Image Encryption using chaos functions and fractal key
Directory of Open Access Journals (Sweden)
Houman Kashanian
2016-09-01
Full Text Available Many image in recent years are transmitted via internet and stored on it. Maintain the confidentiality of these data has become a major issue. So that encryption algorithms permit only authorized users to access data which is a proper solution to this problem.This paper presents a novel scheme for image encryption. At first, a two dimensional logistic mapping is applied to permutation relations between image pixels. We used a fractal image as an encryption key. Given that the chaotic mapping properties such as extreme sensitivity to initial values, random behavior, non-periodic, certainty and so on, we used theses mappings in order to select fractal key for encryption. Experimental results show that proposed algorithm to encrypt image has many features. Due to features such as large space key, low relations between the pixels of encrypted image, high sensitivity to key and high security, it can effectively protect the encrypted image security.
Fractal images induce fractal pupil dilations and constrictions.
Moon, P; Muday, J; Raynor, S; Schirillo, J; Boydston, C; Fairbanks, M S; Taylor, R P
2014-09-01
Fractals are self-similar structures or patterns that repeat at increasingly fine magnifications. Research has revealed fractal patterns in many natural and physiological processes. This article investigates pupillary size over time to determine if their oscillations demonstrate a fractal pattern. We predict that pupil size over time will fluctuate in a fractal manner and this may be due to either the fractal neuronal structure or fractal properties of the image viewed. We present evidence that low complexity fractal patterns underlie pupillary oscillations as subjects view spatial fractal patterns. We also present evidence implicating the autonomic nervous system's importance in these patterns. Using the variational method of the box-counting procedure we demonstrate that low complexity fractal patterns are found in changes within pupil size over time in millimeters (mm) and our data suggest that these pupillary oscillation patterns do not depend on the fractal properties of the image viewed.
Directory of Open Access Journals (Sweden)
Amin Qorbani
2011-12-01
Full Text Available Fractal Image Compression is a well-known problem which is in the class of NP-Hard problems.Quantum Evolutionary Algorithm is a novel optimization algorithm which uses a probabilisticrepresentation for solutions and is highly suitable for combinatorial problems like Knapsack problem.Genetic algorithms are widely used for fractal image compression problems, but QEA is not used for thiskind of problems yet. This paper improves QEA whit change population size and used it in fractal imagecompression. Utilizing the self-similarity property of a natural image, the partitioned iterated functionsystem (PIFS will be found to encode an image through Quantum Evolutionary Algorithm (QEA methodExperimental results show that our method has a better performance than GA and conventional fractalimage compression algorithms.
Fractal methods in image analysis and coding
Neary, David
2001-01-01
In this thesis we present an overview of image processing techniques which use fractal methods in some way. We show how these fields relate to each other, and examine various aspects of fractal methods in each area. The three principal fields of image processing and analysis th a t we examine are texture classification, image segmentation and image coding. In the area of texture classification, we examine fractal dimension estimators, comparing these methods to other methods in use, a...
Multispectral image fusion based on fractal features
Tian, Jie; Chen, Jie; Zhang, Chunhua
2004-01-01
Imagery sensors have been one indispensable part of the detection and recognition systems. They are widely used to the field of surveillance, navigation, control and guide, et. However, different imagery sensors depend on diverse imaging mechanisms, and work within diverse range of spectrum. They also perform diverse functions and have diverse circumstance requires. So it is unpractical to accomplish the task of detection or recognition with a single imagery sensor under the conditions of different circumstances, different backgrounds and different targets. Fortunately, the multi-sensor image fusion technique emerged as important route to solve this problem. So image fusion has been one of the main technical routines used to detect and recognize objects from images. While, loss of information is unavoidable during fusion process, so it is always a very important content of image fusion how to preserve the useful information to the utmost. That is to say, it should be taken into account before designing the fusion schemes how to avoid the loss of useful information or how to preserve the features helpful to the detection. In consideration of these issues and the fact that most detection problems are actually to distinguish man-made objects from natural background, a fractal-based multi-spectral fusion algorithm has been proposed in this paper aiming at the recognition of battlefield targets in the complicated backgrounds. According to this algorithm, source images are firstly orthogonally decomposed according to wavelet transform theories, and then fractal-based detection is held to each decomposed image. At this step, natural background and man-made targets are distinguished by use of fractal models that can well imitate natural objects. Special fusion operators are employed during the fusion of area that contains man-made targets so that useful information could be preserved and features of targets could be extruded. The final fused image is reconstructed from the
Experimental Study of Fractal Image Compression Algorithm
Directory of Open Access Journals (Sweden)
Chetan R. Dudhagara
2012-08-01
Full Text Available Image compression applications have been increasing in recent years. Fractal compression is a lossy compression method for digital images, based on fractals. The method is best suited for textures and natural images, relying on the fact that parts of an image often resemble other parts of the same image. In this paper, a study on fractal-based image compression and fixed-size partitioning will be made, analyzed for performance and compared with a standard frequency domain based image compression standard, JPEG. Sample images will be used to perform compression and decompression. Performance metrics such as compression ratio, compression time and decompression time will be measured in JPEG cases. Also the phenomenon of resolution/scale independence will be studied and described with examples. Fractal algorithms convert these parts into mathematical data called "fractal codes" which are used to recreate the encoded image. Fractal encoding is a mathematical process used to encode bitmaps containing a real-world image as a set of mathematical data that describes the fractal properties of the image. Fractal encoding relies on the fact that all natural, and most artificial, objects contain redundant information in the form of similar, repeating patterns called fractals.
Fractal Image Coding with Digital Watermarks
Directory of Open Access Journals (Sweden)
Z. Klenovicova
2000-12-01
Full Text Available In this paper are presented some results of implementation of digitalwatermarking methods into image coding based on fractal principles. Thepaper focuses on two possible approaches of embedding digitalwatermarks into fractal code of images - embedding digital watermarksinto parameters for position of similar blocks and coefficients ofblock similarity. Both algorithms were analyzed and verified on grayscale static images.
A Fast Fractal Image Compression Coding Method
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
Fast algorithms for reducing encoding complexity of fractal image coding have recently been an important research topic. Search of the best matched domain block is the most computation intensive part of the fractal encoding process. In this paper, a fast fractal approximation coding scheme implemented on a personal computer based on matching in range block's neighbours is presented. Experimental results show that the proposed algorithm is very simple in implementation, fast in encoding time and high in compression ratio while PSNR is almost the same as compared with Barnsley's fractal block coding .
Fractal image encoding based on adaptive search
Institute of Scientific and Technical Information of China (English)
Kya Berthe; Yang Yang; Huifang Bi
2003-01-01
Finding the optimal algorithm between an efficient encoding process and the rate distortion is the main research in fractal image compression theory. A new method has been proposed based on the optimization of the Least-Square Error and the orthogonal projection. A large number of domain blocks can be eliminated in order to speed-up fractal image compression. Moreover, since the rate-distortion performance of most fractal image coders is not satisfactory, an efficient bit allocation algorithm to improve the rate distortion is also proposed. The implementation and comparison have been done with the feature extraction method to prove the efficiency of the proposed method.
Estimating fractal dimension of medical images
Penn, Alan I.; Loew, Murray H.
1996-04-01
Box counting (BC) is widely used to estimate the fractal dimension (fd) of medical images on the basis of a finite set of pixel data. The fd is then used as a feature to discriminate between healthy and unhealthy conditions. We show that BC is ineffective when used on small data sets and give examples of published studies in which researchers have obtained contradictory and flawed results by using BC to estimate the fd of data-limited medical images. We present a new method for estimating fd of data-limited medical images. In the new method, fractal interpolation functions (FIFs) are used to generate self-affine models of the underlying image; each model, upon discretization, approximates the original data points. The fd of each FIF is analytically evaluated. The mean of the fds of the FIFs is the estimate of the fd of the original data. The standard deviation of the fds of the FIFs is a confidence measure of the estimate. The goodness-of-fit of the discretized models to the original data is a measure of self-affinity of the original data. In a test case, the new method generated a stable estimate of fd of a rib edge in a standard chest x-ray; box counting failed to generate a meaningful estimate of the same image.
BIVARIATE FRACTAL INTERPOLATION FUNCTIONS ON RECTANGULAR DOMAINS
Institute of Scientific and Technical Information of China (English)
Xiao-yuan Qian
2002-01-01
Non-tensor product bivariate fractal interpolation functions defined on gridded rectangular domains are constructed. Linear spaces consisting of these functions are introduced.The relevant Lagrange interpolation problem is discussed. A negative result about the existence of affine fractal interpolation functions defined on such domains is obtained.
Riemann zeta function is a fractal
Woon, S C
1994-01-01
Voronin's theorem on the "Universality" of Riemann zeta function is shown to imply that Riemann zeta function is a fractal (in the sense that Mandelbrot set is a fractal) and a concrete "representation" of the "giant book of theorems'' that Paul Halmos referred to.
Pre-Service Teachers' Concept Images on Fractal Dimension
Karakus, Fatih
2016-01-01
The analysis of pre-service teachers' concept images can provide information about their mental schema of fractal dimension. There is limited research on students' understanding of fractal and fractal dimension. Therefore, this study aimed to investigate the pre-service teachers' understandings of fractal dimension based on concept image. The…
A fractal-based image encryption system
Abd-El-Hafiz, S. K.
2014-12-01
This study introduces a novel image encryption system based on diffusion and confusion processes in which the image information is hidden inside the complex details of fractal images. A simplified encryption technique is, first, presented using a single-fractal image and statistical analysis is performed. A general encryption system utilising multiple fractal images is, then, introduced to improve the performance and increase the encryption key up to hundreds of bits. This improvement is achieved through several parameters: feedback delay, multiplexing and independent horizontal or vertical shifts. The effect of each parameter is studied separately and, then, they are combined to illustrate their influence on the encryption quality. The encryption quality is evaluated using different analysis techniques such as correlation coefficients, differential attack measures, histogram distributions, key sensitivity analysis and the National Institute of Standards and Technology (NIST) statistical test suite. The obtained results show great potential compared to other techniques.
Three-dimensional tumor perfusion reconstruction using fractal interpolation functions.
Craciunescu, O I; Das, S K; Poulson, J M; Samulski, T V
2001-04-01
It has been shown that the perfusion of blood in tumor tissue can be approximated using the relative perfusion index determined from dynamic contrast-enhanced magnetic resonance imaging (DE-MRI) of the tumor blood pool. Also, it was concluded in a previous report that the blood perfusion in a two-dimensional (2-D) tumor vessel network has a fractal structure and that the evolution of the perfusion front can be characterized using invasion percolation. In this paper, the three-dimensional (3-D) tumor perfusion is reconstructed from the 2-D slices using the method of fractal interpolation functions (FIF), i.e., the piecewise self-affine fractal interpolation model (PSAFIM) and the piecewise hidden variable fractal interpolation model (PHVFIM). The fractal models are compared to classical interpolation techniques (linear, spline, polynomial) by means of determining the 2-D fractal dimension of the reconstructed slices. Using FIFs instead of classical interpolation techniques better conserves the fractal-like structure of the perfusion data. Among the two FIF methods, PHVFIM conserves the 3-D fractality better due to the cross correlation that exists between the data in the 2-D slices and the data along the reconstructed direction. The 3-D structures resulting from PHVFIM have a fractal dimension within 3%-5% of the one reported in literature for 3-D percolation. It is, thus, concluded that the reconstructed 3-D perfusion has a percolation-like scaling. As the perfusion term from bio-heat equation is possibly better described by reconstruction via fractal interpolation, a more suitable computation of the temperature field induced during hyperthermia treatments is expected.
Generalized fragmentation functions for fractal jet observables
Elder, Benjamin T.; Procura, Massimiliano; Thaler, Jesse; Waalewijn, Wouter J.; Zhou, Kevin
2017-06-01
We introduce a broad class of fractal jet observables that recursively probe the collective properties of hadrons produced in jet fragmentation. To describe these collinear-unsafe observables, we generalize the formalism of fragmentation functions, which are important objects in QCD for calculating cross sections involving identified final-state hadrons. Fragmentation functions are fundamentally nonperturbative, but have a calculable renormalization group evolution. Unlike ordinary fragmentation functions, generalized fragmentation functions exhibit nonlinear evolution, since fractal observables involve correlated subsets of hadrons within a jet. Some special cases of generalized fragmentation functions are reviewed, including jet charge and track functions. We then consider fractal jet observables that are based on hierarchical clustering trees, where the nonlinear evolution equations also exhibit tree-like structure at leading order. We develop a numeric code for performing this evolution and study its phenomenological implications. As an application, we present examples of fractal jet observables that are useful in discriminating quark jets from gluon jets.
A Parallel Approach to Fractal Image Compression
Directory of Open Access Journals (Sweden)
Lubomir Dedera
2004-01-01
Full Text Available The paper deals with a parallel approach to coding and decoding algorithms in fractal image compressionand presents experimental results comparing sequential and parallel algorithms from the point of view of achieved bothcoding and decoding time and effectiveness of parallelization.
Fractal Image Editing with PhotoFrac
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Tim McGraw
2016-12-01
Full Text Available In this paper, we describe the development and use of PhotoFrac, an application that allows artists and designers to turn digital images into fractal patterns interactively. Fractal equations are a rich source of procedural texture and detail, but controlling the patterns and incorporating traditional media has been difficult. Additionally, the iterative nature of fractal calculations makes implementation of interactive techniques on mobile devices and web apps challenging. We overcome these problems by using an image coordinate based orbit trapping technique that permits a user-selected image to be embedded into the fractal. Performance challenges are addressed by exploiting the processing power of graphic processing unit (GPU and precomputing some intermediate results for use on mobile devices. This paper presents results and qualitative analyses of the tool by four artists (the authors who used the PhotoFrac application to create new artworks from original digital images. The final results demonstrate a fusion of traditional media with algorithmic art.
Dynamic Fractal Transform with Applications to Image Data Compression
Institute of Scientific and Technical Information of China (English)
王舟; 余英林
1997-01-01
A recent trend in computer graphics and image processing is to use Iterated Function System(IFS)to generate and describe both man-made graphics and natural images.Jacquin was the first to propose a fully automation gray scale image compression algorithm which is referred to as a typical static fractal transform based algorithm in this paper.By using this algorithm,an image can be condensely described as a fractal transform operator which is the combination of a set of reactal mappings.When the fractal transform operator is iteratedly applied to any initial image,a unique attractro(reconstructed image)can be achieved.In this paper,a dynamic fractal transform is presented which is a modification of the static transform.Instea of being fixed,the dynamic transform operator varies in each decoder iteration,thus differs from static transform operators.The new transform has advantages in improving coding efficiency and shows better convergence for the deocder.
A simple method for estimating the fractal dimension from digital images: The compression dimension
Chamorro-Posada, Pedro
2016-10-01
The fractal structure of real world objects is often analyzed using digital images. In this context, the compression fractal dimension is put forward. It provides a simple method for the direct estimation of the dimension of fractals stored as digital image files. The computational scheme can be implemented using readily available free software. Its simplicity also makes it very interesting for introductory elaborations of basic concepts of fractal geometry, complexity, and information theory. A test of the computational scheme using limited-quality images of well-defined fractal sets obtained from the Internet and free software has been performed. Also, a systematic evaluation of the proposed method using computer generated images of the Weierstrass cosine function shows an accuracy comparable to those of the methods most commonly used to estimate the dimension of fractal data sequences applied to the same test problem.
A Novel Fractal Wavelet Image Compression Approach
Institute of Scientific and Technical Information of China (English)
SONG Chun-lin; FENG Rui; LIU Fu-qiang; CHEN Xi
2007-01-01
By investigating the limitation of existing wavelet tree based image compression methods, we propose a novel wavelet fractal image compression method in this paper. Briefly, the initial errors are appointed given the different levels of importance accorded the frequency sublevel band wavelet coefficients. Higher frequency sublevel bands would lead to larger initial errors. As a result, the sizes of sublevel blocks and super blocks would be changed according to the initial errors. The matching sizes between sublevel blocks and super blocks would be changed according to the permitted errors and compression rates. Systematic analyses are performed and the experimental results demonstrate that the proposed method provides a satisfactory performance with a clearly increasing rate of compression and speed of encoding without reducing SNR and the quality of decoded images. Simulation results show that our method is superior to the traditional wavelet tree based methods of fractal image compression.
Hybrid Prediction and Fractal Hyperspectral Image Compression
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Shiping Zhu
2015-01-01
Full Text Available The data size of hyperspectral image is too large for storage and transmission, and it has become a bottleneck restricting its applications. So it is necessary to study a high efficiency compression method for hyperspectral image. Prediction encoding is easy to realize and has been studied widely in the hyperspectral image compression field. Fractal coding has the advantages of high compression ratio, resolution independence, and a fast decoding speed, but its application in the hyperspectral image compression field is not popular. In this paper, we propose a novel algorithm for hyperspectral image compression based on hybrid prediction and fractal. Intraband prediction is implemented to the first band and all the remaining bands are encoded by modified fractal coding algorithm. The proposed algorithm can effectively exploit the spectral correlation in hyperspectral image, since each range block is approximated by the domain block in the adjacent band, which is of the same size as the range block. Experimental results indicate that the proposed algorithm provides very promising performance at low bitrate. Compared to other algorithms, the encoding complexity is lower, the decoding quality has a great enhancement, and the PSNR can be increased by about 5 dB to 10 dB.
Pyramidal fractal dimension for high resolution images
Mayrhofer-Reinhartshuber, Michael; Ahammer, Helmut
2016-07-01
Fractal analysis (FA) should be able to yield reliable and fast results for high-resolution digital images to be applicable in fields that require immediate outcomes. Triggered by an efficient implementation of FA for binary images, we present three new approaches for fractal dimension (D) estimation of images that utilize image pyramids, namely, the pyramid triangular prism, the pyramid gradient, and the pyramid differences method (PTPM, PGM, PDM). We evaluated the performance of the three new and five standard techniques when applied to images with sizes up to 8192 × 8192 pixels. By using artificial fractal images created by three different generator models as ground truth, we determined the scale ranges with minimum deviations between estimation and theory. All pyramidal methods (PM) resulted in reasonable D values for images of all generator models. Especially, for images with sizes ≥1024 ×1024 pixels, the PMs are superior to the investigated standard approaches in terms of accuracy and computation time. A measure for the possibility to differentiate images with different intrinsic D values did show not only that the PMs are well suited for all investigated image sizes, and preferable to standard methods especially for larger images, but also that results of standard D estimation techniques are strongly influenced by the image size. Fastest results were obtained with the PDM and PGM, followed by the PTPM. In terms of absolute D values best performing standard methods were magnitudes slower than the PMs. Concluding, the new PMs yield high quality results in short computation times and are therefore eligible methods for fast FA of high-resolution images.
Image compression with a hybrid wavelet-fractal coder.
Li, J; Kuo, C J
1999-01-01
A hybrid wavelet-fractal coder (WFC) for image compression is proposed. The WFC uses the fractal contractive mapping to predict the wavelet coefficients of the higher resolution from those of the lower resolution and then encode the prediction residue with a bitplane wavelet coder. The fractal prediction is adaptively applied only to regions where the rate saving offered by fractal prediction justifies its overhead. A rate-distortion criterion is derived to evaluate the fractal rate saving and used to select the optimal fractal parameter set for WFC. The superior performance of the WFC is demonstrated with extensive experimental results.
STUDY ON IMAGE EDGE PROPERTY LOCATION BASED ON FRACTAL THEORY
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
A novel approach of printed circuit board(PCB)image locating is presentedBased on the rectangle mark image edge of PCB,the featur es is used to describe the image edge and the fractal properby of image edge is analyzedIt is proved that the rectangle mark image edge of PCB has some fracta l featuresA method of deleting unordinary curve noise and compensating the l ength of the fractal curve is put forward,which can get the fractal dimension value from one complex edge fractal property curveThe relation between the dim ension of the fractal curve and the turning angle of image can be acquired from an equation,as a result,the angle value of the PCB image is got exactlyA real image edge analysis result confirms that the method based on the fractal theory is a new powerful tool for angle locating on PCB and related image area
New Approach to Fractal Approximation of Vector-Functions
Directory of Open Access Journals (Sweden)
Konstantin Igudesman
2015-01-01
Full Text Available This paper introduces new approach to approximation of continuous vector-functions and vector sequences by fractal interpolation vector-functions which are multidimensional generalization of fractal interpolation functions. Best values of fractal interpolation vector-functions parameters are found. We give schemes of approximation of some sets of data and consider examples of approximation of smooth curves with different conditions.
A fast and efficient hybrid fractal-wavelet image coder.
Iano, Yuzo; da Silva, Fernando Silvestre; Cruz, Ana Lúcia Mendes
2006-01-01
The excellent visual quality and compression rate of fractal image coding have limited applications due to exhaustive inherent encoding time. This paper presents a new fast and efficient image coder that applies the speed of the wavelet transform to the image quality of the fractal compression. Fast fractal encoding using Fisher's domain classification is applied to the lowpass subband of wavelet transformed image and a modified set partitioning in hierarchical trees (SPIHT) coding, on the remaining coefficients. Furthermore, image details and wavelet progressive transmission characteristics are maintained, no blocking effects from fractal techniques are introduced, and the encoding fidelity problem common in fractal-wavelet hybrid coders is solved. The proposed scheme promotes an average of 94% reduction in encoding-decoding time comparing to the pure accelerated Fractal coding results. The simulations also compare the results to the SPIHT wavelet coding. In both cases, the new scheme improves the subjective quality of pictures for high-medium-low bitrates.
An Approach to Extracting Fractal in Remote Sensing Image
Institute of Scientific and Technical Information of China (English)
ZHU Ji; LIN Ziyu; WANG Angsheng; CUI Peng
2006-01-01
In order to apply the spatial structure information to remote sensing interpretation through fractal theory,an algorithm is introduced to compute the single pixel fractal dimension in remote sensing images. After a computer program was written according to the algorithm, the ETM+ images were calculated to obtain their fractal data through the program. The algorithm has following characteristics: The obtained fractal values indicate the complexity of image, and have positive correlation with the complexity of images and ground objects. Moreover, the algorithm is simple and reliable, and easy to be implemented.
Fractals and spectra related to fourier analysis and function spaces
Triebel, Hans
1997-01-01
Fractals and Spectra Hans Triebel This book deals with the symbiotic relationship between the theory of function spaces, fractal geometry, and spectral theory of (fractal) pseudodifferential operators as it has emerged quite recently. Atomic and quarkonial (subatomic) decompositions in scalar and vector valued function spaces on the euclidean n-space pave the way to study properties (compact embeddings, entropy numbers) of function spaces on and of fractals. On this basis, distributions of eigenvalues of fractal (pseudo)differential operators are investigated. Diverse versions of fractal drums are played. The book is directed to mathematicians interested in functional analysis, the theory of function spaces, fractal geometry, partial and pseudodifferential operators, and, in particular, in how these domains are interrelated. ------ It is worth mentioning that there is virtually no literature on this topic and hence the most of the presented material is published here the first time. - Zentralblatt MATH (…) ...
Smitha, K A; Gupta, A K; Jayasree, R S
2015-09-07
Glioma, the heterogeneous tumors originating from glial cells, generally exhibit varied grades and are difficult to differentiate using conventional MR imaging techniques. When this differentiation is crucial in the disease prognosis and treatment, even the advanced MR imaging techniques fail to provide a higher discriminative power for the differentiation of malignant tumor from benign ones. A powerful image processing technique applied to the imaging techniques is expected to provide a better differentiation. The present study focuses on the fractal analysis of fluid attenuation inversion recovery MR images, for the differentiation of glioma. For this, we have considered the most important parameters of fractal analysis, fractal dimension and lacunarity. While fractal analysis assesses the malignancy and complexity of a fractal object, lacunarity gives an indication on the empty space and the degree of inhomogeneity in the fractal objects. Box counting method with the preprocessing steps namely binarization, dilation and outlining was used to obtain the fractal dimension and lacunarity in glioma. Statistical analysis such as one-way analysis of variance and receiver operating characteristic (ROC) curve analysis helped to compare the mean and to find discriminative sensitivity of the results. It was found that the lacunarity of low and high grade gliomas vary significantly. ROC curve analysis between low and high grade glioma for fractal dimension and lacunarity yielded 70.3% sensitivity and 66.7% specificity and 70.3% sensitivity and 88.9% specificity, respectively. The study observes that fractal dimension and lacunarity increases with an increase in the grade of glioma and lacunarity is helpful in identifying most malignant grades.
Beyond maximum entropy: Fractal Pixon-based image reconstruction
Puetter, Richard C.; Pina, R. K.
1994-01-01
We have developed a new Bayesian image reconstruction method that has been shown to be superior to the best implementations of other competing methods, including Goodness-of-Fit methods such as Least-Squares fitting and Lucy-Richardson reconstruction, as well as Maximum Entropy (ME) methods such as those embodied in the MEMSYS algorithms. Our new method is based on the concept of the pixon, the fundamental, indivisible unit of picture information. Use of the pixon concept provides an improved image model, resulting in an image prior which is superior to that of standard ME. Our past work has shown how uniform information content pixons can be used to develop a 'Super-ME' method in which entropy is maximized exactly. Recently, however, we have developed a superior pixon basis for the image, the Fractal Pixon Basis (FPB). Unlike the Uniform Pixon Basis (UPB) of our 'Super-ME' method, the FPB basis is selected by employing fractal dimensional concepts to assess the inherent structure in the image. The Fractal Pixon Basis results in the best image reconstructions to date, superior to both UPB and the best ME reconstructions. In this paper, we review the theory of the UPB and FPB pixon and apply our methodology to the reconstruction of far-infrared imaging of the galaxy M51. The results of our reconstruction are compared to published reconstructions of the same data using the Lucy-Richardson algorithm, the Maximum Correlation Method developed at IPAC, and the MEMSYS ME algorithms. The results show that our reconstructed image has a spatial resolution a factor of two better than best previous methods (and a factor of 20 finer than the width of the point response function), and detects sources two orders of magnitude fainter than other methods.
Determination of fish gender using fractal analysis of ultrasound images
DEFF Research Database (Denmark)
McEvoy, Fintan J.; Tomkiewicz, Jonna; Støttrup, Josianne;
2009-01-01
The gender of cod Gadus morhua can be determined by considering the complexity in their gonadal ultrasonographic appearance. The fractal dimension (DB) can be used to describe this feature in images. B-mode gonadal ultrasound images in 32 cod, where gender was known, were collected. Fractal...... by subjective analysis alone. The mean (and standard deviation) of the fractal dimension DB for male fish was 1.554 (0.073) while for female fish it was 1.468 (0.061); the difference was statistically significant (P=0.001). The area under the ROC curve was 0.84 indicating the value of fractal analysis in gender...... result. Fractal analysis is useful for gender determination in cod. This or a similar form of analysis may have wide application in veterinary imaging as a tool for quantification of complexity in images...
Fast Fractal Image Encoding Based on Special Image Features
Institute of Scientific and Technical Information of China (English)
ZHANG Chao; ZHOU Yiming; ZHANG Zengke
2007-01-01
The fractal image encoding method has received much attention for its many advantages over other methods,such as high decoding quality at high compression ratios. However, because every range block must be compared to all domain blocks in the codebook to find the best-matched one during the coding procedure, baseline fractal coding (BFC) is quite time consuming. To speed up fractal coding, a new fast fractal encoding algorithm is proposed. This algorithm aims at reducing the size of the search window during the domain-range matching process to minimize the computational cost. A new theorem presented in this paper shows that a special feature of the image can be used to do this work. Based on this theorem, the most inappropriate domain blocks, whose features are not similar to that of the given range block, are excluded before matching. Thus, the best-matched block can be captured much more quickly than in the BFC approachThe experimental results show that the runtime of the proposed method is reduced greatly compared to the BFC method. At the same time,the new algorithm also achieves high reconstructed image quality. In addition,the method can be incorporated with other fast algorithms to achieve better performance.Therefore, the proposed algorithm has a much better application potential than BFC.
An image retrieval system based on fractal dimension
Institute of Scientific and Technical Information of China (English)
无
2003-01-01
This paper presents a new kind of image retrieval system which obtains the feature vectors of images by estimating their fractal dimension; and at the same time establishes a tree-structure image database. After preprocessing and feature extracting, a given image is matched with the standard images in the image database using a hierarchical method of image indexing.
An image retrieval system based on fractal dimension.
Yao, Min; Yi, Wen-Sheng; Shen, Bin; Dai, Hong-Hua
2003-01-01
This paper presents a new kind of image retrieval system which obtains the feature vectors of images by estimating their fractal dimension; and at the same time establishes a tree-structure image database. After preprocessing and feature extracting, a given image is matched with the standard images in the image database using a hierarchical method of image indexing.
Image edge detection based on multi-fractal spectrum analysis
Institute of Scientific and Technical Information of China (English)
WANG Shao-yuan; WANG Yao-nan
2006-01-01
In this paper,an image edge detection method based on multi-fractal spectrum analysis is presented.The coarse grain H(o)lder exponent of the image pixels is first computed,then,its multi-fractal spectrum is estimated by the kernel estimation method.Finally,the image edge detection is done by means of different multi-fractal spectrum values.Simulation results show that this method is efficient and has better locality compared with the traditional edge detection methods such as the Sobel method.
Fractal structures and fractal functions as disease indicators
Escos, J.M; Alados, C.L.; Emlen, J.M.
1995-01-01
Developmental instability is an early indicator of stress, and has been used to monitor the impacts of human disturbance on natural ecosystems. Here we investigate the use of different measures of developmental instability on two species, green peppers (Capsicum annuum), a plant, and Spanish ibex (Capra pyrenaica), an animal. For green peppers we compared the variance in allometric relationship between control plants, and a treatment group infected with the tomato spotted wilt virus. The results show that infected plants have a greater variance about the allometric regression line than the control plants. We also observed a reduction in complexity of branch structure in green pepper with a viral infection. Box-counting fractal dimension of branch architecture declined under stress infection. We also tested the reduction in complexity of behavioral patterns under stress situations in Spanish ibex (Capra pyrenaica). Fractal dimension of head-lift frequency distribution measures predator detection efficiency. This dimension decreased under stressful conditions, such as advanced pregnancy and parasitic infection. Feeding distribution activities reflect food searching efficiency. Power spectral analysis proves to be the most powerful tool for character- izing fractal behavior, revealing a reduction in complexity of time distribution activity under parasitic infection.
A NOVEL APPROACH TO GENERATE FRACTAL IMAGES USING CHAOS THEORY
Directory of Open Access Journals (Sweden)
K. Thamizhchelvy
2014-08-01
Full Text Available We propose the fractal generation method to generate the different types of fractals using chaos theory. The fractals are generated by Iterated Function System (IFS technique. The chaos theory is an unpredictable behavior arises in the dynamical system. Chaos in turns explains the nonlinearity and randomness. Chaotic behavior depends upon the initial condition called as “seed” or “key”. Pseudo Random Number Generator (PRNG fixes the initial condition from the difference equations. The system uses the PRNG value and it generates the fractals, also it is hard to break. We apply the rules to generate the fractals. The different types of fractals are generated for the same data, because of the great sensitivity to the initial condition. It can be used as a digital signature in online applications such as e-Banking and online shopping.
MR imaging and osteoporosis: fractal lacunarity analysis of trabecular bone.
Zaia, Annamaria; Eleonori, Roberta; Maponi, Pierluigi; Rossi, Roberto; Murri, Roberto
2006-07-01
We develop a method of magnetic resonance (MR) image analysis able to provide parameter(s) sensitive to bone microarchitecture changes in aging, and to osteoporosis onset and progression. The method has been built taking into account fractal properties of many anatomic and physiologic structures. Fractal lacunarity analysis has been used to determine relevant parameter(s) to differentiate among three types of trabecular bone structure (healthy young, healthy perimenopausal, and osteoporotic patients) from lumbar vertebra MR images. In particular, we propose to approximate the lacunarity function by a hyperbola model function that depends on three coefficients, alpha, beta, and gamma, and to compute these coefficients as the solution of a least squares problem. This triplet of coefficients provides a model function that better represents the variation of mass density of pixels in the image considered. Clinical application of this preliminary version of our method suggests that one of the three coefficients, beta, may represent a standard for the evaluation of trabecular bone architecture and a potentially useful parametric index for the early diagnosis of osteoporosis.
Dougherty, G; Henebry, G M
2001-07-01
Fractal analysis is a method of characterizing complex shapes such as the trabecular structure of bone. Numerous algorithms for estimating fractal dimension have been described, but the Fourier power spectrum method is particularly applicable to self-affine fractals, and facilitates corrections for the effects of noise and blurring in an image. We found that it provided accurate estimates of fractal dimension for synthesized fractal images. For natural texture images fractality is limited to a range of scales, and the fractal dimension as a function of spatial frequency presents as a fractal signature. We found that the fractal signature was more successful at discriminating between these textures than either the global fractal dimension or other metrics such as the mean width and root-mean-square width of the spectral density plots. Different natural textures were also readily distinguishable using lacunarity plots, which explicitly characterize the average size and spatial organization of structural sub-units within an image. The fractal signatures of small regions of interest (32x32 pixels), computed in the frequency domain after corrections for imaging system noise and MTF, were able to characterize the texture of vertebral trabecular bone in CT images. Even small differences in texture due to acquisition slice thickness resulted in measurably different fractal signatures. These differences were also readily apparent in lacunarity plots, which indicated that a slice thickness of 1 mm or less is necessary if essential architectural information is not to be lost. Since lacunarity measures gap size and is not predicated on fractality, it may be particularly useful for characterizing the texture of trabecular bone.
FRACTAL IMAGE FEATURE VECTORS WITH APPLICATIONS IN FRACTOGRAPHY
Directory of Open Access Journals (Sweden)
Hynek Lauschmann
2011-05-01
Full Text Available The morphology of fatigue fracture surface (caused by constant cycle loading is strictly related to crack growth rate. This relation may be expressed, among other methods, by means of fractal analysis. Fractal dimension as a single numerical value is not sufficient. Two types of fractal feature vectors are discussed: multifractal and multiparametric. For analysis of images, the box-counting method for 3D is applied with respect to the non-homogeneity of dimensions (two in space, one in brightness. Examples of application are shown: images of several fracture surfaces are analyzed and related to crack growth rate.
Laser image denoising technique based on multi-fractal theory
Du, Lin; Sun, Huayan; Tian, Weiqing; Wang, Shuai
2014-02-01
The noise of laser images is complex, which includes additive noise and multiplicative noise. Considering the features of laser images, the basic processing capacity and defects of the common algorithm, this paper introduces the fractal theory into the research of laser image denoising. The research of laser image denoising is implemented mainly through the analysis of the singularity exponent of each pixel in fractal space and the feature of multi-fractal spectrum. According to the quantitative and qualitative evaluation of the processed image, the laser image processing technique based on fractal theory not only effectively removes the complicated noise of the laser images obtained by range-gated laser active imaging system, but can also maintains the detail information when implementing the image denoising processing. For different laser images, multi-fractal denoising technique can increase SNR of the laser image at least 1~2dB compared with other denoising techniques, which basically meet the needs of the laser image denoising technique.
Construction and Dimension Analysis for a Class of Fractal Functions
Institute of Scientific and Technical Information of China (English)
Hong-yong Wang; Zong-ben Xu
2002-01-01
In this paper, we construct a class of nowhere differentiable continuous functions by means of the Cantor series expression of real numbers. The constructed functions include some known nondifferentiable functions, such as Bush type functions. These functions are fractal functions since their graphs are in general fractal sets. Under certain conditions, we investigate the fractal dimensions of the graphs of these functions,compute the precise values of Box and Packing dimensions, and evaluate the Hausdorff dimension. Meanwhile,the Holder continuity of such functions is also discussed.
Xianyu Jin; Bei Li; Ye Tian; Nanguo Jin; An Duan
2013-01-01
Based on the fractal theory, this study presents a numerical analysis on the fractal characteristics of cracks and pore structure of concrete with the help of digital image technology. The results show that concrete cracks and the micro pore distribution of concrete are of fractal characteristics and the fractal dimension ranges from 1 to 2. The fractal characteristics of pores in cracked concrete and un-cracked concrete is similar and the former fractal dimension of the micro pore structure ...
Structured-light Image Compression Based on Fractal Theory
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
The method of fractal image compression is introduced which is applied to compress the line structured-light image. Based on the self-similarity of the structured-light image, we attain satisfactory compression ratio and higher peak signal-to-noise ratio (PSNR). The experimental results indicate that this method can achieve high performance.
Fractal-based image texture analysis of trabecular bone architecture.
Jiang, C; Pitt, R E; Bertram, J E; Aneshansley, D J
1999-07-01
Fractal-based image analysis methods are investigated to extract textural features related to the anisotropic structure of trabecular bone from the X-ray images of cubic bone specimens. Three methods are used to quantify image textural features: power spectrum, Minkowski dimension and mean intercept length. The global fractal dimension is used to describe the overall roughness of the image texture. The anisotropic features formed by the trabeculae are characterised by a fabric ellipse, whose orientation and eccentricity reflect the textural anisotropy of the image. Tests of these methods with synthetic images of known fractal dimension show that the Minkowski dimension provides a more accurate and consistent estimation of global fractal dimension. Tests on bone x-ray (eccentricity range 0.25-0.80) images indicate that the Minkowski dimension is more sensitive to the changes in textural orientation. The results suggest that the Minkowski dimension is a better measure for characterising trabecular bone anisotropy in the x-ray images of thick specimens.
A New Approach in Cryptographic Systems Using Fractal Image Coding
Directory of Open Access Journals (Sweden)
Nadia M.G. Al-Saidi
2009-01-01
Full Text Available Problem statement: With the rapid development in the communications and information transmissions there is a growing demand for new approaches that increase the security of cryptographic systems. Approach: Therefore some emerging theories, such as fractals, can be adopted to provide a contribution toward this goal. In this study we proposed a new cryptographic system utilizing fractal theories; this approach exploited the main feature of fractals generated by IFS techniques. Results: Double enciphering and double deciphering methods performed to enhance the security of the system. The encrypted date represented the attractor generated by the IFS transformation, collage theorem was used to find the IFSM for decrypting data. Conclusion/Recommendations: The proposed method gave the possibility to hide maximum amount of data in an image that represent the attractor of the IFS without degrading its quality and to make the hidden data robust enough to withstand known cryptographic attacks and image processing techniques which did not change the appearance of image.
Trabecular architecture analysis in femur radiographic images using fractals.
Udhayakumar, G; Sujatha, C M; Ramakrishnan, S
2013-04-01
Trabecular bone is a highly complex anisotropic material that exhibits varying magnitudes of strength in compression and tension. Analysis of the trabecular architectural alteration that manifest as loss of trabecular plates and connection has been shown to yield better estimation of bone strength. In this work, an attempt has been made toward the development of an automated system for investigation of trabecular femur bone architecture using fractal analysis. Conventional radiographic femur bone images recorded using standard protocols are used in this study. The compressive and tensile regions in the images are delineated using preprocessing procedures. The delineated images are analyzed using Higuchi's fractal method to quantify pattern heterogeneity and anisotropy of trabecular bone structure. The results show that the extracted fractal features are distinct for compressive and tensile regions of normal and abnormal human femur bone. As the strength of the bone depends on architectural variation in addition to bone mass, this study seems to be clinically useful.
Liver ultrasound image classification by using fractal dimension of edge
Moldovanu, Simona; Bibicu, Dorin; Moraru, Luminita
2012-08-01
Medical ultrasound image edge detection is an important component in increasing the number of application of segmentation, and hence it has been subject of many studies in the literature. In this study, we have classified the liver ultrasound images (US) combining Canny and Sobel edge detectors with fractal analysis in order to provide an indicator about of the US images roughness. We intend to provide a classification rule of the focal liver lesions as: cirrhotic liver, liver hemangioma and healthy liver. For edges detection the Canny and Sobel operators were used. Fractal analyses have been applied for texture analysis and classification of focal liver lesions according to fractal dimension (FD) determined by using the Box Counting method. To assess the performance and accuracy rate of the proposed method the contrast-to-noise (CNR) is analyzed.
Fractal zeta functions and fractal drums higher-dimensional theory of complex dimensions
Lapidus, Michel L; Žubrinić, Darko
2017-01-01
This monograph gives a state-of-the-art and accessible treatment of a new general higher-dimensional theory of complex dimensions, valid for arbitrary bounded subsets of Euclidean spaces, as well as for their natural generalization, relative fractal drums. It provides a significant extension of the existing theory of zeta functions for fractal strings to fractal sets and arbitrary bounded sets in Euclidean spaces of any dimension. Two new classes of fractal zeta functions are introduced, namely, the distance and tube zeta functions of bounded sets, and their key properties are investigated. The theory is developed step-by-step at a slow pace, and every step is well motivated by numerous examples, historical remarks and comments, relating the objects under investigation to other concepts. Special emphasis is placed on the study of complex dimensions of bounded sets and their connections with the notions of Minkowski content and Minkowski measurability, as well as on fractal tube formulas. It is shown for the f...
Fractal image perception provides novel insights into hierarchical cognition.
Martins, M J; Fischmeister, F P; Puig-Waldmüller, E; Oh, J; Geissler, A; Robinson, S; Fitch, W T; Beisteiner, R
2014-08-01
Hierarchical structures play a central role in many aspects of human cognition, prominently including both language and music. In this study we addressed hierarchy in the visual domain, using a novel paradigm based on fractal images. Fractals are self-similar patterns generated by repeating the same simple rule at multiple hierarchical levels. Our hypothesis was that the brain uses different resources for processing hierarchies depending on whether it applies a "fractal" or a "non-fractal" cognitive strategy. We analyzed the neural circuits activated by these complex hierarchical patterns in an event-related fMRI study of 40 healthy subjects. Brain activation was compared across three different tasks: a similarity task, and two hierarchical tasks in which subjects were asked to recognize the repetition of a rule operating transformations either within an existing hierarchical level, or generating new hierarchical levels. Similar hierarchical images were generated by both rules and target images were identical. We found that when processing visual hierarchies, engagement in both hierarchical tasks activated the visual dorsal stream (occipito-parietal cortex, intraparietal sulcus and dorsolateral prefrontal cortex). In addition, the level-generating task specifically activated circuits related to the integration of spatial and categorical information, and with the integration of items in contexts (posterior cingulate cortex, retrosplenial cortex, and medial, ventral and anterior regions of temporal cortex). These findings provide interesting new clues about the cognitive mechanisms involved in the generation of new hierarchical levels as required for fractals.
Fractal Image Filters for Specialized Image Recognition Tasks
2010-02-11
The Fractal Geometry of Nature, [24], Mandelbrot argues that random frac- tals provide geometrical models for naturally occurring shapes and forms...Fractal Properties of Number Systems, Period. Math. Hungar 42 (2001) 51-68. [24] Benoit Mandelbrot , The Fractal Geometry of Nature, W. H. Freeman, San
Chaos-based encryption for fractal image coding
Institute of Scientific and Technical Information of China (English)
Yuen Ching-Hung; Wong Kwok-Wo
2012-01-01
A chaos-based cryptosystem for fractal image coding is proposed.The Rényi chaotic map is employed to determine the order of processing the range blocks and to generate the keystream for masking the encoded sequence.Compared with the standard approach of fractal image coding followed by the Advanced Encryption Standard,our scheme offers a higher sensitivity to both plaintext and ciphertext at a comparable operating efficiency.The keystream generated by the Rényi chaotic map passes the randomness tests set by the United States National Institute of Standards and Technology,and so the proposed scheme is sensitive to the key.
Fractal Analysis of Laplacian Pyramidal Filters Applied to Segmentation of Soil Images
Directory of Open Access Journals (Sweden)
J. de Castro
2014-01-01
Full Text Available The laplacian pyramid is a well-known technique for image processing in which local operators of many scales, but identical shape, serve as the basis functions. The required properties to the pyramidal filter produce a family of filters, which is unipara metrical in the case of the classical problem, when the length of the filter is 5. We pay attention to gaussian and fractal behaviour of these basis functions (or filters, and we determine the gaussian and fractal ranges in the case of single parameter a. These fractal filters loose less energy in every step of the laplacian pyramid, and we apply this property to get threshold values for segmenting soil images, and then evaluate their porosity. Also, we evaluate our results by comparing them with the Otsu algorithm threshold values, and conclude that our algorithm produce reliable test results.
Novel welding image processing method based on fractal theory
Institute of Scientific and Technical Information of China (English)
陈强; 孙振国; 肖勇; 路井荣
2002-01-01
Computer vision has come into used in the fields of welding process control and automation. In order to improve precision and rapidity of welding image processing, a novel method based on fractal theory has been put forward in this paper. Compared with traditional methods, the image is preliminarily processed in the macroscopic regions then thoroughly analyzed in the microscopic regions in the new method. With which, an image is divided up to some regions according to the different fractal characters of image edge, and the fuzzy regions including image edges are detected out, then image edges are identified with Sobel operator and curved by LSM (Lease Square Method). Since the data to be processed have been decreased and the noise of image has been reduced, it has been testified through experiments that edges of weld seam or weld pool could be recognized correctly and quickly.
Fractal Dimension of Certain Continuous Functions of Unbounded Variation
Liang, Y. S.; Su, W. Y.
Continuous functions on closed intervals are composed of bounded variation functions and unbounded variation functions. Fractal dimension of continuous functions with bounded variation must be one-dimensional (1D). While fractal dimension of continuous functions with unbounded variation may be 1 or not. Certain continuous functions of unbounded variation whose fractal dimensions are 1 have been mainly investigated in the paper. A continuous function on a closed interval with finite unbounded variation points has been proved to be 1D. Furthermore, we deal with continuous functions which have infinite unbounded variation points and part of them have been proved to be 1D. Certain examples of 1D continuous functions which have uncountable unbounded variation points have been given in the present paper.
A new modified fast fractal image compression algorithm
DEFF Research Database (Denmark)
Salarian, Mehdi; Nadernejad, Ehsan; MiarNaimi, Hossein
2013-01-01
In this paper, a new fractal image compression algorithm is proposed, in which the time of the encoding process is considerably reduced. The algorithm exploits a domain pool reduction approach, along with the use of innovative predefined values for contrast scaling factor, S, instead of searching...
The Generating of Fractal Images using MathCAD Program
Directory of Open Access Journals (Sweden)
Laura Stefan
2008-01-01
Full Text Available This paper presents the graphic representation in the z–plane of the first three iterations of the algorithm that generates the Sierpinski Gasket. It analyses the influence of the f(z map when we represent fractal images.
Do-It-Yourself Fractal Functions
Shriver, Janet; Willard, Teri; McDaniel, Mandy
2017-01-01
In the set of fractal activities described in this article, students will accomplish much more than just creating a fun set of cards that simply resemble an art project. Goals of this activity, designed for an algebra 1 class, are to encourage students to generate data, look for and analyze patterns, and create their own models--all from a set of…
arXiv Generalized Fragmentation Functions for Fractal Jet Observables
Elder, Benjamin T.; Thaler, Jesse; Waalewijn, Wouter J.; Zhou, Kevin
2017-06-15
We introduce a broad class of fractal jet observables that recursively probe the collective properties of hadrons produced in jet fragmentation. To describe these collinear-unsafe observables, we generalize the formalism of fragmentation functions, which are important objects in QCD for calculating cross sections involving identified final-state hadrons. Fragmentation functions are fundamentally nonperturbative, but have a calculable renormalization group evolution. Unlike ordinary fragmentation functions, generalized fragmentation functions exhibit nonlinear evolution, since fractal observables involve correlated subsets of hadrons within a jet. Some special cases of generalized fragmentation functions are reviewed, including jet charge and track functions. We then consider fractal jet observables that are based on hierarchical clustering trees, where the nonlinear evolution equations also exhibit tree-like structure at leading order. We develop a numeric code for performing this evolution and study its phen...
FIRE: fractal indexing with robust extensions for image databases.
Distasi, Riccardo; Nappi, Michele; Tucci, Maurizio
2003-01-01
As already documented in the literature, fractal image encoding is a family of techniques that achieves a good compromise between compression and perceived quality by exploiting the self-similarities present in an image. Furthermore, because of its compactness and stability, the fractal approach can be used to produce a unique signature, thus obtaining a practical image indexing system. Since fractal-based indexing systems are able to deal with the images in compressed form, they are suitable for use with large databases. We propose a system called FIRE, which is then proven to be invariant under three classes of pixel intensity transformations and under geometrical isometries such as rotations by multiples of /spl pi//2 and reflections. This property makes the system robust with respect to a large class of image transformations that can happen in practical applications: the images can be retrieved even in the presence of illumination and/or color alterations. Additionally, the experimental results show the effectiveness of FIRE in terms of both compression and retrieval accuracy.
Fractal Dimension-Based Damage Imaging for Composites
Directory of Open Access Journals (Sweden)
Li Zhou
2013-01-01
Full Text Available In this paper, a damage imaging algorithm based on fractal dimension is developed for quantitative damage detection of composite structures. Box-counting dimension, a typical fractal dimension, is employed to analyze the difference of Lamb wave signals, extract damage feature and define damage index. An enhanced reconstruction algorithm for probabilistic inspection of damage is developed for damage imaging. Experimental investigation in a composite laminate and a stiffened composite panel shows that the developed algorithm could quantitatively predict the location and size of not only single but also multiple damages. The influence of parameters in the developed algorithm on the imaging quality and accuracy is studied, and reference values for parameters are presented.
A simple method for estimating the fractal dimension from digital images: The compression dimension
Chamorro-Posada, P
2016-01-01
The fractal structure of real world objects is often analyzed using digital images. In this context, the compression fractal dimension is put forward. It provides a simple method for the direct estimation of the dimension of fractals stored as digital image files. The computational scheme can be implemented using readily available free software. Its simplicity also makes it very interesting for introductory elaborations of basic concepts of fractal geometry, complexity, and information theory. A test of the computational scheme using limited-quality images of well-defined fractal sets obtained from the Internet and free software has been performed.
Greylevel Difference Classification Algorithm inFractal Image Compression
Institute of Scientific and Technical Information of China (English)
陈毅松; 卢坚; 孙正兴; 张福炎
2002-01-01
This paper proposes the notion of a greylevel difference classification algorithm in fractal image compression. Then an example of the greylevel difference classification algo rithm is given as an improvement of the quadrant greylevel and variance classification in the quadtree-based encoding algorithm. The algorithm incorporates the frequency feature in spatial analysis using the notion of average quadrant greylevel difference, leading to an enhancement in terms of encoding time, PSNR value and compression ratio.
Fast Fractal Image Encoding Using an Improved Search Scheme
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
As fractal image encoding algorithms can yield high-resolution reconstructed images at very high compression ratio, and therefore, have a great potential for improving the efficiency of image storage and image transmission. However, the baseline fractal encoding algorithm requires a great deal of time to complete the best matching search between the range and domain blocks, which greatly limits practical applications of the algorithm. In order to solve this problem, a necessary condition of the best matching search based on an image feature is proposed in this paper. The proposed method can reduce the search space significantly and excludes the most inappropriate domain blocks for each range block before carrying out the best matching search. Experimental results show that the proposed algorithm can produce good quality reconstructed images and requires much less time than the baseline encoding algorithm. Specifically, the new algorithm can speed up encoding by about 85 times with a loss of just 3 dB in the peak signal to noise ratio (PSNR), and yields compression ratios close to 34.
Detection of Glaucomatous Eye via Color Fundus Images Using Fractal Dimensions
Directory of Open Access Journals (Sweden)
J. Jan
2008-09-01
Full Text Available This paper describes a method for glaucomatous eye detection based on fractal description, followed by classification. Two methods for fractal dimensions estimation, which give a different image/tissue description, are presented. The fundus color images are used, in which the areas with retinal nerve fibers are analyzed. The presented method shows that fractal dimensions can be used as features for retinal nerve fibers losses detection, which is a sign of glaucomatous eye.
Fractal dimension metric for quantifying noise texture of computed tomography images
Khobragade, P.; Fan, Jiahua; Rupcich, Franco; Crotty, Dominic J.; Gilat Schmidt, Taly
2017-03-01
This study investigated a fractal dimension algorithm for noise texture quantification in CT images. Quantifying noise in CT images is important for assessing image quality. Noise is typically quantified by calculating noise standard deviation and noise power spectrum (NPS). Different reconstruction kernels and iterative reconstruction approaches affect both the noise magnitude and noise texture. The shape of the NPS can be used as a noise texture descriptor. However, the NPS requires numerous images for calculation and is a vector quantity. This study proposes the metric of fractal dimension to quantify noise texture, because fractal dimension is a single scalar metric calculated from a small number of images. Fractal dimension measures the complexity of a pattern. In this study, the ACR CT phantom was scanned and images were reconstructed using filtered back-projection with three reconstruction kernels: bone, soft and standard. Regions of interest were extracted from the uniform section of the phantom for NPS and fractal dimension calculation. The results demonstrated a mean fractal dimension of 1.86 for soft kernel, 1.92 for standard kernel, and 2.16 for bone kernel. Increasing fractal dimension corresponded to shift in the NPS towards higher spatial frequencies and grainier noise appearance. Stable fractal dimension was calculated from two ROI's compared to more than 250 ROI's used for NPS calculation. The scalar fractal dimension metric may be a useful noise texture descriptor for evaluating or optimizing reconstruction algorithms.
An efficient fractal image coding algorithm using unified feature and DCT
Energy Technology Data Exchange (ETDEWEB)
Zhou Yiming [Department of Automation, Tsinghua University, Beijing 100084 (China)], E-mail: zhouym02@mails.tsinghua.edu.cn; Zhang Chao; Zhang Zengke [Department of Automation, Tsinghua University, Beijing 100084 (China)
2009-02-28
Fractal image compression is a promising technique to improve the efficiency of image storage and image transmission with high compression ratio, however, the huge time consumption for the fractal image coding is a great obstacle to the practical applications. In order to improve the fractal image coding, efficient fractal image coding algorithms using a special unified feature and a DCT coder are proposed in this paper. Firstly, based on a necessary condition to the best matching search rule during fractal image coding, the fast algorithm using a special unified feature (UFC) is addressed, and it can reduce the search space obviously and exclude most inappropriate matching subblocks before the best matching search. Secondly, on the basis of UFC algorithm, in order to improve the quality of the reconstructed image, a DCT coder is combined to construct a hybrid fractal image algorithm (DUFC). Experimental results show that the proposed algorithms can obtain good quality of the reconstructed images and need much less time than the baseline fractal coding algorithm.
Improved Fractal Method for Singularity Detection in Fingerprint Images
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
A new technique that uses Discrete Fractal Brownian Motion todescribe a fingerprint is presented. By computing certain fractal parameters, a fingerprints core and delta fields can be roughly detected. Experimental results demonstrate this method to be not only more efficient than the single fractal dimension method, but also more noise-resistant than the traditional schemes.
Fractal Interpolation Function and its Dimension%分形插值函数及其维数
Institute of Scientific and Technical Information of China (English)
马林涛; 陈德勇; 张琰
2012-01-01
主要从分形插值函数的理论出发，利用Matlab软件绘制分形插值函数的图像，绘出确定的垂直压缩因子与随机垂直压缩因子的函数图像，定性地分析垂直压缩因子的变化所引起的分形插值函数图像的变化．最后，通过计算得到分形插值函数的图像的盒维数随着垂直压缩因子的变大而变大．%Based on the theories of fractal interpolation functions, by using Matlab software, we draw the images of fractal interpolation functions for the determined vertical compression factors and random vertical compression factors. Quantitatively analyze the change of the images of the fractal interpolation functions caused by the vertical compression factors. Finally, we calculate Box dimension of the fractal interpolation function. Therefore, the relationships between the vertical compression factors and Box dimensions of fractal interpolation functions are obtained.
FRACTAL DIMENSION OF URBAN EXPANSION BASED ON REMOTE SENSING IMAGES
Directory of Open Access Journals (Sweden)
IACOB I. CIPRIAN
2012-11-01
Full Text Available Fractal Dimension of Urban Expansion Based on Remote Sensing Images: In Cluj-Napoca city the process of urbanization has been accelerated during the years and implication of local authorities reflects a relevant planning policy. A good urban planning framework should take into account the society demands and also it should satisfy the natural conditions of local environment. The expansion of antropic areas it can be approached by implication of 5D variables (time as a sequence of stages, space: with x, y, z and magnitude of phenomena into the process, which will allow us to analyse and extract the roughness of city shape. Thus, to improve the decision factor we take a different approach in this paper, looking at geometry and scale composition. Using the remote sensing (RS and GIS techniques we manage to extract a sequence of built-up areas (from 1980 to 2012 and used the result as an input for modelling the spatialtemporal changes of urban expansion and fractal theory to analysed the geometric features. Taking the time as a parameter we can observe behaviour and changes in urban landscape, this condition have been known as self-organized – a condition which in first stage the system was without any turbulence (before the antropic factor and during the time tend to approach chaotic behaviour (entropy state without causing an disequilibrium in the main system.
Log-periodic route to fractal functions.
Gluzman, S; Sornette, D
2002-03-01
Log-periodic oscillations have been found to decorate the usual power-law behavior found to describe the approach to a critical point, when the continuous scale-invariance symmetry is partially broken into a discrete-scale invariance symmetry. For Ising or Potts spins with ferromagnetic interactions on hierarchical systems, the relative magnitude of the log-periodic corrections are usually very small, of order 10(-5). In growth processes [diffusion limited aggregation (DLA)], rupture, earthquake, and financial crashes, log-periodic oscillations with amplitudes of the order of 10% have been reported. We suggest a "technical" explanation for this 4 order-of-magnitude difference based on the property of the "regular function" g(x) embodying the effect of the microscopic degrees of freedom summed over in a renormalization group (RG) approach F(x)=g(x)+mu(-1)F(gamma x) of an observable F as a function of a control parameter x. For systems for which the RG equation has not been derived, the previous equation can be understood as a Jackson q integral, which is the natural tool for describing discrete-scale invariance. We classify the "Weierstrass-type" solutions of the RG into two classes characterized by the amplitudes A(n) of the power-law series expansion. These two classes are separated by a novel "critical" point. Growth processes (DLA), rupture, earthquake, and financial crashes thus seem to be characterized by oscillatory or bounded regular microscopic functions that lead to a slow power-law decay of A(n), giving strong log-periodic amplitudes. If in addition, the phases of A(n) are ergodic and mixing, the observable presents self-affine nondifferentiable properties. In contrast, the regular function of statistical physics models with "ferromagnetic"-type interactions at equilibrium involves unbound logarithms of polynomials of the control variable that lead to a fast exponential decay of A(n) giving weak log-periodic amplitudes and smoothed observables.
An improved fast fractal image compression using spatial texture correlation
Institute of Scientific and Technical Information of China (English)
Wang Xing-Yuan; Wang Yuan-Xing; Yun Jiao-Jiao
2011-01-01
This paper utilizes a spatial texture correlation and the intelligent classification algorithm (ICA) search strategy to speed up the encoding process and improve the bit rate for fractal image compression.Texture features is one of the most important properties for the representation of an image.Entropy and maximum entry from co-occurrence matrices are used for representing texture features in an image.For a range block,concerned domain blocks of neighbouring range blocks with similar texture features can be searched.In addition,domain blocks with similar texture features are searched in the ICA search process.Experiments show that in comparison with some typical methods,the proposed algorithm significantly speeds up the encoding process and achieves a higher compression ratio,with a slight diminution in the quality of the reconstructed image; in comparison with a spatial correlation scheme,the proposed scheme spends much less encoding time while the compression ratio and the quality of the reconstructed image are almost the same.
Osler, Thomas J.
1999-01-01
Because fractal images are by nature very complex, it can be inspiring and instructive to create the code in the classroom and watch the fractal image evolve as the user slowly changes some important parameter or zooms in and out of the image. Uses programming language that permits the user to store and retrieve a graphics image as a disk file.…
Fractal analysis of en face tomographic images obtained with full field optical coherence tomography
Energy Technology Data Exchange (ETDEWEB)
Gao, Wanrong; Zhu, Yue [Department of Optical Engineering, Nanjing University of Science and Technology, Jiangsu (China)
2017-03-15
The quantitative modeling of the imaging signal of pathological areas and healthy areas is necessary to improve the specificity of diagnosis with tomographic en face images obtained with full field optical coherence tomography (FFOCT). In this work, we propose to use the depth-resolved change in the fractal parameter as a quantitative specific biomarker of the stages of disease. The idea is based on the fact that tissue is a random medium and only statistical parameters that characterize tissue structure are appropriate. We successfully relate the imaging signal in FFOCT to the tissue structure in terms of the scattering function and the coherent transfer function of the system. The formula is then used to analyze the ratio of the Fourier transforms of the cancerous tissue to the normal tissue. We found that when the tissue changes from the normal to cancerous the ratio of the spectrum of the index inhomogeneities takes the form of an inverse power law and the changes in the fractal parameter can be determined by estimating slopes of the spectra of the ratio plotted on a log-log scale. The fresh normal and cancer liver tissues were imaged to demonstrate the potential diagnostic value of the method at early stages when there are no significant changes in tissue microstructures. (copyright 2016 by WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Fractal analysis of scatter imaging signatures to distinguish breast pathologies
Eguizabal, Alma; Laughney, Ashley M.; Krishnaswamy, Venkataramanan; Wells, Wendy A.; Paulsen, Keith D.; Pogue, Brian W.; López-Higuera, José M.; Conde, Olga M.
2013-02-01
Fractal analysis combined with a label-free scattering technique is proposed for describing the pathological architecture of tumors. Clinicians and pathologists are conventionally trained to classify abnormal features such as structural irregularities or high indices of mitosis. The potential of fractal analysis lies in the fact of being a morphometric measure of the irregular structures providing a measure of the object's complexity and self-similarity. As cancer is characterized by disorder and irregularity in tissues, this measure could be related to tumor growth. Fractal analysis has been probed in the understanding of the tumor vasculature network. This work addresses the feasibility of applying fractal analysis to the scattering power map (as a physical modeling) and principal components (as a statistical modeling) provided by a localized reflectance spectroscopic system. Disorder, irregularity and cell size variation in tissue samples is translated into the scattering power and principal components magnitude and its fractal dimension is correlated with the pathologist assessment of the samples. The fractal dimension is computed applying the box-counting technique. Results show that fractal analysis of ex-vivo fresh tissue samples exhibits separated ranges of fractal dimension that could help classifier combining the fractal results with other morphological features. This contrast trend would help in the discrimination of tissues in the intraoperative context and may serve as a useful adjunct to surgeons.
Fractal analysis of AFM images of the surface of Bowman's membrane of the human cornea.
Ţălu, Ştefan; Stach, Sebastian; Sueiras, Vivian; Ziebarth, Noël Marysa
2015-04-01
The objective of this study is to further investigate the ultrastructural details of the surface of Bowman's membrane of the human cornea, using atomic force microscopy (AFM) images. One representative image acquired of Bowman's membrane of a human cornea was investigated. The three-dimensional (3-D) surface of the sample was imaged using AFM in contact mode, while the sample was completely submerged in optisol solution. Height and deflection images were acquired at multiple scan lengths using the MFP-3D AFM system software (Asylum Research, Santa Barbara, CA), based in IGOR Pro (WaveMetrics, Lake Oswego, OR). A novel approach, based on computational algorithms for fractal analysis of surfaces applied for AFM data, was utilized to analyze the surface structure. The surfaces revealed a fractal structure at the nanometer scale. The fractal dimension, D, provided quantitative values that characterize the scale properties of surface geometry. Detailed characterization of the surface topography was obtained using statistical parameters, in accordance with ISO 25178-2: 2012. Results obtained by fractal analysis confirm the relationship between the value of the fractal dimension and the statistical surface roughness parameters. The surface structure of Bowman's membrane of the human cornea is complex. The analyzed AFM images confirm a fractal nature of the surface, which is not taken into account by classical surface statistical parameters. Surface fractal dimension could be useful in ophthalmology to quantify corneal architectural changes associated with different disease states to further our understanding of disease evolution.
Energy Technology Data Exchange (ETDEWEB)
Gomez-Carracedo, A.; Alvarez-Lorenzo, C.; Coca, R.; Martinez-Pacheco, R.; Concheiro, A. [Departamento de Farmacia y Tecnologia Farmaceutica, Universidad de Santiago de Compostela, Santiago de Compostela 15782 (Spain); Gomez-Amoza, J.L. [Departamento de Farmacia y Tecnologia Farmaceutica, Universidad de Santiago de Compostela, Santiago de Compostela 15782 (Spain)], E-mail: joseluis.gomez.amoza@usc.es
2009-01-15
The microstructure of theophylline pellets prepared from microcrystalline cellulose, carbopol and dicalcium phosphate dihydrate, according to a mixture design, was characterized using textural analysis of gray-level scanning electron microscopy (SEM) images and thermodynamic analysis of the cumulative pore volume distribution obtained by mercury intrusion porosimetry. Surface roughness evaluated in terms of gray-level non-uniformity and fractal dimension of pellet surface depended on agglomeration phenomena during extrusion/spheronization. Pores at the surface, mainly 1-15 {mu}m in diameter, determined both the mechanism and the rate of theophylline release, and a strong negative correlation between the fractal geometry and the b parameter of the Weibull function was found for pellets containing >60% carbopol. Theophylline mean dissolution time from these pellets was about two to four times greater. Textural analysis of SEM micrographs and fractal analysis of mercury intrusion data are complementary techniques that enable complete characterization of multiparticulate drug dosage forms.
Intelligent fuzzy approach for fast fractal image compression
Nodehi, Ali; Sulong, Ghazali; Al-Rodhaan, Mznah; Al-Dhelaan, Abdullah; Rehman, Amjad; Saba, Tanzila
2014-12-01
Fractal image compression (FIC) is recognized as a NP-hard problem, and it suffers from a high number of mean square error (MSE) computations. In this paper, a two-phase algorithm was proposed to reduce the MSE computation of FIC. In the first phase, based on edge property, range and domains are arranged. In the second one, imperialist competitive algorithm (ICA) is used according to the classified blocks. For maintaining the quality of the retrieved image and accelerating algorithm operation, we divided the solutions into two groups: developed countries and undeveloped countries. Simulations were carried out to evaluate the performance of the developed approach. Promising results thus achieved exhibit performance better than genetic algorithm (GA)-based and Full-search algorithms in terms of decreasing the number of MSE computations. The number of MSE computations was reduced by the proposed algorithm for 463 times faster compared to the Full-search algorithm, although the retrieved image quality did not have a considerable change.
Region-Based Fractal Image Coding with Freely-Shaped Partition
Institute of Scientific and Technical Information of China (English)
SUNYunda; ZHAOYao; YUANBaozong
2004-01-01
In Fractal image coding (FIC), a partitioning of the original image into ranges and domains is required, which greatly affects the coding performance. Usually, the more adaptive to the image content the partition is, the higher performance it can achieve. Nowadays, some alleged Region-based fractal coders (RBFC) using split-and-merge strategy can achieve better adaptivity andperformance compared with traditional rectangular block partitions. However, the regions are still with linear contour. In this paper, we present a Freely-shaped Regionbased fractal coder (FS-RBFC) using a two-step partitioning, i.e. coarse partitioning based on fractal dimension and fine partitioning based on region growth, which brings freely-shaped regions. Our highly image-adaptive scheme can achieve better rate-distortion curve than conventional scheme, even more visually pleasing results at the same performance.
Memory Function and Fractional Intergral Associated to the Random Self—similar Fractal
Institute of Scientific and Technical Information of China (English)
LIANGHong-liang; Hong-liang; LIUXiao-shu
2003-01-01
For a physics system which exhibits memory,if memory is preserved only at points of random self-similar fractals,we define random memory functions and give the connection between the expectation of flux and the fractional integral.In particular,when memory sets degenerate to Cantor type fractals or non-random self-similar fractals our results coincide with that of Nigmatullin and Ren et al.
Mishra, Jibitesh
2007-01-01
The book covers all the fundamental aspects of generating fractals through L-system. Also it provides insight to various researches in this area for generating fractals through L-system approach & estimating dimensions. Also it discusses various applications of L-system fractals. Key Features: - Fractals generated from L-System including hybrid fractals - Dimension calculation for L-system fractals - Images & codes for L-system fractals - Research directions in the area of L-system fractals - Usage of various freely downloadable tools in this area - Fractals generated from L-System including hybrid fractals- Dimension calculation for L-system fractals- Images & codes for L-system fractals- Research directions in the area of L-system fractals- Usage of various freely downloadable tools in this area
The fractal measurement of experimental images of supersonic turbulent mixing layer
Institute of Scientific and Technical Information of China (English)
ZHAO YuXin; YI ShiHe; TIAN LiFeng; HE Lin; CHENG ZhongYu
2008-01-01
Flow Visualization of supersonic mixing layer has been studied based on the high spatiotemporal resolution Nano-based Planar Laser Scattering (NPLS) method in SML-1 wind tunnel. The corresponding images distinctly reproduced the flow structure of laminar, transitional and turbulent region, with which the fractal meas-urement can be implemented. Two methods of measuring fractal dimension wereintroduced and compared. The fractal dimension of the transitional region and the fully developing turbulence region of supersonic mixing layer were measured based on the box-counting method. In the transitional region, the fractal dimension will increase with turbulent intensity. In the fully developing turbulent region, the fractal dimension will not vary apparently for different flow structures, which em-bodies the self-similarity of supersonic turbulence.
The fractal measurement of experimental images of supersonic turbulent mixing layer
Institute of Scientific and Technical Information of China (English)
2008-01-01
Flow visualization of supersonic mixing layer has been studied based on the high spatiotemporal resolution Nano-based Planar Laser Scattering(NPLS) method in SML-1 wind tunnel. The corresponding images distinctly reproduced the flow structure of laminar,transitional and turbulent region,with which the fractal measurement can be implemented. Two methods of measuring fractal dimension were introduced and compared. The fractal dimension of the transitional region and the fully developing turbulence region of supersonic mixing layer were measured based on the box-counting method. In the transitional region,the fractal dimension will increase with turbulent intensity. In the fully developing turbulent region,the fractal dimension will not vary apparently for different flow structures,which em-bodies the self-similarity of supersonic turbulence.
Zaia, Annamaria
2015-03-18
Osteoporosis represents one major health condition for our growing elderly population. It accounts for severe morbidity and increased mortality in postmenopausal women and it is becoming an emerging health concern even in aging men. Screening of the population at risk for bone degeneration and treatment assessment of osteoporotic patients to prevent bone fragility fractures represent useful tools to improve quality of life in the elderly and to lighten the related socio-economic impact. Bone mineral density (BMD) estimate by means of dual-energy X-ray absorptiometry is normally used in clinical practice for osteoporosis diagnosis. Nevertheless, BMD alone does not represent a good predictor of fracture risk. From a clinical point of view, bone microarchitecture seems to be an intriguing aspect to characterize bone alteration patterns in aging and pathology. The widening into clinical practice of medical imaging techniques and the impressive advances in information technologies together with enhanced capacity of power calculation have promoted proliferation of new methods to assess changes of trabecular bone architecture (TBA) during aging and osteoporosis. Magnetic resonance imaging (MRI) has recently arisen as a useful tool to measure bone structure in vivo. In particular, high-resolution MRI techniques have introduced new perspectives for TBA characterization by non-invasive non-ionizing methods. However, texture analysis methods have not found favor with clinicians as they produce quite a few parameters whose interpretation is difficult. The introduction in biomedical field of paradigms, such as theory of complexity, chaos, and fractals, suggests new approaches and provides innovative tools to develop computerized methods that, by producing a limited number of parameters sensitive to pathology onset and progression, would speed up their application into clinical practice. Complexity of living beings and fractality of several physio-anatomic structures suggest
Fractal analysis in radiological and nuclear medicine perfusion imaging: a systematic review
Energy Technology Data Exchange (ETDEWEB)
Michallek, Florian; Dewey, Marc [Humboldt-Universitaet zu Berlin, Freie Universitaet Berlin, Charite - Universitaetsmedizin Berlin, Medical School, Department of Radiology, Berlin (Germany)
2014-01-15
To provide an overview of recent research in fractal analysis of tissue perfusion imaging, using standard radiological and nuclear medicine imaging techniques including computed tomography (CT), magnetic resonance imaging (MRI), ultrasound, positron emission tomography (PET) and single-photon emission computed tomography (SPECT) and to discuss implications for different fields of application. A systematic review of fractal analysis for tissue perfusion imaging was performed by searching the databases MEDLINE (via PubMed), EMBASE (via Ovid) and ISI Web of Science. Thirty-seven eligible studies were identified. Fractal analysis was performed on perfusion imaging of tumours, lung, myocardium, kidney, skeletal muscle and cerebral diseases. Clinically, different aspects of tumour perfusion and cerebral diseases were successfully evaluated including detection and classification. In physiological settings, it was shown that perfusion under different conditions and in various organs can be properly described using fractal analysis. Fractal analysis is a suitable method for quantifying heterogeneity from radiological and nuclear medicine perfusion images under a variety of conditions and in different organs. Further research is required to exploit physiologically proven fractal behaviour in the clinical setting. (orig.)
Fractals with point impact in functional linear regression
McKeague, Ian W; 10.1214/10-AOS791
2010-01-01
This paper develops a point impact linear regression model in which the trajectory of a continuous stochastic process, when evaluated at a sensitive time point, is associated with a scalar response. The proposed model complements and is more interpretable than the functional linear regression approach that has become popular in recent years. The trajectories are assumed to have fractal (self-similar) properties in common with a fractional Brownian motion with an unknown Hurst exponent. Bootstrap confidence intervals based on the least-squares estimator of the sensitive time point are developed. Misspecification of the point impact model by a functional linear model is also investigated. Non-Gaussian limit distributions and rates of convergence determined by the Hurst exponent play an important role.
Potts model partition functions on two families of fractal lattices
Gong, Helin; Jin, Xian'an
2014-11-01
The partition function of q-state Potts model, or equivalently the Tutte polynomial, is computationally intractable for regular lattices. The purpose of this paper is to compute partition functions of q-state Potts model on two families of fractal lattices. Based on their self-similar structures and by applying the subgraph-decomposition method, we divide their Tutte polynomials into two summands, and for each summand we obtain a recursive formula involving the other summand. As a result, the number of spanning trees and their asymptotic growth constants, and a lower bound of the number of connected spanning subgraphs or acyclic root-connected orientations for each of such two lattices are obtained.
Border extrapolation using fractal attributes in remote sensing images
Cipolletti, M. P.; Delrieux, C. A.; Perillo, G. M. E.; Piccolo, M. C.
2014-01-01
In management, monitoring and rational use of natural resources the knowledge of precise and updated information is essential. Satellite images have become an attractive option for quantitative data extraction and morphologic studies, assuring a wide coverage without exerting negative environmental influence over the study area. However, the precision of such practice is limited by the spatial resolution of the sensors and the additional processing algorithms. The use of high resolution imagery (i.e., Ikonos) is very expensive for studies involving large geographic areas or requiring long term monitoring, while the use of less expensive or freely available imagery poses a limit in the geographic accuracy and physical precision that may be obtained. We developed a methodology for accurate border estimation that can be used for establishing high quality measurements with low resolution imagery. The method is based on the original theory by Richardson, taking advantage of the fractal nature of geographic features. The area of interest is downsampled at different scales and, at each scale, the border is segmented and measured. Finally, a regression of the dependence of the measured length with respect to scale is computed, which then allows for a precise extrapolation of the expected length at scales much finer than the originally available. The method is tested with both synthetic and satellite imagery, producing accurate results in both cases.
Boychuk, T. M.; Bodnar, B. M.; Vatamanesku, L. I.
2012-01-01
For the first time the complex correlation and fractal analysis was used for the investigation of microscopic images of both tissue images and hemangioma liquids. It was proposed a physical model of description of phase distributions formation of coherent radiation, which was transformed by optical anisotropic biological structures. The phase maps of laser radiation in the boundary diffraction zone were used as the main information parameter. The results of investigating the interrelation between the values of correlation (correlation area, asymmetry coefficient and autocorrelation function excess) and fractal (dispersion of logarithmic dependencies of power spectra) parameters are presented. They characterize the coordinate distributions of phase shifts in the points of laser images of histological sections of hemangioma, hemangioma blood smears and blood plasma with vascular system pathologies. The diagnostic criteria of hemangioma nascency are determined.
Institute of Scientific and Technical Information of China (English)
杨旭红; 李栋高
2004-01-01
Nonwovens are fiber materials which are based on nonwoven technologies. For the complexity and randomness of nonwovens morphologic structures, it is difficult to express them effectively using classical method. Fractal geometry gives us a new idea and a powerful tool to study on irregularity of geometric objects. Therefore, we studied on the pore size, pore shape, pore size distribution and fiber orientation distribution of real nonwovens using fractal geometry combined with computer image analysis to evaluate nonwovens' morphologic structures.
On the fractal distribution of primes and prime-indexed primes by the binary image analysis
Cattani, Carlo; Ciancio, Armando
2016-10-01
In this paper, the distribution of primes and prime-indexed primes (PIPs) is studied by mapping primes into a binary image which visualizes the distribution of primes. These images show that the distribution of primes (and PIPs) is similar to a Cantor dust, moreover the self-similarity with respect to the order of PIPs (already proven in Batchko (2014)) can be seen as an invariance of the binary images. The index of primes plays the same role of the scale for fractals, so that with respect to the index the distribution of prime-indexed primes is characterized by the self-similarity alike any other fractal. In particular, in order to single out the scale dependence, the PIPs fractal distribution will be evaluated by limiting to two parameters, fractal dimension (δ) and lacunarity (λ), that are usually used to measure the fractal nature. Because of the invariance of the corresponding binary plots, the fractal dimension and lacunarity of primes distribution are invariant with respect to the index of PIPs.
A Lossless hybrid wavelet-fractal compression for welding radiographic images.
Mekhalfa, Faiza; Avanaki, Mohammad R N; Berkani, Daoud
2016-01-01
In this work a lossless wavelet-fractal image coder is proposed. The process starts by compressing and decompressing the original image using wavelet transformation and fractal coding algorithm. The decompressed image is removed from the original one to obtain a residual image which is coded by using Huffman algorithm. Simulation results show that with the proposed scheme, we achieve an infinite peak signal to noise ratio (PSNR) with higher compression ratio compared to typical lossless method. Moreover, the use of wavelet transform speeds up the fractal compression algorithm by reducing the size of the domain pool. The compression results of several welding radiographic images using the proposed scheme are evaluated quantitatively and compared with the results of Huffman coding algorithm.
Lahmiri, Salim
2016-08-01
The main purpose of this work is to explore the usefulness of fractal descriptors estimated in multi-resolution domains to characterize biomedical digital image texture. In this regard, three multi-resolution techniques are considered: the well-known discrete wavelet transform (DWT) and the empirical mode decomposition (EMD), and; the newly introduced; variational mode decomposition mode (VMD). The original image is decomposed by the DWT, EMD, and VMD into different scales. Then, Fourier spectrum based fractal descriptors is estimated at specific scales and directions to characterize the image. The support vector machine (SVM) was used to perform supervised classification. The empirical study was applied to the problem of distinguishing between normal and abnormal brain magnetic resonance images (MRI) affected with Alzheimer disease (AD). Our results demonstrate that fractal descriptors estimated in VMD domain outperform those estimated in DWT and EMD domains; and also those directly estimated from the original image.
Fractal scaling of apparent soil moisture estimated from vertical planes of Vertisol pit images
Cumbrera, Ramiro; Tarquis, Ana M.; Gascó, Gabriel; Millán, Humberto
2012-07-01
SummaryImage analysis could be a useful tool for investigating the spatial patterns of apparent soil moisture at multiple resolutions. The objectives of the present work were (i) to define apparent soil moisture patterns from vertical planes of Vertisol pit images and (ii) to describe the scaling of apparent soil moisture distribution using fractal parameters. Twelve soil pits (0.70 m long × 0.60 m width × 0.30 m depth) were excavated on a bare Mazic Pellic Vertisol. Six of them were excavated in April/2011 and six pits were established in May/2011 after 3 days of a moderate rainfall event. Digital photographs were taken from each Vertisol pit using a Kodak™ digital camera. The mean image size was 1600 × 945 pixels with one physical pixel ≈373 μm of the photographed soil pit. Each soil image was analyzed using two fractal scaling exponents, box counting (capacity) dimension (DBC) and interface fractal dimension (Di), and three prefractal scaling coefficients, the total number of boxes intercepting the foreground pattern at a unit scale (A), fractal lacunarity at the unit scale (Λ1) and Shannon entropy at the unit scale (S1). All the scaling parameters identified significant differences between both sets of spatial patterns. Fractal lacunarity was the best discriminator between apparent soil moisture patterns. Soil image interpretation with fractal exponents and prefractal coefficients can be incorporated within a site-specific agriculture toolbox. While fractal exponents convey information on space filling characteristics of the pattern, prefractal coefficients represent the investigated soil property as seen through a higher resolution microscope. In spite of some computational and practical limitations, image analysis of apparent soil moisture patterns could be used in connection with traditional soil moisture sampling, which always renders punctual estimates.
Time Series Analysis OF SAR Image Fractal Maps: The Somma-Vesuvio Volcanic Complex Case Study
Pepe, Antonio; De Luca, Claudio; Di Martino, Gerardo; Iodice, Antonio; Manzo, Mariarosaria; Pepe, Susi; Riccio, Daniele; Ruello, Giuseppe; Sansosti, Eugenio; Zinno, Ivana
2016-04-01
The fractal dimension is a significant geophysical parameter describing natural surfaces representing the distribution of the roughness over different spatial scale; in case of volcanic structures, it has been related to the specific nature of materials and to the effects of active geodynamic processes. In this work, we present the analysis of the temporal behavior of the fractal dimension estimates generated from multi-pass SAR images relevant to the Somma-Vesuvio volcanic complex (South Italy). To this aim, we consider a Cosmo-SkyMed data-set of 42 stripmap images acquired from ascending orbits between October 2009 and December 2012. Starting from these images, we generate a three-dimensional stack composed by the corresponding fractal maps (ordered according to the acquisition dates), after a proper co-registration. The time-series of the pixel-by-pixel estimated fractal dimension values show that, over invariant natural areas, the fractal dimension values do not reveal significant changes; on the contrary, over urban areas, it correctly assumes values outside the natural surfaces fractality range and show strong fluctuations. As a final result of our analysis, we generate a fractal map that includes only the areas where the fractal dimension is considered reliable and stable (i.e., whose standard deviation computed over the time series is reasonably small). The so-obtained fractal dimension map is then used to identify areas that are homogeneous from a fractal viewpoint. Indeed, the analysis of this map reveals the presence of two distinctive landscape units corresponding to the Mt. Vesuvio and Gran Cono. The comparison with the (simplified) geological map clearly shows the presence in these two areas of volcanic products of different age. The presented fractal dimension map analysis demonstrates the ability to get a figure about the evolution degree of the monitored volcanic edifice and can be profitably extended in the future to other volcanic systems with
Image fractal coding algorithm based on complex exponent moments and minimum variance
Yang, Feixia; Ping, Ziliang; Zhou, Suhua
2017-02-01
Image fractal coding possesses very high compression ratio, the main problem is low speed of coding. The algorithm based on Complex Exponent Moments(CEM) and minimum variance is proposed to speed up the fractal coding compression. The definition of CEM and its FFT algorithm are presented, and the multi-distorted invariance of CEM are discussed. The multi-distorted invariance of CEM is fit to the fractal property of an image. The optimal matching pair of range blocks and domain blocks in an image is determined by minimizing the variance of their CEM. Theory analysis and experimental results have proved that the algorithm can dramatically reduce the iteration time and speed up image encoding and decoding process.
A Method for Generating Super Large Fractal Images useful for Decoration Art
Institute of Scientific and Technical Information of China (English)
HuajieLIU; JunLUO
1996-01-01
Many authors have reported the techniques to iterate nonlinear equations on complex plane,but generally,the size of image calculated by usual VGA style(640×480) is too small to fit the needs for high quality publications or ecorative patterns.We describe a universal method for generating and storing(in *.GIF format)fractal image large enough as you need,such as an image 5000×5000 256-color(25,000,774 bytes≈23.8MB),which can thoroughly display the intricate beauty of fractals.
K-Dimension and H(o)lder Exponent for Bush Type Fractal Functions
Institute of Scientific and Technical Information of China (English)
Wang Hongyong
2006-01-01
Bush type fractal functions were defined by means of the expression of Cantor series of real numbers. The upper and lower bound estimates for the K-dimension of such functions were given. In a typical case, the fractal dimensional relations in which the K-dimension equals the box dimension and packing dimension were presented; moreover, the exact H(o)lder exponent were obtained for such Bush type functions.
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
The linear relationship between fractal dimensions of a type of generalized Weierstrass functions and the order of their fractional calculus has been proved. The graphs and numerical results given here further indicate the corresponding relationship.
Morphology and functions of astrocytes cultured on water-repellent fractal tripalmitin surfaces.
Hu, Wei-wei; Wang, Zhe; Zhang, Shan-shan; Jiang, Lei; Zhang, Jing; Zhang, Xiangnan; Lei, Qun-fang; Park, Hyun-Joo; Fang, Wen-jun; Chen, Zhong
2014-08-01
In the brain, astrocytes play an essential role with their multiple functions and sophisticated structure, as surrounded by a fractal environment which has not been available in our traditional cell culture. Water-repellent fractal tripalmitin (PPP) surfaces can imitate the fractal environment in vivo, so the morphology and biochemical characterization of astrocytes on these surfaces are examined. Water-repellent fractal PPP surface can induce astrocytes to display sophisticated morphology with smaller size of cell area, longer and finer filopodium-like processes, and higher morphological complexity. The super water-repellent fractal PPP surface with water contact angle of 150°∼160° produces the maximal effects compared with other surfaces at lower water contact angles. The trends of characteristic protein expression, including that of nestin, vimentin, GFAP and glutamine synthetase, for astrocytes cultured on super water-repellent fractal PPP surfaces approximate more to in vivo pattern. The super water-repellent PPP surface also render astrocytes to perform more pronounced promotion of neurogenesis by increasing the release of nerve growth factor in a co-culture system. Altogether, our results suggest that the super water-repellent fractal PPP surface facilitates the astrocytes to mimic their in vivo performance, thus provides a closer-to-natural culture environment for experimental assessment of glial structure and functions.
A CLASS OF FUNCTIONAL EQUATION AND FRACTAL INTERPOLATION FUNCTIONS
Institute of Scientific and Technical Information of China (English)
ShaZhen
1999-01-01
A new class of functional equation in C0(I) is investigated. It is proved that some class of FIF satisfies the functional equation. Another functional equation is constructed. Theirsolutions can approximate FIF arbitrarily. And a new approximate estimate between FIF andinterpolated function is given.
Tremberger, George, Jr.; Flamholz, A.; Cheung, E.; Sullivan, R.; Subramaniam, R.; Schneider, P.; Brathwaite, G.; Boteju, J.; Marchese, P.; Lieberman, D.; Cheung, T.; Holden, Todd
2007-09-01
The absorption effect of the back surface boundary of a diffuse layer was studied via laser generated reflection speckle pattern. The spatial speckle intensity provided by a laser beam was measured. The speckle data were analyzed in terms of fractal dimension (computed by NIH ImageJ software via the box counting fractal method) and weak localization theory based on Mie scattering. Bar code imaging was modeled as binary absorption contrast and scanning resolution in millimeter range was achieved for diffusive layers up to thirty transport mean free path thick. Samples included alumina, porous glass and chicken tissue. Computer simulation was used to study the effect of speckle spatial distribution and observed fractal dimension differences were ascribed to variance controlled speckle sizes. Fractal dimension suppressions were observed in samples that had thickness dimensions around ten transport mean free path. Computer simulation suggested a maximum fractal dimension of about 2 and that subtracting information could lower fractal dimension. The fractal dimension was shown to be sensitive to sample thickness up to about fifteen transport mean free paths, and embedded objects which modified 20% or more of the effective thickness was shown to be detectable. The box counting fractal method was supplemented with the Higuchi data series fractal method and application to architectural distortion mammograms was demonstrated. The use of fractals in diffusive analysis would provide a simple language for a dialog between optics experts and mammography radiologists, facilitating the applications of laser diagnostics in tissues.
Automatic Method to Classify Images Based on Multiscale Fractal Descriptors and Paraconsistent Logic
Pavarino, E.; Neves, L. A.; Nascimento, M. Z.; Godoy, M. F.; Arruda, P. F.; Neto, D. S.
2015-01-01
In this study is presented an automatic method to classify images from fractal descriptors as decision rules, such as multiscale fractal dimension and lacunarity. The proposed methodology was divided in three steps: quantification of the regions of interest with fractal dimension and lacunarity, techniques under a multiscale approach; definition of reference patterns, which are the limits of each studied group; and, classification of each group, considering the combination of the reference patterns with signals maximization (an approach commonly considered in paraconsistent logic). The proposed method was used to classify histological prostatic images, aiming the diagnostic of prostate cancer. The accuracy levels were important, overcoming those obtained with Support Vector Machine (SVM) and Best- first Decicion Tree (BFTree) classifiers. The proposed approach allows recognize and classify patterns, offering the advantage of giving comprehensive results to the specialists.
Detection of Rice Leaf Diseases Using Chaos and Fractal Dimension in Image Processing
Directory of Open Access Journals (Sweden)
V.Surendrababu
2014-01-01
Full Text Available A novel method for detecting rice leaf disease using image processing technique called fractal dimension and chaos theory is proposed in this paper. The analysis of a diseased leaf is carried out according to its image pattern and fractal dimension, and especially box-counting ratio calculation, and chaos, are applied to be able to identify the disease pattern’s self-similarity and to recreate the fractal. The image’s self-similarity is the disease infected one which is same as when it is fully infected. This method is proposed as preliminary information for the development of an early detection system or for developing knowledge based expert system or decision support system.
Dewdney, A. K.
1991-01-01
Explores the subject of fractal geometry focusing on the occurrence of fractal-like shapes in the natural world. Topics include iterated functions, chaos theory, the Lorenz attractor, logistic maps, the Mandelbrot set, and mini-Mandelbrot sets. Provides appropriate computer algorithms, as well as further sources of information. (JJK)
On the fractal geometry of DNA by the binary image analysis.
Cattani, Carlo; Pierro, Gaetano
2013-09-01
The multifractal analysis of binary images of DNA is studied in order to define a methodological approach to the classification of DNA sequences. This method is based on the computation of some multifractality parameters on a suitable binary image of DNA, which takes into account the nucleotide distribution. The binary image of DNA is obtained by a dot-plot (recurrence plot) of the indicator matrix. The fractal geometry of these images is characterized by fractal dimension (FD), lacunarity, and succolarity. These parameters are compared with some other coefficients such as complexity and Shannon information entropy. It will be shown that the complexity parameters are more or less equivalent to FD, while the parameters of multifractality have different values in the sense that sequences with higher FD might have lower lacunarity and/or succolarity. In particular, the genome of Drosophila melanogaster has been considered by focusing on the chromosome 3r, which shows the highest fractality with a corresponding higher level of complexity. We will single out some results on the nucleotide distribution in 3r with respect to complexity and fractality. In particular, we will show that sequences with higher FD also have a higher frequency distribution of guanine, while low FD is characterized by the higher presence of adenine.
Extension Theorem for Complex Clifford Algebras-Valued Functions on Fractal Domains
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Bory-Reyes Juan
2010-01-01
Full Text Available Monogenic extension theorem of complex Clifford algebras-valued functions over a bounded domain with fractal boundary is obtained. The paper is dealing with the class of Hölder continuous functions. Applications to holomorphic functions theory of several complex variables as well as to that of the so-called biregular functions will be deduced directly from the isotonic approach.
Tomomitsu, Tatsushi; Mimura, Hiroaki; Murase, Kenya; Tamada, Tsutomu; Sone, Teruki; Fukunaga, Masao
2005-06-20
Many analyses of bone microarchitecture using three-dimensional images of micro CT (microCT) have been reported recently. However, as extirpated bone is the subject of measurement on microCT, various kinds of information are not available clinically. Our aim is to evaluate usefulness of fractal dimension as an index of bone strength different from bone mineral density in in-vivo, to which microCT could not be applied. In this fundamental study, the relation between pixel size and the slice thickness of images was examined when fractal analysis was applied to clinical images. We examined 40 lumbar spine specimens extirpated from 16 male cadavers (30-88 years; mean age, 60.8 years). Three-dimensional images of the trabeculae of 150 slices were obtained by a microCT system under the following conditions: matrix size, 512 x 512; slice thickness, 23.2 em; and pixel size, 18.6 em. Based on images of 150 slices, images of four different matrix sizes and nine different slice thicknesses were made using public domain software (NIH Image). The threshold value for image binarization, and the relation between pixel size and the slice thickness of an image used for two-dimensional and three-dimensional fractal analyses were studied. In addition, the box counting method was used for fractal analysis. One hundred forty-five in box counting was most suitable as the threshold value for image binarization on the 256 gray levels. The correlation coefficients between two-dimensional fractal dimensions of processed images and three-dimensional fractal dimensions of original images were more than 0.9 for pixel sizes fractal dimension of processed images and three-dimensional fractal dimension of original images, when pixel size was less than 74.4 microm, a correlation coefficient of more than 0.9 was obtained even for the maximal slice thickness (1.74 mm) examined in this study.
Fractal analysis of granular ore media based on computed tomography image processing
Institute of Scientific and Technical Information of China (English)
WU Ai-xiang; YANG Bao-hua; ZHOU Xu
2008-01-01
The cross-sectional images of nine groups of ore samples were obtained by X-ray computed tomography(CT) scanner.Based on CT image analysis,the fractal dimensions of solid matrix,pore space and matrix/pore interface of each sample were measured by using box counting method.The correlation of the three fractal dimensions with particle size,porosity,and seepage coefficient was investigated.The results show that for all images of these samples,the matrix phase has the highest dimension,followed by the pore phase,and the dimension of matrix-pore interface has the smallest value; the dimensions of matrix phase and matrix-pore interface are negatively and linearly correlated with porosity while the dimension of pore phase relates positively and linearly with porosity; the fractal dimension of matrix-pore interface relates negatively and linearly with seepage coefficient.Larger fractal dimension of matrix/pore interface indicates more irregular complicated channels for solution flow,resulting in low permeability.
Directory of Open Access Journals (Sweden)
Tatjana eStadnitski
2012-05-01
Full Text Available When investigating fractal phenomena, the following questions are fundamental for the applied researcher: (1 What are essential statistical properties of 1/f noise? (2 Which estimators are available for measuring fractality? (3 Which measurement instruments are appropriate and how are they applied? The purpose of this article is to give clear and comprehensible answers to these questions. First, theoretical characteristics of a fractal pattern (self-similarity, long memory, power law and the related fractal parameters (the Hurst coefficient, the scaling exponent, the fractional differencing parameter d of the ARFIMA methodology, the power exponent of the spectral analysis are discussed. Then, estimators of fractal parameters from different software packages commonly used by applied researchers (R, SAS, SPSS are introduced and evaluated. Advantages, disadvantages, and constrains of the popular estimators are illustrated by elaborate examples. Finally, crucial steps of fractal analysis (plotting time series data, autocorrelation and spectral functions; performing stationarity tests; choosing an adequate estimator; estimating fractal parameters; distinguishing fractal processes from short memory patterns are demonstrated with empirical time series.
Stadnitski, Tatjana
2012-01-01
WHEN INVESTIGATING FRACTAL PHENOMENA, THE FOLLOWING QUESTIONS ARE FUNDAMENTAL FOR THE APPLIED RESEARCHER: (1) What are essential statistical properties of 1/f noise? (2) Which estimators are available for measuring fractality? (3) Which measurement instruments are appropriate and how are they applied? The purpose of this article is to give clear and comprehensible answers to these questions. First, theoretical characteristics of a fractal pattern (self-similarity, long memory, power law) and the related fractal parameters (the Hurst coefficient, the scaling exponent α, the fractional differencing parameter d of the autoregressive fractionally integrated moving average methodology, the power exponent β of the spectral analysis) are discussed. Then, estimators of fractal parameters from different software packages commonly used by applied researchers (R, SAS, SPSS) are introduced and evaluated. Advantages, disadvantages, and constrains of the popular estimators ([Formula: see text] power spectral density, detrended fluctuation analysis, signal summation conversion) are illustrated by elaborate examples. Finally, crucial steps of fractal analysis (plotting time series data, autocorrelation, and spectral functions; performing stationarity tests; choosing an adequate estimator; estimating fractal parameters; distinguishing fractal processes from short-memory patterns) are demonstrated with empirical time series.
Barnsley, Michael F
2012-01-01
""Difficult concepts are introduced in a clear fashion with excellent diagrams and graphs."" - Alan E. Wessel, Santa Clara University""The style of writing is technically excellent, informative, and entertaining."" - Robert McCartyThis new edition of a highly successful text constitutes one of the most influential books on fractal geometry. An exploration of the tools, methods, and theory of deterministic geometry, the treatment focuses on how fractal geometry can be used to model real objects in the physical world. Two sixteen-page full-color inserts contain fractal images, and a bonus CD of
An image retrieval system based on fractal dimension
Institute of Scientific and Technical Information of China (English)
姚敏; 易文晟; 沈斌; DAIHong-hua
2003-01-01
This paper presents a new kind of image retrieval system which obtains the feature vectors of im-ages by estimating their fraetal dimension; and at the same time establishes a tree-structure image database. After preproeessing and feature extracting, a given image is matched with the standard images in the image da-tabase using a hierarchical method of image indexing.
2013-01-01
Changes in the concentration profiles of β-carotene caused by diffusion through parenchymatic dried apple tissue were characterized by image and fractal analysis. Apple slices were dried by convection, and then impregnated with an aqueous β-carotene solution. Scanning electron microscopy images of dried apple slices were captured and the fractal dimension (FD) values of the textures of the images were obtained (FDSEM). It was observed that the microstructure of the foodstuff being impregnated...
The conundrum of functional brain networks: small-world efficiency or fractal modularity
Gallos, Lazaros K; Makse, Hernan A
2012-01-01
The human brain has been studied at multiple scales, from neurons, circuits, areas with well defined anatomical and functional boundaries, to large-scale functional networks which mediate coherent cognition. In a recent work, we addressed the problem of the hierarchical organization in the brain through network analysis. Our analysis identified functional brain modules of fractal structure that were inter-connected in a small-world topology. Here, we provide more details on the use of network science tools to elaborate on this behavior. We indicate the importance of using percolation theory to highlight the modular character of the functional brain network. These modules present a fractal, self-similar topology, identified through fractal network methods. When we lower the threshold of correlations to include weaker ties, the network as a whole assumes a small-world character. These weak ties are organized precisely as predicted by theory maximizing information transfer with minimal wiring costs.
Reduction of Transmitted Information Using Similarities between Range Blocks in Fractal Image Coding
Hu, Xiaotong; Qiu, Shuping; Kuroda, Hideo
2007-01-01
Fractal image coding uses the similarities between the best matching domain blocks and range blocks to reconstruct image. In the transmitted information, the information about the best matching domain blocks occupies a large percentage, so the reduction of information about the best matching domain blocks is the most effective method to reduce the quality of transmitted information. On the other hand, there are similarities between range blocks from each other. So, when range blocks are simil...
Directory of Open Access Journals (Sweden)
Amir Lashgari
2015-01-01
Full Text Available Bimetallic materials, which have the ability to convert heat change into mechanical movement, normally consist of two bonded strips of dissimilar metals that expand at different rates. We describe how we made a manganese-chromium (Mn-Cr bimetallic nanocomposite using the centrifuge method and a low-to-high approach. We conducted scanning electron microscope (SEM imaging, energy-dispersive X-ray spectroscopy (EDX analysis, and X-ray diffraction spectra of the nanocomposite to prove its identity. We examined how centrifuge speed, process time, and the use of an “intruder agent” affected the properties of the material. The fractal dimension is a significant factor that can be used to approximate the surface roughness, the texture segmentation, and an image of the studied compounds. We calculated the technique of fractal dimensions using image-processing values on a computer and histogram plot with the SEM image of the Mn-Cr bimetallic nanocomposite using MATLAB software. We applied the Statistical Package for the Social Sciences software for statistics data extracted from the SEM image of the nanocomposite and obtained the following results: mean = 1.778, median = 1.770, max = 1.98, min = 1.60, skewness = 0.177, range = 0.38, and harmonic mean = 1.771 for fractal dimension of the SEM image.
Enhancing Volumetric Bouligand-Minkowski Fractal Descriptors by using Functional Data Analysis
Florindo, João Batista; Bruno, Odemir Martinez; 10.1142/S0129183111016701
2012-01-01
This work proposes and study the concept of Functional Data Analysis transform, applying it to the performance improving of volumetric Bouligand-Minkowski fractal descriptors. The proposed transform consists essentially in changing the descriptors originally defined in the space of the calculus of fractal dimension into the space of coefficients used in the functional data representation of these descriptors. The transformed decriptors are used here in texture classification problems. The enhancement provided by the FDA transform is measured by comparing the transformed to the original descriptors in terms of the correctness rate in the classification of well known datasets.
Breki, Christina-Marina; Hassel, Jessica; Theoharis, Theoharis; Sachpekidis, Christos; Pan, Leyun; Provata, Astero
2016-01-01
PET/CT with F-18-Fluorodeoxyglucose (FDG) images of patients suffering from metastatic melanoma have been analysed using fractal and multifractal analysis to assess the impact of monoclonal antibody ipilimumab treatment with respect to therapy outcome. Our analysis shows that the fractal dimensions which describe the tracer dispersion in the body decrease consistently with the deterioration of the patient therapeutic outcome condition. In 20 out-of 24 cases the fractal analysis results match those of the medical records, while 7 cases are considered as special cases because the patients have non-tumour related medical conditions or side effects which affect the results. The decrease in the fractal dimensions with the deterioration of the patient conditions (in terms of disease progression) are attributed to the hierarchical localisation of the tracer which accumulates in the affected lesions and does not spread homogeneously throughout the body. Fractality emerges as a result of the migration patterns which t...
Detecting abrupt dynamic change based on changes in the fractal properties of spatial images
Liu, Qunqun; He, Wenping; Gu, Bin; Jiang, Yundi
2016-08-01
Many abrupt climate change events often cannot be detected timely by conventional abrupt detection methods until a few years after these events have occurred. The reason for this lag in detection is that abundant and long-term observational data are required for accurate abrupt change detection by these methods, especially for the detection of a regime shift. So, these methods cannot help us understand and forecast the evolution of the climate system in a timely manner. Obviously, spatial images, generated by a coupled spatiotemporal dynamical model, contain more information about a dynamic system than a single time series, and we find that spatial images show the fractal properties. The fractal properties of spatial images can be quantitatively characterized by the Hurst exponent, which can be estimated by two-dimensional detrended fluctuation analysis (TD-DFA). Based on this, TD-DFA is used to detect an abrupt dynamic change of a coupled spatiotemporal model. The results show that the TD-DFA method can effectively detect abrupt parameter changes in the coupled model by monitoring the changing in the fractal properties of spatial images. The present method provides a new way for abrupt dynamic change detection, which can achieve timely and efficient abrupt change detection results.
ITERATION FREE FRACTAL COMPRESSION USING GENETIC ALGORITHM FOR STILL COLOUR IMAGES
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A.R. Nadira Banu Kamal
2014-02-01
Full Text Available The storage requirements for images can be excessive, if true color and a high-perceived image quality are desired. An RGB image may be viewed as a stack of three gray-scale images that when fed into the red, green and blue inputs of a color monitor, produce a color image on the screen. The abnormal size of many images leads to long, costly, transmission times. Hence, an iteration free fractal algorithm is proposed in this research paper to design an efficient search of the domain pools for colour image compression using Genetic Algorithm (GA. The proposed methodology reduces the coding process time and intensive computation tasks. Parameters such as image quality, compression ratio and coding time are analyzed. It is observed that the proposed method achieves excellent performance in image quality with reduction in storage space.
Discriminating between photorealistic computer graphics and natural images using fractal geometry
Institute of Scientific and Technical Information of China (English)
PAN Feng; CHEN JiongBin; HUANG JiWu
2009-01-01
Rendering technology in computer graphics (CG) Is now capable of producing highly photorealistlc Images, giving rise to the problem of how to identify CG Images from natural images. Some methods were proposed to solve this problem. In this paper, we give a novel method from a new point of view of Image perception. Although the photorealisUc CG images are very similar to natural images, they are surrealistic and smoother than natural images, thus leading to the difference in perception. A part of features are derived from fractal dimension to capture the difference In color perception between CG images and natural Images, and several generalized dimensions are used as the rest features to capture difference in coarseness. The effect of these features is verified by experiments. The average accuracy is over 91.2%.
Institute of Scientific and Technical Information of China (English)
HU; Xingtang; ZHANG; Bing; ZHANG; Xia; ZHENG; Lanfen; TONG; Qingxi
2006-01-01
Starting with a fractal-based image-compression algorithm based on wavelet transformation for hyperspectral images, the authors were able to obtain more spectral bands with the help of of hyperspectral remote sensing. Because large amounts of data and limited bandwidth complicate the storage and transmission of data measured by TB-level bits, it is important to compress image data acquired by hyperspectral sensors such as MODIS, PHI, and OMIS; otherwise, conventional lossless compression algorithms cannot reach adequate compression ratios. Other loss-compression methods can reach high compression ratios but lack good image fidelity, especially for hyperspectral image data. Among the third generation of image compression algorithms, fractal image compression based on wavelet transformation is superior to traditional compression methods,because it has high compression ratios and good image fidelity, and requires less computing time. To keep the spectral dimension invariable, the authors compared the results of two compression algorithms based on the storage-file structures of BSQ and of BIP, and improved the HV and Quadtree partitioning and domain-range matching algorithms in order to accelerate their encode/decode efficiency. The authors' Hyperspectral Image Process and Analysis System (HIPAS) software used a VC++6.0 integrated development environment (IDE), with which good experimental results were obtained. Possible modifications of the algorithm and limitations of the method are also discussed.
Radial distribution function for hard spheres in fractal dimensions. A heuristic approximation
Santos, Andrés
2016-01-01
Analytic approximations for the radial distribution function, the structure factor, and the equation of state of hard-core fluids in fractal dimension $d$ ($1 \\leq d \\leq 3$) are developed as heuristic interpolations from the knowledge of the exact and Percus-Yevick results for the hard-rod and hard-sphere fluids, respectively. In order to assess their value, such approximate results are compared with those of recent Monte Carlo simulations and numerical solutions of the Percus-Yevick equation for fractal dimension [M. Heinen et al., Phys. Rev. Lett. \\textbf{115}, 097801 (2015)], a good agreement being observed.
Liang, Yingjie; Ye, Allen Q.; Chen, Wen; Gatto, Rodolfo G.; Colon-Perez, Luis; Mareci, Thomas H.; Magin, Richard L.
2016-10-01
Non-Gaussian (anomalous) diffusion is wide spread in biological tissues where its effects modulate chemical reactions and membrane transport. When viewed using magnetic resonance imaging (MRI), anomalous diffusion is characterized by a persistent or 'long tail' behavior in the decay of the diffusion signal. Recent MRI studies have used the fractional derivative to describe diffusion dynamics in normal and post-mortem tissue by connecting the order of the derivative with changes in tissue composition, structure and complexity. In this study we consider an alternative approach by introducing fractal time and space derivatives into Fick's second law of diffusion. This provides a more natural way to link sub-voxel tissue composition with the observed MRI diffusion signal decay following the application of a diffusion-sensitive pulse sequence. Unlike previous studies using fractional order derivatives, here the fractal derivative order is directly connected to the Hausdorff fractal dimension of the diffusion trajectory. The result is a simpler, computationally faster, and more direct way to incorporate tissue complexity and microstructure into the diffusional dynamics. Furthermore, the results are readily expressed in terms of spectral entropy, which provides a quantitative measure of the overall complexity of the heterogeneous and multi-scale structure of biological tissues. As an example, we apply this new model for the characterization of diffusion in fixed samples of the mouse brain. These results are compared with those obtained using the mono-exponential, the stretched exponential, the fractional derivative, and the diffusion kurtosis models. Overall, we find that the order of the fractal time derivative, the diffusion coefficient, and the spectral entropy are potential biomarkers to differentiate between the microstructure of white and gray matter. In addition, we note that the fractal derivative model has practical advantages over the existing models from the
Energy Technology Data Exchange (ETDEWEB)
N' Diaye, Mambaye [LUNAM Université, GEROM Groupe Etudes Remodelage Osseux et bioMatériaux-LHEA, IRIS-IBS Institut de Biologie en Santé, CHU d' Angers, 49933 ANGERS Cedex (France); Degeratu, Cristinel [LUNAM Université, GEROM Groupe Etudes Remodelage Osseux et bioMatériaux-LHEA, IRIS-IBS Institut de Biologie en Santé, CHU d' Angers, 49933 ANGERS Cedex (France); University Politehnica of Bucharest, Faculty of Applied Chemistry and Materials Science, Department of Bioresources and Polymer Science, Calea Victoriei 149, 010072, Sector 1, Bucharest (Romania); Bouler, Jean-Michel [Inserm UMR 791, LIOAD, University of Nantes, 44000 Nantes (France); Chappard, Daniel, E-mail: daniel.chappard@univ-angers.fr [LUNAM Université, GEROM Groupe Etudes Remodelage Osseux et bioMatériaux-LHEA, IRIS-IBS Institut de Biologie en Santé, CHU d' Angers, 49933 ANGERS Cedex (France)
2013-05-01
Porous structures are becoming more and more important in biology and material science because they help in reducing the density of the grafted material. For biomaterials, porosity also increases the accessibility of cells and vessels inside the grafted area. However, descriptors of porosity are scanty. We have used a series of biomaterials with different types of porosity (created by various porogens: fibers, beads …). Blocks were studied by microcomputed tomography for the measurement of 3D porosity. 2D sections were re-sliced to analyze the microarchitecture of the pores and were transferred to image analysis programs: star volumes, interconnectivity index, Minkowski–Bouligand and Kolmogorov fractal dimensions were determined. Lacunarity and succolarity, two recently described fractal dimensions, were also computed. These parameters provided a precise description of porosity and pores' characteristics. Non-linear relationships were found between several descriptors e.g. succolarity and star volume of the material. A linear correlation was found between lacunarity and succolarity. These techniques appear suitable in the study of biomaterials usable as bone substitutes. Highlights: ► Interconnected porosity is important in the development of bone substitutes. ► Porosity was evaluated by 2D and 3D morphometry on microCT images. ► Euclidean and fractal descriptors measure interconnectivity on 2D microCT images. ► Lacunarity and succolarity were evaluated on a series of porous biomaterials.
Fractal analyses of osseous healing using Tuned Aperture Computed Tomography images
Energy Technology Data Exchange (ETDEWEB)
Nair, M.K.; Nair, U.P. [Dept. of Oral and Maxillofacial Radiology, Univ. of Pittsburgh, PA (United States); Seyedain, A. [Dept. of Periodontics, Univ. of Pittsburgh, PA (United States); Webber, R.L. [Dept. of Dentistry, Wake Forest University School of Medicine, Winston-Salem (United States); Piesco, N.P.; Agarwal, S.; Mooney, M.P. [Dept. of Oral Biology, School of Dental Medicine, Univ. of Pittsburgh, PA (Ukraine); Groendahl, H.G. [Dept. of Oral and Maxillofacial Radiology, Goteborg Univ. (Sweden)
2001-08-01
The aim of this study was to evaluate osseous healing in mandibular defects using fractal analyses on conventional radiographs and tuned aperture computed tomography (TACT; OrthoTACT, Instrumentarium Imaging, Helsinki, Finland) images. Eighty test sites on the inferior margins of rabbit mandibles were subject to lesion induction and treated with one of the following: no treatment (controls); osteoblasts only; polymer matrix only; or osteoblast-polymer matrix (OPM) combination. Images were acquired using conventional radiography and TACT, including unprocessed TACT (TACT-U) and iteratively restored TACT (TACT-IR). Healing was followed up over time and images acquired at 3, 6, 9, and 12 weeks post-surgery. Fractal dimension (FD) was computed within regions of interest in the defects using the TACT workbench. Results were analyzed for effects produced by imaging modality, treatment modality, time after surgery and lesion location. Histomorphometric data were available to assess ground truth. Significant differences (p<0.0001) were noted based on imaging modality with TACT-IR recording the highest mean fractal dimension (MFD), followed by TACT-U and conventional images, in that order. Sites treated with OPM recorded the highest MFDs among all treatment modalities (p<0.0001). The highest MFD based on time was recorded at 3 weeks and differed significantly with 12 weeks (p<0.035). Correlation of FD with results of histomorphometric data was high (r=0.79; p<0.001). The FD computed on TACT-IR showed the highest correlation with histomorphometric data, thus establishing the fact TACT is a more efficient and accurate imaging modality for quantification of osseous changes within healing bony defects. (orig.)
Astaneh, Amin Faraji
2015-01-01
We use the Heat Kernel method to calculate the Entanglement Entropy for a given entangling region on a fractal. The leading divergent term of the entropy is obtained as a function of the fractal dimension as well as the walk dimension. The power of the UV cut-off parameter is (generally) a fractional number which indeed is a certain combination of these two indices. This exponent is known as the spectral dimension. We show that there is a novel log periodic oscillatory behavior in the entropy which has root in the complex dimension of a fractal. We finally indicate that the Holographic calculation in a certain Hyper-scaling violating bulk geometry yields the same leading term for the entanglement entropy, if one identifies the effective dimension of the hyper-scaling violating theory with the spectral dimension of the fractal. We provide more supports with comparing the behavior of the thermal entropy in terms of the temperature in these two cases.
Classification of diabetic retinopathy using fractal dimension analysis of eye fundus image
Safitri, Diah Wahyu; Juniati, Dwi
2017-08-01
Diabetes Mellitus (DM) is a metabolic disorder when pancreas produce inadequate insulin or a condition when body resist insulin action, so the blood glucose level is high. One of the most common complications of diabetes mellitus is diabetic retinopathy which can lead to a vision problem. Diabetic retinopathy can be recognized by an abnormality in eye fundus. Those abnormalities are characterized by microaneurysms, hemorrhage, hard exudate, cotton wool spots, and venous's changes. The diabetic retinopathy is classified depends on the conditions of abnormality in eye fundus, that is grade 1 if there is a microaneurysm only in the eye fundus; grade 2, if there are a microaneurysm and a hemorrhage in eye fundus; and grade 3: if there are microaneurysm, hemorrhage, and neovascularization in the eye fundus. This study proposed a method and a process of eye fundus image to classify of diabetic retinopathy using fractal analysis and K-Nearest Neighbor (KNN). The first phase was image segmentation process using green channel, CLAHE, morphological opening, matched filter, masking, and morphological opening binary image. After segmentation process, its fractal dimension was calculated using box-counting method and the values of fractal dimension were analyzed to make a classification of diabetic retinopathy. Tests carried out by used k-fold cross validation method with k=5. In each test used 10 different grade K of KNN. The accuracy of the result of this method is 89,17% with K=3 or K=4, it was the best results than others K value. Based on this results, it can be concluded that the classification of diabetic retinopathy using fractal analysis and KNN had a good performance.
Fast Fractal Compression of Satellite and Medical Images Based on Domain-Range Entropy
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Ramesh Babu Inampudi
2010-01-01
Full Text Available Fractal image Compression is a lossy compression technique developed in the early 1990s. It makes use of the local self-similarity property existing in an image and finds a contractive mapping affine transformation (fractal transformT, such that the fixed point of T is close to the given image in a suitable metric. It has generated much interest due to its promise of high compression ratios with good decompression quality. The other advantage is its multi resolution property, i.e. an image can be decoded at higher or lower resolutions than the original without much degradation in quality. However, the encoding time is computationally intensive. In this paper, a fast fractal image compression method based on the domain-range entropy is proposed to reduce the encoding time, while maintaining the fidelity and compression ratio of the decoded image. The method is a two-step process. First, domains that are similar i.e. domains having nearly equal variances are eliminated from the domain pool. Second, during the encoding phase, only domains and ranges having equal entropies (with an adaptive error threshold, λdepth for each quadtree depth are compared for a match within the rms error tolerance. As a result, many unqualified domains are removed from comparison and a significant reduction in encoding time is expected. The method is applied for compression of satellite and medical images (512x512, 8-bit gray scale. Experimental results show that the proposed method yields superior performance over Fisher’s classified search and other methods.
Zone Specific Fractal Dimension of Retinal Images as Predictor of Stroke Incidence
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Behzad Aliahmad
2014-01-01
Full Text Available Fractal dimensions (FDs are frequently used for summarizing the complexity of retinal vascular. However, previous techniques on this topic were not zone specific. A new methodology to measure FD of a specific zone in retinal images has been developed and tested as a marker for stroke prediction. Higuchi’s fractal dimension was measured in circumferential direction (FDC with respect to optic disk (OD, in three concentric regions between OD boundary and 1.5 OD diameter from its margin. The significance of its association with future episode of stroke event was tested using the Blue Mountain Eye Study (BMES database and compared against spectrum fractal dimension (SFD and box-counting (BC dimension. Kruskal-Wallis analysis revealed FDC as a better predictor of stroke (H=5.80, P=0.016, α=0.05 compared with SFD (H=0.51, P=0.475, α=0.05 and BC (H=0.41, P=0.520, α=0.05 with overall lower median value for the cases compared to the control group. This work has shown that there is a significant association between zone specific FDC of eye fundus images with future episode of stroke while this difference is not significant when other FD methods are employed.
Texture image classification using multi-fractal dimension
Institute of Scientific and Technical Information of China (English)
LIU Zhuo-fu; SANG En-fang
2003-01-01
This paper presents a supervised classification metelet analysis. In the process of feature extraction, image transformation and wasion is obtained. In the part of classifier construction, the Learning Vector Quantization (LVQ) network is adopted as a classifier. Experiments of sonar image classification were carried out with satisfactory results, which verify the effectiveness of this method.
Fractal coding of wavelet image based on human vision contrast-masking effect
Wei, Hai; Shen, Lansun
2000-06-01
In this paper, a fractal-based compression approach of wavelet image is presented. The scheme tries to make full use of the sensitivity features of the human visual system. With the wavelet-based multi-resolution representation of image, detail vectors of each high frequency sub-image are constructed in accordance with its spatial orientation in order to grasp the edge information to which human observer is sensitive. Then a multi-level selection algorithm based on human vision's contrast masking effect is proposed to make the decision whether a detail vector is coded or not. Those vectors below the contrast threshold are discarded without introducing visual artifacts because of the ignorance of human vision. As for the redundancy of the retained vectors, different fractal- based methods are employed to decrease the correlation in single sub-image and between the different resolution sub- images with the same orientation. Experimental results suggest the efficiency of the proposed scheme. With the standard test image, our approach outperforms the EZW algorithm and the JPEG method.
A Novel Semi-blind Watermarking Algorithm Based on Fractal Dimension and Image Feature
Institute of Scientific and Technical Information of China (English)
NIRongrong; RUANQiuqi
2004-01-01
This paper presents a novel semi-blind watermarking algorithm based on fractal dimension and image feature. An original image is divided into blocks with fixed size. According to the idea of the second generation watermarking[1], the image is analyzed using fractal dimension to attain its feature blocks containing edges and textures that are used in the later embedding process and used to form a feature label. The watermark that is the fusion of the feature label and a binary copyright symbol not only represents the copyright symbol, but also reflects the feature of the image. Arnold iteration transform is employed to increase the security of watermark. Then,DCT (Discrete cosine transform) is applied to the feature blocks. The secure watermark that is adaptive to the individual image is embedded into the relations between middle-frequency coefficients and corresponding DC coefficients. The detection and extraction procedure is a semiblind one which does not use the original image but the watermark. Only those who have the original watermarkand the key can detect and extract the right watermark.This makes the approach authentic and have high securitylevel. Experimental results show that this algorithm can get good perceptual invisibility, adaptability and security.And it is robust against cropping, scribbling, low or highpass filtering, adding noise and JPEG compression.
Directory of Open Access Journals (Sweden)
Alexandru Florin Badea
2013-01-01
Full Text Available The geometry of some medical images of tissues, obtained by elastography and ultrasonography, is characterized in terms of complexity parameters such as the fractal dimension (FD. It is well known that in any image there are very subtle details that are not easily detectable by the human eye. However, in many cases like medical imaging diagnosis, these details are very important since they might contain some hidden information about the possible existence of certain pathological lesions like tissue degeneration, inflammation, or tumors. Therefore, an automatic method of analysis could be an expedient tool for physicians to give a faultless diagnosis. The fractal analysis is of great importance in relation to a quantitative evaluation of “real-time” elastography, a procedure considered to be operator dependent in the current clinical practice. Mathematical analysis reveals significant discrepancies among normal and pathological image patterns. The main objective of our work is to demonstrate the clinical utility of this procedure on an ultrasound image corresponding to a submandibular diffuse pathology.
Construction of Fractal Surfaces by Recurrent Fractal Interpolation Curves
Yun, Chol-Hui; O., Hyong-chol; Choi, Hui-chol
2013-01-01
A method to construct fractal surfaces by recurrent fractal curves is provided. First we construct fractal interpolation curves using a recurrent iterated functions system(RIFS) with function scaling factors and estimate their box-counting dimension. Then we present a method of construction of wider class of fractal surfaces by fractal curves and Lipschitz functions and calculate the box-counting dimension of the constructed surfaces. Finally, we combine both methods to have more flexible con...
After notes on self-similarity exponent for fractal structures
Fernández-Martínez, Manuel; Caravaca Garratón, Manuel
2017-06-01
Previous works have highlighted the suitability of the concept of fractal structure, which derives from asymmetric topology, to propound generalized definitions of fractal dimension. The aim of the present article is to collect some results and approaches allowing to connect the self-similarity index and the fractal dimension of a broad spectrum of random processes. To tackle with, we shall use the concept of induced fractal structure on the image set of a sample curve. The main result in this paper states that given a sample function of a random process endowed with the induced fractal structure on its image, it holds that the self-similarity index of that function equals the inverse of its fractal dimension.
Wang, Heming; Liu, Yu; Song, Yongchen; Zhao, Yuechao; Zhao, Jiafei; Wang, Dayong
2012-11-01
Pore structure is one of important factors affecting the properties of porous media, but it is difficult to describe the complexity of pore structure exactly. Fractal theory is an effective and available method for quantifying the complex and irregular pore structure. In this paper, the fractal dimension calculated by box-counting method based on fractal theory was applied to characterize the pore structure of artificial cores. The microstructure or pore distribution in the porous material was obtained using the nuclear magnetic resonance imaging (MRI). Three classical fractals and one sand packed bed model were selected as the experimental material to investigate the influence of box sizes, threshold value, and the image resolution when performing fractal analysis. To avoid the influence of box sizes, a sequence of divisors of the image was proposed and compared with other two algorithms (geometric sequence and arithmetic sequence) with its performance of partitioning the image completely and bringing the least fitted error. Threshold value selected manually and automatically showed that it plays an important role during the image binary processing and the minimum-error method can be used to obtain an appropriate or reasonable one. Images obtained under different pixel matrices in MRI were used to analyze the influence of image resolution. Higher image resolution can detect more quantity of pore structure and increase its irregularity. With benefits of those influence factors, fractal analysis on four kinds of artificial cores showed the fractal dimension can be used to distinguish the different kinds of artificial cores and the relationship between fractal dimension and porosity or permeability can be expressed by the model of D = a - bln(x + c).
An effective fractal image compression algorithm based on plane fitting
Institute of Scientific and Technical Information of China (English)
Wang Xing-Yuan; Guo Xing; Zhang Dan-Dan
2012-01-01
A new method using plane fitting to decide whether a domain block is similar enough to a given range block is proposed in this paper.First,three coefficients are computed for describing each range and domain block.Then,the best-matched one for every range block is obtained by analysing the relation between their coefficients.Experimental results show that the proposed method can shorten encoding time markedly,while the retrieved image quality is still acceptable.In the decoding step,a kind of simple line fitting on block boundaries is used to reduce blocking effects.At the same time,the proposed method can also achieve a high compression ratio.
Bells Galore: Oscillations and circle-map dynamics from space-filling fractal functions
Energy Technology Data Exchange (ETDEWEB)
Puente, C.E.; Cortis, A.; Sivakumar, B.
2008-10-15
The construction of a host of interesting patterns over one and two dimensions, as transformations of multifractal measures via fractal interpolating functions related to simple affine mappings, is reviewed. It is illustrated that, while space-filling fractal functions most commonly yield limiting Gaussian distribution measures (bells), there are also situations (depending on the affine mappings parameters) in which there is no limit. Specifically, the one-dimensional case may result in oscillations between two bells, whereas the two-dimensional case may give rise to unexpected circle map dynamics of an arbitrary number of two-dimensional circular bells. It is also shown that, despite the multitude of bells over two dimensions, whose means dance making regular polygons or stars inscribed on a circle, the iteration of affine maps yields exotic kaleidoscopes that decompose such an oscillatory pattern in a way that is similar to the many cases that converge to a single bell.
Azevedo-Marques, P M; Spagnoli, H F; Frighetto-Pereira, L; Menezes-Reis, R; Metzner, G A; Rangayyan, R M; Nogueira-Barbosa, M H
2015-08-01
Fractures with partial collapse of vertebral bodies are generically referred to as "vertebral compression fractures" or VCFs. VCFs can have different etiologies comprising trauma, bone failure related to osteoporosis, or metastatic cancer affecting bone. VCFs related to osteoporosis (benign fractures) and to cancer (malignant fractures) are commonly found in the elderly population. In the clinical setting, the differentiation between benign and malignant fractures is complex and difficult. This paper presents a study aimed at developing a system for computer-aided diagnosis to help in the differentiation between malignant and benign VCFs in magnetic resonance imaging (MRI). We used T1-weighted MRI of the lumbar spine in the sagittal plane. Images from 47 consecutive patients (31 women, 16 men, mean age 63 years) were studied, including 19 malignant fractures and 54 benign fractures. Spectral and fractal features were extracted from manually segmented images of 73 vertebral bodies with VCFs. The classification of malignant vs. benign VCFs was performed using the k-nearest neighbor classifier with the Euclidean distance. Results obtained show that combinations of features derived from Fourier and wavelet transforms, together with the fractal dimension, were able to obtain correct classification rate up to 94.7% with area under the receiver operating characteristic curve up to 0.95.
Wang, Jianji; Zheng, Nanning
2013-09-01
Fractal image compression (FIC) is an image coding technology based on the local similarity of image structure. It is widely used in many fields such as image retrieval, image denoising, image authentication, and encryption. FIC, however, suffers from the high computational complexity in encoding. Although many schemes are published to speed up encoding, they do not easily satisfy the encoding time or the reconstructed image quality requirements. In this paper, a new FIC scheme is proposed based on the fact that the affine similarity between two blocks in FIC is equivalent to the absolute value of Pearson's correlation coefficient (APCC) between them. First, all blocks in the range and domain pools are chosen and classified using an APCC-based block classification method to increase the matching probability. Second, by sorting the domain blocks with respect to APCCs between these domain blocks and a preset block in each class, the matching domain block for a range block can be searched in the selected domain set in which these APCCs are closer to APCC between the range block and the preset block. Experimental results show that the proposed scheme can significantly speed up the encoding process in FIC while preserving the reconstructed image quality well.
Realization of Fractal Affine Transformation
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
This paper gives the definition of fractal affine transformation and presents a specific method for its realization and its cor responding mathematical equations which are essential in fractal image construction.
Modeling Fractal Structure of Systems of Cities Using Spatial Correlation Function
Chen, Yanguang
2016-01-01
This paper proposes a new method to analyze the spatial structure of urban systems using ideas from fractals. Regarding a system of cities as a set of "particles" distributed randomly on a triangular lattice, we construct a spatial correlation function of cities. Suppose that the spatial correlation follows the power law. It can be proved that the correlation exponent is the second order generalized dimension. The spatial correlation model is applied to the system of cities in China. The results show that the Chinese urban system can be described by the correlation dimension ranging from 1.3 to 1.6. The fractality of self-organized network of cities in both the conventional geographic space and the "time" space is revealed with the empirical evidence. The spatial correlation analysis is significant in that it is applicable to both large and small sizes of samples and can be used to link different fractal dimensions in urban study, including box dimension and radial dimension.
Alonso, Carmelo; Tarquis, Ana M.; Zúñiga, Ignacio; Benito, Rosa M.
2017-03-01
Several studies have shown that vegetation indexes can be used to estimate root zone soil moisture. Earth surface images, obtained by high-resolution satellites, presently give a lot of information on these indexes, based on the data of several wavelengths. Because of the potential capacity for systematic observations at various scales, remote sensing technology extends the possible data archives from the present time to several decades back. Because of this advantage, enormous efforts have been made by researchers and application specialists to delineate vegetation indexes from local scale to global scale by applying remote sensing imagery. In this work, four band images have been considered, which are involved in these vegetation indexes, and were taken by satellites Ikonos-2 and Landsat-7 of the same geographic location, to study the effect of both spatial (pixel size) and radiometric (number of bits coding the image) resolution on these wavelength bands as well as two vegetation indexes: the Normalized Difference Vegetation Index (NDVI) and the Enhanced Vegetation Index (EVI). In order to do so, a multi-fractal analysis of these multi-spectral images was applied in each of these bands and the two indexes derived. The results showed that spatial resolution has a similar scaling effect in the four bands, but radiometric resolution has a larger influence in blue and green bands than in red and near-infrared bands. The NDVI showed a higher sensitivity to the radiometric resolution than EVI. Both were equally affected by the spatial resolution. From both factors, the spatial resolution has a major impact in the multi-fractal spectrum for all the bands and the vegetation indexes. This information should be taken in to account when vegetation indexes based on different satellite sensors are obtained.
Yang, Y.; Li, H. T.; Han, Y. S.; Gu, H. Y.
2015-06-01
Image segmentation is the foundation of further object-oriented image analysis, understanding and recognition. It is one of the key technologies in high resolution remote sensing applications. In this paper, a new fast image segmentation algorithm for high resolution remote sensing imagery is proposed, which is based on graph theory and fractal net evolution approach (FNEA). Firstly, an image is modelled as a weighted undirected graph, where nodes correspond to pixels, and edges connect adjacent pixels. An initial object layer can be obtained efficiently from graph-based segmentation, which runs in time nearly linear in the number of image pixels. Then FNEA starts with the initial object layer and a pairwise merge of its neighbour object with the aim to minimize the resulting summed heterogeneity. Furthermore, according to the character of different features in high resolution remote sensing image, three different merging criterions for image objects based on spectral and spatial information are adopted. Finally, compared with the commercial remote sensing software eCognition, the experimental results demonstrate that the efficiency of the algorithm has significantly improved, and the result can maintain good feature boundaries.
N'Diaye, Mambaye; Degeratu, Cristinel; Bouler, Jean-Michel; Chappard, Daniel
2013-05-01
Porous structures are becoming more and more important in biology and material science because they help in reducing the density of the grafted material. For biomaterials, porosity also increases the accessibility of cells and vessels inside the grafted area. However, descriptors of porosity are scanty. We have used a series of biomaterials with different types of porosity (created by various porogens: fibers, beads …). Blocks were studied by microcomputed tomography for the measurement of 3D porosity. 2D sections were re-sliced to analyze the microarchitecture of the pores and were transferred to image analysis programs: star volumes, interconnectivity index, Minkowski-Bouligand and Kolmogorov fractal dimensions were determined. Lacunarity and succolarity, two recently described fractal dimensions, were also computed. These parameters provided a precise description of porosity and pores' characteristics. Non-linear relationships were found between several descriptors e.g. succolarity and star volume of the material. A linear correlation was found between lacunarity and succolarity. These techniques appear suitable in the study of biomaterials usable as bone substitutes. Copyright © 2013 Elsevier B.V. All rights reserved.
Review on Fractal Analysis of Porous Metal Materials
Directory of Open Access Journals (Sweden)
J. Z. Wang
2015-01-01
Full Text Available Porous metal materials are multifunctional lightweight materials and have been used widely in industry. The structural and functional characters of porous metal materials depend on the pore structure which can be described effectively by the fractal theory. This paper reviews the major achievements on fractal analysis of pore structure of porous metal materials made by State Key Laboratory of Porous Metal Materials, China, over the past few years. These include (i designing and developing a set of novel fractal analytical software of porous metal materials, (ii the influence of material characterization and image processing method on the fractal dimension, and (iii the relationship between the material performance and the fractal dimension. Finally, the outlooks of fractal theory applied in porous metal materials are discussed.
Esbenshade, Donald H., Jr.
1991-01-01
Develops the idea of fractals through a laboratory activity that calculates the fractal dimension of ordinary white bread. Extends use of the fractal dimension to compare other complex structures as other breads and sponges. (MDH)
Esbenshade, Donald H., Jr.
1991-01-01
Develops the idea of fractals through a laboratory activity that calculates the fractal dimension of ordinary white bread. Extends use of the fractal dimension to compare other complex structures as other breads and sponges. (MDH)
A Distributed Web GIS Application Based on Component Technology and Fractal Image Compression
Institute of Scientific and Technical Information of China (English)
HAN Jie
2006-01-01
Geographic information system (GIS) technology is a combination of computer's graphic and database to store and process spatial information. According to the users' demands, GIS exports the exact geographic information and related information for users with map and description through associating geographic place and related attributes. Based on the existing popular technology, this paper presents a distributed web GIS application based on component technology and fractal image compression. It presents the basic framework of the proposed system at first, and then discusses the key technology of implementing this system; finally it designs a three-layer WEB GIS instance using VC++ ATL based on Geo Beans. The example suggests the proposed design is correct, feasible and valid.
Fractal dimensions of wave functions and local spectral measures on the Fibonacci chain
Macé, Nicolas; Jagannathan, Anuradha; Piéchon, Frédéric
2016-05-01
We present a theoretical framework for understanding the wave functions and spectrum of an extensively studied paradigm for quasiperiodic systems, namely the Fibonacci chain. Our analytical results, which are obtained in the limit of strong modulation of the hopping amplitudes, are in good agreement with published numerical data. In the perturbative limit, we show a symmetry of wave functions under permutation of site and energy indices. We compute the wave-function renormalization factors and from them deduce analytical expressions for the fractal exponents corresponding to individual wave functions, as well as their global averages. The multifractality of wave functions is seen to appear at next-to-leading order in ρ . Exponents for the local spectral density are given, in extremely good accord with numerical calculations. Interestingly, our analytical results for exponents are observed to describe the system rather well even for values of ρ well outside the domain of applicability of perturbation theory.
An Allometric Algorithm for Fractal-Based Cobb-Douglas Function of Geographical Systems
Directory of Open Access Journals (Sweden)
Hongyu Luo
2014-01-01
Full Text Available The generalized Cobb-Douglas production function has been derived from a general input-output relation based on fractality assumptions. It was proved to be a useful self-affine model for geographical analysis. However, the ordinary least square calculation is always an ineffectual method for the Cobb-Douglas modeling because of the multicollinearity in the logarithmic linear regression. In this paper, a novel approach is proposed to build the geographical Cobb-Douglas models. Combining the concept of allometric scaling with the linear regression technique, we obtain a simple algorithm that can be employed to estimate the parameters of the Cobb-Douglas function. As a case, the algorithm and models are applied to the public transportation of China’s cities, and the results validate the allometric algorithm. A conclusion can be drawn that the allometric analysis is an effective way of modeling geographical systems with the general Cobb-Douglas function. This study is significant for integrating the notions of allometry, fractals, and scaling into a new framework to form a quantitative methodology of spatial analysis.
Jitaree, Sirinapa; Phinyomark, Angkoon; Boonyaphiphat, Pleumjit; Phukpattaranont, Pornchai
2015-01-01
Having a classifier of cell types in a breast cancer microscopic image (BCMI), obtained with immunohistochemical staining, is required as part of a computer-aided system that counts the cancer cells in such BCMI. Such quantitation by cell counting is very useful in supporting decisions and planning of the medical treatment of breast cancer. This study proposes and evaluates features based on texture analysis by fractal dimension (FD), for the classification of histological structures in a BCMI into either cancer cells or non-cancer cells. The cancer cells include positive cells (PC) and negative cells (NC), while the normal cells comprise stromal cells (SC) and lymphocyte cells (LC). The FD feature values were calculated with the box-counting method from binarized images, obtained by automatic thresholding with Otsu's method of the grayscale images for various color channels. A total of 12 color channels from four color spaces (RGB, CIE-L*a*b*, HSV, and YCbCr) were investigated, and the FD feature values from them were used with decision tree classifiers. The BCMI data consisted of 1,400, 1,200, and 800 images with pixel resolutions 128 × 128, 192 × 192, and 256 × 256, respectively. The best cross-validated classification accuracy was 93.87%, for distinguishing between cancer and non-cancer cells, obtained using the Cr color channel with window size 256. The results indicate that the proposed algorithm, based on fractal dimension features extracted from a color channel, performs well in the automatic classification of the histology in a BCMI. This might support accurate automatic cell counting in a computer-assisted system for breast cancer diagnosis.
Tikhonov, K. Â. S.; Mirlin, A. Â. D.
2016-11-01
We investigate analytically and numerically eigenfunction statistics in a disordered system on a finite Bethe lattice (Cayley tree). We show that the wave-function amplitude at the root of a tree is distributed fractally in a large part of the delocalized phase. The fractal exponents are expressed in terms of the decay rate and the velocity in a problem of propagation of a front between unstable and stable phases. We demonstrate a crucial difference between a loopless Cayley tree and a locally treelike structure without a boundary (random regular graph) where extended wave functions are ergodic.
Using texture synthesis in fractal pattern design
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
Traditional fractal pattern design has some disadvantages such as inability to effectively reflect the characteristics of real scenery and texture. We propose a novel pattern design technique combining fractal geometry and image texture synthesis to solve these problems. We have improved Wei and Levoy (2000)'s texture synthesis algorithm by first using two-dimensional autocorrelation function to analyze the structure and distribution of textures, and then determining the size of L neighborhood.Several special fractal sets were adopted and HSL (Hue, Saturation, and Light) color space was chosen. The fractal structure was used to manipulate the texture synthesis in HSL color space where the pattern's color can be adjusted conveniently. Experiments showed that patterns with different styles and different color characteristics can be more efficiently generated using the new technique.
Modeling fractal structure of city-size distributions using correlation function
Chen, Yanguang
2011-01-01
Zipf's law is one the most conspicuous empirical facts for cities, however, there is no convincing explanation for the scaling relation between rank and size and its scaling exponent. Based on the idea from general fractals and scaling, this paper proposes a dual competition hypothesis of city develop to explain the value intervals and the special value, 1, of the power exponent. Zipf's law and Pareto's law can be mathematically transformed into one another. Based on the Pareto distribution, a frequency correlation function can be constructed. By scaling analysis and multifractals spectrum, the parameter interval of Pareto exponent is derived as (0.5, 1]; Based on the Zipf distribution, a size correlation function can be built, and it is opposite to the first one. By the second correlation function and multifractals notion, the Pareto exponent interval is derived as [1, 2). Thus the process of urban evolution falls into two effects: one is Pareto effect indicating city number increase (external complexity), a...
Wang, Qiang; Bi, Sheng
2017-01-01
To predict the peak signal-to-noise ratio (PSNR) quality of decoded images in fractal image coding more efficiently and accurately, an improved method is proposed. After some derivations and analyses, we find that the linear correlation coefficients between coded range blocks and their respective best-matched domain blocks can determine the dynamic range of their collage errors, which can also provide the minimum and the maximum of the accumulated collage error (ACE) of uncoded range blocks. Moreover, the dynamic range of the actual percentage of accumulated collage error (APACE), APACEmin to APACEmax, can be determined as well. When APACEmin reaches a large value, such as 90%, APACEmin to APACEmax will be limited in a small range and APACE can be computed approximately. Furthermore, with ACE and the approximate APACE, the ACE of all range blocks and the average collage error (ACER) can be obtained. Finally, with the logarithmic relationship between ACER and the PSNR quality of decoded images, the PSNR quality of decoded images can be predicted directly. Experiments show that compared with the previous similar method, the proposed method can predict the PSNR quality of decoded images more accurately and needs less computation time simultaneously.
Extreme value laws for fractal intensity functions in dynamical systems: Minkowski analysis
Mantica, Giorgio; Perotti, Luca
2016-09-01
Typically, in the dynamical theory of extremal events, the function that gauges the intensity of a phenomenon is assumed to be convex and maximal, or singular, at a single, or at most a finite collection of points in phase-space. In this paper we generalize this situation to fractal landscapes, i.e. intensity functions characterized by an uncountable set of singularities, located on a Cantor set. This reveals the dynamical rôle of classical quantities like the Minkowski dimension and content, whose definition we extend to account for singular continuous invariant measures. We also introduce the concept of extremely rare event, quantified by non-standard Minkowski constants and we study its consequences to extreme value statistics. Limit laws are derived from formal calculations and are verified by numerical experiments. Dedicated to the memory of Joseph Ford, on the twentieth anniversary of his departure.
Jaroniec, Mietek; Kruk, Michal; Olivier, James
1995-11-01
Methods of calculating the fractal dimension (D) on the basis of single adsorption isotherms were critically tested by using argon composite adsorption isotherms for fractally porous solids. These isotherms were obtained from adsorption data for homogeneous slit-like pores calculated by employing the density functional theory (DFT). The composite adsorption isotherms were used to test the validity of the method based on the Frenkel-Halsey-Hill equation and so called "thermodynamic method" proposed by Neimark. The applicability of these methods was confirmed. However, our studies reveal new aspects of practical usage of both approaches, which need to be taken into consideration in analysis of experimental data.
Field Emission and Radial Distribution Function Studies of Fractal-like Amorphous Carbon Nanotips
Solá, F.; Biaggi-Labiosa, A.; Fonseca, L. F.; Resto, O.; Lebrón-Colón, M.; Meador, M. A.
2009-05-01
The short-range order of individual fractal-like amorphous carbon nanotips was investigated by means of energy-filtered electron diffraction in a transmission electron microscope (TEM). The nanostructures were grown in porous silicon substrates in situ within the TEM by the electron beam-induced deposition method. The structure factor S( k) and the reduced radial distribution function G( r) were calculated. From these calculations a bond angle of 124° was obtained which suggests a distorted graphitic structure. Field emission was obtained from individual nanostructures using two micromanipulators with sub-nanometer positioning resolution. A theoretical three-stage model that accounts for the geometry of the nanostructures provides a value for the field enhancement factor close to the one obtained experimentally from the Fowler-Nordheim law.
Directory of Open Access Journals (Sweden)
M. A. Navascués
2013-01-01
Full Text Available This paper tackles the construction of fractal maps on the unit sphere. The functions defined are a generalization of the classical spherical harmonics. The methodology used involves an iterated function system and a linear and bounded operator of functions on the sphere. For a suitable choice of the coefficients of the system, one obtains classical maps on the sphere. The different values of the system parameters provide Bessel sequences, frames, and Riesz fractal bases for the Lebesgue space of the square integrable functions on the sphere. The Laplace series expansion is generalized to a sum in terms of the new fractal mappings.
Hermitean Téodorescu Transform Decomposition of Continuous Matrix Functions on Fractal Hypersurfaces
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Hennie De Schepper
2010-01-01
Full Text Available We consider Hölder continuous circulant (2×2 matrix functions G21 defined on the fractal boundary Γ of a domain Ω in ℝ2n. The main goal is to study under which conditions such a function G21 can be decomposed as G21=G21+−G21−, where the components G21± are extendable to H-monogenic functions in the interior and the exterior of Ω, respectively. H-monogenicity are a concept from the framework of Hermitean Clifford analysis, a higher-dimensional function theory centered around the simultaneous null solutions of two first-order vector-valued differential operators, called Hermitean Dirac operators. H-monogenic functions then are the null solutions of a (2×2 matrix Dirac operator, having these Hermitean Dirac operators as its entries; such matrix functions play an important role in the function theoretic development of Hermitean Clifford analysis. In the present paper a matricial Hermitean Téodorescu transform is the key to solve the problem under consideration. The obtained results are then shown to include the ones where domains with an Ahlfors-David regular boundary were considered.
Hermitean Téodorescu Transform Decomposition of Continuous Matrix Functions on Fractal Hypersurfaces
Directory of Open Access Journals (Sweden)
Bory-Reyes Juan
2010-01-01
Full Text Available We consider Hölder continuous circulant ( matrix functions defined on the fractal boundary of a domain in . The main goal is to study under which conditions such a function can be decomposed as , where the components are extendable to -monogenic functions in the interior and the exterior of , respectively. -monogenicity are a concept from the framework of Hermitean Clifford analysis, a higher-dimensional function theory centered around the simultaneous null solutions of two first-order vector-valued differential operators, called Hermitean Dirac operators. -monogenic functions then are the null solutions of a ( matrix Dirac operator, having these Hermitean Dirac operators as its entries; such matrix functions play an important role in the function theoretic development of Hermitean Clifford analysis. In the present paper a matricial Hermitean Téodorescu transform is the key to solve the problem under consideration. The obtained results are then shown to include the ones where domains with an Ahlfors-David regular boundary were considered.
Functional Magnetic Resonance Imaging
Voos, Avery; Pelphrey, Kevin
2013-01-01
Functional magnetic resonance imaging (fMRI), with its excellent spatial resolution and ability to visualize networks of neuroanatomical structures involved in complex information processing, has become the dominant technique for the study of brain function and its development. The accessibility of in-vivo pediatric brain-imaging techniques…
Functional Magnetic Resonance Imaging
Voos, Avery; Pelphrey, Kevin
2013-01-01
Functional magnetic resonance imaging (fMRI), with its excellent spatial resolution and ability to visualize networks of neuroanatomical structures involved in complex information processing, has become the dominant technique for the study of brain function and its development. The accessibility of in-vivo pediatric brain-imaging techniques…
Fractal Structure in Galactic Star Fields
Elmegreen, B G; Elmegreen, Bruce G.; Elmegreen, Debra Meloy
2001-01-01
The fractal structure of star formation on large scales in disk galaxies is studied using the size distribution function of stellar aggregates in kpc-scale star fields. Achival HST images of 10 galaxies are Gaussian smoothed to define the aggregates, and a count of these aggregates versus smoothing scale gives the fractal dimension. Fractal and Poisson models confirm the procedure. The fractal dimension of star formation in all of the galaxies is ~2.3. This is the same as the fractal dimension of interstellar gas in the Milky Way and nearby galaxies, suggesting that star formation is a passive tracer of gas structure defined by self-gravity and turbulence. Dense clusters like the Pleiades form at the bottom of the hierarchy of structures, where the protostellar gas is densest. If most stars form in such clusters, then the fractal arises from the spatial distribution of their positions, giving dispersed star fields from continuous cluster disruption. Dense clusters should have an upper mass limit that increase...
Functional imaging and endoscopy
Institute of Scientific and Technical Information of China (English)
Jian-Guo Zhang; Hai-Feng Liu
2011-01-01
The emergence of endoscopy for the diagnosis of gastrointestinal diseases and the treatment of gastrointestinal diseases has brought great changes.The mere observation of anatomy with the imaging mode using modern endoscopy has played a significant role in this regard.However,increasing numbers of endoscopies have exposed additional deficiencies and defects such as anatomically similar diseases.Endoscopy can be used to examine lesions that are difficult to identify and diagnose.Early disease detection requires that substantive changes in biological function should be observed,but in the absence of marked morphological changes,endoscopic detection and diagnosis are difficult.Disease detection requires not only anatomic but also functional imaging to achieve a comprehensive interpretation and understanding.Therefore,we must ask if endoscopic examination can be integrated with both anatomic imaging and functional imaging.In recent years,as molecular biology and medical imaging technology have further developed,more functional imaging methods have emerged.This paper is a review of the literature related to endoscopic optical imaging methods in the hopes of initiating integration of functional imaging and anatomical imaging to yield a new and more effective type of endoscopy.
Fractal Dimension Invariant Filtering and Its CNN-based Implementation
Xu, Hongteng; Yan, Junchi; Persson, Nils; Lin, Weiyao; Zha, Hongyuan
2016-01-01
Fractal analysis has been widely used in computer vision, especially in texture image processing and texture analysis. The key concept of fractal-based image model is the fractal dimension, which is invariant to bi-Lipschitz transformation of image, and thus capable of representing intrinsic structural information of image robustly. However, the invariance of fractal dimension generally does not hold after filtering, which limits the application of fractal-based image model. In this paper, we...
DEFF Research Database (Denmark)
Bruun Jensen, Casper
2007-01-01
. Instead, I outline a fractal approach to the study of space, society, and infrastructure. A fractal orientation requires a number of related conceptual reorientations. It has implications for thinking about scale and perspective, and (sociotechnical) relations, and for considering the role of the social...... and a fractal social theory....
Liu, Shuai; Wang, Yinyan; Xu, Kaibin; Wang, Zheng; Fan, Xing; Zhang, Chuanbao; Li, Shaowu; Qiu, Xiaoguang; Jiang, Tao
2017-08-16
Necrosis is a hallmark feature of glioblastoma (GBM). This study investigated the prognostic role of necrotic patterns in GBM using fractal dimension (FD) and lacunarity analyses of magnetic resonance imaging (MRI) data and evaluated the role of lacunarity in the biological processes leading to necrosis. We retrospectively reviewed clinical and MRI data of 95 patients with GBM. FD and lacunarity of the necrosis on MRI were calculated by fractal analysis and subjected to survival analysis. We also performed gene ontology analysis in 32 patients with available RNA-seq data. Univariate analysis revealed that FD lacunarity > 0.46 significantly correlated with poor progression-free survival (p = 0.006 and p = 0.012, respectively) and overall survival (p = 0.008 and p = 0.005, respectively). Multivariate analysis revealed that both parameters were independent factors for unfavorable progression-free survival (p = 0.001 and p = 0.015, respectively) and overall survival (p = 0.002 and p = 0.007, respectively). Gene ontology analysis revealed that genes positively correlated with lacunarity were involved in the suppression of apoptosis and necrosis-associated biological processes. We demonstrate that the fractal parameters of necrosis in GBM can predict patient survival and are associated with the biological processes of tumor necrosis.
Simoson, Andrew J.
2009-01-01
This article presents a fun activity of generating a double-minded fractal image for a linear algebra class once the idea of rotation and scaling matrices are introduced. In particular the fractal flip-flops between two words, depending on the level at which the image is viewed. (Contains 5 figures.)
Energy Technology Data Exchange (ETDEWEB)
Conte, Elio [Department of Pharmacology and Human Physiology and Tires, Center for Innovative Technologies for Signal Detection and Processing, University of Bari (Italy); School of Advanced International Studies on Theoretical and Nonlinear Methodologies-Bari (Italy)], E-mail: elio.conte@fastwebnet.it; Khrennikov, Andrei [International Center for Mathematical Modelling in Physics and Cognitive Sciences, M.S.I., University of Vaexjoe, S-35195 (Sweden); Federici, Antonio [Department of Pharmacology and Human Physiology and Tires, Center for Innovative Technologies for Signal Detection and Processing, University of Bari (Italy); Zbilut, Joseph P. [Department of Molecular Biophysics and Physiology, Rush University Medical Center, 1653W Congress, Chicago, IL 60612 (United States)
2009-09-15
We develop a new method for analysis of fundamental brain waves as recorded by the EEG. To this purpose we introduce a Fractal Variance Function that is based on the calculation of the variogram. The method is completed by using Random Matrix Theory. Some examples are given. We also discuss the link of such formulation with H. Weiss and V. Weiss golden ratio found in the brain, and with El Naschie fractal Cantorian space-time theory.
Surface-enhanced Raman imaging of fractal shaped periodic metal nanostructures
DEFF Research Database (Denmark)
Beermann, Jonas; Novikov, Sergey Mikhailovich; Albrektsen, Ole;
2009-01-01
Surface-enhanced Raman scattering (SERS) from Rhodamine 6G (R6G) homogenously adsorbed on fractal shaped 170-nm-period square arrays formed by 50-nm-high gold nanoparticles (diameters of 80, 100, or 120 nm are constant within each array), fabricated on a smooth gold film by electron-beam lithogra......Surface-enhanced Raman scattering (SERS) from Rhodamine 6G (R6G) homogenously adsorbed on fractal shaped 170-nm-period square arrays formed by 50-nm-high gold nanoparticles (diameters of 80, 100, or 120 nm are constant within each array), fabricated on a smooth gold film by electron...
Matlab Simulation of Jacquin Fractal Image Coding%基于Jacquin分形法图像编码的Matlab仿真实现
Institute of Scientific and Technical Information of China (English)
李丹; 张梁斌; 梁世斌
2011-01-01
Fractal image coding, which has the potential high compression ratio and simple decoding characteristics, has been a research focus of the lossy image coding over the past decade. This paper describes the mathematical basis of fractal image coding, the traditional Jacquin fractal image coding principle of encoding and decoding, and the experimental simulation of Jacquin fractal image coding using Matlab tool. Experimental result shows that Jacquin fractal image coding needs a long time of searching the best matching domain block, but image decoding is easy and fast.How to improve image coding time will be the main content of Jacquin fractal coding in the future.%分形图像编码具有潜在的高压缩比、解码简单等特点成为近十年来有损编码中的一个研究热点。文章阐述了分形编码的数学基础和传统分形编码Jacquin方法的编解码原理，最后利用Matlab工具对图像的Jacquin分形法进行了实验仿真。实验结果表明，Jacquin分形法搜索最佳匹配块的编码时间较长，而解码过程简单快捷。提高图像编码速度将是Jacquin分形法今后改进的主要内容。
Shahi Ferdows, Mohammad; Ramazi, Hamidreza
2015-12-01
The selection of a suitable membership function and its parameters plays a critical role in the integration of layer information by the fuzzy method. In this paper, parameters of membership function for induced polarization (IP) and resistivity (RS) data (in the Hamyj copper deposit) have been determined by the threshold parameter of IP and resistivity data, already determined by expert opinion or drilling data. The Hamyj deposit is located about 80 km west of Birjand city, South Khorasan province, Iran. In this area, resistivity and induced polarization data have been surveyed by dipole-dipole array. In this paper, outlier-induced polarization data have been corrected by the Doerffel method and then IP and resistivity data have been inversed by the Newton and Gauss-Newton methods. The threshold of the IP data is recognized by statistical (gap statistic) and fractal (concentration-area) methods. The determined threshold by the fractal method is higher than the gap statistic. These two thresholds have been used to determine the S-shape function for the IP data. The thresholds of the RS data are recognized by the fractal method. These two thresholds have been used to determine the Z-shape function for the RS data. The integration of geoelectrical layer information has been carried out by the Gama method. Finally, the best drilling points were proposed based on fuzzy modelling for the area. The results show that the optimum exploration borehole is located at a depth of 25 m.
Raupov, Dmitry S.; Myakinin, Oleg O.; Bratchenko, Ivan A.; Kornilin, Dmitry V.; Zakharov, Valery P.; Khramov, Alexander G.
2016-04-01
Optical coherence tomography (OCT) is usually employed for the measurement of tumor topology, which reflects structural changes of a tissue. We investigated the possibility of OCT in detecting changes using a computer texture analysis method based on Haralick texture features, fractal dimension and the complex directional field method from different tissues. These features were used to identify special spatial characteristics, which differ healthy tissue from various skin cancers in cross-section OCT images (B-scans). Speckle reduction is an important pre-processing stage for OCT image processing. In this paper, an interval type-II fuzzy anisotropic diffusion algorithm for speckle noise reduction in OCT images was used. The Haralick texture feature set includes contrast, correlation, energy, and homogeneity evaluated in different directions. A box-counting method is applied to compute fractal dimension of investigated tissues. Additionally, we used the complex directional field calculated by the local gradient methodology to increase of the assessment quality of the diagnosis method. The complex directional field (as well as the "classical" directional field) can help describe an image as set of directions. Considering to a fact that malignant tissue grows anisotropically, some principal grooves may be observed on dermoscopic images, which mean possible existence of principal directions on OCT images. Our results suggest that described texture features may provide useful information to differentiate pathological from healthy patients. The problem of recognition melanoma from nevi is decided in this work due to the big quantity of experimental data (143 OCT-images include tumors as Basal Cell Carcinoma (BCC), Malignant Melanoma (MM) and Nevi). We have sensitivity about 90% and specificity about 85%. Further research is warranted to determine how this approach may be used to select the regions of interest automatically.
Algorithm of Fractal Image Compression on CUDA%CUDA平台的分形图像压缩方法
Institute of Scientific and Technical Information of China (English)
余莉
2011-01-01
In fractal image compression, the matching procedure between range blocks and domain blocks can be executed in parallel manner. Therefore, in order to accelerate fractal image compression by using GPU, we apply compute unified device architecture CU-DA to it. This paper presents a hybrid quad tree compression approach of GPU and CPU, which accelerates the distance calculation that consumes time mostly in GPU side, and handles quad tree division, initialization and so on in CPU side. In GPU part, we discuss two methods, single range block and multiple range blocks. Analysis and experiments show that the latter can achieve better parallel performance than the former. When our approach is compared with traditional pure CPU ones, it can improve fractal compression speed greatly.%考虑到分形图像压缩中,值域块与定义域块之间的匹配能够并行计算这一特点,利用计算统一设备平台CUDA进行GPU加速.提出一种GPU、CPU相结合的四叉树压缩算法,通过GPU加速最耗时的距离计算部分,而四叉树分割、初始化等部分仍采用CPU完成.在GPU加速部分,讨论了单值域块与多值域块的方法,通过分析与实验表明,后者比前者能进一步提高并行性能.与传统的纯CPU方法相比,本文的方法能够显著提高压缩速度.
Fractal Solutions of the Nizhnik-Novikov-Veselov Equation
Institute of Scientific and Technical Information of China (English)
楼森岳; 唐晓艳; 陈春丽
2002-01-01
Considering that some types of fractal solutions may appear in many (2+ l )-dimensional soliton equations because some arbitrary functions can be included in the exact solutions, we use some special types of lower dimensional fractal functions to construct higher dimensional fractal solutions of the Nizhnik Novikov-Veselov equation. The static eagle-shape fractal solutions, fractal dromion solutions and the fractal lump solutions are given in detail.
Galindo-Hernández, Félix; Portales, Benjamín; Domínguez, José M.; Angeles-Beltrán, Deyanira
2014-12-01
Carbon nanofibers are produced by siliceous SBA-15 type materials and the casting method. The nanofibers are functionalized by HNO3 attack in aqueous phase under microwave radiation. N2 sorption data are treated by Non-Local Density Functional Theory and Quenched Solid Density Functional Theory to determine advanced adsorption among other textural properties. The functionalization degree of carbon nanofibers and their hydrogen storage capacity are mainly investigated by FTIR spectroscopy, capacitance studies and analysis of the fractal dimension of the surface. This latter in two ways: i) using the Neimark-Kiselev equation with N2 sorption data and ii) using Box-counting, Information and Perimeter-area methods on TEM photomicrographs. The hydrogen storage testing reveals that functionalized carbon nanofibers adsorb hydrogen above 200% with respect to unfunctionalized carbon nanofibers. This effect is attributed to: i) the creation of extra spacing between contiguous nanofibers, as a consequence of mutual repulsion between the -COOH groups and ii) increase of volume intrawall.
Modeling fractal structure of city-size distributions using correlation functions.
Directory of Open Access Journals (Sweden)
Yanguang Chen
Full Text Available Zipf's law is one the most conspicuous empirical facts for cities, however, there is no convincing explanation for the scaling relation between rank and size and its scaling exponent. Using the idea from general fractals and scaling, I propose a dual competition hypothesis of city development to explain the value intervals and the special value, 1, of the power exponent. Zipf's law and Pareto's law can be mathematically transformed into one another, but represent different processes of urban evolution, respectively. Based on the Pareto distribution, a frequency correlation function can be constructed. By scaling analysis and multifractals spectrum, the parameter interval of Pareto exponent is derived as (0.5, 1]; Based on the Zipf distribution, a size correlation function can be built, and it is opposite to the first one. By the second correlation function and multifractals notion, the Pareto exponent interval is derived as [1, 2. Thus the process of urban evolution falls into two effects: one is the Pareto effect indicating city number increase (external complexity, and the other the Zipf effect indicating city size growth (internal complexity. Because of struggle of the two effects, the scaling exponent varies from 0.5 to 2; but if the two effects reach equilibrium with each other, the scaling exponent approaches 1. A series of mathematical experiments on hierarchical correlation are employed to verify the models and a conclusion can be drawn that if cities in a given region follow Zipf's law, the frequency and size correlations will follow the scaling law. This theory can be generalized to interpret the inverse power-law distributions in various fields of physical and social sciences.
Modeling fractal structure of city-size distributions using correlation functions.
Chen, Yanguang
2011-01-01
Zipf's law is one the most conspicuous empirical facts for cities, however, there is no convincing explanation for the scaling relation between rank and size and its scaling exponent. Using the idea from general fractals and scaling, I propose a dual competition hypothesis of city development to explain the value intervals and the special value, 1, of the power exponent. Zipf's law and Pareto's law can be mathematically transformed into one another, but represent different processes of urban evolution, respectively. Based on the Pareto distribution, a frequency correlation function can be constructed. By scaling analysis and multifractals spectrum, the parameter interval of Pareto exponent is derived as (0.5, 1]; Based on the Zipf distribution, a size correlation function can be built, and it is opposite to the first one. By the second correlation function and multifractals notion, the Pareto exponent interval is derived as [1, 2). Thus the process of urban evolution falls into two effects: one is the Pareto effect indicating city number increase (external complexity), and the other the Zipf effect indicating city size growth (internal complexity). Because of struggle of the two effects, the scaling exponent varies from 0.5 to 2; but if the two effects reach equilibrium with each other, the scaling exponent approaches 1. A series of mathematical experiments on hierarchical correlation are employed to verify the models and a conclusion can be drawn that if cities in a given region follow Zipf's law, the frequency and size correlations will follow the scaling law. This theory can be generalized to interpret the inverse power-law distributions in various fields of physical and social sciences.
Fractal design concepts for stretchable electronics.
Fan, Jonathan A; Yeo, Woon-Hong; Su, Yewang; Hattori, Yoshiaki; Lee, Woosik; Jung, Sung-Young; Zhang, Yihui; Liu, Zhuangjian; Cheng, Huanyu; Falgout, Leo; Bajema, Mike; Coleman, Todd; Gregoire, Dan; Larsen, Ryan J; Huang, Yonggang; Rogers, John A
2014-01-01
Stretchable electronics provide a foundation for applications that exceed the scope of conventional wafer and circuit board technologies due to their unique capacity to integrate with soft materials and curvilinear surfaces. The range of possibilities is predicated on the development of device architectures that simultaneously offer advanced electronic function and compliant mechanics. Here we report that thin films of hard electronic materials patterned in deterministic fractal motifs and bonded to elastomers enable unusual mechanics with important implications in stretchable device design. In particular, we demonstrate the utility of Peano, Greek cross, Vicsek and other fractal constructs to yield space-filling structures of electronic materials, including monocrystalline silicon, for electrophysiological sensors, precision monitors and actuators, and radio frequency antennas. These devices support conformal mounting on the skin and have unique properties such as invisibility under magnetic resonance imaging. The results suggest that fractal-based layouts represent important strategies for hard-soft materials integration.
Fractal design concepts for stretchable electronics
Fan, Jonathan A.; Yeo, Woon-Hong; Su, Yewang; Hattori, Yoshiaki; Lee, Woosik; Jung, Sung-Young; Zhang, Yihui; Liu, Zhuangjian; Cheng, Huanyu; Falgout, Leo; Bajema, Mike; Coleman, Todd; Gregoire, Dan; Larsen, Ryan J.; Huang, Yonggang; Rogers, John A.
2014-02-01
Stretchable electronics provide a foundation for applications that exceed the scope of conventional wafer and circuit board technologies due to their unique capacity to integrate with soft materials and curvilinear surfaces. The range of possibilities is predicated on the development of device architectures that simultaneously offer advanced electronic function and compliant mechanics. Here we report that thin films of hard electronic materials patterned in deterministic fractal motifs and bonded to elastomers enable unusual mechanics with important implications in stretchable device design. In particular, we demonstrate the utility of Peano, Greek cross, Vicsek and other fractal constructs to yield space-filling structures of electronic materials, including monocrystalline silicon, for electrophysiological sensors, precision monitors and actuators, and radio frequency antennas. These devices support conformal mounting on the skin and have unique properties such as invisibility under magnetic resonance imaging. The results suggest that fractal-based layouts represent important strategies for hard-soft materials integration.
Fractal characterization and wettability of ion treated silicon surfaces
Yadav, R. P.; Kumar, Tanuj; Baranwal, V.; Vandana, Kumar, Manvendra; Priya, P. K.; Pandey, S. N.; Mittal, A. K.
2017-02-01
Fractal characterization of surface morphology can be useful as a tool for tailoring the wetting properties of solid surfaces. In this work, rippled surfaces of Si (100) are grown using 200 keV Ar+ ion beam irradiation at different ion doses. Relationship between fractal and wetting properties of these surfaces are explored. The height-height correlation function extracted from atomic force microscopic images, demonstrates an increase in roughness exponent with an increase in ion doses. A steep variation in contact angle values is found for low fractal dimensions. Roughness exponent and fractal dimensions are found correlated with the static water contact angle measurement. It is observed that after a crossover of the roughness exponent, the surface morphology has a rippled structure. Larger values of interface width indicate the larger ripples on the surface. The contact angle of water drops on such surfaces is observed to be lowest. Autocorrelation function is used for the measurement of ripple wavelength.
Spina, Maria E; Saraceno, Marcos
2010-01-01
It has been conjectured that for a class of piecewise linear maps the closure of the set of images of the discontinuity has the structure of a fat fractal, that is, a fractal with positive measure. An example of such maps is the sawtooth map in the elliptic regime. In this work we analyze this problem quantum mechanically in the semiclassical regime. We find that the fraction of states localized on the unstable set satisfies a modified fractal Weyl law, where the exponent is given by the exterior dimension of the fat fractal.
Fractals in several electrode materials
Energy Technology Data Exchange (ETDEWEB)
Zhang, Chunyong, E-mail: zhangchy@njau.edu.cn [Department of Chemistry, College of Science, Nanjing Agricultural University, Nanjing 210095 (China); Suzhou Key Laboratory of Environment and Biosafety, Suzhou Academy of Southeast University, Dushuhu lake higher education town, Suzhou 215123 (China); Wu, Jingyu [Department of Chemistry, College of Science, Nanjing Agricultural University, Nanjing 210095 (China); Fu, Degang [Suzhou Key Laboratory of Environment and Biosafety, Suzhou Academy of Southeast University, Dushuhu lake higher education town, Suzhou 215123 (China); State Key Laboratory of Bioelectronics, Southeast University, Nanjing 210096 (China)
2014-09-15
Highlights: • Fractal geometry was employed to characterize three important electrode materials. • The surfaces of all studied electrodes were proved to be very rough. • The fractal dimensions of BDD and ACF were scale dependent. • MMO film was more uniform than BDD and ACF in terms of fractal structures. - Abstract: In the present paper, the fractal properties of boron-doped diamond (BDD), mixed metal oxide (MMO) and activated carbon fiber (ACF) electrode have been studied by SEM imaging at different scales. Three materials are self-similar with mean fractal dimension in the range of 2.6–2.8, confirming that they all exhibit very rough surfaces. Specifically, it is found that MMO film is more uniform in terms of fractal structure than BDD and ACF. As a result, the intriguing characteristics make these electrodes as ideal candidates for high-performance decontamination processes.
Study of fractal dimension in chest images using normal and interstitial lung disease cases
Tucker, Douglas M.; Correa, Jose L.; Souto, Miguel; Malagari, Katerina S.
1993-09-01
A quantitative computerized method which provides accurate discrimination between chest radiographs with positive findings of interstitial disease patterns and normal chest radiographs may increase the efficacy of radiologic screening of the chest and the utility of digital radiographic systems. This report is a comparison of fractal dimension measured in normal chest radiographs and in radiographs with abnormal lungs having reticular, nodular, reticulonodular and linear patterns of interstitial disease. Six regions of interest (ROI's) from each of 33 normal chest radiographs and 33 radiographs with positive findings of interstitial disease were studied. Results indicate that there is a statistically significant difference between the distribution of the fractal dimension in normal radiographs and radiographs where disease is present.
Fractal metrology for biogeosystems analysis
Directory of Open Access Journals (Sweden)
V. Torres-Argüelles
2010-06-01
Full Text Available The solid-pore distribution pattern plays an important role in soil functioning being related with the main physical, chemical and biological multiscale and multitemporal processes. In the present research, this pattern is extracted from the digital images of three soils (Chernozem, Solonetz and "Chocolate'' Clay and compared in terms of roughness of the gray-intensity distribution (the measurand quantified by several measurement techniques. Special attention was paid to the uncertainty of each of them and to the measurement function which best fits to the experimental results. Some of the applied techniques are known as classical in the fractal context (box-counting, rescaling-range and wavelets analyses, etc. while the others have been recently developed by our Group. The combination of all these techniques, coming from Fractal Geometry, Metrology, Informatics, Probability Theory and Statistics is termed in this paper Fractal Metrology (FM. We show the usefulness of FM through a case study of soil physical and chemical degradation applying the selected toolbox to describe and compare the main structural attributes of three porous media with contrasting structure but similar clay mineralogy dominated by montmorillonites.
Institute of Scientific and Technical Information of China (English)
惠红梅
2013-01-01
分形是近四十年刚刚发展起来的一门新兴学科，隶属于非线性领域，分形能够描述传统数学无法表达的形态如树木、山脉等。千姿万态的自然界构成大部分是无序的、不确定的、也是随机的。而传统的欧式几何学它所描述的对象是规则光滑平整的。那要准确表达自然界中的复杂事物，用传统的几何方法很难描述。人类认识领域开始呼唤产生一种新的能够更好地描述自然图形的几何学----分形几何学。人们形象的把分形几何学称之为大自然的几何学。在分形编程绘图中，迭代函数系统(IFS)的各种算法，依据IFS码可以生成自然景物中的各种分形图。在本文中主要通过IFS码生成分形图的特性研究及IFS迭代规律(分形图生成规律)的研究。%Abctrat:Fractal is nearly forty years just to the development of an emerging discipline, it belongs to the field of nonlinear, it makes the traditional mathematics to express the form such as trees, mountains to the expression profile of. The nature of most varied types and poses is disordered, uncertain, is random. But the traditional Euclidean geometry which objects are described by rules is smooth. The accurate expression of the complexity in nature, with the traditional geometric method is difficult to describe. Human understanding of the field began calling for a new can better describe the natural graphics geometry, fractal geometry People image fractal geometry is called the geometry of nature. In the fractal program drawing, iterated function system ( IFS ) algorithms, based on the IFS code can generate natural scenery in a variety of fractal images. In this paper mainly through the IFS code generating fractal characteristics and IFS iterative law ( Law of fractal graph generation ).
The fractal heart — embracing mathematics in the cardiology clinic
Captur, Gabriella; Karperien, Audrey L.; Hughes, Alun D.; Francis, Darrel P.; Moon, James C.
2017-01-01
For clinicians grappling with quantifying the complex spatial and temporal patterns of cardiac structure and function (such as myocardial trabeculae, coronary microvascular anatomy, tissue perfusion, myocyte histology, electrical conduction, heart rate, and blood-pressure variability), fractal analysis is a powerful, but still underused, mathematical tool. In this Perspectives article, we explain some fundamental principles of fractal geometry and place it in a familiar medical setting. We summarize studies in the cardiovascular sciences in which fractal methods have successfully been used to investigate disease mechanisms, and suggest potential future clinical roles in cardiac imaging and time series measurements. We believe that clinical researchers can deploy innovative fractal solutions to common cardiac problems that might ultimately translate into advancements for patient care. PMID:27708281
基于小波分形的图像分割算法%Wavelet Fractal-Based Image Segment Algorithm
Institute of Scientific and Technical Information of China (English)
叶俊勇; 汪同庆; 彭健; 杨波
2002-01-01
The image of shoe leather lumen is not very satisfaction because of technology of CT. The smart imagesegment is the base of getting smart measurement data. An algorithm of image segment based on wavelet and fractalhas been proposed after analyzing the specialty of images. The image is decomposed through wavelet multi-resolutiondecomposition , and the fractal dimension is calculated by the decomposed image. This approach is more satisfied thangeneral method in image segment of shoe leather lumen image by CT. This algorithm can segment the edge of shoe lu-men exactly. The experimentations prove the approach is rational.
Fractal Metrology for biogeosystems analysis
Directory of Open Access Journals (Sweden)
V. Torres-Argüelles
2010-11-01
Full Text Available The solid-pore distribution pattern plays an important role in soil functioning being related with the main physical, chemical and biological multiscale and multitemporal processes of this complex system. In the present research, we studied the aggregation process as self-organizing and operating near a critical point. The structural pattern is extracted from the digital images of three soils (Chernozem, Solonetz and "Chocolate" Clay and compared in terms of roughness of the gray-intensity distribution quantified by several measurement techniques. Special attention was paid to the uncertainty of each of them measured in terms of standard deviation. Some of the applied methods are known as classical in the fractal context (box-counting, rescaling-range and wavelets analyses, etc. while the others have been recently developed by our Group. The combination of these techniques, coming from Fractal Geometry, Metrology, Informatics, Probability Theory and Statistics is termed in this paper Fractal Metrology (FM. We show the usefulness of FM for complex systems analysis through a case study of the soil's physical and chemical degradation applying the selected toolbox to describe and compare the structural attributes of three porous media with contrasting structure but similar clay mineralogy dominated by montmorillonites.
Fractal Metrology for biogeosystems analysis
Torres-Argüelles, V.; Oleschko, K.; Tarquis, A. M.; Korvin, G.; Gaona, C.; Parrot, J.-F.; Ventura-Ramos, E.
2010-11-01
The solid-pore distribution pattern plays an important role in soil functioning being related with the main physical, chemical and biological multiscale and multitemporal processes of this complex system. In the present research, we studied the aggregation process as self-organizing and operating near a critical point. The structural pattern is extracted from the digital images of three soils (Chernozem, Solonetz and "Chocolate" Clay) and compared in terms of roughness of the gray-intensity distribution quantified by several measurement techniques. Special attention was paid to the uncertainty of each of them measured in terms of standard deviation. Some of the applied methods are known as classical in the fractal context (box-counting, rescaling-range and wavelets analyses, etc.) while the others have been recently developed by our Group. The combination of these techniques, coming from Fractal Geometry, Metrology, Informatics, Probability Theory and Statistics is termed in this paper Fractal Metrology (FM). We show the usefulness of FM for complex systems analysis through a case study of the soil's physical and chemical degradation applying the selected toolbox to describe and compare the structural attributes of three porous media with contrasting structure but similar clay mineralogy dominated by montmorillonites.
Thermodynamic fractals and formalism. Fractales y formalismo termodinamico
Energy Technology Data Exchange (ETDEWEB)
Chacon, R.; Morales, J.J.
1994-01-01
We give a brief introduction to the so called ''thermodynamical description of fractals'' restricting our attention to Cantor sets generated by chaotic motion of a dynamical system. In particular, an entropy function and a free energy are introduced for multi fractals. (Author) 14 refs.
Configuration entropy of fractal landscapes
National Research Council Canada - National Science Library
Rodríguez‐Iturbe, Ignacio; D'Odorico, Paolo; Rinaldo, Andrea
1998-01-01
.... The spatial arrangement of two‐dimensional images is found to be an effective way to characterize fractal landscapes and the configurational entropy of these arrangements imposes demanding conditions for models attempting to represent these fields.
Contour fractal analysis of grains
Guida, Giulia; Casini, Francesca; Viggiani, Giulia MB
2017-06-01
Fractal analysis has been shown to be useful in image processing to characterise the shape and the grey-scale complexity in different applications spanning from electronic to medical engineering (e.g. [1]). Fractal analysis consists of several methods to assign a dimension and other fractal characteristics to a dataset describing geometric objects. Limited studies have been conducted on the application of fractal analysis to the classification of the shape characteristics of soil grains. The main objective of the work described in this paper is to obtain, from the results of systematic fractal analysis of artificial simple shapes, the characterization of the particle morphology at different scales. The long term objective of the research is to link the microscopic features of granular media with the mechanical behaviour observed in the laboratory and in situ.
Institute of Scientific and Technical Information of China (English)
梁洪亮; 刘孝书
2003-01-01
For a physics system which exhibits memory, if memory is preserved only at points of random self-similar fractals, we define random memory functions and give the connection between the expectation of flux and the fractional integral. In particular, when memory sets degenerate to Cantor type fractals or non-random self-similar fractals our results coincide with that of Nigmatullin and Ren et al..
Upper Bound and Lower Bound Estimate of Monotone Increasing Fractal Function%单调递增分形函数上、下界的估计
Institute of Scientific and Technical Information of China (English)
马冠忠; 袁瑰霞; 崔振文
2008-01-01
Mass distribution principle is one of important tools in studying Hausdorff dimension and Hausdorff measure.In this paper we will give a numerical approximate method of upper bound and lower bound of mass distribution function f(x)(it is a monotone increasing fractal function)and its some applications.
Deppman, Airton
2016-01-01
The non extensive aspects of $p_T$ distributions obtained in high energy collisions are discussed in relation to possible fractal structure in hadrons, in the sense of the thermofractal structure recently introduced. The evidences of self-similarity in both theoretical and experimental works in High Energy and in Hadron Physics are discussed, to show that the idea of fractal structure of hadrons and fireballs have being under discussion for decades. The non extensive self-consistent thermodynamics and the thermofractal structure allow one to connect non extensivity to intermittence and possibly to parton distribution functions in a single theoretical framework.
Waliszewski, Przemyslaw
2016-01-01
The subjective evaluation of tumor aggressiveness is a cornerstone of the contemporary tumor pathology. A large intra- and interobserver variability is a known limiting factor of this approach. This fundamental weakness influences the statistical deterministic models of progression risk assessment. It is unlikely that the recent modification of tumor grading according to Gleason criteria for prostate carcinoma will cause a qualitative change and improve significantly the accuracy. The Gleason system does not allow the identification of low aggressive carcinomas by some precise criteria. The ontological dichotomy implies the application of an objective, quantitative approach for the evaluation of tumor aggressiveness as an alternative. That novel approach must be developed and validated in a manner that is independent of the results of any subjective evaluation. For example, computer-aided image analysis can provide information about geometry of the spatial distribution of cancer cell nuclei. A series of the interrelated complexity measures characterizes unequivocally the complex tumor images. Using those measures, carcinomas can be classified into the classes of equivalence and compared with each other. Furthermore, those measures define the quantitative criteria for the identification of low- and high-aggressive prostate carcinomas, the information that the subjective approach is not able to provide. The co-application of those complexity measures in cluster analysis leads to the conclusion that either the subjective or objective classification of tumor aggressiveness for prostate carcinomas should comprise maximal three grades (or classes). Finally, this set of the global fractal dimensions enables a look into dynamics of the underlying cellular system of interacting cells and the reconstruction of the temporal-spatial attractor based on the Taken's embedding theorem. Both computer-aided image analysis and the subsequent fractal synthesis could be performed
Lung cancer-a fractal viewpoint.
Lennon, Frances E; Cianci, Gianguido C; Cipriani, Nicole A; Hensing, Thomas A; Zhang, Hannah J; Chen, Chin-Tu; Murgu, Septimiu D; Vokes, Everett E; Vannier, Michael W; Salgia, Ravi
2015-11-01
Fractals are mathematical constructs that show self-similarity over a range of scales and non-integer (fractal) dimensions. Owing to these properties, fractal geometry can be used to efficiently estimate the geometrical complexity, and the irregularity of shapes and patterns observed in lung tumour growth (over space or time), whereas the use of traditional Euclidean geometry in such calculations is more challenging. The application of fractal analysis in biomedical imaging and time series has shown considerable promise for measuring processes as varied as heart and respiratory rates, neuronal cell characterization, and vascular development. Despite the advantages of fractal mathematics and numerous studies demonstrating its applicability to lung cancer research, many researchers and clinicians remain unaware of its potential. Therefore, this Review aims to introduce the fundamental basis of fractals and to illustrate how analysis of fractal dimension (FD) and associated measurements, such as lacunarity (texture) can be performed. We describe the fractal nature of the lung and explain why this organ is particularly suited to fractal analysis. Studies that have used fractal analyses to quantify changes in nuclear and chromatin FD in primary and metastatic tumour cells, and clinical imaging studies that correlated changes in the FD of tumours on CT and/or PET images with tumour growth and treatment responses are reviewed. Moreover, the potential use of these techniques in the diagnosis and therapeutic management of lung cancer are discussed.
WEAR PARTICLE IMAGE SEGMENTATION BASED ON FRACTAL FEATURE%基于分形特征的磨粒图像分割
Institute of Scientific and Technical Information of China (English)
郭恒光; 瞿军; 汪兴海
2014-01-01
磨粒图像分割是磨粒图像分析的关键一步，分割结果的准确性将直接影响磨粒的最终识别和分类。分形理论在表征磨粒的轮廓特征和表面特征方面得到了广泛应用。结合磨粒图像的分形特征和自组织特征映射神经网络，提出基于分形特征的磨粒图像分割方法。首先，计算磨粒图像的分形维数，多重分形维数，结合图像的灰度信息，共得到图像的8个特征；然后，利用自组织特征映射神经网络的自组织、自学习特性，实现磨粒图像的分割。磨粒图像分割的结果表明，该算法是可行的、有效的。%Wear particle image segmentation is the key step of wear particle image analysis,and the accuracy of the segmentation result affects directly the final recognition and classification of wear particles.Fractal geometry has been used widely in characterising wear particle profile and surface features.We propose a fractal features-based wear particle image segmentation method by combining the fractal features of ware particle image with self-organising feature mapping (SOFM)neural network.First,we calculate the fractal dimensions and multi-fractal dimensions of the ware particle image,in combination with its grey information,we acquire total eight features of the image.Then,we use the characteristics of self-organising and self-learning of SOFM neural network to implement the wear particle image segmentation.Result of the wear particle image segmentation shows that this algorithm is feasible and effective.
On the fractal properties microaccelerations
Sedelnikov, A V
2012-01-01
In this paper the fractal property of the internal environment of space laboratory microaccelerations that occur. Changing the size of the space lab leads to the fact that the dependence of microaccelerations from time to time has the property similar to the self-affinity of fractal functions. With the help of microaccelerations, based on the model of the real part of the fractal Weierstrass-Mandelbrot function is proposed to form the inertial-mass characteristics of laboratory space with a given level of microaccelerations.
2011-01-01
Objective The aim of this study was to use fractal dimension (FD) analysis on multidetector CT (MDCT) images for quantifying the morphological changes of the pulmonary artery tree in patients with pulmonary hypertension (PH). Materials and Methods Fourteen patients with PH and 17 patients without PH as controls were studied. All of the patients underwent contrast-enhanced helical CT and transthoracic echocardiography. The pulmonary artery trees were generated using post-processing software, a...
Fractal Trigonometric Polynomials for Restricted Range Approximation
Chand, A. K. B.; Navascués, M. A.; Viswanathan, P.; Katiyar, S. K.
2016-05-01
One-sided approximation tackles the problem of approximation of a prescribed function by simple traditional functions such as polynomials or trigonometric functions that lie completely above or below it. In this paper, we use the concept of fractal interpolation function (FIF), precisely of fractal trigonometric polynomials, to construct one-sided uniform approximants for some classes of continuous functions.
Dougherty, G
2001-06-01
The structural integrity of trabecular bone is an important factor characterizing the biomechanical strength of the vertebra, and is determined by the connectivity of the bone network and the trabeculation pattern. These can be assessed using texture measures such as the fractal signature and lacunarity from a high resolution projection radiograph. Using central sections of lumbar vertebrae we compared the results obtained from high-resolution transverse projection images with those obtained from spatially registered low-resolution images from a conventional clinical CT scanner to determine whether clinical CT data can provide useful structural information. Provided the power spectra of the CT images are corrected for image system blurring, the resulting fractal signature is similar for both modalities. Although the CT images are blurred relative to the projection images, with a consequent reduction in lacunarity, the estimated trabecular separation obtained from the lacunarity plots is similar for both modalities. This suggests that these texture measures contain essential information on trabecular microarchitecture, which is present even in low resolution CT images. Such quantitative texture measurements from CT or MRI images are potentially useful in monitoring bone strength and predicting future fracture risk.
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
The main contents in this note are: 1. introduction; 2. locally compact groups and local fields ; 3. calcaius on fractals based upon local fields; 4. fractional calculus and fractals; 5. fractal function spaces and PDE on fractals.
Pelletier, J D
1997-01-01
The power spectrum S of linear transects of the earth's topography is often observed to be a power-law function of wave number k with exponent close to -2: S(k) is proportional to k^-2. In addition, river networks are fractal trees that satisfy many power-law or fractal relationships between their morphologic components. A model equation for the evolution of the earth's topography by erosional processes which produces fractal topography and fractal river networks is presented and its solutions compared in detail to real topography. The model is the diffusion equation for sediment transport on hillslopes and channels with the local diffusivity proportional to the square of the discharge. The dependence of diffusivity on discharge follows from fundamental equations of sediment transport. We study the model in two ways. In the first analysis the diffusivity is parameterized as a function of relief and a Taylor expansion procedure is carried out to obtain a differential equation for the landform elevation which i...
Ofstatistical and Fractal Properties of Semiconductor Surface Roughness
Directory of Open Access Journals (Sweden)
Stanislav Jurecka
2008-01-01
Full Text Available Surface morphology evolution is of primary significance for the thin-film growth and modification of surface andinterface states. Surface and interface states substantially influence the electrical and optical properties of the semiconductorstructure. Statistical and fractal properties of semiconductor rough surfaces were determined by analysis of the AFM images.In this paper statistical characteristics of the AFM height function distribution, fractal dimension, lacunarity and granulometric density values are used for the surface morphology of the SiC samples description. The results can be used for solution ofthe microstructural and optical properties of given semiconductor structure.
Pippa, Natassa; Pispas, Stergios; Demetzos, Costas
2014-09-01
The major advance of mixed liposomes (the so-called chimeric systems) is to control the size, structure, and morphology of these nanoassemblies, and therefore, system colloidal properties, with the aid of a large variety of parameters, such as chemical architecture and composition. The goal of this study is to investigate the alterations of the physicochemical and morphological characteristics of chimeric dipalmitoylphosphatidylcholine (DPPC) liposomes, caused by the incorporation of block and gradient copolymers (different macromolecular architecture) with different chemical compositions (different amounts of hydrophobic component). Light scattering techniques were utilized in order to characterize physicochemically and to delineate the fractal morphology of chimeric liposomes. In this study, we also investigated the structural differences between the prepared chimeric liposomes as are visualized by scanning electron microscopy (SEM). It could be concluded that all the chimeric liposomes have regular structure, as SEM images revealed, while their fractal dimensionality was found to be dependent on the macromolecular architecture of the polymeric guest.
Directory of Open Access Journals (Sweden)
Xiuqing Zheng
2013-01-01
box-counting dimension (PWBCD, is computed for each image pixel. PWBCD uses a fixed size local window centered at the considered image pixel to fit the different local structures of images. Then based on PWBCD, a new method that uses PWBCD to improve SA of NLMs directly is proposed. That is, PWBCD is combined with the weight of the difference between local comparison windows for NLMs. Smoothing results for test images and real sinograms show that PWBCD-NLMs with well-chosen parameters can preserve anatomical features better while suppressing the noises efficiently. In addition, PWBCD-NLMs also has better performance both in visual quality and peak signal to noise ratio (PSNR than NLMs in LDCT imaging.
A Parallel Implementation of Improved Fractal Image Coding Based on Tree Topology
Institute of Scientific and Technical Information of China (English)
SUNYunda,; ZHAOYao; YUANBaozong
2003-01-01
One of the main drawbacks of fractai im-age coding (FIC) is its time-consuming encoding process.So how to speed up the encoding process is a challenging issue of FIC research. As both sequential solutions and parallel ones have their advantages and disadvantages, we combine them together to further speed up the encoding phase. In this paper a derivative tree topology is first pro-posed to provide support for complex parallelism. Then a dual-classification technique is designed for speeding up the fractai image coding with Same-Sized Block Mapping,which improves the decoded image quality. Finally, some experimental results with good performance are presented.
Directory of Open Access Journals (Sweden)
P. K. Dutta
2012-04-01
Full Text Available Satellite imagery for 2011 earthquake off the Pacific coast of Tohoku has provided an opportunity to conduct image transformation analyses by employing multi-temporal images retrieval techniques. In this study, we used a new image segmentation algorithm to image coastline deformation by adopting graph cut energy minimization framework. Comprehensive analysis of available INSAR images using coastline deformation analysis helped extract disaster information of the affected region of the 2011 Tohoku tsunamigenic earthquake source zone. We attempted to correlate fractal analysis of seismic clustering behavior with image processing analogies and our observations suggest that increase in fractal dimension distribution is associated with clustering of events that may determine the level of devastation of the region. The implementation of graph cut based image registration technique helps us to detect the devastation across the coastline of Tohoku through change of intensity of pixels that carries out regional segmentation for the change in coastal boundary after the tsunami. The study applies transformation parameters on remotely sensed images by manually segmenting the image to recovering translation parameter from two images that differ by rotation. Based on the satellite image analysis through image segmentation, it is found that the area of 0.997 sq km for the Honshu region was a maximum damage zone localized in the coastal belt of NE Japan forearc region. The analysis helps infer using matlab that the proposed graph cut algorithm is robust and more accurate than other image registration methods. The analysis shows that the method can give a realistic estimate for recovered deformation fields in pixels corresponding to coastline change which may help formulate the strategy for assessment during post disaster need assessment scenario for the coastal belts associated with damages due to strong shaking and tsunamis in the world under disaster risk
Functional imaging in the fetus.
Schöpf, Veronika; Kasprian, Gregor; Prayer, Daniela
2011-06-01
This review focuses on the application of magnetic resonance imaging methods in utero studying functional brain development of spontaneous brain activity generated under resting conditions and of task-evoked activity using stimulation. These imaging approaches have been useful to explore the brain's functional organization during development, as already shown in different substantial resting-state studies in preterms. We also discuss emerging future directions regarding analyzing methods and combination of functional and structural connectivity approaches.
Khokhlov, D L
1999-01-01
The model of the universe is considered in which background of the universe is not defined by the matter but is a priori specified as a homogenous and isotropic flat space. The scale factor of the universe follows the linear law. The scale of mass changes proportional to the scale factor. This leads to that the universe has the fractal structure with a power index of 2.
Fractal signatures in the aperiodic Fibonacci grating.
Verma, Rupesh; Banerjee, Varsha; Senthilkumaran, Paramasivam
2014-05-01
The Fibonacci grating (FbG) is an archetypal example of aperiodicity and self-similarity. While aperiodicity distinguishes it from a fractal, self-similarity identifies it with a fractal. Our paper investigates the outcome of these complementary features on the FbG diffraction profile (FbGDP). We find that the FbGDP has unique characteristics (e.g., no reduction in intensity with increasing generations), in addition to fractal signatures (e.g., a non-integer fractal dimension). These make the Fibonacci architecture potentially useful in image forming devices and other emerging technologies.
Conference on Fractals and Related Fields III
Seuret, Stéphane
2017-01-01
This contributed volume provides readers with an overview of the most recent developments in the mathematical fields related to fractals, including both original research contributions, as well as surveys from many of the leading experts on modern fractal theory and applications. It is an outgrowth of the Conference of Fractals and Related Fields III, that was held on September 19-25, 2015 in île de Porquerolles, France. Chapters cover fields related to fractals such as harmonic analysis, multifractal analysis, geometric measure theory, ergodic theory and dynamical systems, probability theory, number theory, wavelets, potential theory, partial differential equations, fractal tilings, combinatorics, and signal and image processing. The book is aimed at pure and applied mathematicians in these areas, as well as other researchers interested in discovering the fractal domain.
Bhat, C K
2010-01-01
We show from a simulations-based study of the TACTIC telescope that fractal and wavelet analysis of Cerenkov images, recorded in a single imaging Cerenkov telescope, enables almost complete segregation of isotropic gamma-ray initiated events from the overwhelming background of cosmic-ray hadron-initiated events. This presents a new method for measuring galactic and extragalactic gamma-ray background above 1 TeV energy. Preliminary results based on this method are reported here. Primary aim is to explore the possibility of using data recorded by a single imaging atmospheric Cerenkov telescope(IACT) for making accurate measurements of diffuse galactic and extragalactic gamma-ray flux above ~1 TeV energy. Using simulated data of atmospheric Cerenkov images recorded in an IACT, initiated both by cosmic ray protons and diffuse gamma-rays with energies above 4 TeV and 2 TeV respectively, we identify the most efficient fractal /wavelet parameters of the recorded images for primary identification. The method is based...
Comparison of two fractal interpolation methods
Fu, Yang; Zheng, Zeyu; Xiao, Rui; Shi, Haibo
2017-03-01
As a tool for studying complex shapes and structures in nature, fractal theory plays a critical role in revealing the organizational structure of the complex phenomenon. Numerous fractal interpolation methods have been proposed over the past few decades, but they differ substantially in the form features and statistical properties. In this study, we simulated one- and two-dimensional fractal surfaces by using the midpoint displacement method and the Weierstrass-Mandelbrot fractal function method, and observed great differences between the two methods in the statistical characteristics and autocorrelation features. From the aspect of form features, the simulations of the midpoint displacement method showed a relatively flat surface which appears to have peaks with different height as the fractal dimension increases. While the simulations of the Weierstrass-Mandelbrot fractal function method showed a rough surface which appears to have dense and highly similar peaks as the fractal dimension increases. From the aspect of statistical properties, the peak heights from the Weierstrass-Mandelbrot simulations are greater than those of the middle point displacement method with the same fractal dimension, and the variances are approximately two times larger. When the fractal dimension equals to 1.2, 1.4, 1.6, and 1.8, the skewness is positive with the midpoint displacement method and the peaks are all convex, but for the Weierstrass-Mandelbrot fractal function method the skewness is both positive and negative with values fluctuating in the vicinity of zero. The kurtosis is less than one with the midpoint displacement method, and generally less than that of the Weierstrass-Mandelbrot fractal function method. The autocorrelation analysis indicated that the simulation of the midpoint displacement method is not periodic with prominent randomness, which is suitable for simulating aperiodic surface. While the simulation of the Weierstrass-Mandelbrot fractal function method has
Fractal Characterization of Hyperspectral Imagery
Qiu, Hon-Iie; Lam, Nina Siu-Ngan; Quattrochi, Dale A.; Gamon, John A.
1999-01-01
Two Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) hyperspectral images selected from the Los Angeles area, one representing urban and the other, rural, were used to examine their spatial complexity across their entire spectrum of the remote sensing data. Using the ICAMS (Image Characterization And Modeling System) software, we computed the fractal dimension values via the isarithm and triangular prism methods for all 224 bands in the two AVIRIS scenes. The resultant fractal dimensions reflect changes in image complexity across the spectral range of the hyperspectral images. Both the isarithm and triangular prism methods detect unusually high D values on the spectral bands that fall within the atmospheric absorption and scattering zones where signature to noise ratios are low. Fractal dimensions for the urban area resulted in higher values than for the rural landscape, and the differences between the resulting D values are more distinct in the visible bands. The triangular prism method is sensitive to a few random speckles in the images, leading to a lower dimensionality. On the contrary, the isarithm method will ignore the speckles and focus on the major variation dominating the surface, thus resulting in a higher dimension. It is seen where the fractal curves plotted for the entire bandwidth range of the hyperspectral images could be used to distinguish landscape types as well as for screening noisy bands.
Pribic, Jelena; Vasiljevic, Jelena; Kanjer, Ksenija; Konstantinovic, Zora Neskovic; Milosevic, Nebojsa T; Vukosavljevic, Dragica Nikolic; Radulovic, Marko
2015-01-01
Research in the field of breast cancer outcome prognosis has been focused on molecular biomarkers, while neglecting the discovery of novel tumor histology structural clues. We thus aimed to improve breast cancer prognosis by fractal analysis of tumor histomorphology. This retrospective study included 92 breast cancer patients without systemic treatment. Fractal dimension and lacunarity of the breast tumor microscopic histology possess prognostic value comparable to the major clinicopathological prognostic parameters. Fractal analysis was performed for the first time on routinely produced archived pan-tissue stained primary breast tumor sections, indicating its potential for clinical use as a simple and cost-effective prognostic indicator of distant metastasis risk to complement the molecular approaches for cancer risk prognosis.
Fractals and Scars on a Compact Octagon
Levin, J; Levin, Janna; Barrow, John D.
2000-01-01
A finite universe naturally supports chaotic classical motion. An ordered fractal emerges from the chaotic dynamics which we characterize in full for a compact 2-dimensional octagon. In the classical to quantum transition, the underlying fractal can persist in the form of scars, ridges of enhanced amplitude in the semiclassical wave function. Although the scarring is weak on the octagon, we suggest possible subtle implications of fractals and scars in a finite universe.
Modeling Fractal Dimension Curve of Urban Growth in Developing Countries
Chen, Yanguang
2016-01-01
The growth curve of fractal dimension of cities can be described with sigmoid function such as Boltzmann's equation and logistic function. The logistic models of fractal dimension curves have been presented for the cities in developed countries. However, these models cannot be well fitted to the observational data of fractal dimension of urban form in developing countries (e.g. China). By statistic experiments of fractal parameters, we find that the quadratic Boltzmann's equation can be used to describe fractal dimension change of Chinese cities. For the normalized fractal dimension values, the Boltzmann's equation can be reduced to a quadratic logistic function. In practice, a fractal dimension dataset of urban growth can be approximately fitted with the quadratic logistic function. Thus, a series of models of fractal dimension curve can be proposed for the cities in developing countries. The models are applied to the city of Beijing, Chinese capital, and yield satisfying trend lines of the observational dat...
Segmentation of histological structures for fractal analysis
Dixon, Vanessa; Kouznetsov, Alexei; Tambasco, Mauro
2009-02-01
Pathologists examine histology sections to make diagnostic and prognostic assessments regarding cancer based on deviations in cellular and/or glandular structures. However, these assessments are subjective and exhibit some degree of observer variability. Recent studies have shown that fractal dimension (a quantitative measure of structural complexity) has proven useful for characterizing structural deviations and exhibits great potential for automated cancer diagnosis and prognosis. Computing fractal dimension relies on accurate image segmentation to capture the architectural complexity of the histology specimen. For this purpose, previous studies have used techniques such as intensity histogram analysis and edge detection algorithms. However, care must be taken when segmenting pathologically relevant structures since improper edge detection can result in an inaccurate estimation of fractal dimension. In this study, we established a reliable method for segmenting edges from grayscale images. We used a Koch snowflake, an object of known fractal dimension, to investigate the accuracy of various edge detection algorithms and selected the most appropriate algorithm to extract the outline structures. Next, we created validation objects ranging in fractal dimension from 1.3 to 1.9 imitating the size, structural complexity, and spatial pixel intensity distribution of stained histology section images. We applied increasing intensity thresholds to the validation objects to extract the outline structures and observe the effects on the corresponding segmentation and fractal dimension. The intensity threshold yielding the maximum fractal dimension provided the most accurate fractal dimension and segmentation, indicating that this quantitative method could be used in an automated classification system for histology specimens.
Speckle interferometry from fiber-reinforced materials:A fractal geometry approach
Horta, J. M.; Castano, V. M.
Speckle field studies were performed on fiber-modified Portland cement-based microconcrete beam models subjected to flexural loading. The resulting speckle fields were analyzed in terms of their associated mass fractal dimension by using digital image processing techniques. The experiments showed a change in the fractal dimension of the speckle fields as a function both of the loading and the structure of the microconcrete beams. A study was also conducted on the free-damped frequencies of the beams, which allowed to draw a fractal dimension vs. frequency plot on each loading cycle. These results allow to foresee the use of fractal geometry as a promising tool for better understanding the mechanical behavior of structures.
An Optical Demonstration of Fractal Geometry
Scannel, Billy; Taylor, Richard
2012-01-01
We have built a Sinai cube to illustrate and investigate the scaling properties that result by iterating chaotic trajectories into a well ordered system. We allow red, green and blue light to reflect off a mirrored sphere, which is contained in an otherwise, closed mirrored cube. The resulting images are modeled by ray tracing procedures and both sets of images undergo fractal analysis. We offer this as a novel demonstration of fractal geometry, utilizing the aesthetic appeal of these images to motivate an intuitive understanding of the resulting scaling plots and associated fractal dimensions.
Inversion problem for the dimension of fractal rough surface
Institute of Scientific and Technical Information of China (English)
ZHAO Donghua; CAI Zhijie; RUAN Jiong
2005-01-01
In the present paper, the fractal rough surface is described by a band-limited Weierstrass-Mandelbrot function. By using the Monte Carlo method and optimal method,a minimal target function method is applied to inverting the fractal dimension of the fractal rough surface. Numerical simulations show that the method can avoid the influence of the fractal characteristic scale, and that the method is of high precision.
Fractal organization of feline oocyte cytoplasm.
De Vico, G; Peretti, V; Losa, G A
2005-01-01
The present study aimed at verifying whether immature cat oocytes with morphologic irregular cytoplasm display self-similar features which can be analytically described by fractal analysis. Original images of oocytes collected by ovariectomy were acquired at a final magnification of 400x with a CCD video camera connected to an optic microscope. After greyscale thresholding segmentation of cytoplasm, image profiles were submitted to fractal analysis using FANAL++, a program which provided an analytical standard procedure for determining the fractal dimension (FD). The presentation of the oocyte influenced the magnitude of the fractal dimension with the highest FD of 1.91 measured on grey-dark cytoplasm characterized by a highly connected network of lipid droplets and intracellular membranes. Fractal analysis provides an effective quantitative descriptor of the real cytoplasm morphology, which can influence the acquirement of in vitro developmental competence, without introducing any bias or shape approximation and thus contributes to an objective and reliable classification of feline oocytes.
Fractal organization of feline oocyte cytoplasm
Directory of Open Access Journals (Sweden)
G De Vico
2009-06-01
Full Text Available The present study aimed at verifying whether immature cat oocytes with morphologic irregular cytoplasm display selfsimilar features which can be analytically described by fractal analysis. Original images of oocytes collected by ovariectomy were acquired at a final magnification of 400 X with a CCD video camera connected to an optic microscope. After greyscale thresholding segmentation of cytoplasm, image profiles were submitted to fractal analysis using FANAL++, a program which provided an analytical standard procedure for determining the fractal dimension (FD. The presentation of the oocyte influenced the magnitude of the fractal dimension with the highest FD of 1.91 measured on grey-dark cytoplasm characterized by a highly connected network of lipid droplets and intracellular membranes. Fractal analysis provides an effective quantitative descriptor of the real cytoplasm morphology, which can influence the acquirement of in vitro developmental competence, without introducing any bias or shape approximation and thus contributes to an objective and reliable classification of feline oocytes.
Retinal Vascular Fractals and Cognitive Impairment
Directory of Open Access Journals (Sweden)
Yi-Ting Ong
2014-08-01
Full Text Available Background: Retinal microvascular network changes have been found in patients with age-related brain diseases such as stroke and dementia including Alzheimer's disease. We examine whether retinal microvascular network changes are also present in preclinical stages of dementia. Methods: This is a cross-sectional study of 300 Chinese participants (age: ≥60 years from the ongoing Epidemiology of Dementia in Singapore study who underwent detailed clinical examinations including retinal photography, brain imaging and neuropsychological testing. Retinal vascular parameters were assessed from optic disc-centered photographs using a semiautomated program. A comprehensive neuropsychological battery was administered, and cognitive function was summarized as composite and domain-specific Z-scores. Cognitive impairment no dementia (CIND and dementia were diagnosed according to standard diagnostic criteria. Results: Among 268 eligible nondemented participants, 78 subjects were categorized as CIND-mild and 69 as CIND-moderate. In multivariable adjusted models, reduced retinal arteriolar and venular fractal dimensions were associated with an increased risk of CIND-mild and CIND-moderate. Reduced fractal dimensions were associated with poorer cognitive performance globally and in the specific domains of verbal memory, visuoconstruction and visuomotor speed. Conclusion: A sparser retinal microvascular network, represented by reduced arteriolar and venular fractal dimensions, was associated with cognitive impairment, suggesting that early microvascular damage may be present in preclinical stages of dementia.
Kunze, Herb; La Torre, Davide; Lin, Jianyi
2017-01-01
We consider the inverse problem associated with IFSM: Given a target function f , find an IFSM, such that its fixed point f ¯ is sufficiently close to f in the Lp distance. Forte and Vrscay [1] showed how to reduce this problem to a quadratic optimization model. In this paper, we extend the collage-based method developed by Kunze, La Torre and Vrscay ([2][3][4]), by proposing the minimization of the 1-norm instead of the 0-norm. In fact, optimization problems involving the 0-norm are combinatorial in nature, and hence in general NP-hard. To overcome these difficulties, we introduce the 1-norm and propose a Sequential Quadratic Programming algorithm to solve the corresponding inverse problem. As in Kunze, La Torre and Vrscay [3] in our formulation, the minimization of collage error is treated as a multi-criteria problem that includes three different and conflicting criteria i.e., collage error, entropy and sparsity. This multi-criteria program is solved by means of a scalarization technique which reduces the model to a single-criterion program by combining all objective functions with different trade-off weights. The results of some numerical computations are presented.
Institute of Scientific and Technical Information of China (English)
CHEN Xiufa; YANG Xiaomei; LI Yunju; LIU Baoyin; WANG Jinggui; ZHANG Zichuan
2004-01-01
The fractal characteristics of tidal creeks in the Gaizhou Beach are analyzed based on high-resolution images fusion of Landsat TM and ERS-2, and then the graphic models and characteristics of converse information tree of tidal creeks in the Gaizhou Beach are established. A calculation model is established based on the above results, and at the same time, quantitative calculation of the evolution characteristics and the diversity between the northern and the southern parts of the Gaizhou Beach is carried out. By the supervised classification of these images, distribution and areas of high tidal flats, middle tidal flats and low tidal flats in the Gaizhou Beach are studied quantitatively, and image charactistics of seashell habitats in the Gaizhou Beach and the correlation between mudflat distribution and seashell habitats are studied. At last, the engineering problems in the Gaizhou Beach are discussed.
The Art of Space Filling in Penrose Tilings and Fractals
Le, San
2011-01-01
Incorporating designs into the tiles that form tessellations presents an interesting challenge for artists. Creating a viable MC Escher like image that works esthetically as well as functionally requires resolving incongruencies at a tile's edge while constrained by its shape. Escher was the most well known practitioner in this style of mathematical visualization, but there are significant mathematical shapes to which he never applied his artistry. These shapes can incorporate designs that form images as appealing as those produced by Escher, and our paper explores this for traditional tessellations, Penrose Tilings, fractals, and fractal/tessellation combinations. To illustrate the versatility of tiling art, images were created with multiple figures and negative space leading to patterns distinct from the work of others.
Fractals in art and nature: why do we like them?
Spehar, Branka; Taylor, Richard P.
2013-03-01
Fractals have experienced considerable success in quantifying the visual complexity exhibited by many natural patterns, and continue to capture the imagination of scientists and artists alike. Fractal patterns have also been noted for their aesthetic appeal, a suggestion further reinforced by the discovery that the poured patterns of the American abstract painter Jackson Pollock are also fractal, together with the findings that many forms of art resemble natural scenes in showing scale-invariant, fractal-like properties. While some have suggested that fractal-like patterns are inherently pleasing because they resemble natural patterns and scenes, the relation between the visual characteristics of fractals and their aesthetic appeal remains unclear. Motivated by our previous findings that humans display a consistent preference for a certain range of fractal dimension across fractal images of various types we turn to scale-specific processing of visual information to understand this relationship. Whereas our previous preference studies focused on fractal images consisting of black shapes on white backgrounds, here we extend our investigations to include grayscale images in which the intensity variations exhibit scale invariance. This scale-invariance is generated using a 1/f frequency distribution and can be tuned by varying the slope of the rotationally averaged Fourier amplitude spectrum. Thresholding the intensity of these images generates black and white fractals with equivalent scaling properties to the original grayscale images, allowing a direct comparison of preferences for grayscale and black and white fractals. We found no significant differences in preferences between the two groups of fractals. For both set of images, the visual preference peaked for images with the amplitude spectrum slopes from 1.25 to 1.5, thus confirming and extending the previously observed relationship between fractal characteristics of images and visual preference.
Determination of permeability using fractal method for porous media
Institute of Scientific and Technical Information of China (English)
施明恒; 陈永平
2001-01-01
A theoretical formulation was developed to express permeability as a function of different fractal dimensions and other scales for porous media . The effective fractal void ratio, the spectral dimension and the fractal dimension of particle mass distribution were introduced. The permeabilities for different soils in China are calculated. The predicted permeability for rice soil was compared with the measured data available in literature.
ON FRACTAL MECHANISM OF COASTLINE -A Case Study of China
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
MANDELBROT enunciated the uncertainty of the length of a coastline in his paper" How long is the coastline of Britain?" published in " Science" in 1967. The fractal concept was presented for the first time in that paper and has been applied to many fields ever since. According to the fractal theory and conditions of fractal research of coastline, the controls of faults and biologic function on the fractal character of coastline are preliminarily discussed on the basis of GIS in this paper . Finally, some significant conclusions are drawn: 1) the faults control the basic trends of coastlines of two study areas;2) the fractal dimension of coastline of Taiwan is smaller than that of Changle- Lufeng, because the faults of Taiwan more intensely control the trend and fractal dimension of the coastline;3) the larger the fractal dimension of the faults or the major faults, the more the controlling effect of them on the trend and fractal dimension of coastline; 4) the larger fractal dimension of the coastline of Changle- Lufeng indicates that the biologic function intensely shapes the coastline. In a word, the controls of faults and biologic function on the fractal character of coastline are discussed with a case study of China in this paper, it can be seen that faults and biologic function both have influence over the trend and fractal dimension of coastline, the fractal mechanism of coastline of two study areas may be so.
Functional near-infrared imager
Luo, Qingming; Nioka, Shoko; Chance, Britton
1997-08-01
We developed a continuous wave (cw) light imaging probe which includes 9 light sources and four pairs detectors (each pair has one 850 nm filtered detector and one 760 nm filtered detector). The light sources are controlled by a computer and the signals from the detectors are converted and processed in the computer. There are 16 measurement sections and total detection area is 9 cm multiplied by 4 cm which can be scanned every 8 seconds. The detector-source uses 2.5 cm spacing. In this study, we present the noise, drift, detectivity and spatial resolution test results of the imager. Changes of oxygenation and blood volume in about 2 cm depth from the surface of brain model can be detected. The temporal resolution is 8 seconds and spatial resolution is about 2 cm. The detectivity of OD changes can reach 0.008. With this cw imaging probe, we measured motor function in motor cortex area, visual function in occipital area, and cognitive activity in frontal forehead area of the human brian when the subjects are stimulated by moving fingers, viewing a flashing light and doing an analogy test, respectively. The experimental results show that the cw imaging probe can be used for functional images of brain activity, base upon changes of oxygenation and blood volume due to the stimulus.
Surface topography characterization of automotive cylinder liner surfaces using fractal methods
Lawrence K, Deepak; Ramamoorthy, B.
2013-09-01
This paper explores the use of fractal approaches for the possible characterization of automotive cylinder bore surface topography by employing methods such as differential box counting method, power spectral method and structure function method. Three stage plateau honing experiments were conducted to manufacture sixteen cylinder liner surfaces with different surface topographies, for the study. The three fractal methods are applied on the image data obtained using a computer vision system and 3-D profile data obtained using vertical scanning white light interferometer from the cylinder liner surfaces. The computed fractal parameters (fractal dimension and topothesy) are compared and correlated with the measured 3-D Abbott-Firestone curve parameters (Sk, Spk, Svk, Sr1 and Sr2) that are currently used for the surface topography characterization cylinder liner surfaces. The analyses of the results indicated that the fractal dimension (D) computed using the vision data as well as 3-D profile data by employing three different fractal methods consistantly showed a negative correlation with the functional surface topographical parameters that represents roughness at peak (Spk),core (Sk) and valley (Svk) regions and positive correlation with the upper bearing area (Sr1) and lower bearing area (Sr2) of the automotive of cylinder bore surface.
Fractal differential equations and fractal-time dynamical systems
Indian Academy of Sciences (India)
Abhay Parvate; A D Gangal
2005-03-01
Differential equations and maps are the most frequently studied examples of dynamical systems and may be considered as continuous and discrete time-evolution processes respectively. The processes in which time evolution takes place on Cantor- like fractal subsets of the real line may be termed as fractal-time dynamical systems. Formulation of these systems requires an appropriate framework. A new calculus called -calculus, is a natural calculus on subsets ⊂ R of dimension , 0 < ≤ 1. It involves integral and derivative of order , called -integral and -derivative respectively. The -integral is suitable for integrating functions with fractal support of dimension , while the -derivative enables us to differentiate functions like the Cantor staircase. The functions like the Cantor staircase function occur naturally as solutions of -differential equations. Hence the latter can be used to model fractal-time processes or sublinear dynamical systems. We discuss construction and solutions of some fractal differential equations of the form $$D^{}_{F,t} x = h(x, t),$$ where ℎ is a vector field and $D^{}_{F,t}$ is a fractal differential operator of order in time . We also consider some equations of the form $$D^{}_{F,t} W(x, t) = L[W(x, t)],$$ where is an ordinary differential operator in the real variable , and $(t, x) F × \\mathbf{R}^{n}$ where is a Cantor-like set of dimension . Further, we discuss a method of finding solutions to -differential equations: They can be mapped to ordinary differential equations, and the solutions of the latter can be transformed back to get those of the former. This is illustrated with a couple of examples.
Experiments in the use of fractal in computer pattern recognition
Sadjadi, Firooz A.
1993-10-01
The results of a study in the uses of fractal for the automatic detection of man made objects in infrared (IR) and millimeter wave (MMW) radar imagery are discussed in this paper. The fractal technique that is used is based on the estimation of the fractal dimensions of sequential blocks of an image of a scene and then by slicing the histogram of the computed fractal dimensions. The fractal dimension is computed by a Fourier regression approach. The technique is shown to be effective for the detection of tactical military vehicles in IR, and for the detection of airport attributes in MMW radar imagery.
Quantitating the subtleties of microglial morphology with fractal analysis.
Karperien, Audrey; Ahammer, Helmut; Jelinek, Herbert F
2013-01-01
It is well established that microglial form and function are inextricably linked. In recent years, the traditional view that microglial form ranges between "ramified resting" and "activated amoeboid" has been emphasized through advancing imaging techniques that point to microglial form being highly dynamic even within the currently accepted morphological categories. Moreover, microglia adopt meaningful intermediate forms between categories, with considerable crossover in function and varying morphologies as they cycle, migrate, wave, phagocytose, and extend and retract fine and gross processes. From a quantitative perspective, it is problematic to measure such variability using traditional methods, but one way of quantitating such detail is through fractal analysis. The techniques of fractal analysis have been used for quantitating microglial morphology, to categorize gross differences but also to differentiate subtle differences (e.g., amongst ramified cells). Multifractal analysis in particular is one technique of fractal analysis that may be useful for identifying intermediate forms. Here we review current trends and methods of fractal analysis, focusing on box counting analysis, including lacunarity and multifractal analysis, as applied to microglial morphology.
Quantitating the Subtleties of Microglial Morphology with Fractal Analysis
Directory of Open Access Journals (Sweden)
Audrey eKarperien
2013-01-01
Full Text Available It is well established that microglial form and function are inextricably linked. In recent years, the traditional view that microglial form ranges between "ramified resting" and "activated amoeboid" has been emphasized through advancing imaging techniques that point to microglial form being highly dynamic even within the currently accepted morphological categories. Moreover, microglia adopt meaningful intermediate forms between categories, with considerable crossover in function and varying morphologies as they cycle, migrate, wave, phagocytose, and extend and retract fine and gross processes. From a quantitative perspective, it is problematic to measure such variability using traditional methods, but one way of quantitating such detail is through fractal analysis. The techniques of fractal analysis have been used for quantitating microglial morphology, to categorize gross differences but also to differentiate subtle differences (e.g., amongst ramified cells. Multifractal analysis in particular is one technique of fractal analysis that may be useful for identifying intermediate forms. Here we review current trends and methods of fractal analysis, focusing on box counting analysis, including lacunarity and multifractal analysis, as applied to microglial morphology.
The conundrum of functional brain networks: small-world or fractal modularity
Gallos, Lazaros K; Sigman, Mariano
2011-01-01
The human brain is organized in functional modules. Such an organization poses a conundrum: modules ought to be sufficiently independent to guarantee functional specialization and sufficiently connected to bind multiple processors for efficient information transfer. It is commonly accepted that small-world architecture may solve this problem. However, there is intrinsic tension between shortcuts generating small-worlds and the persistence of modules. Here we provide a solution to this puzzle. We show that the functional brain network formed by percolation of strong links is highly modular. Contrary to the common view, modules are self-similar and therefore are very far from being small-world. Incorporating the weak ties to the network converts it into a small-world preserving an underlying backbone of well-defined modules. Weak ties are organized precisely as predicted by theory maximizing information transfer with minimal wiring costs. This trade-off architecture is reminiscent of the "strength of weak ties"...
Fractals of the Julia and Mandelbrot sets of the Riemann $zeta$ Function
Woon, S C
1998-01-01
Computations of the Julia and Mandelbrot sets of the Riemann zeta function and observations of their properties are made. In the appendix section, a corollary of Voronin's theorem is derived and a scale-invariant equation for the bounds in Goldbach conjecture is conjectured.
Raupov, Dmitry S.; Myakinin, Oleg O.; Bratchenko, Ivan A.; Zakharov, Valery P.; Khramov, Alexander G.
2016-10-01
In this paper, we propose a report about our examining of the validity of OCT in identifying changes using a skin cancer texture analysis compiled from Haralick texture features, fractal dimension, Markov random field method and the complex directional features from different tissues. Described features have been used to detect specific spatial characteristics, which can differentiate healthy tissue from diverse skin cancers in cross-section OCT images (B- and/or C-scans). In this work, we used an interval type-II fuzzy anisotropic diffusion algorithm for speckle noise reduction in OCT images. The Haralick texture features as contrast, correlation, energy, and homogeneity have been calculated in various directions. A box-counting method is performed to evaluate fractal dimension of skin probes. Markov random field have been used for the quality enhancing of the classifying. Additionally, we used the complex directional field calculated by the local gradient methodology to increase of the assessment quality of the diagnosis method. Our results demonstrate that these texture features may present helpful information to discriminate tumor from healthy tissue. The experimental data set contains 488 OCT-images with normal skin and tumors as Basal Cell Carcinoma (BCC), Malignant Melanoma (MM) and Nevus. All images were acquired from our laboratory SD-OCT setup based on broadband light source, delivering an output power of 20 mW at the central wavelength of 840 nm with a bandwidth of 25 nm. We obtained sensitivity about 97% and specificity about 73% for a task of discrimination between MM and Nevus.
Energy Technology Data Exchange (ETDEWEB)
Sun, Haitao; Li, Ning; Guo, Lijun; Gao, Fei; Liu, Cheng [Shandong University, Shandong Medical Imaging Research Institute, Shandong (Korea, Republic of)
2011-06-15
The aim of this study was to use fractal dimension (FD) analysis on multidetector CT (MDCT) images for quantifying the morphological changes of the pulmonary artery tree in patients with pulmonary hypertension (PH). Fourteen patients with PH and 17 patients without PH as controls were studied. All of the patients underwent contrast-enhanced helical CT and transthoracic echocardiography. The pulmonary artery trees were generated using post-processing software, and the FD and projected image area of the pulmonary artery trees were determined with Image J software in a personal computer. The FD, the projected image area and the pulmonary artery pressure (PAP) were statistically evaluated in the two groups. The FD, the projected image area and the PAP of the patients with PH were higher than those values of the patients without PH (p < 0.05, t-test). There was a high correlation of FD with the PAP (r = 0.82, p < 0.05, partial correlation analysis). There was a moderate correlation of FD with the projected image area (r = 0.49, p < 0.05, partial correlation analysis). There was a correlation of the PAP with the projected image area (r = 0.65, p < 0.05, Pearson correlation analysis). The FD of the pulmonary arteries in the PH patients was significantly higher than that of the controls. There is a high correlation of FD with the PAP.
GENERALIZED FRACTAL TRANSFORMS AND SELF-SIMILARITY: RECENT RESULTS AND APPLICATIONS
Davide La Torre; Edward R. Vrscay
2011-01-01
Most practical as well as theoretical works in image processing and mathematical imaging consider images as real-valued functions, u : X → ℝg, where X denotes the base space or pixel space over which the images are defined and ℝg ⊂ ℝ is a suitable greyscale space. A variety of function spaces ℱ(X) may be considered depending on the application. Fractal image coding seeks to approximate an image function as a union of spatially-contracted and greyscale-modified copies of subsets of itself, i.e...
Wicks, Keith R
1991-01-01
Addressed to all readers with an interest in fractals, hyperspaces, fixed-point theory, tilings and nonstandard analysis, this book presents its subject in an original and accessible way complete with many figures. The first part of the book develops certain hyperspace theory concerning the Hausdorff metric and the Vietoris topology, as a foundation for what follows on self-similarity and fractality. A major feature is that nonstandard analysis is used to obtain new proofs of some known results much more slickly than before. The theory of J.E. Hutchinson's invariant sets (sets composed of smaller images of themselves) is developed, with a study of when such a set is tiled by its images and a classification of many invariant sets as either regular or residual. The last and most original part of the book introduces the notion of a "view" as part of a framework for studying the structure of sets within a given space. This leads to new, elegant concepts (defined purely topologically) of self-similarity and fracta...
FRACTAL ANALYSIS OF TRABECULAR BONE: A STANDARDISED METHODOLOGY
Directory of Open Access Journals (Sweden)
Ian Parkinson
2011-05-01
Full Text Available A standardised methodology for the fractal analysis of histological sections of trabecular bone has been established. A modified box counting method has been developed for use on a PC based image analyser (Quantimet 500MC, Leica Cambridge. The effect of image analyser settings, magnification, image orientation and threshold levels, was determined. Also, the range of scale over which trabecular bone is effectively fractal was determined and a method formulated to objectively calculate more than one fractal dimension from the modified Richardson plot. The results show that magnification, image orientation and threshold settings have little effect on the estimate of fractal dimension. Trabecular bone has a lower limit below which it is not fractal (λ<25 μm and the upper limit is 4250 μm. There are three distinct fractal dimensions for trabecular bone (sectional fractals, with magnitudes greater than 1.0 and less than 2.0. It has been shown that trabecular bone is effectively fractal over a defined range of scale. Also, within this range, there is more than 1 fractal dimension, describing spatial structural entities. Fractal analysis is a model independent method for describing a complex multifaceted structure, which can be adapted for the study of other biological systems. This may be at the cell, tissue or organ level and compliments conventional histomorphometric and stereological techniques.
Correlation of optical properties with the fractal microstructure of black molybdenum coatings
Energy Technology Data Exchange (ETDEWEB)
Barrera, Enrique; Gonzalez, Federico [Area de Energia, Division de Ciencias Basicas e Ingenieria, Universidad Autonoma Metropolitana-Iztapalapa, Apartado Postal 55-534, Mexico, D.F. 09340 (Mexico); Rodriguez, Eduardo [Area de Computacion y Sistemas, Division de Ciencias Basicas e Ingenieria, Universidad Autonoma Metropolitana-Iztapalapa, Apartado Postal 55-534, Mexico, D.F. 09340 (Mexico); Alvarez-Ramirez, Jose, E-mail: jjar@xanum.uam.mx [Area de Energia, Division de Ciencias Basicas e Ingenieria, Universidad Autonoma Metropolitana-Iztapalapa, Apartado Postal 55-534, Mexico, D.F. 09340 (Mexico)
2010-01-01
Coating is commonly used for improving the optical properties of surfaces for solar collector applications. The coating morphology depends on the deposition conditions, and this determines the final optical characteristics. Coating morphologies are irregular and of fractal nature, so a suitable approach for its characterization should use methods borrowed from fractal analysis. The aim of this work is to study the fractal characteristics of black molybdenum coatings on copper and to relate the fractal parameters to the optical properties. To this end, coating surfaces were prepared via immersion in a solution of ammonium paramolybdate for different deposition periods. The fractal analysis was carried out for SEM and AFM images of the coating surface and the fractal properties were obtained with a recently developed high-dimensional extension of the well-known detrended fluctuation analysis (DFA). The most salient parameter drawn from the application of the DFA is the Hurst index, a parameter related to the roughness of the coating surface, and the multifractality index, which is related to the non-linearity features of the coating morphology. The results showed that optical properties, including absorptance and emittance, are decreasing functions of the Hurst and multifractality indices. This suggests that coating surfaces with high absorptance and emittance values are related to complex coating morphologies conformed within a non-linear structure.
Fractality in the neuron axonal topography of the human brain based on 3-D diffusion MRI
Katsaloulis, P.; Ghosh, A.; Philippe, A. C.; Provata, A.; Deriche, R.
2012-05-01
In this work the fractal architecture of the neuron axonal topography of the human brain is evaluated, as derived from 3-D diffusion MRI (dMRI) acquisitions. This is a 3D extension of work performed previously in 2D regions of interest (ROIs), where the fractal dimension of the neuron axonal topography was computed from dMRI data. A group study with 18 subjects is here conducted and the fractal dimensions D f of the entire 3-D volume of the brains is estimated via the box counting, the correlation dimension and the fractal mass dimension methods. The neuron axon data is obtained using tractography algorithms on diffusion tensor imaging of the brain. We find that all three calculations of D f give consistent results across subjects, namely, they demonstrate fractal characteristics in the short and medium length scales: different fractal exponents prevail at different length scales, an indication of multifractality. We surmise that this complexity stems as a collective property emerging when many local brain units, performing different functional tasks and having different local topologies, are recorded together.
Hashemi, S. M.; Jagodič, U.; Mozaffari, M. R.; Ejtehadi, M. R.; Muševič, I.; Ravnik, M.
2017-01-01
Fractals are remarkable examples of self-similarity where a structure or dynamic pattern is repeated over multiple spatial or time scales. However, little is known about how fractal stimuli such as fractal surfaces interact with their local environment if it exhibits order. Here we show geometry-induced formation of fractal defect states in Koch nematic colloids, exhibiting fractal self-similarity better than 90% over three orders of magnitude in the length scales, from micrometers to nanometres. We produce polymer Koch-shaped hollow colloidal prisms of three successive fractal iterations by direct laser writing, and characterize their coupling with the nematic by polarization microscopy and numerical modelling. Explicit generation of topological defect pairs is found, with the number of defects following exponential-law dependence and reaching few 100 already at fractal iteration four. This work demonstrates a route for generation of fractal topological defect states in responsive soft matter. PMID:28117325
Neutron scattering from fractals
DEFF Research Database (Denmark)
Kjems, Jørgen; Freltoft, T.; Richter, D.
1986-01-01
The scattering formalism for fractal structures is presented. Volume fractals are exemplified by silica particle clusters formed either from colloidal suspensions or by flame hydrolysis. The determination of the fractional dimensionality through scattering experiments is reviewed, and recent small...
Fractal Aggregation Under Rotation
Institute of Scientific and Technical Information of China (English)
WU Feng-Min; WU Li-Li; LU Hang-Jun; LI Qiao-Wen; YE Gao-Xiang
2004-01-01
By means of the Monte Carlo simulation, a fractal growth model is introduced to describe diffusion-limited aggregation (DLA) under rotation. Patterns which are different from the classical DLA model are observed and the fractal dimension of such clusters is calculated. It is found that the pattern of the clusters and their fractal dimension depend strongly on the rotation velocity of the diffusing particle. Our results indicate the transition from fractal to non-fractal behavior of growing cluster with increasing rotation velocity, i.e. for small enough angular velocity ω the fractal dimension decreases with increasing ω, but then, with increasing rotation velocity, the fractal dimension increases and the cluster becomes compact and tends to non-fractal.
Thamrin, Cindy; Stern, Georgette; Frey, Urs
2010-06-01
There is increasing interest in the study of fractals in medicine. In this review, we provide an overview of fractals, of techniques available to describe fractals in physiological data, and we propose some reasons why a physician might benefit from an understanding of fractals and fractal analysis, with an emphasis on paediatric respiratory medicine where possible. Among these reasons are the ubiquity of fractal organisation in nature and in the body, and how changes in this organisation over the lifespan provide insight into development and senescence. Fractal properties have also been shown to be altered in disease and even to predict the risk of worsening of disease. Finally, implications of a fractal organisation include robustness to errors during development, ability to adapt to surroundings, and the restoration of such organisation as targets for intervention and treatment.
Hashemi, S. M.; Jagodič, U.; Mozaffari, M. R.; Ejtehadi, M. R.; Muševič, I.; Ravnik, M.
2017-01-01
Fractals are remarkable examples of self-similarity where a structure or dynamic pattern is repeated over multiple spatial or time scales. However, little is known about how fractal stimuli such as fractal surfaces interact with their local environment if it exhibits order. Here we show geometry-induced formation of fractal defect states in Koch nematic colloids, exhibiting fractal self-similarity better than 90% over three orders of magnitude in the length scales, from micrometers to nanometres. We produce polymer Koch-shaped hollow colloidal prisms of three successive fractal iterations by direct laser writing, and characterize their coupling with the nematic by polarization microscopy and numerical modelling. Explicit generation of topological defect pairs is found, with the number of defects following exponential-law dependence and reaching few 100 already at fractal iteration four. This work demonstrates a route for generation of fractal topological defect states in responsive soft matter.
Ji-Huan He
2011-01-01
A new fractal derive is defined, which is very easy for engineering applications to discontinuous problems, two simple examples are given to elucidate to establish governing equations with fractal derive and how to solve such equations, respectively.
Fractal Structure of Molecular Clouds
Datta, Srabani
2001-01-01
Compelling evidence exists to show that the structure of molecular clouds is fractal in nature. In this paper, the author reiterates this view and, in addition, asserts that not only is cloud geometry fractal, but that they also have a common characteristic - they are similar in shape to the Horsehead nebula in Orion. This shape can be described by the Julia function f(x)= z^2 + c,where both z and c are complex quantities and c = -0.745429 + 0.113008i. The dynamical processes responsible for ...
Time evolution of quantum fractals
Wojcik; Bialynicki-Birula; Zyczkowski
2000-12-11
We propose a general construction of wave functions of arbitrary prescribed fractal dimension, for a wide class of quantum problems, including the infinite potential well, harmonic oscillator, linear potential, and free particle. The box-counting dimension of the probability density P(t)(x) = |Psi(x,t)|(2) is shown not to change during the time evolution. We prove a universal relation D(t) = 1+Dx/2 linking the dimensions of space cross sections Dx and time cross sections D(t) of the fractal quantum carpets.
Time Evolution of Quantum Fractals
Wójcik, D; Zyczkowski, K; Wojcik, Daniel; Bialynicki-Birula, Iwo; Zyczkowski, Karol
2000-01-01
We propose a general construction of wave functions of arbitrary prescribed fractal dimension, for a wide class of quantum problems, including the infinite potential well, harmonic oscillator, linear potential and free particle. The box-counting dimension of the probability density $P_t(x)=|\\Psi(x,t)|^2$ is shown not to change during the time evolution. We prove a universal relation $D_t=1+D_x/2$ linking the dimensions of space cross-sections $D_x$ and time cross-sections $D_t$ of the fractal quantum carpets.
Fraboni, Michael; Moller, Trisha
2008-01-01
Fractal geometry offers teachers great flexibility: It can be adapted to the level of the audience or to time constraints. Although easily explained, fractal geometry leads to rich and interesting mathematical complexities. In this article, the authors describe fractal geometry, explain the process of iteration, and provide a sample exercise.…
Routes to fractality and entropy in Liesegang systems
Energy Technology Data Exchange (ETDEWEB)
Kalash, Leen; Sultan, Rabih, E-mail: rsultan@aub.edu.lb [Department of Chemistry, American University of Beirut, Riad El Solh, 1107 2020 Beirut (Lebanon)
2014-06-01
Liesegang bands are formed when solutions of co-precipitate ions interdiffuse in a 1D gel matrix. In a recent study [R. F. Sultan, Acta. Mech. Sin. 27, 119 (2011)], Liesegang patterns have been characterized as fractal structures. In addition to experimentally obtained patterns, geometric Liesegang patterns were constructed in conformity with the well-known empirical laws. Both mathematical fractal dimensions and box count dimensions for images of PbF{sub 2} and PbI{sub 2} Liesegang patterns have been calculated. Liesegang patterns can also be described by the entropy state function, and categorized as more or less ordered structures. We revisit the relation between entropy and fractal dimension, and apply it to simulated geometrical Liesegang patterns. We have resort to three different routes for the estimation of the entropy of a Liesegang pattern. The HarFA software enabled the calculation of the Hausdorff dimension and the topological entropy, then the information dimension and the Shannon entropy. In a third pathway, analytical calculations were carried out by estimating the probability of occurrence of a fractal element or coverage. The product of Shannon entropy and Boltzmann constant yields the thermodynamic entropy. The values for PbF{sub 2} and PbI{sub 2} Liesegang patterns attained the order of magnitude of the reported Third Law entropies, but yet remained lower, in conformity with the more ordered Liesegang structures.
Fractals Generated by Statistical Contraction Operators
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
In the theory of random fractal, there are two important classes of random sets, one is the class of fractals generated by the paths of stochastic processes and another one is the class of factals generated by statistical contraction operators. Now we will introduce some things about the probability basis and fractal properties of fractals in the last class. The probability basis contains (1) the convergence and measurability of a random recursive set K(ω) as a random element, (2) martingals property. The fractal properties include (3) the character of various similarity, (4) the separability property, (5) the support and zero-one law of distribution Pk=PK-1, (6) the Hausdorff dimension and Hausdorff exact measure function.
Modeling Soil Water Retention Curve with a Fractal Method
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
Many empirical models have been developed to describe the soil water retention curve (SWRC). In this study, a fractal model for SWRC was derived with a specially constructed Menger sponge to describe the fractal scaling behavior of soil; relationships were established among the fractal dimension of SWRC, the fractal dimension of soil mass, and soil texture; and the model was used to estimate SWRC with the estimated results being compared to experimental data for verification. The derived fractal model was in a power-law form, similar to the Brooks-Corey and Campbell empirical functions. Experimental data of particle size distribution (PSD), texture, and soil water retention for 10 soils collected at different places in China were used to estimate the fractal dimension of SWRC and the mass fractal dimension. The fractal dimension of SWRC and the mass fractal dimension were linearly related. Also, both of the fractal dimensions were dependent on soil texture, i.e., clay and sand contents. Expressions were proposed to quantify the relationships. Based on the relationships, four methods were used to determine the fractal dimension of SWRC and the model was applied to estimate soil water content at a wide range of tension values. The estimated results compared well with the measured data having relative errors less than 10% for over 60% of the measurements. Thus, this model, estimating the fractal dimension using soil textural data, offered an alternative for predicting SWRC.
Impact factors of fractal analysis of porous structure
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
Characterization of pore structure is one of the key problems for fabrication and application research on porous materials. But, complexity of pore structure makes it difficult to characterize pore structure by Euclidean geometry and traditional experimental methods. Fractal theory has been proved effective to characterize the complex pore structure. The box dimension method based on fractal theory was applied to characterizing the pore structure of fiber porous materials by analyzing the electronic scanning microscope (SEM) images of the porous materials in this paper. The influences of image resolution, threshold value, and image magnification on fractal analysis were investigated. The results indicate that such factors greatly affect fractal analysis process and results. The appropriate magnification threshold and fractal analysis are necessary for fractal analysis.
High Efficient Tunable Fractal Axicon Based on LCoS
Institute of Scientific and Technical Information of China (English)
WANG Xin; DAI Hai-Tao; Xu Ke-Shu
2008-01-01
@@ Based on the Cantor function and phase modulation,a tunable fractal axicon is formed on a liquid crystal on silicon(LCos)with an improved generating method.It has higher focusing efficiency in higher fractal stage and approaches to 100% theoretically.The on-axis intensity keeps its fractal structure unchanged in operation of fractal stages.The tunability of the axicon is demonstrated by tune fractal stage from 1 to 3 and focal length from 0.8m to 1 m.We also provide details of theoretical analyses and experimental results.
Marks-Tarlow, Terry
2010-01-01
In this article, the author draws on contemporary science to illuminate the relationship between early play experiences, processes of self-development, and the later emergence of the fractal self. She argues that orientation within social space is a primary function of early play and developmentally a two-step process. With other people and with…
Exploring fractal behaviour of blood oxygen saturation in preterm babies
Zahari, Marina; Hui, Tan Xin; Zainuri, Nuryazmin Ahmat; Darlow, Brian A.
2017-04-01
Recent evidence has been emerging that oxygenation instability in preterm babies could lead to an increased risk of retinal injury such as retinopathy of prematurity. There is a potential that disease severity could be better understood using nonlinear methods for time series data such as fractal theories [1]. Theories on fractal behaviours have been employed by researchers in various disciplines who were motivated to look into the behaviour or structure of irregular fluctuations in temporal data. In this study, an investigation was carried out to examine whether fractal behaviour could be detected in blood oxygen time series. Detection for the presence of fractals in oxygen data of preterm infants was performed using the methods of power spectrum, empirical probability distribution function and autocorrelation function. The results from these fractal identification methods indicate the possibility that these data exhibit fractal nature. Subsequently, a fractal framework for future research was suggested for oxygen time series.
Directory of Open Access Journals (Sweden)
FELICIA RAMONA BIRAU
2012-05-01
Full Text Available In this article, the concept of capital market is analysed using Fractal Market Hypothesis which is a modern, complex and unconventional alternative to classical finance methods. Fractal Market Hypothesis is in sharp opposition to Efficient Market Hypothesis and it explores the application of chaos theory and fractal geometry to finance. Fractal Market Hypothesis is based on certain assumption. Thus, it is emphasized that investors did not react immediately to the information they receive and of course, the manner in which they interpret that information may be different. Also, Fractal Market Hypothesis refers to the way that liquidity and investment horizons influence the behaviour of financial investors.
Computation of the Fractal Pattern in Manganese Dendrites
Institute of Scientific and Technical Information of China (English)
Z. Merdan; M. Bayirli
2005-01-01
@@ The images of manganese flowers (clusters) on the surface of the natural magnesium silicate substance are scanned and the pictures of them are transferred to computer atmosphere. By using these scanning parameters, the exponents of density correlation function and fractal dimension values are calculated. For all different groups between the least and the most dense in the samples, the correlation function exponents may range from 0.141 to 0.178 and the fractal dimension values may vary between 1.61 and 1.88. In addition, the manganese flowers are divided into seven different groups according to their smallest- and largest-density features. The formation of the natural manganese clusters (flowers, dendrites) on the surface of the magnesium silicate substance can be defined by using the deposition, diffusion and aggregation model.
Functional Brain Imaging: A Comprehensive Survey
Sarraf, Saman
2016-01-01
Functional brain imaging allows measuring dynamic functionality in all brain regions. It is broadly used in clinical cognitive neuroscience as, well as in research. It will allow the observation of neural activities in the brain simultaneously. From the beginning when functional brain imaging was initiated by the mapping of brain functions proposed by phrenologists, many scientists were asking why we need to image brain functionality since we have already structural information. Simply, their important question was including a great answer. Functional information of the human brain would definitely complement structural information, helping to have a better understanding of what is happening in the brain. This paper, which could be useful to those who have an interest in functional brain imaging, such as engineers, will present a quick review of modalities used in functional brain imaging. We will concentrate on the most used techniques in functional imaging which are functional magnetic resonance imaging (fM...
Fractal Aggregation Under Rotation
Institute of Scientific and Technical Information of China (English)
WUFeng-Min; WULi-Li; LUHang-Jun; LIQiao-Wen; YEGao-Xiang
2004-01-01
By means of the Monte Carlo simulation, a fractal growth model is introduced to describe diffusion-limited aggregation (DLA) under rotation. Patterns which are different from the classical DLA model are observed and the fractal dimension of such clusters is calculated. It is found that the pattern of the clusters and their fractal dimension depend strongly on the rotation velocity of the diffusing particle. Our results indicate the transition from fractal to non-fractal behavior of growing cluster with increasing rotation velocity, i.e. for small enough angular velocity ω; thefractal dimension decreases with increasing ω;, but then, with increasing rotation velocity, the fractal dimension increases and the cluster becomes compact and tends to non-fractal.
Functional imaging in Tourette's syndrome.
Adams, J R; Troiano, A R; Calne, D B
2004-10-01
The cause or causes of Tourette's syndrome (TS) remain unknown. Functional imaging studies have evaluated several implicated neurotransmitter systems and focused predominantly on the frequency or severity of tics. The results have been inconclusive and frequently contradictory with little light shed on pathogenetic mechanisms. However, metabolic derangements have been demonstrated within regions of the basal ganglia, limbic system and sensori-motor cortex and are in keeping with the concept of TS as both a motor and behavioral disorder. TS has long been regarded an involuntary movement disorder. However, many patients have stated that without the premonitory sensation, there would be no tics. For this reason, it has been suggested that the premonitory urge may be considered the involuntary component of TS and the performance of the tic merely a voluntary response. Future studies are needed to differentiate functional changes relating to urge from those associated with the performance of tics and tic suppression.
Quantitative evaluation of midpalatal suture maturation via fractal analysis
Kwak, Kyoung Ho; Kim, Yong-Il; Kim, Yong-Deok
2016-01-01
Objective The purpose of this study was to determine whether the results of fractal analysis can be used as criteria for midpalatal suture maturation evaluation. Methods The study included 131 subjects aged over 18 years of age (range 18.1–53.4 years) who underwent cone-beam computed tomography. Skeletonized images of the midpalatal suture were obtained via image processing software and used to calculate fractal dimensions. Correlations between maturation stage and fractal dimensions were calculated using Spearman's correlation coefficient. Optimal fractal dimension cut-off values were determined using a receiver operating characteristic curve. Results The distribution of maturation stages of the midpalatal suture according to the cervical vertebrae maturation index was highly variable, and there was a strong negative correlation between maturation stage and fractal dimension (−0.623, p Fractal dimension was a statistically significant indicator of dichotomous results with regard to maturation stage (area under curve = 0.794, p fractal dimension was used to predict the resulting variable that splits maturation stages into ABC and D or E yielded an optimal fractal dimension cut-off value of 1.0235. Conclusions There was a strong negative correlation between fractal dimension and midpalatal suture maturation. Fractal analysis is an objective quantitative method, and therefore we suggest that it may be useful for the evaluation of midpalatal suture maturation. PMID:27668195
Functional brain imaging across development.
Rubia, Katya
2013-12-01
The developmental cognitive neuroscience literature has grown exponentially over the last decade. This paper reviews the functional magnetic resonance imaging (fMRI) literature on brain function development of typically late developing functions of cognitive and motivation control, timing and attention as well as of resting state neural networks. Evidence shows that between childhood and adulthood, concomitant with cognitive maturation, there is progressively increased functional activation in task-relevant lateral and medial frontal, striatal and parieto-temporal brain regions that mediate these higher level control functions. This is accompanied by progressively stronger functional inter-regional connectivity within task-relevant fronto-striatal and fronto-parieto-temporal networks. Negative age associations are observed in earlier developing posterior and limbic regions, suggesting a shift with age from the recruitment of "bottom-up" processing regions towards "top-down" fronto-cortical and fronto-subcortical connections, leading to a more mature, supervised cognition. The resting state fMRI literature further complements this evidence by showing progressively stronger deactivation with age in anti-correlated task-negative resting state networks, which is associated with better task performance. Furthermore, connectivity analyses during the resting state show that with development increasingly stronger long-range connections are being formed, for example, between fronto-parietal and fronto-cerebellar connections, in both task-positive networks and in task-negative default mode networks, together with progressively lesser short-range connections, suggesting progressive functional integration and segregation with age. Overall, evidence suggests that throughout development between childhood and adulthood, there is progressive refinement and integration of both task-positive fronto-cortical and fronto-subcortical activation and task-negative deactivation, leading to
Energy Technology Data Exchange (ETDEWEB)
Conte, Elio [Department of Pharmacology and Human Physiology and Tires, Center for Innovative Technologies for Signal Detection and Processing, University of Bari, Bari (Italy); School of Advanced International Studies on Nuclear, Theoretical and Nonlinear Methodologies-Bari (Italy)], E-mail: fisio2@fisiol.uniba.it; Federici, Antonio [Department of Pharmacology and Human Physiology and Tires, Center for Innovative Technologies for Signal Detection and Processing, University of Bari, Bari (Italy); Zbilut, Joseph P. [Department of Molecular Biophysics and Physiology, Rush University Medical Center, 1653W Congress, Chicago, IL 60612 (United States)
2009-08-15
It is known that R-R time series calculated from a recorded ECG, are strongly correlated to sympathetic and vagal regulation of the sinus pacemaker activity. In human physiology it is a crucial question to estimate such components with accuracy. Fourier analysis dominates still to day the data analysis efforts of such data ignoring that FFT is valid under some crucial restrictions that results largely violated in R-R time series data as linearity and stationarity. In order to go over such approach, we introduce a new method, called CZF. It is based on variogram analysis. It is aimed from a profound link with Recurrence Quantification Analysis that is a basic tool for investigation of non linear and non stationary time series. Therefore, a relevant feature of the method is that it finally may be applied also in cases of non linear and non stationary time series analysis. In addition, the method enables also to analyze the fractal variance function, the Generalized Fractal Dimension and, finally, the relative probability density function of the data. The CZF gives very satisfactory results. In the present paper it has been applied to direct experimental cases of normal subjects, patients with hypertension before and after therapy and in children under some different conditions of experimentation.
Fractal parameters and vascular networks: facts & artifacts
Directory of Open Access Journals (Sweden)
Maniero Fabrizio
2008-07-01
Full Text Available Abstract Background Several fractal and non-fractal parameters have been considered for the quantitative assessment of the vascular architecture, using a variety of test specimens and of computational tools. The fractal parameters have the advantage of being scale invariant, i.e. to be independent of the magnification and resolution of the images to be investigated, making easier the comparison among different setups and experiments. Results The success of several commercial and/or free codes in computing the fractal parameters has been tested on well known exact models. Based on such a preliminary study, we selected the code Frac-lac in order to analyze images obtained by visualizing the angiogenetic process occurring in chick Chorio Allontoic Membranes (CAM, assumed to be paradigmatic of a realistic 2D vascular network. Among the parameters investigated, the fractal dimension Df proved to be the most robust estimator for CAM vascular networks. Moreover, only Df was able to discriminate between effective and elusive increases in vascularization after drug-induced angiogenic stimulations on CAMs. Conclusion The fractal dimension Df is likely to be the most promising tool for monitoring the effectiveness of anti-angiogenic therapies in various clinical contexts.
Graphics with Mathematica fractals, Julia sets, patterns and natural forms
Getz, Chonat
2004-01-01
In this book we generate graphic images using the software Mathematica thus providing a gentle and enjoyable introduction to this rather technical software and its graphic capabilities. The programs we use for generating these graphics are easily adaptable to many variations.These graphic images are enhanced by introducing a variety of different coloring techniques.Detailed instructions are given for the construction of some interesting 2D and 3D fractals using iterated functions systems as well as the construction of many different types of Julia sets and parameter sets such as the Mandelbrot
Functional imaging of decision conflict.
Pochon, Jean-Baptiste; Riis, Jason; Sanfey, Alan G; Nystrom, Leigh E; Cohen, Jonathan D
2008-03-26
Decision conflict occurs when people feel uncertain as to which option to choose from a set of similarly attractive (or unattractive) options, with many studies demonstrating that this conflict can lead to suboptimal decision making. In this article, we investigate the neurobiological underpinnings of decision conflict, in particular, the involvement of the anterior cingulate cortex (ACC). Previous studies have implicated the ACC in conflict monitoring during perceptual tasks, but there is considerable controversy as to whether the ACC actually indexes conflict related to choice, or merely conflict related to selection of competing motor responses. In a functional magnetic resonance imaging study, we dissociate the decision and response phases of a decision task, and show that the ACC does indeed index conflict at the decision stage. Furthermore, we show that it does so for a complex decision task, one that requires the integration of beliefs and preferences and not just perceptual judgments.
Fractal Character of China Bedrock Coastline
Institute of Scientific and Technical Information of China (English)
朱晓华
2004-01-01
Fractal theory was applied to a preliminary discussion of the fractal character and formation mechanism of the coastline of the bedrock coast of China on the basis of GIS (Geographical Information System). Some significant conclusions were drawn:(1) The fractal dimensions of the coastline and linear structures of Liaodong Peninsula are 1.0093 and 1.0246 respectively, those of Shandong Peninsula are 1.019 and 1.021 respectively, etc.(2) The fractal dimensions of coastlines of Liaodong Peninsula, Shandong Peninsula, Zhejiang and Fujian-Guangdong tend to increase with the spatial change from north to south.(3)The regional linear structures(including faults)control the basic trends and fractal dimensions of coastlines as a whole in the regions of the bedrock coast of China:the more the controlling effect of linear structures, the smaller the fractal dimensions of coastlines.(4)The substantial constituents of coast and biologic function both play an important role in affecting the fractal dimensions of coastlines of Liaodong Peninsula, Shandong Peninsula, Zhejiang, Fujian-Guangdong and Taiwan Island.
Finite element contact analysis of fractal surfaces
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Sahoo, Prasanta; Ghosh, Niloy [Department of Mechanical Engineering, Jadavpur University, Kolkata 700032 (India)
2007-07-21
The present study considers finite element analysis of non-adhesive, frictionless elastic/elastic-plastic contact between a rigid flat plane and a self-affine fractal rough surface using the commercial finite element package ANSYS. Three-dimensional rough surfaces are generated using a modified two-variable Weierstrass-Mandelbrot function with given fractal parameters. Parametric studies are done to consider the general relations between contact properties and key material and surface parameters. The present analysis is validated with available experimental results in the literature. Non-dimensional contact area and displacement are obtained as functions of non-dimensional load for varying fractal surface parameters in the case of elastic contact and for varying rates of strain hardening in the case of elastic-plastic contact of fractal surfaces.
Functional brain imaging; Funktionelle Hirnbildgebung
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Gizewski, E.R. [Medizinische Universitaet Innsbruck, Universitaetsklinik fuer Neuroradiologie, Innsbruck (Austria)
2016-02-15
Functional magnetic resonance imaging (fMRI) is a non-invasive method that has become one of the major tools for understanding human brain function and in recent years has also been developed for clinical applications. Changes in hemodynamic signals correspond to changes in neuronal activity with good spatial and temporal resolution in fMRI. Using high-field MR systems and increasingly dedicated statistics and postprocessing, activated brain areas can be detected and superimposed on anatomical images. Currently, fMRI data are often combined in multimodal imaging, e. g. with diffusion tensor imaging (DTI) sequences. This method is helping to further understand the physiology of cognitive brain processes and is also being used in a number of clinical applications. In addition to the blood oxygenation level-dependent (BOLD) signals, this article deals with the construction of fMRI investigations, selection of paradigms and evaluation in the clinical routine. Clinically, this method is mainly used in the planning of brain surgery, analyzing the location of brain tumors in relation to eloquent brain areas and the lateralization of language processing. As the BOLD signal is dependent on the strength of the magnetic field as well as other limitations, an overview of recent developments is given. Increases of magnetic field strength (7 T), available head coils and advances in MRI analytical methods have led to constant improvement in fMRI signals and experimental design. Especially the depiction of eloquent brain regions can be done easily and quickly and has become an essential part of presurgical planning. (orig.) [German] Mittlerweile ist die funktionelle MRT (fMRT) eine Methode, die nicht mehr nur in der neurowissenschaftlichen Routine verwendet wird. Die fMRT ermoeglicht die nichtinvasive Darstellung der Hirnaktivitaet in guter raeumlicher und zeitlicher Aufloesung unter Ausnutzung der Durchblutungsaenderung aufgrund der erhoehten Nervenzellaktivitaet. Unter
Applications of Fractal Signals
Directory of Open Access Journals (Sweden)
Ion TUTĂNESCU
2008-05-01
Full Text Available "Fractal" term - which in Latin languagedefines something fragmented anomalous - wasintroduced in mathematics by B. B. Mandelbrot in1975. He avoided to define it rigorously and used it todesignate some "rugged" and "self-similar"geometrical forms. Fractals were involved in the theoryof chaotic dynamic systems and used to designatecertain specific sets; finally, they were “captured” bygeometry and remarked in tackling of the boundaryproblems. It proved that the fractals can be of interesteven in the signal’s theory.
Fractal Geometry of Architecture
Lorenz, Wolfgang E.
In Fractals smaller parts and the whole are linked together. Fractals are self-similar, as those parts are, at least approximately, scaled-down copies of the rough whole. In architecture, such a concept has also been known for a long time. Not only architects of the twentieth century called for an overall idea that is mirrored in every single detail, but also Gothic cathedrals and Indian temples offer self-similarity. This study mainly focuses upon the question whether this concept of self-similarity makes architecture with fractal properties more diverse and interesting than Euclidean Modern architecture. The first part gives an introduction and explains Fractal properties in various natural and architectural objects, presenting the underlying structure by computer programmed renderings. In this connection, differences between the fractal, architectural concept and true, mathematical Fractals are worked out to become aware of limits. This is the basis for dealing with the problem whether fractal-like architecture, particularly facades, can be measured so that different designs can be compared with each other under the aspect of fractal properties. Finally the usability of the Box-Counting Method, an easy-to-use measurement method of Fractal Dimension is analyzed with regard to architecture.
Baryshev, Yuri
2002-01-01
This is the first book to present the fascinating new results on the largest fractal structures in the universe. It guides the reader, in a simple way, to the frontiers of astronomy, explaining how fractals appear in cosmic physics, from our solar system to the megafractals in deep space. It also offers a personal view of the history of the idea of self-similarity and of cosmological principles, from Plato's ideal architecture of the heavens to Mandelbrot's fractals in the modern physical cosmos. In addition, this invaluable book presents the great fractal debate in astronomy (after Luciano Pi
Automatic detection of microcalcifications with multi-fractal spectrum.
Ding, Yong; Dai, Hang; Zhang, Hang
2014-01-01
For improving the detection of micro-calcifications (MCs), this paper proposes an automatic detection of MC system making use of multi-fractal spectrum in digitized mammograms. The approach of automatic detection system is based on the principle that normal tissues possess certain fractal properties which change along with the presence of MCs. In this system, multi-fractal spectrum is applied to reveal such fractal properties. By quantifying the deviations of multi-fractal spectrums between normal tissues and MCs, the system can identify MCs altering the fractal properties and finally locate the position of MCs. The performance of the proposed system is compared with the leading automatic detection systems in a mammographic image database. Experimental results demonstrate that the proposed system is statistically superior to most of the compared systems and delivers a superior performance.
Hyperspectral image classification using functional data analysis.
Li, Hong; Xiao, Guangrun; Xia, Tian; Tang, Y Y; Li, Luoqing
2014-09-01
The large number of spectral bands acquired by hyperspectral imaging sensors allows us to better distinguish many subtle objects and materials. Unlike other classical hyperspectral image classification methods in the multivariate analysis framework, in this paper, a novel method using functional data analysis (FDA) for accurate classification of hyperspectral images has been proposed. The central idea of FDA is to treat multivariate data as continuous functions. From this perspective, the spectral curve of each pixel in the hyperspectral images is naturally viewed as a function. This can be beneficial for making full use of the abundant spectral information. The relevance between adjacent pixel elements in the hyperspectral images can also be utilized reasonably. Functional principal component analysis is applied to solve the classification problem of these functions. Experimental results on three hyperspectral images show that the proposed method can achieve higher classification accuracies in comparison to some state-of-the-art hyperspectral image classification methods.
Paradigms of Complexity: Fractals and Structures in the Sciences
Novak, Miroslav M.
The Table of Contents for the book is as follows: * Preface * The Origin of Complexity (invited talk) * On the Existence of Spatially Uniform Scaling Laws in the Climate System * Multispectral Backscattering: A Fractal-Structure Probe * Small-Angle Multiple Scattering on a Fractal System of Point Scatterers * Symmetric Fractals Generated by Cellular Automata * Bispectra and Phase Correlations for Chaotic Dynamical Systems * Self-Organized Criticality Models of Neural Development * Altered Fractal and Irregular Heart Rate Behavior in Sick Fetuses * Extract Multiple Scaling in Long-Term Heart Rate Variability * A Semi-Continous Box Counting Method for Fractal Dimension Measurement of Short Single Dimension Temporal Signals - Preliminary Study * A Fractional Brownian Motion Model of Cracking * Self-Affine Scaling Studies on Fractography * Coarsening of Fractal Interfaces * A Fractal Model of Ocean Surface Superdiffusion * Stochastic Subsurface Flow and Transport in Fractal Fractal Conductivity Fields * Rendering Through Iterated Function Systems * The σ-Hull - The Hull Where Fractals Live - Calculating a Hull Bounded by Log Spirals to Solve the Inverse IFS-Problem by the Detected Orbits * On the Multifractal Properties of Passively Convected Scalar Fields * New Statistical Textural Transforms for Non-Stationary Signals: Application to Generalized Mutlifractal Analysis * Laplacian Growth of Parallel Needles: Their Mullins-Sekerka Instability * Entropy Dynamics Associated with Self-Organization * Fractal Properties in Economics (invited talk) * Fractal Approach to the Regional Seismic Event Discrimination Problem * Fractal and Topological Complexity of Radioactive Contamination * Pattern Selection: Nonsingular Saffman-Taylor Finger and Its Dynamic Evolution with Zero Surface Tension * A Family of Complex Wavelets for the Characterization of Singularities * Stabilization of Chaotic Amplitude Fluctuations in Multimode, Intracavity-Doubled Solid-State Lasers * Chaotic
Spatial Entropy and Fractal Dimension of Urban Form
Chen, Yanguang; Feng, Jian
2016-01-01
Entropy is an important concept in the studies on complex systems such as cities. Spatial patterns and processes can be described with varied entropy functions. However, spatial entropy always depends on the scale of measurement, and we cannot find a characteristic value for it. In contrast, entropy-based fractal parameters can be employed to characterize scale-free phenomena. This paper is devoted to exploring the similarities and differences between spatial entropy and fractal dimension in urban description. Drawing an analogy between cities and growing fractals, we illustrate the definitions of fractal dimension based on several entropy formulae. Three representative fractal dimensions in the multifractal dimension set, capacity dimension, information dimension, and correlation dimension, are utilized to make an empirical analysis of Beijing's and Hangzhou's urban form using functional box-counting method. The results show that the entropy values are not determinate, but the fractal dimension value is cert...
The Gompertzian curve reveals fractal properties of tumor growth
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Waliszewski, Przemyslaw; Konarski, Jerzy
2003-06-01
The normalized Gompertzian curve reflecting growth of experimental malignant tumors in time can be fitted by the power function y(t)=at{sup b} with the coefficient of nonlinear regression r{>=}0.95, in which the exponent b is a temporal fractal dimension, (i.e., a real number), and time t is a scalar. This curve is a fractal, (i.e., fractal dimension b exists, it changes along the time scale, the Gompertzian function is a contractable mapping of the Banach space R of the real numbers, holds the Banach theorem about the fix point, and its derivative is {<=}1). This denotes that not only space occupied by the interacting cancer cells, but also local, intrasystemic time, in which tumor growth occurs, possesses fractal structure. The value of the mean temporal fractal dimension decreases along the curve approaching eventually integer values; a fact consistent with our hypothesis that the fractal structure is lost during tumor progression.
Fractal dimension and architecture of trabecular bone.
Fazzalari, N L; Parkinson, I H
1996-01-01
The fractal dimension of trabecular bone was determined for biopsies from the proximal femur of 25 subjects undergoing hip arthroplasty. The average age was 67.7 years. A binary profile of the trabecular bone in the biopsy was obtained from a digitized image. A program written for the Quantimet 520 performed the fractal analysis. The fractal dimension was calculated for each specimen, using boxes whose sides ranged from 65 to 1000 microns in length. The mean fractal dimension for the 25 subjects was 1.195 +/- 0.064 and shows that in Euclidean terms the surface extent of trabecular bone is indeterminate. The Quantimet 520 was also used to perform bone histomorphometric measurements. These were bone volume/total volume (BV/TV) (per cent) = 11.05 +/- 4.38, bone surface/total volume (BS/TV) (mm2/mm3) = 1.90 +/- 0.51, trabecular thickness (Tb.Th) (mm) = 0.12 +/- 0.03, trabecular spacing (Tb.Sp) (mm) = 1.03 +/- 0.36, and trabecular number (Tb.N) (number/mm) = 0.95 +/- 0.25. Pearsons' correlation coefficients showed a statistically significant relationship between the fractal dimension and all the histomorphometric parameters, with BV/TV (r = 0.85, P fractal dimension shows that trabecular bone exhibits fractal properties over a defined box size, which is within the dimensions of a structural unit for trabecular bone. Therefore, the fractal dimension of trabecular bone provides a measure which does not rely on Euclidean descriptors in order to describe a complex geometry.
Fractal properties of financial markets
Budinski-Petković, Lj.; Lončarević, I.; Jakšić, Z. M.; Vrhovac, S. B.
2014-09-01
We present an analysis of the USA stock market using a simple fractal function. Financial bubbles preceding the 1987, 2000 and 2007 crashes are investigated using the Besicovitch-Ursell fractal function. Fits show a good agreement with the S&P 500 data when a complete financial growth is considered, starting at the threshold of the abrupt growth and ending at the peak. Moving the final time of the fitting interval towards earlier dates causes growing discrepancy between two curves. On the basis of a detailed analysis of the financial index behavior we propose a method for identifying the stage of the current financial growth and estimating the time in which the index value is going to reach the maximum.
Namazi, Hamidreza; Kulish, Vladimir V.; Akrami, Amin
2016-01-01
One of the major challenges in vision research is to analyze the effect of visual stimuli on human vision. However, no relationship has been yet discovered between the structure of the visual stimulus, and the structure of fixational eye movements. This study reveals the plasticity of human fixational eye movements in relation to the ‘complex’ visual stimulus. We demonstrated that the fractal temporal structure of visual dynamics shifts towards the fractal dynamics of the visual stimulus (image). The results showed that images with higher complexity (higher fractality) cause fixational eye movements with lower fractality. Considering the brain, as the main part of nervous system that is engaged in eye movements, we analyzed the governed Electroencephalogram (EEG) signal during fixation. We have found out that there is a coupling between fractality of image, EEG and fixational eye movements. The capability observed in this research can be further investigated and applied for treatment of different vision disorders. PMID:27217194
Namazi, Hamidreza; Kulish, Vladimir V.; Akrami, Amin
2016-05-01
One of the major challenges in vision research is to analyze the effect of visual stimuli on human vision. However, no relationship has been yet discovered between the structure of the visual stimulus, and the structure of fixational eye movements. This study reveals the plasticity of human fixational eye movements in relation to the ‘complex’ visual stimulus. We demonstrated that the fractal temporal structure of visual dynamics shifts towards the fractal dynamics of the visual stimulus (image). The results showed that images with higher complexity (higher fractality) cause fixational eye movements with lower fractality. Considering the brain, as the main part of nervous system that is engaged in eye movements, we analyzed the governed Electroencephalogram (EEG) signal during fixation. We have found out that there is a coupling between fractality of image, EEG and fixational eye movements. The capability observed in this research can be further investigated and applied for treatment of different vision disorders.
Fractal analysis of cervical intraepithelial neoplasia.
Directory of Open Access Journals (Sweden)
Markus Fabrizii
Full Text Available INTRODUCTION: Cervical intraepithelial neoplasias (CIN represent precursor lesions of cervical cancer. These neoplastic lesions are traditionally subdivided into three categories CIN 1, CIN 2, and CIN 3, using microscopical criteria. The relation between grades of cervical intraepithelial neoplasia (CIN and its fractal dimension was investigated to establish a basis for an objective diagnosis using the method proposed. METHODS: Classical evaluation of the tissue samples was performed by an experienced gynecologic pathologist. Tissue samples were scanned and saved as digital images using Aperio scanner and software. After image segmentation the box counting method as well as multifractal methods were applied to determine the relation between fractal dimension and grades of CIN. A total of 46 images were used to compare the pathologist's neoplasia grades with the predicted groups obtained by fractal methods. RESULTS: Significant or highly significant differences between all grades of CIN could be found. The confusion matrix, comparing between pathologist's grading and predicted group by fractal methods showed a match of 87.1%. Multifractal spectra were able to differentiate between normal epithelium and low grade as well as high grade neoplasia. CONCLUSION: Fractal dimension can be considered to be an objective parameter to grade cervical intraepithelial neoplasia.
Warchalowski, Wiktor; Krawczyk, Malgorzata J.
2017-03-01
We found the Lindenmayer systems for line graphs built on selected fractals. We show that the fractal dimension of such obtained graphs in all analysed cases is the same as for their original graphs. Both for the original graphs and for their line graphs we identified classes of nodes which reflect symmetry of the graph.
Perepelitsa, VA; Sergienko, [No Value; Kochkarov, AM
1999-01-01
Definitions of prefractal and fractal graphs are introduced, and they are used to formulate mathematical models in different fields of knowledge. The topicality of fractal-graph recognition from the point of view, of fundamental improvement in the efficiency of the solution of algorithmic problems i
Enhancement of critical temperature in fractal metamaterial superconductors
Smolyaninov, Igor I
2016-01-01
Fractal metamaterial superconductor geometry has been suggested and analyzed based on the recently developed theoretical description of critical temperature increase in epsilon near zero (ENZ) metamaterial superconductors. Considerable enhancement of critical temperature has been predicted in such materials due to appearance of large number of additional poles in the inverse dielectric response function of the fractal. Our results agree with the recent observation (Fratini et al. Nature 466, 841 (2010)) that fractal defect structure promotes superconductivity.
Enhancement of critical temperature in fractal metamaterial superconductors
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Smolyaninov, Igor I., E-mail: smoly@umd.edu [Department of Electrical and Computer Engineering, University of Maryland, College Park, MD 20742 (United States); Smolyaninova, Vera N. [Department of Physics Astronomy and Geosciences, Towson University, 8000 York Road, Towson, MD 21252 (United States)
2017-04-15
Fractal metamaterial superconductor geometry has been suggested and analyzed based on the recently developed theoretical description of critical temperature increase in epsilon near zero (ENZ) metamaterial superconductors. Considerable enhancement of critical temperature has been predicted in such materials due to appearance of large number of additional poles in the inverse dielectric response function of the fractal. Our results agree with the recent observation (Fratini et al. Nature 466, 841 (2010)) that fractal defect structure promotes superconductivity.
Heterogeneity of cerebral blood flow: a fractal approach
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Kuikka, J.T.; Hartikainen, P. [Department of Clinical Physiology, Kuopioo Univ. Hospital (Finland); Department of Neurology, Kuopio Univ. Hosspital (Finland); Niuvanniemi Hospital, Kuopio (Finland)
2000-07-01
Aim: We demonstrate the heterogeneity of regional cerebral blood flow using a fractal approach and single-photon emission computed tomography (SPECT). Method: Tc-99m-labelled ethylcysteine dimer was injected intravenously in 10 healthy controls and in 10 patients with dementia of frontal lobe type. The head was imaged with a gamma camera and transaxial, sagittal and coronal slices were reconstructed. Two hundred fifty-six symmetrical regions of interest (ROIs) were drawn onto each hemisphere of functioning brain matter. Fractal analysis was used to examine the spatial heterogeneity of blood flow as a function of the number of ROIs. Results: Relative dispersion (=coefficient of variation of the regional flows) was fractal-like in healthy subjects and could be characterized by a fractal dimension of 1.17{+-}0.05 (mean{+-}SD) for the left hemisphere and 1.15{+-}0.04 for the right hemisphere, respectively. The fractal dimension of 1.0 reflects completely homogeneous blood flow and 1.5 indicates a random blood flow distribution. Patients with dementia of frontal lobe type had a significantly lower fractal dimension of 1.04{+-}0.03 than in healthy controls. (orig.) [German] Ziel: Unter Einsatz einer fraktalen Annaeherung und SPECT wird die Heterogenitaet der regionalen Hirndruchblutung demonstriert. Methode: Tc-99m-ECD wurde nach intravenoeser Injektion bei zehn Gesunden sowie bei zehn Patienten mit Demenz vom Frontallappen-Typ eingesetzt. Aus dem SPECT-Umlauf wurden transaxiale, sagittale und koronare Schnitte rekonstruiert. 265 symmetrische Regions of Interest wurden im Gebiet der funktionellen grauen Substanz fuer jede Hemisphaere markiert. Die fraktale Analyse wurde eingesetzt zur Bestimmung der raeumlichen Heterogenitaet der Hirndurchblutung als Funktion der ROI-Anzahl. Ergebnisse: Die relative Streuung (Variationskoeffizient der regionalen Durchblutung) war bei Gesunden fraktalaehnlich geordnet und konnte durch eine Fraktaldimension von 1,17{+-}0,05 (Mittelwert
Stereotactic imaging in functional neurosurgery
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Hirabayashi, Hidehiro
2012-07-01
Background: The birth of stereotactic functional neurosurgery in 1947 was to a great extent dependent on the development of ventriculography. The last decades have witnessed a renaissance of functional stereotactic neurosurgery in the treatment of patients with movement disorders. Initially, these procedures were largely based on the same imaging technique that had been used since the birth of this technique, and that is still used in some centers. The introduction of new imaging modalities such as Computed Tomography (CT) and Magnetic Resonance Imaging (MRI) provided new potentials, but also new challenges for accurate identification and visualisation of the targets in the basal ganglia and the thalamus with an urge to thoroughly evaluate and optimize the stereotactic targeting technique, as well as evaluate accurately in stereotactic space the location and extent of stereotactic Radiofrequency (RF) lesions and the position of deep brain stimulation (DBS) electrodes. Aims: To study the differences between CT and MRI regarding indirect atlas coordinates in thalamic and pallidal procedures and to evaluate and validate visualisation of the pallidum and the subthalamic nucleus in view of direct targeting irrespective of atlas-derived coordinates. Furthermore, to evaluate the contribution of RF parameters on the size of stereotactic lesions, as well as the impact of size and location on clinical outcome. Method: The coordinates in relation to the landmarks of the 3{sup rd} ventricle of the targets in the pallidum and ventrolateral thalamus were compared between CT and MRI in 34 patients. In another 48 patients direct visualization of the pallidum was evaluated and compared to indirect atlas based targeting. The possibility and versatility of visualizing the Subthalamic Nucleus (STN) on short acquisition MRI were evaluated in a multicentre study, and the use of alternative landmarks in identification of the STN was demonstrated in another study. In 46 patients CT and
Equivalent Relation between Normalized Spatial Entropy and Fractal Dimension
Chen, Yanguang
2016-01-01
Fractal dimension is defined on the base of entropy, including macro state entropy and information entropy. The generalized dimension of multifractals is based on Renyi entropy. However, the mathematical transform from entropy to fractal dimension is not yet clear in both theory and practice. This paper is devoted to revealing the equivalence relation between spatial entropy and fractal dimension using box-counting method. Based on varied regular fractals, the numerical relationship between spatial entropy and fractal dimension is examined. The results show that the ratio of actual entropy (Mq) to the maximum entropy (Mmax) equals the ratio of actual dimension (Dq) to the maximum dimension (Dmax), that is, Mq/Mmax=Dq/Dmax. For real systems, the spatial entropy and fractal dimension of complex spatial systems such as cities can be converted into one another by means of functional box-counting method. The theoretical inference is verified by observational data of urban form. A conclusion is that normalized spat...
Ultra wide band electromagnetic scattering of a fractal profile
Rouvier, S.; Borderies, P.; Chênerie, I.
1997-03-01
The relationship between the fractal dimension of a perfectly conducting bidimensionnal profile and the fractal dimension of the time domain scattered field is investigated. The first part of the paper is dedicated to the profile itself; implementation of the counting box method for fractal dimension estimation is described and improved by the adjunction of an iterative process involving a correlation criterion. The second part is about the field scattered by a fractal profile which is calculated by the method of moments; polarizations, directions of incidence and observation effects are studied. Influence of spectral window and of noise is also investigated. Results show that fractal dimensions of the field and of the profile are linked by a monotonous increasing function which weakly depends on the polarizations and on the directions of incidence and observation. Moreover, the fractal dimension shows robustness to noise.
A simple method to estimate fractal dimension of mountain surfaces
Kolwankar, Kiran M
2014-01-01
Fractal surfaces are ubiquitous in nature as well as in the sciences. The examples range from the cloud boundaries to the corroded surfaces. Fractal dimension gives a measure of the irregularity in the object under study. We present a simple method to estimate the fractal dimension of mountain surface. We propose to use easily available satellite images of lakes for this purpose. The fractal dimension of the boundary of a lake, which can be extracted using image analysis softwares, can be determined easily which gives the estimate of the fractal dimension of the mountain surface and hence a quantitative characterization of the irregularity of the topography of the mountain surface. This value will be useful in validating models of mountain formation
Energy Technology Data Exchange (ETDEWEB)
Yadav, R.P. [Department of Physics, University of Allahabad, Allahabad, UP 211002 (India); Kumar, T. [Department of Physics, Central University of Haryana, Jant-Pali, Mahendergarh, Haryana 123029 (India); Mittal, A.K. [Department of Physics, University of Allahabad, Allahabad, UP 211002 (India); K Banerjee Centre of Atmospheric and Ocean Studies, University of Allahabad, Allahabad, UP 211002 (India); Dwivedi, S., E-mail: suneetdwivedi@gmail.com [K Banerjee Centre of Atmospheric and Ocean Studies, University of Allahabad, Allahabad, UP 211002 (India); Kanjilal, D. [Inter-University Accelerator Centre, Aruna Asaf Ali Marg, PO Box 10502, New Delhi 110 067 (India)
2015-08-30
Highlights: • Fractal analysis of Si(1 0 0) surface morphology at varying ion fluences. • Autocorrelation function and height–height correlation function as fractal measures. • Surface roughness and lateral correlation length increases with ion fluence. • Ripple pattern of the surfaces is found at higher ion fluences. • Wavelength of the ripple surfaces is computed for each fluence. - Abstract: Si (1 0 0) is bombarded with 200 keV Ar{sup +} ion beam at oblique incidence with fluences ranging from 3 × 10{sup 17} ions/cm{sup 2} to 3 × 10{sup 18} ions/cm{sup 2}. The surface morphology of the irradiated surfaces is captured by the atomic force microscopy (AFM) for each ion fluence. The fractal analysis is performed on the AFM images. The autocorrelation function and height–height correlation function are used as fractal measures. It is found that the average roughness, interface width, lateral correlation length as well as roughness exponent increase with ions fluence. The analysis reveals the ripple pattern of the surfaces at higher fluences. The wavelength of the ripple surfaces is computed for each ion fluence.
Fractals and Spatial Statistics of Point Patterns
Institute of Scientific and Technical Information of China (English)
Frederik P Agterberg
2013-01-01
The relationship between fractal point pattern modeling and statistical methods of parameter estimation in point-process modeling is reviewed.Statistical estimation of the cluster fractal dimension by using Ripley's K-function has advantages in comparison with the more commonly used methods of box-counting and cluster fractal dimension estimation because it corrects for edge effects,not only for rectangular study areas but also for study areas with curved boundaries determined by regional geology.Application of box-counting to estimate the fractal dimension of point patterns has the disadvantage that,in general,it is subject to relatively strong "roll-off" effects for smaller boxes.Point patterns used for example in this paper are mainly for gold deposits in the Abitibi volcanic belt on the Canadian Shield.Additionally,it is proposed that,worldwide,the local point patterns of podiform Cr,volcanogenic massive sulphide and porphyry copper deposits,which are spatially distributed within irregularly shaped favorable tracts,satisfy the fractal clustering model with similar fractal dimensions.The problem of deposit size (metal tonnage) is also considered.Several examples are provided of cases in which the Pareto distribution provides good results for the largest deposits in metal size-frequency distribution modeling.
Functional Magnetic Resonance Imaging and Pediatric Anxiety
Pine, Daniel S.; Guyer, Amanda E.; Leibenluft, Ellen; Peterson, Bradley S.; Gerber, Andrew
2008-01-01
The use of functional magnetic resonance imaging in investigating pediatric anxiety disorders is studied. Functional magnetic resonance imaging can be utilized in demonstrating parallels between the neural architecture of difference in anxiety of humans and the neural architecture of attention-orienting behavior in nonhuman primates or rodents.…
Functional Magnetic Resonance Imaging and Pediatric Anxiety
Pine, Daniel S.; Guyer, Amanda E.; Leibenluft, Ellen; Peterson, Bradley S.; Gerber, Andrew
2008-01-01
The use of functional magnetic resonance imaging in investigating pediatric anxiety disorders is studied. Functional magnetic resonance imaging can be utilized in demonstrating parallels between the neural architecture of difference in anxiety of humans and the neural architecture of attention-orienting behavior in nonhuman primates or rodents.…
A curious arithmetic of fractal dimension for polyadic Cantor sets
Villatoro, Francisco R
2009-01-01
Fractal sets, by definition, are non-differentiable, however their dimension can be continuous, differentiable, and arithmetically manipulable as function of their construction parameters. A new arithmetic for fractal dimension of polyadic Cantor sets is introduced by means of properly defining operators for the addition, subtraction, multiplication, and division. The new operators have the usual properties of the corresponding operations with real numbers. The combination of an infinitesimal change of fractal dimension with these arithmetic operators allows the manipulation of fractal dimension with the tools of calculus.
Application of the Autocorrelation Function and Fractal Geometry Methods for Analysis of MFM Images
Directory of Open Access Journals (Sweden)
Bramowicz M.
2014-06-01
Full Text Available Niniejsza praca dotyczy zastosowania metod korelacyjnych do numerycznej analizy obrazów rozkładu pola magnetycznego emitowanego z obszarów spontanicznego namagnesowania. W pracy przedstawiono kontynuację badań nad zastosowaniem funkcji autokorelacji oraz metod analizy fraktalnej w badaniach struktury domenowej oraz charakterystyki emitowanego z nich pola magnetycznego.
McAteer, R. T. J.
2013-06-01
When Mandelbrot, the father of modern fractal geometry, made this seemingly obvious statement he was trying to show that we should move out of our comfortable Euclidean space and adopt a fractal approach to geometry. The concepts and mathematical tools of fractal geometry provides insight into natural physical systems that Euclidean tools cannot do. The benet from applying fractal geometry to studies of Self-Organized Criticality (SOC) are even greater. SOC and fractal geometry share concepts of dynamic n-body interactions, apparent non-predictability, self-similarity, and an approach to global statistics in space and time that make these two areas into naturally paired research techniques. Further, the iterative generation techniques used in both SOC models and in fractals mean they share common features and common problems. This chapter explores the strong historical connections between fractal geometry and SOC from both a mathematical and conceptual understanding, explores modern day interactions between these two topics, and discusses how this is likely to evolve into an even stronger link in the near future.
Fractal Dimension Study of Non-metallic Inclusion Images in Steel%钢中非金属夹杂物图像分形维数的研究
Institute of Scientific and Technical Information of China (English)
岳强; 张雅丽; 孔辉; 周俐; 王建军; 汪诚
2012-01-01
Binary images of non-metallic inclusions boundary were obtained by processing images of rolling material of 304/304L stainless steel with large inclusions and ingots with micro inclusions. Box-counting method was employed to compute fractal dimension of inclusion contour. Algorithm was implemented with MATLAB programming. Results show that the fractal dimension of inclusion is closely related to its composition and melting point. Morphologies of low melting point Al2O3-SiO2-CaO compound inclusion are sphere or similar sphere, their fractal dimensions are small, morphologies of high melting point Al2O3 inclusions and SiO2 inclusions are irregular, their fractal dimensions are large.%通过对304/304L不锈钢轧材中大型夹杂物和铸锭中显微夹杂物的图像进行处理,得到夹杂物边界的二值图像.采用计盒维数法对夹杂物轮廓的分形维数进行计算与分析,算法利用MATLAB编程实现.结果表明,夹杂物的分形维数与其组成和熔点密切相关,低熔点的Al2O3-SiO2-CaO系复合夹杂的形貌多为球形或类球形,其分形维数较小；高熔点的Al2O3夹杂物与SiQ2夹杂物的形貌多为不规则形,其分形维数较大.
Magnetic resonance imaging based functional imaging in paediatric oncology.
Manias, Karen A; Gill, Simrandip K; MacPherson, Lesley; Foster, Katharine; Oates, Adam; Peet, Andrew C
2017-02-01
Imaging is central to management of solid tumours in children. Conventional magnetic resonance imaging (MRI) is the standard imaging modality for tumours of the central nervous system (CNS) and limbs and is increasingly used in the abdomen. It provides excellent structural detail, but imparts limited information about tumour type, aggressiveness, metastatic potential or early treatment response. MRI based functional imaging techniques, such as magnetic resonance spectroscopy, diffusion and perfusion weighted imaging, probe tissue properties to provide clinically important information about metabolites, structure and blood flow. This review describes the role of and evidence behind these functional imaging techniques in paediatric oncology and implications for integrating them into routine clinical practice. Copyright © 2016 Elsevier Ltd. All rights reserved.
Objetos fractales y arquitectura
MARTÍNEZ REQUENA, CELIA ANA
2015-01-01
Este trabajo final de grado versa acerca de la fractalidad y su posible aplicación arquitectónica. Se parte del concepto de fractal quedándose con la idea de que “un fractal es un diseño que se repite indefinidamente hacia el infinito cada vez a escala menor” y se presentan los diferentes conjuntos haciendo especial hincapié en los fractales clásicos. La fractalidad se puede apreciar en la naturaleza (p.e: un árbol tiene un tronco, este se divide en ramas, cada una de ellas en ...
Objetos fractales y arquitectura
MARTÍNEZ REQUENA, CELIA ANA
2015-01-01
Este trabajo final de grado versa acerca de la fractalidad y su posible aplicación arquitectónica. Se parte del concepto de fractal quedándose con la idea de que “un fractal es un diseño que se repite indefinidamente hacia el infinito cada vez a escala menor” y se presentan los diferentes conjuntos haciendo especial hincapié en los fractales clásicos. La fractalidad se puede apreciar en la naturaleza (p.e: un árbol tiene un tronco, este se divide en ramas, cada una de ellas en ...
Fractal frontiers in cardiovascular magnetic resonance: towards clinical implementation.
Captur, Gabriella; Karperien, Audrey L; Li, Chunming; Zemrak, Filip; Tobon-Gomez, Catalina; Gao, Xuexin; Bluemke, David A; Elliott, Perry M; Petersen, Steffen E; Moon, James C
2015-09-07
Many of the structures and parameters that are detected, measured and reported in cardiovascular magnetic resonance (CMR) have at least some properties that are fractal, meaning complex and self-similar at different scales. To date however, there has been little use of fractal geometry in CMR; by comparison, many more applications of fractal analysis have been published in MR imaging of the brain.This review explains the fundamental principles of fractal geometry, places the fractal dimension into a meaningful context within the realms of Euclidean and topological space, and defines its role in digital image processing. It summarises the basic mathematics, highlights strengths and potential limitations of its application to biomedical imaging, shows key current examples and suggests a simple route for its successful clinical implementation by the CMR community.By simplifying some of the more abstract concepts of deterministic fractals, this review invites CMR scientists (clinicians, technologists, physicists) to experiment with fractal analysis as a means of developing the next generation of intelligent quantitative cardiac imaging tools.
The role of the circadian system in fractal neurophysiological control.
Pittman-Polletta, Benjamin R; Scheer, Frank A J L; Butler, Matthew P; Shea, Steven A; Hu, Kun
2013-11-01
Many neurophysiological variables such as heart rate, motor activity, and neural activity are known to exhibit intrinsic fractal fluctuations - similar temporal fluctuation patterns at different time scales. These fractal patterns contain information about health, as many pathological conditions are accompanied by their alteration or absence. In physical systems, such fluctuations are characteristic of critical states on the border between randomness and order, frequently arising from nonlinear feedback interactions between mechanisms operating on multiple scales. Thus, the existence of fractal fluctuations in physiology challenges traditional conceptions of health and disease, suggesting that high levels of integrity and adaptability are marked by complex variability, not constancy, and are properties of a neurophysiological network, not individual components. Despite the subject's theoretical and clinical interest, the neurophysiological mechanisms underlying fractal regulation remain largely unknown. The recent discovery that the circadian pacemaker (suprachiasmatic nucleus) plays a crucial role in generating fractal patterns in motor activity and heart rate sheds an entirely new light on both fractal control networks and the function of this master circadian clock, and builds a bridge between the fields of circadian biology and fractal physiology. In this review, we sketch the emerging picture of the developing interdisciplinary field of fractal neurophysiology by examining the circadian system's role in fractal regulation.
ON FRACTAL MECHANISM OF COASTLINE —A Case Study of China
Institute of Scientific and Technical Information of China (English)
ZHUXiao－hua; WANGJian
2002-01-01
MANDELBROT enunciated the uncertainty of the length of a coastline in his paper"How long is the coast-line of Britain?" published in "Science"in 1967.The fractal concept was presented for the first time in that paper and has been applied to many fields ever since.According to the fractal theory and conditions of fractal research of coastline,the controls of faults and biologic function on the fractal character of coastline are preliminarily discussed on the basis of GIS in this paper.Finally,some significant conclusions are drawn:1)the faults control the basic trends of coastlines of two study areas;2)the fractal dimension of coastline of Taiwan is smaller than that of Changle-Lufent,because the faults of Taiwan more intensely control the trend and fractal dimension of the coastline;3)the larger the fractal dimension of the faults or the major faults ,the more the controlling effect of them on the trend and fractal dimension of coastline;4)the larger fractal dimension of the coastline of Changle-Lufeng indicates that the biologic function intensely shapes the coastline .In a word ,the controls of faults and biologic function on the fractal character of coastline are discussed with a case study of China in this paper,it can be seen that faults and biologic function both have influence over the trend and fractal dimension of coastline,the fractal mechanism of coastline of two study areas may be so.
Fractal Property in the Light Curve of BL Lac Object S5 0716+714
Indian Academy of Sciences (India)
J. W. Ou; Y. G. Zheng
2014-09-01
In this paper, we compile the historical R-band data of S5 0716+714 from literature and obtain its fractal dimension by using a fractal method and then simulate the data with the Weierstrass–Mandelbrot (W–M) function. It is considered that the light curve has a fractal property.
Fractal Property in the Light Curve of BL Lac Object S5 0716 + 714
Ou, J. W.; Zheng, Y. G.
2014-09-01
In this paper, we compile the historical R-band data of S5 0716 + 714 from literature and obtain its fractal dimension by using a fractal method and then simulate the data with the Weierstrass-Mandelbrot (W-M) function. It is considered that the light curve has a fractal property.
Relativistic Fractal Cosmologies
Ribeiro, Marcelo B
2009-01-01
This article reviews an approach for constructing a simple relativistic fractal cosmology whose main aim is to model the observed inhomogeneities of the distribution of galaxies by means of the Lemaitre-Tolman solution of Einstein's field equations for spherically symmetric dust in comoving coordinates. This model is based on earlier works developed by L. Pietronero and J.R. Wertz on Newtonian cosmology, whose main points are discussed. Observational relations in this spacetime are presented, together with a strategy for finding numerical solutions which approximate an averaged and smoothed out single fractal structure in the past light cone. Such fractal solutions are shown, with one of them being in agreement with some basic observational constraints, including the decay of the average density with the distance as a power law (the de Vaucouleurs' density power law) and the fractal dimension in the range 1 <= D <= 2. The spatially homogeneous Friedmann model is discussed as a special case of the Lemait...
A transfer matrix method for the analysis of fractal quantum potentials
Energy Technology Data Exchange (ETDEWEB)
Monsoriu, Juan A [Departamento de Fisica Aplicada, Universidad Politecnica de Valencia, E-46022 Valencia (Spain); Villatoro, Francisco R [Departamento de Lenguajes y Ciencias de la Computacion, Universidad de Malaga, E-29071 Malaga (Spain); Marin, Maria J [Departamento de Termodinamica, Universitat de Valencia, E-46100 Burjassot (Spain); UrchueguIa, Javier F [Departamento de Fisica Aplicada, Universidad Politecnica de Valencia, E-46022 Valencia (Spain); Cordoba, Pedro Fernandez de [Departamento de Matematica Aplicada, Universidad Politecnica de Valencia, E-46022 Valencia (Spain)
2005-07-01
The scattering properties of quantum particles on a sequence of potentials converging towards a fractal one are obtained by means of the transfer matrix method. The reflection coefficients for both the fractal potential and finite periodic potential are calculated and compared. It is shown that the reflection coefficient for the fractal potential has a self-similar structure associated with the fractal distribution of the potential whose degree of self-similarity has been quantified by means of the correlation function.
A Fractal Model for the Effective Thermal Conductivity of Granular Flow with Non-uniform Particles
Institute of Scientific and Technical Information of China (English)
ZHANG Duan-Ming; LEI Ya-Jie; YU Bo-Ming; ZHANG Mei-Jun; HUANG Ming-Tao; LI Zhi-Hua; GUAN Li
2002-01-01
The equipartition of energy applied in binary mixture of granular flow is extended to granular flow withnon-uniform particles. Based on the fractal characteristic of granular flow with non-uniform particles as well as energyequipartition, a fractal velocity distribution function and a fractal model of effective thermal conductivity are derived.Thermal conduction resulted from motions of particles in the granular flow, as well as the effect of fractal dimension oneffective thermal conductivity, is discussed.
Iris Recognition System Using Fractal Dimensions of Haar Patterns
Directory of Open Access Journals (Sweden)
Patnala S. R. Chandra Murty
2009-09-01
Full Text Available Classification of iris templates based on their texture patterns is one of the most effective methods in iris recognition systems. This paper proposes a novel algorithm for automatic iris classification based on fractal dimensions of Haar wavelet transforms is presented. Fractal dimensions obtained from multiple scale features are used to characterize the textures completely. Haar wavelet is applied in order to extract the multiple scale features at different resolutions from the iris image. Fractal dimensions are estimated from these patterns and a classifier is used to recognize the given image from a data base. Performance comparison was made among different classifiers.
Trabajando fractales con Winlogo
Sabogal, Sonia; Arenas, Gilberto
2007-01-01
Después de una breve introducción en la cual se establecerán algunos conceptos teóricos básicos de la geometría fractal, se realizarán talleres en los cuales, con ayuda de las herramientas que trabaja el software WinLogo, se construirán diversos fractales, analizando sus principales características (autosimilitud, dimensión, etc.)
Turcotte, Donald L.
Tectonic processes build landforms that are subsequently destroyed by erosional processes. Landforms exhibit fractal statistics in a variety of ways; examples include (1) lengths of coast lines; (2) number-size statistics of lakes and islands; (3) spectral behavior of topography and bathymetry both globally and locally; and (4) branching statistics of drainage networks. Erosional processes are dominant in the development of many landforms on this planet, but similar fractal statistics are also applicable to the surface of Venus where minimal erosion has occurred. A number of dynamical systems models for landforms have been proposed, including (1) cellular automata; (2) diffusion limited aggregation; (3) self-avoiding percolation; and (4) advective-diffusion equations. The fractal statistics and validity of these models will be discussed. Earthquakes also exhibit fractal statistics. The frequency-magnitude statistics of earthquakes satisfy the fractal Gutenberg-Richter relation both globally and locally. Earthquakes are believed to be a classic example of self-organized criticality. One model for earthquakes utilizes interacting slider-blocks. These slider block models have been shown to behave chaotically and to exhibit self-organized criticality. The applicability of these models will be discussed and alternative approaches will be presented. Fragmentation has been demonstrated to produce fractal statistics in many cases. Comminution is one model for fragmentation that yields fractal statistics. It has been proposed that comminution is also responsible for much of the deformation in the earth's crust. The brittle disruption of the crust and the resulting earthquakes present an integrated problem with many fractal aspects.
Local connected fractal dimensions and lacunarity analyses of 60 degrees fluorescein angiograms.
Landini, G; Murray, P I; Misson, G P
1995-12-01
The retinal vascular tree exhibits fractal characteristics. These findings relate to the mechanisms involved in the vascularization process and to the objective morphologic characterization of retinal vessels using fractal analysis. Although normal retinas show uniform patterns of blood vessels, in pathologic retinas with central vein or artery occlusions, the patterns are irregular. Because the generalized box fractal dimension fails to differentiate successfully between normal and abnormal retinal vessels in 60 degrees fluorescein angiograms, the authors have further investigated this problem using the local connected fractal dimension (alpha). The authors studied 24 digitized 60 degrees fluorescein angiograms of patients with normal retinas and 5 angiograms of patients with central retinal vein or artery occlusion. The pointwise method estimated the local complexity of the angiogram within a finite window centered on those pixels that belong to the retinal vessels. Color-coded dimensional images of the angiograms were constructed by plotting the pixels forming the object with a color that corresponded to specific values of alpha +/- delta alpha. The color-coded representation allowed recognition of areas with increased or decreased local angiogram complexity. The alpha distributions showed differences between normal and pathologic retinas, which overcomes problems encountered when using the methods of calculating the generalized fractal dimensions. A multivariate linear discriminant function using parameters from the alpha distribution and a further fractal parameter--lacunarity--reclassified 23 of the 24 normal and 4 of the 5 pathologic angiograms in their original groups (total: 92.1% correct). This methodology may be used for automatic detection and objective characterization of local retinal vessel abnormalities.
Use of fractal zone plates for transmission X-ray microscopy.
Ge, Xin; Wang, Zhili; Gao, Kun; Wang, Dajiang; Wu, Zhao; Chen, Jian; Pan, Zhiyun; Zhang, Kai; Hong, Youli; Zhu, Peiping; Wu, Ziyu
2012-09-01
In this contribution we discuss the possibility of designing a modified transmission X-ray microscope by using fractal zone plates (Fzps) as diffractive optical elements. In the modified transmission X-ray microscope optical layout, we first introduced a fractal zone plate as the microscope objective. Indeed, a fractal zone plate cannot only be used as an image-forming component but also as a condenser element to achieve an extended depth of field. Numerical analysis reveals that fractal zone plates and conventional Fresnel zone plates have similar imaging capabilities under different coherent illumination. Using a fractal zone plate as a condenser we also simulated axial irradiance. Results confirm that fractal zone plates can improve focusing capability with an extended depth of field. Although preliminary, these simulations clearly reveal that fractal zone plates, when available, will be of great help in microscope layouts, in particular for foreseen high-resolution applications in the "water window" as strongly required in biological research.
Rheological and fractal hydrodynamics of aerobic granules.
Tijani, H I; Abdullah, N; Yuzir, A; Ujang, Zaini
2015-06-01
The structural and hydrodynamic features for granules were characterized using settling experiments, predefined mathematical simulations and ImageJ-particle analyses. This study describes the rheological characterization of these biologically immobilized aggregates under non-Newtonian flows. The second order dimensional analysis defined as D2=1.795 for native clusters and D2=1.099 for dewatered clusters and a characteristic three-dimensional fractal dimension of 2.46 depicts that these relatively porous and differentially permeable fractals had a structural configuration in close proximity with that described for a compact sphere formed via cluster-cluster aggregation. The three-dimensional fractal dimension calculated via settling-fractal correlation, U∝l(D) to characterize immobilized granules validates the quantitative measurements used for describing its structural integrity and aggregate complexity. These results suggest that scaling relationships based on fractal geometry are vital for quantifying the effects of different laminar conditions on the aggregates' morphology and characteristics such as density, porosity, and projected surface area.
Molecular and Functional Imaging of Internet Addiction
Directory of Open Access Journals (Sweden)
Yunqi Zhu
2015-01-01
Full Text Available Maladaptive use of the Internet results in Internet addiction (IA, which is associated with various negative consequences. Molecular and functional imaging techniques have been increasingly used for analysis of neurobiological changes and neurochemical correlates of IA. This review summarizes molecular and functional imaging findings on neurobiological mechanisms of IA, focusing on magnetic resonance imaging (MRI and nuclear imaging modalities including positron emission tomography (PET and single photon emission computed tomography (SPECT. MRI studies demonstrate that structural changes in frontal cortex are associated with functional abnormalities in Internet addicted subjects. Nuclear imaging findings indicate that IA is associated with dysfunction of the brain dopaminergic systems. Abnormal dopamine regulation of the prefrontal cortex (PFC could underlie the enhanced motivational value and uncontrolled behavior over Internet overuse in addicted subjects. Further investigations are needed to determine specific changes in the Internet addictive brain, as well as their implications for behavior and cognition.
Molecular and functional imaging of internet addiction.
Zhu, Yunqi; Zhang, Hong; Tian, Mei
2015-01-01
Maladaptive use of the Internet results in Internet addiction (IA), which is associated with various negative consequences. Molecular and functional imaging techniques have been increasingly used for analysis of neurobiological changes and neurochemical correlates of IA. This review summarizes molecular and functional imaging findings on neurobiological mechanisms of IA, focusing on magnetic resonance imaging (MRI) and nuclear imaging modalities including positron emission tomography (PET) and single photon emission computed tomography (SPECT). MRI studies demonstrate that structural changes in frontal cortex are associated with functional abnormalities in Internet addicted subjects. Nuclear imaging findings indicate that IA is associated with dysfunction of the brain dopaminergic systems. Abnormal dopamine regulation of the prefrontal cortex (PFC) could underlie the enhanced motivational value and uncontrolled behavior over Internet overuse in addicted subjects. Further investigations are needed to determine specific changes in the Internet addictive brain, as well as their implications for behavior and cognition.
Fractal Dimension in Epileptic EEG Signal Analysis
Uthayakumar, R.
Fractal Analysis is the well developed theory in the data analysis of non-linear time series. Especially Fractal Dimension is a powerful mathematical tool for modeling many physical and biological time signals with high complexity and irregularity. Fractal dimension is a suitable tool for analyzing the nonlinear behaviour and state of the many chaotic systems. Particularly in analysis of chaotic time series such as electroencephalograms (EEG), this feature has been used to identify and distinguish specific states of physiological function.Epilepsy is the main fatal neurological disorder in our brain, which is analyzed by the biomedical signal called Electroencephalogram (EEG). The detection of Epileptic seizures in the EEG Signals is an important tool in the diagnosis of epilepsy. So we made an attempt to analyze the EEG in depth for knowing the mystery of human consciousness. EEG has more fluctuations recorded from the human brain due to the spontaneous electrical activity. Hence EEG Signals are represented as Fractal Time Series.The algorithms of fractal dimension methods have weak ability to the estimation of complexity in the irregular graphs. Divider method is widely used to obtain the fractal dimension of curves embedded into a 2-dimensional space. The major problem is choosing initial and final step length of dividers. We propose a new algorithm based on the size measure relationship (SMR) method, quantifying the dimensional behaviour of irregular rectifiable graphs with minimum time complexity. The evidence for the suitability (equality with the nature of dimension) of the algorithm is illustrated graphically.We would like to demonstrate the criterion for the selection of dividers (minimum and maximum value) in the calculation of fractal dimension of the irregular curves with minimum time complexity. For that we design a new method of computing fractal dimension (FD) of biomedical waveforms. Compared to Higuchi's algorithm, advantages of this method include
Fractal-Based Exponential Distribution of Urban Density and Self-Affine Fractal Forms of Cities
Chen, Yanguang
2016-01-01
Urban population density always follows the exponential distribution and can be described with Clark's model. Because of this, the spatial distribution of urban population used to be regarded as non-fractal pattern. However, Clark's model differs from the exponential function in mathematics because that urban population is distributed on the fractal support of landform and land-use form. By using mathematical transform and empirical evidence, we argue that there are self-affine scaling relations and local power laws behind the exponential distribution of urban density. The scale parameter of Clark's model indicating the characteristic radius of cities is not a real constant, but depends on the urban field we defined. So the exponential model suggests local fractal structure with two kinds of fractal parameters. The parameters can be used to characterize urban space filling, spatial correlation, self-affine properties, and self-organized evolution. The case study of the city of Hangzhou, China, is employed to ...
Tutte polynomial in functional magnetic resonance imaging
García-Castillón, Marlly V.
2015-09-01
Methods of graph theory are applied to the processing of functional magnetic resonance images. Specifically the Tutte polynomial is used to analyze such kind of images. Functional Magnetic Resonance Imaging provide us connectivity networks in the brain which are represented by graphs and the Tutte polynomial will be applied. The problem of computing the Tutte polynomial for a given graph is #P-hard even for planar graphs. For a practical application the maple packages "GraphTheory" and "SpecialGraphs" will be used. We will consider certain diagram which is depicting functional connectivity, specifically between frontal and posterior areas, in autism during an inferential text comprehension task. The Tutte polynomial for the resulting neural networks will be computed and some numerical invariants for such network will be obtained. Our results show that the Tutte polynomial is a powerful tool to analyze and characterize the networks obtained from functional magnetic resonance imaging.
Institute of Scientific and Technical Information of China (English)
缪志甫
2012-01-01
Fractal image compression （FIC） is an image compression algorithm based on partitioned iterative function system （PIFS）, i. e. self-similarity of natural image is used to conduct data compression, however, its huge time-consuming limits its real application. The time-consuming of FIC is mainly embodied in the aspects of the process of the optimal matched domain block search of every range block in defined domain block, calculation, quantification and storage of all affine transformation parameters and image partition process. In order to overcome the shortcoming of high computation cost, this paper uses optimization algorithm such as GA, ACO and PSO to reduce the search space for finding the self similarity in the given image and to speed up encoding. Experiment results show that optimized FIC can effectively reduce encoding time while peak value of signal-to-noise ratio is maintained.%分形图像压缩（FIC）是基于局部迭代函数系统（PIFS）的图像压缩算法，即用自然景物的自相似性来进行数据压缩；但是巨大的耗时量限制了其实际应用；FIC的耗时量主要体现在以下几方面：每一个值域块的最优匹配块的搜索都要在所有的定义域块中进行，需要花费大量的时间；计算、量化、存储所有的仿射变换参数；图像分割过程；为了克服FIC计算成本高的缺点，采用了遗传算法、蚁群算法和粒子群算法减少寻找相似定义域块的搜索空间，加快编码速度；实验结果表明：优化后的FIC能有效地减少编码时间同时保持峰值信噪比。
A New Model of Urban Population Density Indicating Latent Fractal Structure
Chen, Yanguang
2016-01-01
Fractal structure of a system suggests the optimal way in which parts arranged or put together to form a whole. The ideas from fractals have a potential application to the researches on urban sustainable development. To characterize fractal cities, we need the measure of fractional dimension. However, if the fractal organization is concealed in the complex spatial distributions of geographical phenomena, the common methods of evaluating fractal parameter will be disabled. In this article, a new model is proposed to describe urban density and estimate fractal dimension of urban form. If urban density takes on quasi-fractal pattern or the self-similar pattern is hidden in the negative exponential distribution, the generalized gamma function may be employed to model the urban landscape and estimate its latent fractal dimension. As a case study, the method is applied to the city of Hangzhou, China. The results show that urban form evolves from simple to complex structure with time.
From dendrimers to fractal polymers and beyond
Directory of Open Access Journals (Sweden)
Charles N. Moorefield
2013-01-01
Full Text Available The advent of dendritic chemistry has facilitated materials research by allowing precise control of functional component placement in macromolecular architecture. The iterative synthetic protocols used for dendrimer construction were developed based on the desire to craft highly branched, high molecular weight, molecules with exact mass and tailored functionality. Arborols, inspired by trees and precursors of the utilitarian macromolecules known as dendrimers today, were the first examples to employ predesigned, 1 → 3 C-branched, building blocks; physical characteristics of the arborols, including their globular shapes, excellent solubilities, and demonstrated aggregation, combined to reveal the inherent supramolecular potential (e.g., the unimolecular micelle of these unique species. The architecture that is a characteristic of dendritic materials also exhibits fractal qualities based on self-similar, repetitive, branched frameworks. Thus, the fractal design and supramolecular aspects of these constructs are suggestive of a larger field of fractal materials that incorporates repeating geometries and are derived by complementary building block recognition and assembly. Use of terpyridine-M2+-terpyridine (where, M = Ru, Zn, Fe, etc connectivity in concert with mathematical algorithms, such as forms the basis for the Seirpinski gasket, has allowed the beginning exploration of fractal materials construction. The propensity of the fractal molecules to self-assemble into higher order architectures adds another dimension to this new arena of materials and composite construction.
Fractal Weyl law for quantum fractal eigenstates.
Shepelyansky, D L
2008-01-01
The properties of the resonant Gamow states are studied numerically in the semiclassical limit for the quantum Chirikov standard map with absorption. It is shown that the number of such states is described by the fractal Weyl law, and their Husimi distributions closely follow the strange repeller set formed by classical orbits nonescaping in future times. For large matrices the distribution of escape rates converges to a fixed shape profile characterized by a spectral gap related to the classical escape rate.
Subband/transform functions for image processing
Glover, Daniel
1993-01-01
Functions for image data processing written for use with the MATLAB(TM) software package are presented. These functions provide the capability to transform image data with block transformations (such as the Walsh Hadamard) and to produce spatial frequency subbands of the transformed data. Block transforms are equivalent to simple subband systems. The transform coefficients are reordered using a simple permutation to give subbands. The low frequency subband is a low resolution version of the original image, while the higher frequency subbands contain edge information. The transform functions can be cascaded to provide further decomposition into more subbands. If the cascade is applied to all four of the first stage subbands (in the case of a four band decomposition), then a uniform structure of sixteen bands is obtained. If the cascade is applied only to the low frequency subband, an octave structure of seven bands results. Functions for the inverse transforms are also given. These functions can be used for image data compression systems. The transforms do not in themselves produce data compression, but prepare the data for quantization and compression. Sample quantization functions for subbands are also given. A typical compression approach is to subband the image data, quantize it, then use statistical coding (e.g., run-length coding followed by Huffman coding) for compression. Contour plots of image data and subbanded data are shown.
Fractal Analysis Based on Hierarchical Scaling in Complex Systems
Chen, Yanguang
2016-01-01
A fractal is in essence a hierarchy with cascade structure, which can be described with a set of exponential functions. From these exponential functions, a set of power laws indicative of scaling can be derived. Hierarchy structure and spatial network proved to be associated with one another. This paper is devoted to exploring the theory of fractal analysis of complex systems by means of hierarchical scaling. Two research methods are utilized to make this study, including logic analysis method and empirical analysis method. The main results are as follows. First, a fractal system such as Cantor set is described from the hierarchical angle of view; based on hierarchical structure, three approaches are proposed to estimate fractal dimension. Second, the hierarchical scaling can be generalized to describe multifractals, fractal complementary sets, and self-similar curve such as logarithmic spiral. Third, complex systems such as urban system are demonstrated to be a self-similar hierarchy. The human settlements i...
Prediction of osteoporosis using fractal analysis on periapical radiographs
Energy Technology Data Exchange (ETDEWEB)
Park, Gum Mi; Jung, Yun Hoa; Nah, Kyung Soo [Pusan National University College of Medicine, Busan (Korea, Republic of)
2005-03-15
To purpose of this study was to investigate whether the fractal dimension and radiographic image brightness of periapical radiograph were useful in predicting osteoporosis. Ninety-two postmenopausal women were classified as normal, osteopenia and osteoporosis group according to the bone mineral density of lumbar vertebrae and periapical radiographs of both mandibular molar areas were taken. The ROIs of 358 areas were selected at periapical and interdental areas and fractal dimension and radiographic image brightness were measured. The fractal dimension in normal group was significantly higher than that in osteoporosis group at periapical ROI (p<0.05). The radiographic image brightness in normal group was higher than that in osteopenia and osteoporosis group. There was significant difference not only between normal and osteopenia group (p<0.05) but also within osteopenia and osteoporosis group (p<0.01) at periapical ROI. Significant difference was observed not only between normal and osteopenia group but also between normal and osteoporosis group at interdental ROI (p<0.01). Positive linear relationship was weakly shown at Pearson correlation analysis between fractal dimension and radiographic image brightness. BMD significantly correlated with fractal dimension at periapical ROI (p<0.01), and BMD and radiographic image brightness significantly correlated at both periapical and interdental ROIs (p<0.01). This study suggests that the fractal dimension and radiographic image brightness of periapical ROI may predict BMD.
High speed functional magnetic resonance imaging
Gibson, A M
2002-01-01
The work in this thesis has been undertaken by the except where indicated by reference, within the Magnetic Resonance Centre at the University of Nottingham during the period from October 1998 to October 2001. This thesis documents the implementation and application of a novel high-speed imaging technique, the multi-slice, echo shifted, echo planar imaging technique. This was implemented on the Nottingham 3 T imaging system, for functional magnetic resonance imaging. The technique uses echo shifting over the slices in a multi-slice echo planar imaging acquisition scheme, making the echo time longer than the repetition time per slice. This allows for rapid volumar sampling of the blood oxygen level dependent effect in the human brain. The new high-speed technique was used to investigate the variability of measuring the timing differences between haemodynamic responses, at the same cortical location, to simple cued motor tasks. The technique was also used in an investigation into motor cortex functional connect...
Quantitative amyloid imaging using image-derived arterial input function.
Directory of Open Access Journals (Sweden)
Yi Su
Full Text Available Amyloid PET imaging is an indispensable tool widely used in the investigation, diagnosis and monitoring of Alzheimer's disease (AD. Currently, a reference region based approach is used as the mainstream quantification technique for amyloid imaging. This approach assumes the reference region is amyloid free and has the same tracer influx and washout kinetics as the regions of interest. However, this assumption may not always be valid. The goal of this work is to evaluate an amyloid imaging quantification technique that uses arterial region of interest as the reference to avoid potential bias caused by specific binding in the reference region. 21 participants, age 58 and up, underwent Pittsburgh compound B (PiB PET imaging and MR imaging including a time-of-flight (TOF MR angiography (MRA scan and a structural scan. FreeSurfer based regional analysis was performed to quantify PiB PET data. Arterial input function was estimated based on coregistered TOF MRA using a modeling based technique. Regional distribution volume (VT was calculated using Logan graphical analysis with estimated arterial input function. Kinetic modeling was also performed using the estimated arterial input function as a way to evaluate PiB binding (DVRkinetic without a reference region. As a comparison, Logan graphical analysis was also performed with cerebellar cortex as reference to obtain DVRREF. Excellent agreement was observed between the two distribution volume ratio measurements (r>0.89, ICC>0.80. The estimated cerebellum VT was in line with literature reported values and the variability of cerebellum VT in the control group was comparable to reported variability using arterial sampling data. This study suggests that image-based arterial input function is a viable approach to quantify amyloid imaging data, without the need of arterial sampling or a reference region. This technique can be a valuable tool for amyloid imaging, particularly in population where reference
Quantitative amyloid imaging using image-derived arterial input function.
Su, Yi; Blazey, Tyler M; Snyder, Abraham Z; Raichle, Marcus E; Hornbeck, Russ C; Aldea, Patricia; Morris, John C; Benzinger, Tammie L S
2015-01-01
Amyloid PET imaging is an indispensable tool widely used in the investigation, diagnosis and monitoring of Alzheimer's disease (AD). Currently, a reference region based approach is used as the mainstream quantification technique for amyloid imaging. This approach assumes the reference region is amyloid free and has the same tracer influx and washout kinetics as the regions of interest. However, this assumption may not always be valid. The goal of this work is to evaluate an amyloid imaging quantification technique that uses arterial region of interest as the reference to avoid potential bias caused by specific binding in the reference region. 21 participants, age 58 and up, underwent Pittsburgh compound B (PiB) PET imaging and MR imaging including a time-of-flight (TOF) MR angiography (MRA) scan and a structural scan. FreeSurfer based regional analysis was performed to quantify PiB PET data. Arterial input function was estimated based on coregistered TOF MRA using a modeling based technique. Regional distribution volume (VT) was calculated using Logan graphical analysis with estimated arterial input function. Kinetic modeling was also performed using the estimated arterial input function as a way to evaluate PiB binding (DVRkinetic) without a reference region. As a comparison, Logan graphical analysis was also performed with cerebellar cortex as reference to obtain DVRREF. Excellent agreement was observed between the two distribution volume ratio measurements (r>0.89, ICC>0.80). The estimated cerebellum VT was in line with literature reported values and the variability of cerebellum VT in the control group was comparable to reported variability using arterial sampling data. This study suggests that image-based arterial input function is a viable approach to quantify amyloid imaging data, without the need of arterial sampling or a reference region. This technique can be a valuable tool for amyloid imaging, particularly in population where reference normalization may
Functional magnetic resonance imaging studies of language.
Small, Steven L; Burton, Martha W
2002-11-01
Functional neuroimaging of language builds on almost 150 years of study in neurology, psychology, linguistics, anatomy, and physiology. In recent years, there has been an explosion of research using functional imaging technology, especially positron emission tomography (PET) and functional magnetic resonance imaging (fMRI), to understand the relationship between brain mechanisms and language processing. These methods combine high-resolution anatomic images with measures of language-specific brain activity to reveal neural correlates of language processing. This article reviews some of what has been learned about the neuroanatomy of language from these imaging techniques. We first discuss the normal case, organizing the presentation according to the levels of language, encompassing words (lexicon), sound structure (phonemes), and sentences (syntax and semantics). Next, we delve into some unusual language processing circumstances, including second languages and sign languages. Finally, we discuss abnormal language processing, including developmental and acquired dyslexia and aphasia.
The fractal forest: fractal geometry and applications in forest science.
Nancy D. Lorimer; Robert G. Haight; Rolfe A. Leary
1994-01-01
Fractal geometry is a tool for describing and analyzing irregularity. Because most of what we measure in the forest is discontinuous, jagged, and fragmented, fractal geometry has potential for improving the precision of measurement and description. This study reviews the literature on fractal geometry and its applications to forest measurements.
Surface characterization of proteins using multi-fractal property of heat-denatured aggregates
Lahiri, Tapobrata; Mishra, Hrishikesh; Sarkar, Subrata; Misra, Krishna
2008-01-01
Multi-fractal property of heat-denatured protein aggregates (HDPA) is characteristic of its individual form. The visual similarity between digitally generated microscopic images of HDPA with that of surface-image of its individual X-ray structures in protein databank (PDB) displayed using Visual Molecular Dynamics (VMD) viewer is the basis of the study. We deigned experiments to view the fractal nature of proteins at different aggregate scales. Intensity based multi-fractal dimensions (ILMFD)...
Fractal Patterns and Chaos Games
Devaney, Robert L.
2004-01-01
Teachers incorporate the chaos game and the concept of a fractal into various areas of the algebra and geometry curriculum. The chaos game approach to fractals provides teachers with an opportunity to help students comprehend the geometry of affine transformations.
Oleshko, Klaudia; de Jesús Correa López, María; Romero, Alejandro; Ramírez, Victor; Pérez, Olga
2016-04-01
The effectiveness of fractal toolbox to capture the scaling or fractal probability distribution, and simply fractal statistics of main hydrocarbon reservoir attributes, was highlighted by Mandelbrot (1995) and confirmed by several researchers (Zhao et al., 2015). Notwithstanding, after more than twenty years, it's still common the opinion that fractals are not useful for the petroleum engineers and especially for Geoengineering (Corbett, 2012). In spite of this negative background, we have successfully applied the fractal and multifractal techniques to our project entitled "Petroleum Reservoir as a Fractal Reactor" (2013 up to now). The distinguishable feature of Fractal Reservoir is the irregular shapes and rough pore/solid distributions (Siler, 2007), observed across a broad range of scales (from SEM to seismic). At the beginning, we have accomplished the detailed analysis of Nelson and Kibler (2003) Catalog of Porosity and Permeability, created for the core plugs of siliciclastic rocks (around ten thousand data were compared). We enriched this Catalog by more than two thousand data extracted from the last ten years publications on PoroPerm (Corbett, 2012) in carbonates deposits, as well as by our own data from one of the PEMEX, Mexico, oil fields. The strong power law scaling behavior was documented for the major part of these data from the geological deposits of contrasting genesis. Based on these results and taking into account the basic principles and models of the Physics of Fractals, introduced by Per Back and Kan Chen (1989), we have developed new software (Muukíl Kaab), useful to process the multiscale geological and geophysical information and to integrate the static geological and petrophysical reservoir models to dynamic ones. The new type of fractal numerical model with dynamical power law relations among the shapes and sizes of mesh' cells was designed and calibrated in the studied area. The statistically sound power law relations were established
Small-angle scattering from polymeric mass fractals of arbitrary mass-fractal dimension
Energy Technology Data Exchange (ETDEWEB)
Beaucage, G. [Cincinnati Univ., OH (United States). Dept. of Materials Science and Engineering
1996-04-01
The Debye equation for polymer coils describes scattering from a polymer chain that displays Gaussian statistics. Such a chain is a mass fractal of dimension 2 as evidenced by a power-law decay of -2 in the scattering at intermediate q. At low q, near q{approx_equal}2{pi}/R{sub g}, the Debye equation describes an exponential decay. For polymer chains that are swollen or slightly collapsed, such as is due to good and poor solvent conditions, deviations from a mass-fractal dimension of 2 are expected. A simple description of scattering from such systems is not possible using the approach of Debye. Integral descriptions have been derived. In this paper, asymptotic expansions of these integral forms are used to describe scattering in the power-law regime. These approximations are used to constrain a unified equation for small-angle scattering. A function suitable for data fitting is obtained that describes polymeric mass fractals of arbitrary mass-fractal dimension. Moreover, this approach is extended to describe structural limits to mass-fractal scaling at the persistence length. The unified equation can be substituted for the Debye equation in the RPA (random phase approximation) description of polymer blends when the mass-fractal dimension of a polymer coil deviates from 2. It is also used to gain new insight into materials not conventionally thought of as polymers, such as nanoporous silica aerogels. (orig.).
Functional minimization problems in image processing
Kim, Yunho; Vese, Luminita A.
2008-02-01
In this work we wish to recover an unknown image from a blurry version. We solve this inverse problem by energy minimization and regularization. We seek a solution of the form u + v, where u is a function of bounded variation (cartoon component), while v is an oscillatory component (texture), modeled by a Sobolev function with negative degree of differentiability. Experimental results show that this cartoon + texture model better recovers textured details in natural images, by comparison with the more standard models where the unknown is restricted only to the space of functions of bounded variation.
Perfusion heterogeneity in human skeletal muscle: fractal analysis of PET data
Energy Technology Data Exchange (ETDEWEB)
Kalliokoski, K.K.; Tolvanen, T.; Oikonen, V.; Teraes, M.; Knuuti, J. [Turku PET Centre, University of Turku (Finland); Kuusela, T.A. [Department of Applied Physics, University of Turku, Turku (Finland); Nuutila, P. [Turku PET Centre, University of Turku (Finland); Dept. of Medicine, University of Turku, Turku (Finland); Takala, T.E.S. [Department of Biology of Physical Activity, University of Jyvaeskylae, Jyvaeskylae (Finland)
2001-04-01
Muscle blood flow has been shown to be heterogeneous at the voxel by voxel level in positron emission tomography (PET) studies using oxygen-15 labelled water. However, the limited spatial resolution of the imaging device does not allow direct measurement of true vascular flow heterogeneity. Fractal dimension (D) obtained by fractal analysis describes the relationship between the relative dispersion and the size of the region studied, and has been used for the assessment of perfusion heterogeneity in microvascular units. This study was undertaken to evaluate fractal characteristics of PET perfusion data and to estimate perfusion heterogeneity in microvascular units. Skeletal muscle blood flow was measured in healthy subjects using [{sup 15}O]water PET and the fractal characteristics of blood flow in resting and exercising skeletal muscle were analysed. The perfusion heterogeneity in microvascular units was estimated using the measured heterogeneity (relative dispersion, RD=SD/mean) and D values. Heterogeneity due to methodological factors was estimated with phantoms and subtracted from the flow data. The number of aggregated voxels was inversely correlated with RD both in phantoms (Pearson r=-0.96-0.97) and in muscle (Pearson r=-0.94) when both parameters were expressed using a logarithmic scale. Fractal dimension was similar between exercising (1.13) and resting (1.14) muscles and significantly lower than the values in the phantoms with different activity levels (1.27-1.29). Measured flow heterogeneity values were 20%{+-}6% (exercise) and 27%{+-}5% (rest, P<0.001), whereas estimated flow heterogeneity values in microvascular units (1 mm{sup 3}) were 35%{+-}14% (exercise) and 49%{+-}14% (rest, P<0.01). In conclusion, these results show that it is feasible to apply fractal analysis to PET perfusion data. When microvascular flow heterogeneity is estimated using fractals, perfusion appears to be more heterogeneous in microvascular units than when obtained by routine
Marks-Tarlow, Terry
Linear concepts of time plus the modern capacity to track history emerged out of circular conceptions characteristic of ancient and traditional cultures. A fractal concept of time lies implicitly within the analog clock, where each moment is treated as unique. With fractal geometry the best descriptor of nature, qualities of self-similarity and scale invariance easily model her endless variety and recursive patterning, both in time and across space. To better manage temporal aspects of our lives, a fractal concept of time is non-reductive, based more on the fullness of being than on fragments of doing. By using a fractal concept of time, each activity or dimension of life is multiply and vertically nested. Each nested cycle remains simultaneously present, operating according to intrinsic dynamics and time scales. By adding the vertical axis of simultaneity to the horizontal axis of length, time is already full and never needs to be filled. To attend to time's vertical dimension is to tap into the imaginary potential for infinite depth. To switch from linear to fractal time allows us to relax into each moment while keeping in mind the whole.
Thermodynamics of Fractal Universe
Sheykhi, Ahmad; Wang, Bin
2012-01-01
We investigate the thermodynamical properties of the apparent horizon in a fractal universe. We find that one can always rewrite the Friedmann equation of the fractal universe in the form of the entropy balance relation $ \\delta Q=TdS+Td\\tilde{S}$, where $ \\delta Q $ and $ T $ are the energy flux and Unruh temperature seen by an accelerated observer just inside the apparent horizon, and $d\\tilde{S}$ is the entropy production term due to nonequilibrium thermodynamics of fractal universe. This shows that in a fractal universe, a treatment with nonequilibrium thermodynamics of spacetime may be needed. We also study the generalized second law of thermodynamics in the framework of fractal universe. When the temperature of the apparent horizon and the matter fields inside the horizon are equal, i.e. $T=T_h$, the generalized second law of thermodynamics can be fulfilled provided the deceleration and the equation of state parameters ranges either as $-1 \\leq q < 0 $, $- 1 \\leq w < - 1/3$ or as $q<-1$, $w<...
Ghost quintessence in fractal gravity
Indian Academy of Sciences (India)
Habib Abedi; Mustafa Salti
2015-04-01
In this study, using the time-like fractal theory of gravity, we mainly focus on the ghost dark energy model which was recently suggested to explain the present acceleration of the cosmic expansion. Next, we establish a connection between the quintessence scalar field and fractal ghost dark energy density. This correspondence allows us to reconstruct the potential and the dynamics of a fractal canonical scalar field (the fractal quintessence) according to the evolution of ghost dark energy density.
Lee, Bum Han; Lee, Sung Keun
2013-07-01
Despite the importance of understanding and quantifying the microstructure of porous networks in diverse geologic settings, the effects of the specific surface area and porosity on the key structural parameters of the networks have not been fully understood. We performed cube-counting fractal dimension (Dcc) and lacunarity analyses of 3D porous networks of model sands and configurational entropy analysis of 2D cross sections of model sands using random packing simulations and nuclear magnetic resonance (NMR) micro-imaging. We established relationships among porosity, specific surface area, structural parameters (Dcc and lacunarity), and the corresponding macroscopic properties (configurational entropy and permeability). The Dcc of the 3D porous networks increases with increasing specific surface area at a constant porosity and with increasing porosity at a constant specific surface area. Predictive relationships correlating Dcc, specific surface area, and porosity were also obtained. The lacunarity at the minimum box size decreases with increasing porosity, and that at the intermediate box size (∼0.469 mm in the current model sands) was reproduced well with specific surface area. The maximum configurational entropy increases with increasing porosity, and the entropy length of the pores decreases with increasing specific surface area and was used to calculate the average connectivity among the pores. The correlation among porosity, specific surface area, and permeability is consistent with the prediction from the Kozeny-Carman equation. From the relationship between the permeability and the Dcc of pores, the permeability can be expressed as a function of the Dcc of pores and porosity. The current methods and these newly identified correlations among structural parameters and properties provide improved insights into the nature of porous media and have useful geophysical and hydrological implications for elasticity and shear viscosity of complex composites of rock
Advantages in functional imaging of the brain
Directory of Open Access Journals (Sweden)
Walter eMier
2015-05-01
Full Text Available As neuronal pathologies cause only minor morphological alterations, molecular imaging techniques are a prerequisite for the study of diseases of the brain. The development of molecular probes that specifically bind biochemical markers and the advances of instrumentation have revolutionized the possibilities to gain insight into the human brain organization and beyond this visualize structure-function and brain-behavior relationships. The review describes the development and current applications of functional brain imaging techniques with a focus on applications in psychiatry. A historical overview of the development of functional imaging is followed by the portrayal of the principles and applications of positron emission tomography (PET and functional magnetic resonance imaging (fMRI, two key molecular imaging techniques that have revolutionized the ability to image molecular processes in the brain. In the juxtaposition of PET and fMRI in hybrid PET/MRI scanners enhances the significance of both modalities for research in neurology and psychiatry and might pave the way for a new area of personalized medicine.
Institute of Scientific and Technical Information of China (English)
杨凤霞
2012-01-01
针对当前分形图像编码面临如何改善重建图像视觉效果的问题,利用局部图像的特点,采取自适应的分块方法与缩短编码时间的多种块分类技术相结合设计图像编码算法,该算法明显改善了图像编码视觉效果,编码时间缩短上千倍,具有快速实现分形图像编码之功效.%To improve the reconstructed coding visual effect of fractal image, a new image coding algorithm is developed using adaptive block method integrated with classification techniques for multiple types of blocks which can reduce the coding time. Using proposed coding algorithm, the coding visual effect is improved a lot and the coding time is reduced by thousands of times. Finally,a rapid fractal image coding effect can be realized.
Fractal geometry and stochastics IV
Bandt, Christoph
2010-01-01
Over the years fractal geometry has established itself as a substantial mathematical theory in its own right. This book collects survey articles covering many of the developments, like Schramm-Loewner evolution, fractal scaling limits, exceptional sets for percolation, and heat kernels on fractals.
Vibration modes of 3n-gaskets and other fractals
Energy Technology Data Exchange (ETDEWEB)
Bajorin, N; Chen, T; Dagan, A; Emmons, C; Hussein, M; Khalil, M; Mody, P; Steinhurst, B; Teplyaev, A [Department of Mathematics, University of Connecticut, Storrs CT 06269 (United States)
2008-01-11
We rigorously study eigenvalues and eigenfunctions (vibration modes) on the class of self-similar symmetric finitely ramified fractals, which include the Sierpinski gasket and other 3n-gaskets. We consider the classical Laplacian on fractals which generalizes the usual one-dimensional second derivative, is the generator of the self-similar diffusion process, and has possible applications as the quantum Hamiltonian. We develop a theoretical matrix analysis, including analysis of singularities, which allows us to compute eigenvalues, eigenfunctions and their multiplicities exactly. We support our theoretical analysis by symbolic and numerical computations. Our analysis, in particular, allows the computation of the spectral zeta function on fractals and the limiting distribution of eigenvalues (i.e., integrated density of states). We consider such examples as the level-3 Sierpinski gasket, a fractal 3-tree, and the diamond fractal.
International Conference and Workshop on Fractals and Wavelets
Barnsley, Michael; Devaney, Robert; Falconer, Kenneth; Kannan, V; PB, Vinod
2014-01-01
Fractals and wavelets are emerging areas of mathematics with many common factors which can be used to develop new technologies. This volume contains the selected contributions from the lectures and plenary and invited talks given at the International Workshop and Conference on Fractals and Wavelets held at Rajagiri School of Engineering and Technology, India from November 9-12, 2013. Written by experts, the contributions hope to inspire and motivate researchers working in this area. They provide more insight into the areas of fractals, self similarity, iterated function systems, wavelets and the applications of both fractals and wavelets. This volume will be useful for the beginners as well as experts in the fields of fractals and wavelets.
Determining Effective Thermal Conductivity of Fabrics by Using Fractal Method
Zhu, Fanglong; Li, Kejing
2010-03-01
In this article, a fractal effective thermal conductivity model for woven fabrics with multiple layers is developed. Structural models of yarn and plain woven fabric are derived based on the fractal characteristics of macro-pores (gap or channel) between the yarns and micro-pores inside the yarns. The fractal effective thermal conductivity model can be expressed as a function of the pore structure (fractal dimension) and architectural parameters of the woven fabric. Good agreement is found between the fractal model and the thermal conductivity measurements in the general porosity ranges. It is expected that the model will be helpful in the evaluation of thermal comfort for woven fabric in the whole range of porosity.
Influence Factors of Fractal Characterization of Reciprocating Sliding Wear Surfaces
Institute of Scientific and Technical Information of China (English)
周新聪; 冯伟; 严新平; 萧汉梁
2004-01-01
The principal purpose of this paper is to investigate influence factors of fractal characterization of reciprocating sliding wear surfaces.The wear testing was completed to simulate the real running condition of the diesel engine 8NVD48A-2U.The test results of wear surface morphology dimension characterization show that wear surface profiles have statistical self-affine fractal characteristics.In general, there are no effects of the profilometer sampling spacing and sampling length and evaluation length on the fractal dimensions of the surfaces.However, if the evaluation length is too short, the structure function logarithm of the surface profile is scattered.The sampling length acting as a filter is an important part of the fractal dimension measurement.If the sampling length is too short, the evaluation of the fractal dimension will have a larger standard deviation.The continuous wavelet transform can be used to improve surface profile dimension characterization.
[Recent progress of research and applications of fractal and its theories in medicine].
Cai, Congbo; Wang, Ping
2014-10-01
Fractal, a mathematics concept, is used to describe an image of self-similarity and scale invariance. Some organisms have been discovered with the fractal characteristics, such as cerebral cortex surface, retinal vessel structure, cardiovascular network, and trabecular bone, etc. It has been preliminarily confirmed that the three-dimensional structure of cells cultured in vitro could be significantly enhanced by bionic fractal surface. Moreover, fractal theory in clinical research will help early diagnosis and treatment of diseases, reducing the patient's pain and suffering. The development process of diseases in the human body can be expressed by the fractal theories parameter. It is of considerable significance to retrospectively review the preparation and application of fractal surface and its diagnostic value in medicine. This paper gives an application of fractal and its theories in the medical science, based on the research achievements in our laboratory.
Imaging cellular and molecular biological functions
Energy Technology Data Exchange (ETDEWEB)
Shorte, S.L. [Institut Pasteur, 75 - Paris (France). Plateforme d' Imagerie Dynamique PFID-Imagopole; Frischknecht, F. (eds.) [Heidelberg Univ. Medical School (Germany). Dept. of Parasitology
2007-07-01
'Imaging cellular and molecular biological function' provides a unique selection of essays by leading experts, aiming at scientist and student alike who are interested in all aspects of modern imaging, from its application and up-scaling to its development. Indeed the philosophy of this volume is to provide student, researcher, PI, professional or provost the means to enter this applications field with confidence, and to construct the means to answer their own specific questions. (orig.)
Functional MR Imaging in Chest Malignancies.
Broncano, Jordi; Luna, Antonio; Sánchez-González, Javier; Alvarez-Kindelan, Antonio; Bhalla, Sanjeev
2016-02-01
With recent advances in MR imaging, its application in the thorax has been feasible. The performance of both morphologic and functional techniques in the evaluation of thoracic malignances has improved not only differentiation from benign etiologies but also treatment monitoring based on a multiparametric approach. Several MR imaging-derived parameters have been described as potential biomarkers linked with prognosis and survival. Therefore, an integral approach with a nonradiating and noninvasive technique could be an optimal alternative for evaluating those patients.
Contrast sensitivity function and image discrimination.
Peli, E
2001-02-01
A previous study tested the validity of simulations of the appearance of a natural image (from different observation distances) generated by using a visual model and contrast sensitivity functions of the individual observers [J. Opt. Soc. Am. A 13, 1131 (1996)]. Deleting image spatial-frequency components that should be undetectable made the simulations indistinguishable from the original images at distances larger than the simulated distance. The simulated observation distance accurately predicted the distance at which the simulated image could be discriminated from the original image. Owing to the 1/f characteristic of natural images' spatial spectra, the individual contrast sensitivity functions (CSF's) used in the simulations of the previous study were actually tested only over a narrow range of retinal spatial frequencies. To test the CSF's over a wide range of frequencies, the same simulations and testing procedure were applied to five contrast versions of the images (10-300%). This provides a stronger test of the model, of the simulations, and specifically of the CSF's used. The relevant CSF for a discrimination task was found to be obtained by using 1-octave Gabor stimuli measured in a contrast detection task. The relevant CSF data had to be measured over a range of observation distances, owing to limitations of the displays.
Energy Technology Data Exchange (ETDEWEB)
Benenti, Giuliano; Casati, Giulio; Guarneri, Italo; Terraneo, Marcello
2001-07-02
We numerically analyze quantum survival probability fluctuations in an open, classically chaotic system. In a quasiclassical regime and in the presence of classical mixed phase space, such fluctuations are believed to exhibit a fractal pattern, on the grounds of semiclassical arguments. In contrast, we work in a classical regime of complete chaoticity and in a deep quantum regime of strong localization. We provide evidence that fluctuations are still fractal, due to the slow, purely quantum algebraic decay in time produced by dynamical localization. Such findings considerably enlarge the scope of the existing theory.
Fractal actors and infrastructures
DEFF Research Database (Denmark)
Bøge, Ask Risom
2011-01-01
-network-theory (ANT) into surveillance studies (Ball 2002, Adey 2004, Gad & Lauritsen 2009). In this paper, I further explore the potential of this connection by experimenting with Marilyn Strathern’s concept of the fractal (1991), which has been discussed in newer ANT literature (Law 2002; Law 2004; Jensen 2007). I...... under surveillance. Based on fieldwork conducted in 2008 and 2011 in relation to my Master’s thesis and PhD respectively, I illustrate fractal concepts by describing the acts, actors and infrastructure that make up the ‘DNA surveillance’ conducted by the Danish police....
Institute of Scientific and Technical Information of China (English)
ZhinhongLi; DongWu; Yuhansun; JunWang; YiLiu; BaozhongDong; Zhinhong
2001-01-01
Silica aggregates were prepared by base-catalyzed hydrolysis and condensation of alkoxides in alcohol.Polyethylene glycol(PEG) was used as organic modifier.The sols were characterized using Small Angle X-ray Scattering (SAXS) with synchrotron radiation as X-ray source.The structure evolution during the sol-gel process was determined and described in terms of the fractal geometry.As-produced silica aggregates were found to be mass fractals.The fractl dimensions spanned the regime 2.1-2.6 corresponding to more branched and compact structures.Both RLCA and Eden models dominated the kinetic growth under base-catalyzed condition.
A New Digital Signature Scheme Based on Mandelbrot and Julia Fractal Sets
Directory of Open Access Journals (Sweden)
M. A. Alia
2007-01-01
Full Text Available This paper describes a new cryptographic digital signature scheme based on Mandelbrot and Julia fractal sets. Having fractal based digital signature scheme is possible due to the strong connection between the Mandelbrot and Julia fractal sets. The link between the two fractal sets used for the conversion of the private key to the public key. Mandelbrot fractal function takes the chosen private key as the input parameter and generates the corresponding public-key. Julia fractal function then used to sign the message with receiver's public key and verify the received message based on the receiver's private key. The propose scheme was resistant against attacks, utilizes small key size and performs comparatively faster than the existing DSA, RSA digital signature scheme. Fractal digital signature scheme was an attractive alternative to the traditional number theory digital signature scheme.
The Classification of HEp-2 Cell Patterns Using Fractal Descriptor.
Xu, Rudan; Sun, Yuanyuan; Yang, Zhihao; Song, Bo; Hu, Xiaopeng
2015-07-01
Indirect immunofluorescence (IIF) with HEp-2 cells is considered as a powerful, sensitive and comprehensive technique for analyzing antinuclear autoantibodies (ANAs). The automatic classification of the HEp-2 cell images from IIF has played an important role in diagnosis. Fractal dimension can be used on the analysis of image representing and also on the property quantification like texture complexity and spatial occupation. In this study, we apply the fractal theory in the application of HEp-2 cell staining pattern classification, utilizing fractal descriptor firstly in the HEp-2 cell pattern classification with the help of morphological descriptor and pixel difference descriptor. The method is applied to the data set of MIVIA and uses the support vector machine (SVM) classifier. Experimental results show that the fractal descriptor combining with morphological descriptor and pixel difference descriptor makes the precisions of six patterns more stable, all above 50%, achieving 67.17% overall accuracy at best with relatively simple feature vectors.
Password Authentication Based on Fractal Coding Scheme
Directory of Open Access Journals (Sweden)
Nadia M. G. Al-Saidi
2012-01-01
Full Text Available Password authentication is a mechanism used to authenticate user identity over insecure communication channel. In this paper, a new method to improve the security of password authentication is proposed. It is based on the compression capability of the fractal image coding to provide an authorized user a secure access to registration and login process. In the proposed scheme, a hashed password string is generated and encrypted to be captured together with the user identity using text to image mechanisms. The advantage of fractal image coding is to be used to securely send the compressed image data through a nonsecured communication channel to the server. The verification of client information with the database system is achieved in the server to authenticate the legal user. The encrypted hashed password in the decoded fractal image is recognized using optical character recognition. The authentication process is performed after a successful verification of the client identity by comparing the decrypted hashed password with those which was stored in the database system. The system is analyzed and discussed from the attacker’s viewpoint. A security comparison is performed to show that the proposed scheme provides an essential security requirement, while their efficiency makes it easier to be applied alone or in hybrid with other security methods. Computer simulation and statistical analysis are presented.
Hateren, J.H. van
2013-01-01
A climate response function is introduced that consists of six exponential (low-pass) filters with weights depending as a power law on their e-folding times. The response of this two-parameter function to the combined forcings of solar irradiance, greenhouse gases, and SO2-related aerosols is fitted
Fractal elements and their applications
Gil’mutdinov, Anis Kharisovich; El-Khazali, Reyad
2017-01-01
This book describes a new type of passive electronic components, called fractal elements, from a theoretical and practical point of view. The authors discuss in detail the physical implementation and design of fractal devices for application in fractional-order signal processing and systems. The concepts of fractals and fractal signals are explained, as well as the fundamentals of fractional calculus. Several implementations of fractional impedances are discussed, along with comparison of their performance characteristics. Details of design, schematics, fundamental techniques and implementation of RC-based fractal elements are provided. .
Adolescent body image and psychosocial functioning.
Davison, Tanya E; McCabe, Marita P
2006-02-01
Researchers have highlighted the significance of a poor body image in the development of dysfunctional eating but have systematically investigated few other outcomes. The authors examined the relationships between different aspects of body image and psychosocial functioning. Participants were 245 boys and 173 girls from Grades 8 and 9 (M age = 13.92 years, SD = 0.69 years). Respondents completed measures of physical attractiveness, body satisfaction, body image importance, body image behaviors, appearance comparison, social physique anxiety, self-esteem, depression, anxiety, and same-sex and opposite-sex relations. Whereas girls tended to report a more negative body image than did boys, the relevance of body image to self-esteem was similar for boys and girls. Concern about others' evaluation of their bodies was especially important in understanding low female self-esteem, whereas for boys, ratings of general attractiveness most strongly predicted self-esteem. The authors found a negative body image to be unrelated to symptoms of negative affect but to be strongly associated with poor opposite-sex peer relationships, especially among boys. A negative body image also affected same-sex relations among girls.
Right ventricular plasticity and functional imaging
Brittain, Evan L.; Hemnes, Anna R.; Keebler, Mary; Lawson, Mark; Byrd, Benjamin F.; DiSalvo, Tom
2012-01-01
Right ventricular (RV) function is a strong independent predictor of outcome in a number of distinct cardiopulmonary diseases. The RV has a remarkable ability to sustain damage and recover function which may be related to unique anatomic, physiologic, and genetic factors that differentiate it from the left ventricle. This capacity has been described in patients with RV myocardial infarction, pulmonary arterial hypertension, and chronic thromboembolic disease as well as post-lung transplant and post-left ventricular assist device implantation. Various echocardiographic and magnetic resonance imaging parameters of RV function contribute to the clinical assessment and predict outcomes in these patients; however, limitations remain with these techniques. Early diagnosis of RV function and better insight into the mechanisms of RV recovery could improve patient outcomes. Further refinement of established and emerging imaging techniques is necessary to aid subclinical diagnosis and inform treatment decisions. PMID:23130100
Fractal Representation of Exergy
Directory of Open Access Journals (Sweden)
Yvain Canivet
2016-02-01
Full Text Available We developed a geometrical model to represent the thermodynamic concepts of exergy and anergy. The model leads to multi-scale energy lines (correlons that we characterised by fractal dimension and entropy analyses. A specific attention will be paid to overlapping points, rising interesting remarks about trans-scale dynamics of heat flows.
Earnshow, R; Jones, H
1991-01-01
This volume is based upon the presentations made at an international conference in London on the subject of 'Fractals and Chaos'. The objective of the conference was to bring together some of the leading practitioners and exponents in the overlapping fields of fractal geometry and chaos theory, with a view to exploring some of the relationships between the two domains. Based on this initial conference and subsequent exchanges between the editors and the authors, revised and updated papers were produced. These papers are contained in the present volume. We thank all those who contributed to this effort by way of planning and organisation, and also all those who helped in the production of this volume. In particular, we wish to express our appreciation to Gerhard Rossbach, Computer Science Editor, Craig Van Dyck, Production Director, and Nancy A. Rogers, who did the typesetting. A. J. Crilly R. A. Earnshaw H. Jones 1 March 1990 Introduction Fractals and Chaos The word 'fractal' was coined by Benoit Mandelbrot i...
Multimodality imaging of structure and function
Energy Technology Data Exchange (ETDEWEB)
Townsend, D W [Departments of Medicine and Radiology, University of Tennessee Medical Center, 1924 Alcoa Highway, Knoxville, TN 37920 (United States)], E-mail: dtownsend@mc.utmck.edu
2008-02-21
Historically, medical devices to image either anatomical structure or functional processes have developed along somewhat independent paths. The recognition that combining images from different modalities can nevertheless offer significant diagnostic advantages gave rise to sophisticated software techniques to coregister structure and function. Recently, alternatives to retrospective software-based fusion have become available through instrumentation that combines two imaging modalities within a single device, an approach that has since been termed hardware fusion. As a result, following their recent introduction into the clinic, combined PET/CT and SPECT/CT devices are now playing an increasingly important role in the diagnosis and staging of human disease. Recently, although limited to the brain, the first clinical MR scanner with a PET insert, a technically-challenging design, has been undergoing evaluation. This review will follow the development of multimodality instrumentation for clinical use from conception to present-day technology and assess the status and future potential for such devices. (topical review)
Near-Field Optical Microscopy of Fractal Structures
DEFF Research Database (Denmark)
Coello, Victor; Bozhevolnyi, Sergey I.
1999-01-01
Using a photon scanning tunnelling microscope combined with a shear-force feedback system, we image both topographical and near-field optical images (at the wavelengths of 633 and 594 nm) of silver colloid fractals. Near-field optical imaging is calibrated with a standing evanescent wave pattern...
Functional Magnetic Resonance Imaging in Consumer Research
DEFF Research Database (Denmark)
Reimann, Martin; Schilke, Oliver; Weber, Bernd
2011-01-01
Although the field of psychology is undergoing an immense shift toward the use of functional magnetic resonance imaging (fMRI), the application of this methodology to consumer research is relatively new. To assist consumer researchers in understanding fMRI, this paper elaborates on the findings...
Structural and functional imaging: Particularities in children
Energy Technology Data Exchange (ETDEWEB)
Chiron, C.; Hertz-Pannier, L. [Hop Necker Enfants Malad, INSERM, Serv Neuropediat, U663, F-75015 Paris (France); Chiron, C.; Hertz-Pannier, L. [UnivParis 05, F-75005 Paris (France); Chiron, C.; Hertz-Pannier, L. [CEA, I2BM, Neurospin, SHFJ, F-91191 Orsay (France)
2008-07-01
Surgery of partial epilepsies in childhood has largely benefited from the recent advances of imaging techniques, which carry a triple goal: (1) to contribute to the localization of the epilepsy onset zone, (2) to detect and delineate an underlying lesion, and (3) to study the spatial relationship between the epileptogenic zone and the neighboring functional cortex, in order to select patients and plan the resection. This noninvasive pre-surgical imaging workup must be compared to clinical and electrical data to estimate the postoperative prognosis, while invasive techniques such as SEEG, cortical stimulations, and IAT often remain indispensable in difficult cases, i.e., in cryptogenic epilepsies. As in adults, advances in MRI allow us to detect more and more subtle underlying lesions, but this requires repeating MR studies during early childhood and using adapted sequence parameters to account for ongoing myelination. Ictal SPECT and PET imaging prove especially useful in planning depth electrode placement when video-EEG is not contributive, when MRI looks normal or shows multiple abnormalities, or in cases of discrepant findings. Multimodal imaging greatly enhances the sensitivity of all of these techniques. Finally, functional MRI of motor and language functions provide noninvasive cortical mapping of essential functions, using age-adapted paradigms, in cooperating children from age five to six and from IQs around 60. (authors)
Maslovskaya, A. G.; Barabash, T. K.
2017-01-01
The article presents some results of fractal analysis of ferroelectric domain structure images visualized with scanning electron microscope (SEM) techniques. The fractal and multifractal characteristics were estimated to demonstrate self-similar organization of ferroelectric domain structure registered with static and dynamic contrast modes of SEM. Fractal methods as sensitive analytical tools were used to indicate degree of domain structure and domain boundary imperfections. The electron irradiation-induced erosion effect of ferroelectric domain boundaries in electron beam-stimulated polarization current mode of SEM is characterized by considerable raising of fractal dimension. For dynamic contrast mode of SEM there was revealed that complication of domain structure during its dynamics is specified by increase in fractal dimension of images and slight raising of boundary fractal dimension.
Theoretical study of statistical fractal model with applications to mineral resource prediction
Wei, Shen; Pengda, Zhao
2002-04-01
The statistical estimation of fractal dimensions is an important topic of investigation. Current solutions emphsize visual straight-line fitting, but nonlinear statistical modeling has the potential of making valuable contributions in this field. In this paper, we present the concepts of generalized fractal models and generalized fractal dimension and conclude that many geological models are special cases of the generalized models. We show that the power-function distribution possesses the fractal property of scaling invariance under upper truncation, which may help in lead statistical fractal modeling. A new method is developed on the basis of nonlinear regression to estimate fractal parameters. This method has advantages with respect to the traditional method based on linear regression for estimating the fractal dimension. Finally, the new method is illustrated by means of application to a real data set.
Fractal physiology and the fractional calculus: a perspective
Directory of Open Access Journals (Sweden)
Bruce J West
2010-10-01
Full Text Available This paper presents a restricted overview of Fractal Physiology focusing on the complexity of the human body and the characterization of that complexity through fractal measures and their dynamics, with fractal dynamics being described by the fractional calculus. We review the allometric aggregation approach to the processing of physiologic time series as a way of determining the fractal character of the underlying phenomena. This straight forward method establishes the scaling behavior of complex physiologic networks and some dynamic models capable of generating such scaling are reviewed. These models include simple and fractional random walks, which describe how the scaling of correlation functions and probability densities are related to time series data. Subsequently, it is suggested that a proper methodology for describing the dynamics of fractal time series may well be the fractional calculus, either through the fractional Langevin equation or the fractional diffusion equation. Fractional operators acting on fractal functions yield fractal functions, allowing us to construct a fractional Langevin equation to describe the evolution of a fractal statistical process. Control of physiologic complexity is one of the goals of medicine. Allometric control incorporates long-time memory, inverse power-law (IPL correlations, and long-range interactions in complex phenomena as manifest by IPL distributions. We hypothesize that allometric control, rather than homeostatic control, maintains the fractal character of erratic physiologic time series to enhance the robustness of physiological networks. Moreover, allometric control can be described using the fractional calculus to capture the dynamics of complex physiologic networks. This hypothesis is supported by a number of physiologic time series data.
Image Segmentation via Fractal Dimension
1987-12-01
air intake I external stores stations remain available with the CFTs MSIP improvements include a tactical electronic system use, and McDonnell Douglas...Crapt Tiothy. n.•.itortlon- 1.invariqnt Pattern Aec .nitton In Noen-Randao .olae. MS thesis, AHT Ui’i-!B?-t,0i20. School or Engineertrig. Air Force
Fractal Images: Procedure and Theory.
1987-08-01
impossible to comprehend how anyone ever thought of them." -- Michael Spivak , A Comprehensive Introduction to Differential Geometry In the last few years, the...several results which gave relation- ships between set theory and calculus . In 1874, he produced his proof that there are only countably many algebraic
Visceral Afferent Pathways and Functional Brain Imaging
Directory of Open Access Journals (Sweden)
Stuart W.G. Derbyshire
2003-01-01
Full Text Available The application of functional imaging to study painful sensations has generated considerable interest regarding insight into brain dysfunction that may be responsible for functional pain such as that suffered in patients with irritable bowel syndrome (IBS. This review provides a brief introduction to the development of brain science as it relates to pain processing and a snapshot of recent functional imaging results with somatic and visceral pain. Particular emphasis is placed on current hypotheses regarding dysfunction of the brain-gut axis in IBS patients. There are clear and interpretable differences in brain activation following somatic as compared with visceral noxious sensation. Noxious visceral distension, particularly of the lower gastrointestinal tract, activates regions associated with unpleasant affect and autonomic responses. Noxious somatic sensation, in contrast, activates regions associated with cognition and skeletomotor responses. Differences between IBS patients and control subjects, however, were far less clear and interpretable. While this is in part due to the newness of this field, it also reflects weaknesses inherent within the current understanding of IBS. Future use of functional imaging to examine IBS and other functional disorders will be more likely to succeed by describing clear theoretical and clinical endpoints.
van Hateren, J H
2013-01-01
A climate response function is introduced that consists of six exponential (low-pass) filters with weights depending as a power law on their e-folding times. The response of this function to the combined forcings of solar irradiance, greenhouse gases, and SO2-related aerosols is fitted simultaneously to reconstructed temperatures of the past millennium, the response to solar cycles, the response to the 1991 Pinatubo volcanic eruption, and the modern 1850-2010 temperature trend. The quite adequate fit produces a climate response function with an equilibrium response to doubling of CO2 concentration of 2.0 \\pm 0.3 ^{\\circ}C (mean \\pm standard error), of which about 50% is realized with e-folding times of 0.5 and 2 years, about 30% with e-folding times of 8 and 32 years, and about 20% with e-folding times of 128 and 512 years. The transient climate response (response after 70 years of 1% yearly rise of CO2 concentration) is 1.5 \\pm 0.2 ^{\\circ}C. The temperature rise from 1820-1950 can be attributed for about 70...
Nonlinear interpolation fractal classifier for multiple cardiac arrhythmias recognition
Energy Technology Data Exchange (ETDEWEB)
Lin, C.-H. [Department of Electrical Engineering, Kao-Yuan University, No. 1821, Jhongshan Rd., Lujhu Township, Kaohsiung County 821, Taiwan (China); Institute of Biomedical Engineering, National Cheng-Kung University, Tainan 70101, Taiwan (China)], E-mail: eechl53@cc.kyu.edu.tw; Du, Y.-C.; Chen Tainsong [Institute of Biomedical Engineering, National Cheng-Kung University, Tainan 70101, Taiwan (China)
2009-11-30
This paper proposes a method for cardiac arrhythmias recognition using the nonlinear interpolation fractal classifier. A typical electrocardiogram (ECG) consists of P-wave, QRS-complexes, and T-wave. Iterated function system (IFS) uses the nonlinear interpolation in the map and uses similarity maps to construct various data sequences including the fractal patterns of supraventricular ectopic beat, bundle branch ectopic beat, and ventricular ectopic beat. Grey relational analysis (GRA) is proposed to recognize normal heartbeat and cardiac arrhythmias. The nonlinear interpolation terms produce family functions with fractal dimension (FD), the so-called nonlinear interpolation function (NIF), and make fractal patterns more distinguishing between normal and ill subjects. The proposed QRS classifier is tested using the Massachusetts Institute of Technology-Beth Israel Hospital (MIT-BIH) arrhythmia database. Compared with other methods, the proposed hybrid methods demonstrate greater efficiency and higher accuracy in recognizing ECG signals.
Functional imaging of the pelvic floor
Energy Technology Data Exchange (ETDEWEB)
Lienemann, Andreas E-mail: andreaslienemann@web.de; Fischer, Tanja
2003-08-01
Introduction/Objective: Pelvic floor dysfunction and associated pelvic organ prolapse represent a major problem in our present-day society, mostly afflicting parous women. Magnetic resonance imaging (MRI) is assuming an increasingly important role in the more accurate delineation of the extent of the problem. This article briefly reviews one of the main radiological methods for the dynamic evaluation of the pelvic floor: functional cine MRI. Methods and Material: Out of the literature the smallest common denominator for functional cine MRI can be defined as follows: high field system; patient either in supine or sitting position; fast gradient echo sequence; midsagittal slice orientation; either a stack of slices or repeated measurements at the same slice position with the patient at rest or straining; image analysis using the pubococcygeal reference line. Results: All except two publications stress the usefulness of functional cine MRI in the evaluation of patients with organ descent and prolapse. This well accepted method allows for the visualization of all relevant structures in the anterior, middle and posterior compartment. It is especially useful in the detection of enteroceles, and provides a reliable postoperative follow-up tool. Isolated urinary or stool incontinence are not an indication for functional cine MRI, as is the case in patients with equivocal clinical findings. To date it does not allow for real 3D imaging of the pelvic floor or sufficient determination of fascial defects. Discussion: Functional cine MRI of the pelvic floor is a promising new imaging method for the detection of organ descent and prolapse in patients with equivocal clinical findings. The combination of function and morphology allows for an innovative view of the pelvic floor, and thus adds to our understanding of the various interactions of the structures.
Fractal dimension based corneal fungal infection diagnosis
Balasubramanian, Madhusudhanan; Perkins, A. Louise; Beuerman, Roger W.; Iyengar, S. Sitharama
2006-08-01
We present a fractal measure based pattern classification algorithm for automatic feature extraction and identification of fungus associated with an infection of the cornea of the eye. A white-light confocal microscope image of suspected fungus exhibited locally linear and branching structures. The pixel intensity variation across the width of a fungal element was gaussian. Linear features were extracted using a set of 2D directional matched gaussian-filters. Portions of fungus profiles that were not in the same focal plane appeared relatively blurred. We use gaussian filters of standard deviation slightly larger than the width of a fungus to reduce discontinuities. Cell nuclei of cornea and nerves also exhibited locally linear structure. Cell nuclei were excluded by their relatively shorter lengths. Nerves in the cornea exhibited less branching compared with the fungus. Fractal dimensions of the locally linear features were computed using a box-counting method. A set of corneal images with fungal infection was used to generate class-conditional fractal measure distributions of fungus and nerves. The a priori class-conditional densities were built using an adaptive-mixtures method to reflect the true nature of the feature distributions and improve the classification accuracy. A maximum-likelihood classifier was used to classify the linear features extracted from test corneal images as 'normal' or 'with fungal infiltrates', using the a priori fractal measure distributions. We demonstrate the algorithm on the corneal images with culture-positive fungal infiltrates. The algorithm is fully automatic and will help diagnose fungal keratitis by generating a diagnostic mask of locations of the fungal infiltrates.
Fractal Particles: Titan's Thermal Structure and IR Opacity
McKay, C. P.; Rannou, P.; Guez, L.; Young, E. F.; DeVincenzi, Donald (Technical Monitor)
1998-01-01
Titan's haze particles are the principle opacity at solar wavelengths. Most past work in modeling these particles has assumed spherical particles. However, observational evidence strongly favors fractal shapes for the haze particles. We consider the implications of fractal particles for the thermal structure and near infrared opacity of Titan's atmosphere. We find that assuming fractal particles with the optical properties based on laboratory tholin material and with a production rate that allows for a match to the geometric albedo results in warmer troposphere and surface temperatures compared to spherical particles. In the near infrared (1-3 microns) the predicted opacity of the fractal particles is up to a factor of two less than for spherical particles. This has implications for the ability of Cassini to image Titan's surface at 1 micron.
Fractal analysis of circulating platelets in type 2 diabetic patients.
Bianciardi, G; Tanganelli, I
2015-01-01
This paper investigates the use of computerized fractal analysis for objective characterization by means of transmission electron microscopy of the complexity of circulating platelets collected from healthy individuals and from type 2 diabetic patients, a pathologic condition in which platelet hyperreactivity has been described. Platelet boundaries were extracted by means of automatically image analysis. Local fractal dimension by box counting (measure of geometric complexity) was automatically calculated. The results showed that the platelet boundary observed by electron microscopy is fractal and that the shape of the circulating platelets is significantly more complex in the diabetic patients in comparison to healthy subjects (p fractal analysis of platelet shape by transmission electron microscopy can provide accurate, quantitative, data to study platelet activation in diabetes mellitus.
Numeric character recognition method based on fractal dimension
He, Tao; Xie, Yulang; Chen, Jiuyin; Cheng, Longfei; Yuan, Ye
2013-10-01
An image processing method based on fractal dimension is proposed in this paper. This method uses fractal dimension to process the character images firstly, and rises the analysis of each grid to the analysis of interrelation between the grids to eliminate interference. Box-counting method is commonly used for calculating fractal dimension of fractal, which uses small box whose side length is r ,that is the topological dimension of the box is d, to cover up the image. Because there are various levels of cavities and cracks, some small boxes are empty and some small boxes cover a part of fractal image which is called non-empty box (here refers to the average gray of the part that contained in the small box is larger than a certain threshold). We note down the number of non-empty boxes, analyze and calculate them. The method is used to image process the polluted characters, which can remove ink and scratches around the contour of the characters and remain basic contour, then the characters can be recognized by using template matching. In computer simulation experiment for polluted character recognition, this method can recognize the polluted characters quickly, which improve the accuracy of the recognition of the polluted characters.
Multilayer adsorption on fractal surfaces.
Vajda, Péter; Felinger, Attila
2014-01-10
Multilayer adsorption is often observed in liquid chromatography. The most frequently employed model for multilayer adsorption is the BET isotherm equation. In this study we introduce an interpretation of multilayer adsorption measured on liquid chromatographic stationary phases based on the fractal theory. The fractal BET isotherm model was successfully used to determine the apparent fractal dimension of the adsorbent surface. The nonlinear fitting of the fractal BET equation gives us the estimation of the adsorption equilibrium constants and the monolayer saturation capacity of the adsorbent as well. In our experiments, aniline and proline were used as test molecules on reversed phase and normal phase columns, respectively. Our results suggest an apparent fractal dimension 2.88-2.99 in the case of reversed phase adsorbents, in the contrast with a bare silica column with a fractal dimension of 2.54.
Kinetic properties of fractal media
Chumak, Oleg V
2016-01-01
Kinetic processes in fractal stellar media are analyzed in terms of the approach developed in our earlier paper (Chumak, Rastorguev, 2016) involving a generalization of the nearest neighbor and random force distributions to fractal media. Diffusion is investigated in the approximation of scale-dependent conditional density based on an analysis of the solutions of the corresponding Langevin equations. It is shown that kinetic parameters (time scales, coefficients of dynamic friction, diffusion, etc.) for fractal stellar media can differ significantly both qualitatively and quantitatively from the corresponding parameters for a quasi-uniform random media with limited fluctuations. The most important difference is that in the fractal case kinetic parameters depend on spatial scale length and fractal dimension of the medium studied. A generalized kinetic equation for stellar media (fundamental equation of stellar dynamics) is derived in the Fokker-Planck approximation with the allowance for the fractal properties...
Fractals in geology and geophysics
Turcotte, Donald L.
1989-01-01
The definition of a fractal distribution is that the number of objects N with a characteristic size greater than r scales with the relation N of about r exp -D. The frequency-size distributions for islands, earthquakes, fragments, ore deposits, and oil fields often satisfy this relation. This application illustrates a fundamental aspect of fractal distributions, scale invariance. The requirement of an object to define a scale in photograhs of many geological features is one indication of the wide applicability of scale invariance to geological problems; scale invariance can lead to fractal clustering. Geophysical spectra can also be related to fractals; these are self-affine fractals rather than self-similar fractals. Examples include the earth's topography and geoid.
On the Fractional Calculus of a Type of Weierstrass Functions
Institute of Scientific and Technical Information of China (English)
姚奎; 张霞
2002-01-01
@@ I Introduction In recent years, fractals have shown important applications in many fields. [1, 2] and [3] havedone some excellent initial and conclusion work on fractal and it's mathematical foundations.However, a fractal function: a type of Weierstrass functions defined bybecause of it's special fractal properties, [1,2, 4, 5] have given some detailed discussion about it'sgraph, fractal dimension, etc.
Fast optical imaging of human brain function
Directory of Open Access Journals (Sweden)
Gabriele Gratton
2010-06-01
Full Text Available Great advancements in brain imaging during the last few decades have opened a large number of new possibilities for neuroscientists. The most dominant methodologies (electrophysiological and magnetic resonance-based methods emphasize temporal and spatial information, respectively. However, theorizing about brain function has recently emphasized the importance of rapid (within 100 ms or so interactions between different elements of complex neuronal networks. Fast optical imaging, and in particular the event-related optical signal (EROS, a technology that has emerged over the last 15 years may provide descriptions of localized (to sub-cm level brain activity with a temporal resolution of less than 100 ms. The main limitations of EROS are its limited penetration, which allows us to image cortical structures not deeper than 3 cm from the surface of the head, and its low signal-to-noise ratio. Advantages include the fact that EROS is compatible with most other imaging methods, including electrophysiological, magnetic resonance, and trans-cranial magnetic stimulation techniques, with which can be recorded concurrently. In this paper we present a summary of the research that has been conducted so far on fast optical imaging, including evidence for the possibility of recording neuronal signals with this method, the properties of the signals, and various examples of applications to the study of human cognitive neuroscience. Extant issues, controversies, and possible future developments are also discussed.
Eliazar, Iddo; Klafter, Joseph
2008-06-01
We explore six classes of fractal probability laws defined on the positive half-line: Weibull, Frechét, Lévy, hyper Pareto, hyper beta, and hyper shot noise. Each of these classes admits a unique statistical power-law structure, and is uniquely associated with a certain operation of renormalization. All six classes turn out to be one-dimensional projections of underlying Poisson processes which, in turn, are the unique fixed points of Poissonian renormalizations. The first three classes correspond to linear Poissonian renormalizations and are intimately related to extreme value theory (Weibull, Frechét) and to the central limit theorem (Lévy). The other three classes correspond to nonlinear Poissonian renormalizations. Pareto's law--commonly perceived as the "universal fractal probability distribution"--is merely a special case of the hyper Pareto class.
Institute of Scientific and Technical Information of China (English)
Ren Xin-Cheng; Guo Li-Xin
2008-01-01
A normalized two-dimensional band-limited Weierstrass fractal function is used for modelling the dielectric rough surface. An analytic solution of the scattered field is derived based on the Kirchhoff approximation. The variance of scat-tering intensity is presented to study the fractal characteristics through theoretical analysis and numerical calculations. The important conclusion is obtained that the diffracted envelope slopes of scattering pattern can be approximated as a slope of linear equation. This conclusion will be applicable for solving the inverse problem of reconstructing rough surface and remote sensing.
Turbulent wakes of fractal objects.
Staicu, Adrian; Mazzi, Biagio; Vassilicos, J C; van de Water, Willem
2003-06-01
Turbulence of a windtunnel flow is stirred using objects that have a fractal structure. The strong turbulent wakes resulting from three such objects which have different fractal dimensions are probed using multiprobe hot-wire anemometry in various configurations. Statistical turbulent quantities are studied within inertial and dissipative range scales in an attempt to relate changes in their self-similar behavior to the scaling of the fractal objects.
Fast image coding approach with denoising based on fractal and DWT%带降噪的快速DWT与分形相结合图像编码方法
Institute of Scientific and Technical Information of China (English)
刘波; 房斌; 罗棻; 张世勇
2011-01-01
A new image coding algorithm is presented, which combined the fractal and discrete wavelet transform, based on the statistical character of image blocks, the distance between the value block and its best matched domain block in the baseline fractal coding and the distribution of noise unknown. In the proposed algorithm, ifthe robust regression between the value block and it' s best matched domain block is less than the given threshold value, the value block is compressed by fractal coding, otherwise is compressed by discrete waveform transform. Simulation results show that the proposed algorithm can speed up encoding time greatly and improve on the quality of the reconstructed image. Especially that has good robustness against the outliers caused by salt and pepper noise.%针对图像易受外界噪声干扰,且这种噪声分布通常是未知的这一问题,结合图像的统计特性,基本分形编码中值域块和最佳匹配的定义域块之间的距离统计特性等,提出一种基于方差不变特性、邻域搜索的分形与小波相结合的图像分形编码算法.在该算法中,如果值域决和最佳匹配之间的稳健回归优化目标函数取值小于给定的阈值,则用分形压缩算法编码该块,否则用小波变换压缩该块.实验结果表明,该方法可使编码速度比基本分形算法有较大提高,而且原始图像在受到外界干扰的情况下,该算法表现出了较好的鲁棒特性.
Statistical mechanics and fractals
Dobrushin, Roland Lvovich
1993-01-01
This book is composed of two texts, by R.L. Dobrushin and S. Kusuoka, each representing the content of a course of lectures given by the authors. They are pitched at graduate student level and are thus very accessible introductions to their respective subjects for students and non specialists. CONTENTS: R.L. Dobrushin: On the Way to the Mathematical Foundations of Statistical Mechanics.- S. Kusuoka: Diffusion Processes on Nested Fractals.
Martin, Demetri
2015-03-01
Demetri Maritn prepared this palindromic poem as his project for Michael Frame's fractal geometry class at Yale. Notice the first, fourth, and seventh words in the second and next-to-second lines are palindromes, the first two and last two lines are palindromes, the middle line, "Be still if I fill its ebb" minus its last letter is a palindrome, and the entire poem is a palindrome...
Fractal multifiber microchannel plates
Cook, Lee M.; Feller, W. B.; Kenter, Almus T.; Chappell, Jon H.
1992-01-01
The construction and performance of microchannel plates (MCPs) made using fractal tiling mehtods are reviewed. MCPs with 40 mm active areas having near-perfect channel ordering were produced. These plates demonstrated electrical performance characteristics equivalent to conventionally constructed MCPs. These apparently are the first MCPs which have a sufficiently high degree of order to permit single channel addressability. Potential applications for these devices and the prospects for further development are discussed.
Besselink, R.; Stawski, T. M.; Van Driessche, A. E. S.; Benning, L. G.
2016-12-01
Densely packed surface fractal aggregates form in systems with high local volume fractions of particles with very short diffusion lengths, which effectively means that particles have little space to move. However, there are no prior mathematical models, which would describe scattering from such surface fractal aggregates and which would allow the subdivision between inter- and intraparticle interferences of such aggregates. Here, we show that by including a form factor function of the primary particles building the aggregate, a finite size of the surface fractal interfacial sub-surfaces can be derived from a structure factor term. This formalism allows us to define both a finite specific surface area for fractal aggregates and the fraction of particle interfacial sub-surfaces at the perimeter of an aggregate. The derived surface fractal model is validated by comparing it with an ab initio approach that involves the generation of a "brick-in-a-wall" von Koch type contour fractals. Moreover, we show that this approach explains observed scattering intensities from in situ experiments that followed gypsum (CaSO4 ṡ 2H2O) precipitation from highly supersaturated solutions. Our model of densely packed "brick-in-a-wall" surface fractal aggregates may well be the key precursor step in the formation of several types of mosaic- and meso-crystals.
Darwinian Evolution and Fractals
Carr, Paul H.
2009-05-01
Did nature's beauty emerge by chance or was it intelligently designed? Richard Dawkins asserts that evolution is blind aimless chance. Michael Behe believes, on the contrary, that the first cell was intelligently designed. The scientific evidence is that nature's creativity arises from the interplay between chance AND design (laws). Darwin's ``Origin of the Species,'' published 150 years ago in 1859, characterized evolution as the interplay between variations (symbolized by dice) and the natural selection law (design). This is evident in recent discoveries in DNA, Madelbrot's Fractal Geometry of Nature, and the success of the genetic design algorithm. Algorithms for generating fractals have the same interplay between randomness and law as evolution. Fractal statistics, which are not completely random, characterize such phenomena such as fluctuations in the stock market, the Nile River, rainfall, and tree rings. As chaos theorist Joseph Ford put it: God plays dice, but the dice are loaded. Thus Darwin, in discovering the evolutionary interplay between variations and natural selection, was throwing God's dice!
Fractals a very short introduction
Falconer, Kenneth
2013-01-01
Many are familiar with the beauty and ubiquity of fractal forms within nature. Unlike the study of smooth forms such as spheres, fractal geometry describes more familiar shapes and patterns, such as the complex contours of coastlines, the outlines of clouds, and the branching of trees. In this Very Short Introduction, Kenneth Falconer looks at the roots of the 'fractal revolution' that occurred in mathematics in the 20th century, presents the 'new geometry' of fractals, explains the basic concepts, and explores the wide range of applications in science, and in aspects of economics.This is esse
Bony change of apical lesion healing process using fractal analysis
Energy Technology Data Exchange (ETDEWEB)
Lee, Ji Min; Park, Hyok; Jeong, Ho Gul; Kim, Kee Deog; Park, Chang Seo [Yonsei University College of Medicine, Seoul (Korea, Republic of)
2005-06-15
To investigate the change of bone healing process after endodontic treatment of the tooth with an apical lesion by fractal analysis. Radiographic images of 35 teeth from 33 patients taken on first diagnosis, 6 months, and 1 year after endodontic treatment were selected. Radiographic images were taken by JUPITER computerized Dental X-ray System. Fractal dimensions were calculated three times at each area by Scion Image PC program. Rectangular region of interest (30 x 30) were selected at apical lesion and normal apex of each image. The fractal dimension at apical lesion of first diagnosis (L{sub 0}) is 0.940 {+-} 0.361 and that of normal area (N{sub 0}) is 1.186 {+-} 0.727 (p<0.05). Fractal dimension at apical lesion of 6 months after endodontic treatment (L{sub 1}) is 1.076 {+-} 0.069 and that of normal area (N{sub 1}) is 1.192 {+-} 0.055 (p<0.05). Fractal dimension at apical lesion of 1 year after endodontic treatment (L{sub 2}) is 1.163 {+-} 0.074 and that of normal area (N{sub 2}) is 1.225 {+-} 0.079 (p<0.05). After endodontic treatment, the fractal dimensions at each apical lesions depending on time showed statistically significant difference. And there are statistically significant different between normal area and apical lesion on first diagnosis, 6 months after, 1 year after. But the differences were grow smaller as time flows. The evaluation of the prognosis after the endodontic treatment of the apical lesion was estimated by bone regeneration in apical region. Fractal analysis was attempted to overcome the limit of subjective reading, and as a result the change of the bone during the healing process was able to be detected objectively and quantitatively.
Retinal functional imager (RFI): non-invasive functional imaging of the retina.
Ganekal, S
2013-01-01
Retinal functional imager (RFI) is a unique non-invasive functional imaging system with novel capabilities for visualizing the retina. The objective of this review was to show the utility of non-invasive functional imaging in various disorders. Electronic literature search was carried out using the websites www.pubmed.gov and www.google.com. The search words were retinal functional imager and non-invasive retinal imaging used in combination. The articles published or translated into English were studied. The RFI directly measures hemodynamic parameters such as retinal blood-flow velocity, oximetric state, metabolic responses to photic activation and generates capillary perfusion maps (CPM) that provides retinal vasculature detail similar to flourescein angiography. All of these parameters stand in a direct relationship to the function and therefore the health of the retina, and are known to be degraded in the course of retinal diseases. Detecting changes in retinal function aid early diagnosis and treatment as functional changes often precede structural changes in many retinal disorders.
Stretched Exponential Relaxation in Disordered Complex Systems: Fractal Time Random Walk Model
Institute of Scientific and Technical Information of China (English)
Ekrem Aydmer
2007-01-01
We have analytically derived the relaxation function for one-dimensional disordered complex systems in terms of autocorrelation function of fractal time random walk by using operator formalism. We have shown that the relaxation function has stretched exponential, i.e. the Kohlrausch-Williams-Watts character for a fractal time random walk process.
Thermodynamics with fractal structure, Tsallis statistics and hadrons
Deppman, Airton
2016-01-01
A system presenting fractal structure in its thermodynamical functions is introduced, and it is shown that Tsallis statistics is the correct framework for describing the thermodynamical aspects of such fractal. Its Haussdorf dimension and its Lipshitz-H\\"older exponent are determined in terms of the entropic index $q$. The connections with the intermittency in experimental data is discussed. The thermodynamical aspects of the thermofractal is related to the microscopic interaction of its components through the S-matrix.
Using fractal analysis of thermal signatures for thyroid disease evaluation
Gavriloaia, Gheorghe; Sofron, Emil; Gavriloaia, Mariuca-Roxana; Ghemigean, Adina-Mariana
2010-11-01
The skin is the largest organ of the body and it protects against heat, light, injury and infection. Skin temperature is an important parameter for diagnosing diseases. Thermal analysis is non-invasive, painless, and relatively inexpensive, showing a great potential research. Since the thyroid regulates metabolic rate it is intimately connected to body temperature, more than, any modification of its function generates a specific thermal image on the neck skin. The shapes of thermal signatures are often irregular in size and shape. Euclidean geometry is not able to evaluate their shape for different thyroid diseases, and fractal geometry is used in this paper. Different thyroid diseases generate different shapes, and their complexity are evaluated by specific mathematical approaches, fractal analysis, in order to the evaluate selfsimilarity and lacunarity. Two kinds of thyroid diseases, hyperthyroidism and papillary cancer are analyzed in this paper. The results are encouraging and show the ability to continue research for thermal signature to be used in early diagnosis of thyroid diseases.
Is the human left ventricle partially a fractal pump?
Moore, Brandon; Dasi, Lakshmi
2011-11-01
Ventricular systolic and diastolic dysfunctions represent a large portion of healthcare problems in the United States. Many of these problems are caused and/or characterized by their altered fluid-structure mechanics. The structure of the left ventricle in particular is complex with time dependent multi-scale geometric complexity. At relatively small scales, one facet that is still not well understood is the role of trabeculae in the pumping function of the left ventricle. We utilize fractal geometry tools to help characterize the complexity of the inner surface of the left ventricle at different times during the cardiac cycle. A high-resolution three dimensional model of the time dependent ventricular geometry was constructed from computed tomography (CT) images in a human. The scale dependent fractal dimension of the ventricle was determined using the box-counting algorithm over the cardiac cycle. It is shown that the trabeculae may indeed play an integral role in the biomechanics of pumping by regulating the mechanical leverage available to the cardiac muscle fibers.
Towards Video Quality Metrics Based on Colour Fractal Geometry
Directory of Open Access Journals (Sweden)
Richard Noël
2010-01-01
Full Text Available Vision is a complex process that integrates multiple aspects of an image: spatial frequencies, topology and colour. Unfortunately, so far, all these elements were independently took into consideration for the development of image and video quality metrics, therefore we propose an approach that blends together all of them. Our approach allows for the analysis of the complexity of colour images in the RGB colour space, based on the probabilistic algorithm for calculating the fractal dimension and lacunarity. Given that all the existing fractal approaches are defined only for gray-scale images, we extend them to the colour domain. We show how these two colour fractal features capture the multiple aspects that characterize the degradation of the video signal, based on the hypothesis that the quality degradation perceived by the user is directly proportional to the modification of the fractal complexity. We claim that the two colour fractal measures can objectively assess the quality of the video signal and they can be used as metrics for the user-perceived video quality degradation and we validated them through experimental results obtained for an MPEG-4 video streaming application; finally, the results are compared against the ones given by unanimously-accepted metrics and subjective tests.
Retinal vascular fractals predict long-term microvascular complications in type 1 diabetes mellitus
DEFF Research Database (Denmark)
Broe, Rebecca; Rasmussen, Malin L; Frydkjaer-Olsen, Ulrik
2014-01-01
AIMS/HYPOTHESIS: Fractal analysis of the retinal vasculature provides a global measure of the complexity and density of retinal vessels summarised as a single variable: the fractal dimension. We investigated fractal dimensions as long-term predictors of microvasculopathy in type 1 diabetes. METHODS......: We included 180 patients with type 1 diabetes in a 16 year follow-up study. In baseline retinal photographs (from 1995), all vessels in a zone 0.5-2.0 disc diameters from the disc margin were traced using Singapore Institute Vessel Assessment-Fractal image analysis software. Artefacts were removed...... by a certified grader, and fractal dimensions were calculated using the box-counting method. At follow-up (in 2011), diabetic neuropathy, nephropathy and proliferative retinopathy were assessed and related to baseline fractal dimensions in multiple regressions adjusted for sex and baseline age, diabetes duration...
DEFF Research Database (Denmark)
Mäkikallio, T H; Høiber, S; Køber, L;
1999-01-01
A number of new methods have been recently developed to quantify complex heart rate (HR) dynamics based on nonlinear and fractal analysis, but their value in risk stratification has not been evaluated. This study was designed to determine whether selected new dynamic analysis methods of HR.......17, 95% confidence interval 1.96 to 5.15, p negative predictive accuracies of 65% and 86%, respectively. In the multivariable Cox proportional hazards analysis, mortality was independently predicted by the reduced exponent alpha (p
Characterisation of human non-proliferative diabetic retinopathy using the fractal analysis
Institute of Scientific and Technical Information of China (English)
Stefan; Tǎlu; Dan; Mihai; Cǎlugǎru; Carmen; Alina; Lupascu
2015-01-01
· AIM: To investigate and quantify changes in the branching patterns of the retina vascular network in diabetes using the fractal analysis method.·METHODS: This was a clinic-based prospective study of 172 participants managed at the Ophthalmological Clinic of Cluj-Napoca, Romania, between January 2012 and December 2013. A set of 172 segmented and skeletonized human retinal images, corresponding to both normal(24 images) and pathological(148 images)states of the retina were examined. An automatic unsupervised method for retinal vessel segmentation was applied before fractal analysis. The fractal analyses of the retinal digital images were performed using the fractal analysis software Image J. Statistical analyses were performed for these groups using Microsoft Office Excel2003 and Graph Pad In Stat software.·RESULTS: It was found that subtle changes in the vascular network geometry of the human retina are influenced by diabetic retinopathy(DR) and can be estimated using the fractal geometry. The average of fractal dimensions D for the normal images(segmented and skeletonized versions) is slightly lower than the corresponding values of mild non-proliferative DR(NPDR) images(segmented and skeletonized versions).The average of fractal dimensions D for the normal images(segmented and skeletonized versions) is higher than the corresponding values of moderate NPDR images(segmented and skeletonized versions). The lowestvalues were found for the corresponding values of severe NPDR images(segmented and skeletonized versions).· CONCLUSION: The fractal analysis of fundus photographs may be used for a more complete understanding of the early and basic pathophysiological mechanisms of diabetes. The architecture of the retinal microvasculature in diabetes can be quantitative quantified by means of the fractal dimension.Microvascular abnormalities on retinal imaging may elucidate early mechanistic pathways for microvascular complications and distinguish patients with DR from
Fractal characteristics of fracture morphology of steels irradiated with high-energy ions
Energy Technology Data Exchange (ETDEWEB)
Xian, Yongqiang; Liu, Juan [Institute of Modern Physics, Chinese Academy of Science, Lanzhou 730000 (China); University of Chinese Academy of Science, Beijing 100049 (China); Zhang, Chonghong, E-mail: c.h.zhang@impcas.ac.cn [Institute of Modern Physics, Chinese Academy of Science, Lanzhou 730000 (China); Chen, Jiachao [Paul Scherrer Institute, Villigen PSI (Switzerland); Yang, Yitao; Zhang, Liqing; Song, Yin [Institute of Modern Physics, Chinese Academy of Science, Lanzhou 730000 (China)
2015-06-15
Highlights: • Fractal dimensions of fracture surfaces of steels before and after irradiation were calculated. • Fractal dimension can effectively describe change of fracture surfaces induced by irradiation. • Correlation of change of fractal dimension with embrittlement of irradiated steels is discussed. - Abstract: A fractal analysis of fracture surfaces of steels (a ferritic/martensitic steel and an oxide-dispersion-strengthened ferritic steel) before and after the irradiation with high-energy ions is presented. Fracture surfaces were acquired from a tensile test and a small-ball punch test (SP). Digital images of the fracture surfaces obtained from scanning electron microscopy (SEM) were used to calculate the fractal dimension (FD) by using the pixel covering method. Boundary of binary image and fractal dimension were determined with a MATLAB program. The results indicate that fractal dimension can be an effective parameter to describe the characteristics of fracture surfaces before and after irradiation. The rougher the fracture surface, the larger the fractal dimension. Correlation of the change of fractal dimension with the embrittlement of the irradiated steels is discussed.
Boyko, Anton N.; Pyatilova, Olga V.; Kalmykov, Rustam M.; Gaev, Dahir S.; Timoshenkov, Sergei P.; Gavrilov, Sergei A.
2016-12-01
Study of new materials and composites based on porous silicon is of great interest for electronics and microelectronics industry. Functional characteristics of structured layers are closely associated with their morphology properties and treatment conditions correspondently. In this work a porous silicon layers formed by metal-assisted chemical etching (MACE) with the use of gas adsorption-desorption method, scanning electron microscopy (SEM) and fractal geometry have been examined. Specific surface area given by multi-point BET method was about of 7 m2/g and 13 m2/g for n-Si and p-Si specimens correspondently. Surface fractal dimension Ds was estimated for p-type mesoporous silicon from BET results using Neimark's thermodynamic approach, the value is Ds=2.86. "Slit islands" Mandelbrot's algorithm was applied for analysis of SEM images and calculations of surface fractal dimension Ds, computation gives Ds = 2.52 for n-Si sample and Ds = 2.84 for p-Si sample. The study testified the fractal nature of porous layers formed by MACE and exhibits correlation between different methods of fractal dimension estimation. The results can be applied for improvement of methods of structured solids characterization.
Treatment assessment of radiotherapy using MR functional quantitative imaging
Institute of Scientific and Technical Information of China (English)
Zheng; Chang; Chunhao; Wang
2015-01-01
Recent developments in magnetic resonance(MR) functional quantitative imaging have made it a potentially powerful tool to assess treatment response in radiation therapy. With its abilities to capture functional information on underlying tissue characteristics, MR functional quantitative imaging can be valuable in assessing treatment response and as such to optimize therapeutic outcome. Various MR quantitative imaging techniques, including diffusion weighted imaging, diffusion tensor imaging, MR spectroscopy and dynamic contrastenhanced imaging, have been investigated and found useful for assessment of radiotherapy. However, various aspects including data reproducibility, interpretation of biomarkers, image quality and data analysis impose challenges on applications of MR functional quantitative imaging in radiotherapy assessment. All of these challenging issues shall be addressed to help us understand whether MR functional quantitative imaging is truly beneficial and contributes to future development of radiotherapy. It is evident that individualized therapy is the future direction of patient care. MR functional quantitative imaging might serves as an indispensable tool towards this promising direction.
Fractal analysis of lumbar vertebral cancellous bone architecture.
Feltrin, G P; Macchi, V; Saccavini, C; Tosi, E; Dus, C; Fassina, A; Parenti, A; De Caro, R
2001-11-01
Osteoporosis is characterized by bone mineral density (BMD) decreasing and spongy bone rearrangement with consequent loss of elasticity and increased bone fragility. Quantitative computed tomography (QCT) quantifies bone mineral content but does not describe spongy architecture. Analysis of trabecular pattern may provide additional information to evaluate osteoporosis. The aim of this study was to determine whether the fractal analysis of the microradiography of lumbar vertebrae provides a reliable assessment of bone texture, which correlates with the BMD. The lumbar segment of the spine was removed from 22 cadavers with no history of back pain and examined with standard x-ray, traditional tomography, and quantitative computed tomography to measure BMD. The fractal dimension, which quantifies the image fractal complexity, was calculated on microradiographs of axial sections of the fourth lumbar vertebra to determine its characteristic spongy network. The relationship between the values of the BMD and those of the fractal dimension was evaluated by linear regression and a statistically significant correlation (R = 0.96) was found. These findings suggest that the application of fractal analysis to radiological analyses can provide valuable information on the trabecular pattern of vertebrae. Thus, fractal dimensions of trabecular bone structure should be considered as a supplement to BMD evaluation in the assessment of osteoporosis.
Fractal analysis: methodologies for biomedical researchers.
Ristanović, Dusan; Milosević, Nebojsa T
2012-01-01
Fractal analysis has become a popular method in all branches of scientific investigations including biology and medicine. Although there is a growing interest in the application of fractal analysis in biological sciences, questions about the methodology of fractal analysis have partly restricted its wider and comprehensible application. It is a notable fact that fractal analysis is derived from fractal geometry, but there are some unresolved issues that need to be addressed. In this respect, we discuss several related underlying principles for fractal analysis and establish the meaningful relationship between fractal analysis and fractal geometry. Since some concepts in fractal analysis are determined descriptively and/or qualitatively, this paper provides their exact mathematical definitions or explanations. Another aim of this study is to show that nowadays fractal analysis is an independent mathematical and experimental method based on Mandelbrot's fractal geometry, Euclidean traditiontal geometry and Richardson's coastline method.
Origins of fractality in the growth of complex networks
Song, Chaoming; Havlin, Shlomo; Makse, Hernán A.
2006-04-01
Complex networks from such different fields as biology, technology or sociology share similar organization principles. The possibility of a unique growth mechanism promises to uncover universal origins of collective behaviour. In particular, the emergence of self-similarity in complex networks raises the fundamental question of the growth process according to which these structures evolve. Here we investigate the concept of renormalization as a mechanism for the growth of fractal and non-fractal modular networks. We show that the key principle that gives rise to the fractal architecture of networks is a strong effective `repulsion' (or, disassortativity) between the most connected nodes (that is, the hubs) on all length scales, rendering them very dispersed. More importantly, we show that a robust network comprising functional modules, such as a cellular network, necessitates a fractal topology, suggestive of an evolutionary drive for their existence.
Fractal Dimension as a measure of the scale of Homogeneity
Yadav, Jaswant K; Khandai, Nishikanta
2010-01-01
In the multi-fractal analysis of large scale matter distribution, the scale of transition to homogeneity is defined as the scale above which the fractal dimension of underlying point distribution is equal to the ambient dimension of the space in which points are distributed. With finite sized weakly clustered distribution of tracers obtained from galaxy redshift surveys it is difficult to achieve this equality. Recently we have defined the scale of homogeneity to be the scale above which the deviation of fractal dimension from the ambient dimension becomes smaller than the statistical dispersion. In this paper we use the relation between the fractal dimensions and the correlation function to compute the dispersion for any given model in the limit of weak clustering amplitude. We compare the deviation and dispersion for the LCDM model and discuss the implication of this comparison for the expected scale of homogeneity in the concordant model of cosmology. We estimate the upper limit to the scale of homogeneity...
Functional CT imaging of prostate cancer
Henderson, Elizabeth; Milosevic, Michael F.; Haider, Masoom A.; Yeung, Ivan W. T.
2003-09-01
The purpose of this paper is to investigate the distribution of blood flow (F), mean capillary transit time (Tc), capillary permeability (PS) and blood volume (vb) in prostate cancer using contrast-enhanced CT. Nine stage T2-T3 prostate cancer patients were enrolled in the study. Following bolus injection of a contrast agent, a time series of CT images of the prostate was acquired. Functional maps showing the distribution of F, Tc, PS and vb within the prostate were generated using a distributed parameter tracer kinetic model, the adiabatic approximation to the tissue homogeneity model. The precision of the maps was assessed using covariance matrix analysis. Finally, maps were compared to the findings of standard clinical investigations. Eight of the functional maps demonstrated regions of increased F, PS and vb, the locations of which were consistent with the results of standard clinical investigations. However, model parameters other than F could only be measured precisely within regions of high F. In conclusion functional CT images of cancer-containing prostate glands demonstrate regions of elevated F, PS and vb. However, caution should be used when applying a complex tracer kinetic model to the study of prostate cancer since not all parameters can be measured precisely in all areas.
Seven topics in functional magnetic resonance imaging.
Bandettini, Peter A
2009-09-01
Functional MRI (fMRI) is a non-invasive brain imaging methodology that started in 1991 and allows human brain activation to be imaged at high resolution within only a few minutes. Because it has extremely high sensitivity, is relatively easy to implement, and can be performed on most standard clinical MRI scanners. It continues to grow at an explosive rate throughout the world. Over the years, at any given time, fMRI has been defined by only a handful of major topics that have been the focus of researchers using and developing the methodology. In this review, I attempt to take a snapshot of the field of fMRI as it is in mid-2009 by discussing the seven topics that I feel are most on the minds of fMRI researchers. The topics are, in no particular order or grouping: (1) Clinical impact, (2) Utilization of individual functional maps, (3) fMRI signal interpretation, (4) Pattern effect mapping and decoding, (5) Endogenous oscillations, (6) MRI technology, and (7) Alternative functional contrast mechanisms. Most of these topics are highly interdependent, each advancing as the others advance. While most fMRI involves applications towards clinical or neuroscience questions, all applications are fundamentally dependent on advances in basic methodology as well as advances in our understanding of the relationship between neuronal activity and fMRI signal changes. This review neglects almost completely an in-depth discussion of applications. Rather the discussions are on the methods and interpretation.
Infrared Imaging System for Studying Brain Function
Mintz, Frederick; Mintz, Frederick; Gunapala, Sarath
2007-01-01
A proposed special-purpose infrared imaging system would be a compact, portable, less-expensive alternative to functional magnetic resonance imaging (fMRI) systems heretofore used to study brain function. Whereas a typical fMRI system fills a large room, and must be magnetically isolated, this system would fit into a bicycle helmet. The system would include an assembly that would be mounted inside the padding in a modified bicycle helmet or other suitable headgear. The assembly would include newly designed infrared photodetectors and data-acquisition circuits on integrated-circuit chips on low-thermal-conductivity supports in evacuated housings (see figure) arranged in multiple rows and columns that would define image coordinates. Each housing would be spring-loaded against the wearer s head. The chips would be cooled by a small Stirling Engine mounted contiguous to, but thermally isolated from, the portions of the assembly in thermal contact with the wearer s head. Flexible wires or cables for transmitting data from the aforementioned chips would be routed to an integrated, multichannel transmitter and thence through the top of the assembly to a patch antenna on the outside of the helmet. The multiple streams of data from the infrared-detector chips would be sent to a remote site, where they would be processed, by software, into a three-dimensional display of evoked potentials that would represent firing neuronal bundles and thereby indicate locations of neuronal activity associated with mental or physical activity. The 3D images will be analogous to current fMRI images. The data would also be made available, in real-time, for comparison with data in local or internationally accessible relational databases that already exist in universities and research centers. Hence, this system could be used in research on, and for the diagnosis of response from the wearer s brain to physiological, psychological, and environmental changes in real time. The images would also be
Static friction between rigid fractal surfaces.
Alonso-Marroquin, Fernando; Huang, Pengyu; Hanaor, Dorian A H; Flores-Johnson, E A; Proust, Gwénaëlle; Gan, Yixiang; Shen, Luming
2015-09-01
Using spheropolygon-based simulations and contact slope analysis, we investigate the effects of surface topography and atomic scale friction on the macroscopically observed friction between rigid blocks with fractal surface structures. From our mathematical derivation, the angle of macroscopic friction is the result of the sum of the angle of atomic friction and the slope angle between the contact surfaces. The latter is obtained from the determination of all possible contact slopes between the two surface profiles through an alternative signature function. Our theory is validated through numerical simulations of spheropolygons with fractal Koch surfaces and is applied to the description of frictional properties of Weierstrass-Mandelbrot surfaces. The agreement between simulations and theory suggests that for interpreting macroscopic frictional behavior, the descriptors of surface morphology should be defined from the signature function rather than from the slopes of the contacting surfaces.
Brothers, Harlan J.
2015-03-01
Benoit Mandelbrot always had a strong feeling that music could be viewed from a fractal perspective. However, without our eyes to guide us, how do we gain this perspective? Here we discuss precisely what it means to say that a piece of music is fractal.
Directory of Open Access Journals (Sweden)
Alexander J. Bies
2016-07-01
Full Text Available Two measures are commonly used to describe scale-invariant complexity in images: fractal dimension (D and power spectrum decay rate (β. Although a relationship between these measures has been derived mathematically, empirical validation across measurements is lacking. Here, we determine the relationship between D and β for 1- and 2-dimensional fractals. We find that for 1-dimensional fractals, measurements of D and β obey the derived relationship. Similarly, in 2-dimensional fractals, measurements along any straight-line path across the fractal’s surface obey the mathematically derived relationship. However, the standard approach of vision researchers is to measure β of the surface after 2-dimensional Fourier decomposition rather than along a straight-line path. This surface technique provides measurements of β that do not obey the mathematically derived relationship with D. Instead, this method produces values of β that imply that the fractal’s surface is much smoother than the measurements along the straight lines indicate. To facilitate communication across disciplines, we provide empirically derived equations for relating each measure of β to D. Finally, we discuss implications for future research on topics including stress reduction and the perception of motion in the context of a generalized equation relating β to D.
Image Segmentation Using Two Step Splitting Function
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Gopal Kumar Jha
2013-12-01
Full Text Available Image processing and computer vision is widely using Level Set Method (LSM. In conventional level set formulation, irregularities are developed during evolution of level set function, which cause numerical errors and eventually destroy the stability of the evolution. Therefore a numerical remedy called re-initialization is typically applied periodically to replace the degraded level set function. However re –initialization raises serious problem that is when and how it should be performed and also affects numerical accuracy in an undesirable way. To overcome this drawback of re-initialization process, a new variation level set formulation called Distance regularization level set evolution (DRLSE is introduced in which the regularity of the level set function is internally maintained during the level set evolution. DRLSE allows more general and effective initialization of the level set function. But DRLSE uses relatively large number of steps to ensure efficient numerical accuracy. Here in this thesis we are implementing faster and equally efficient computation technique called two step splitting method (TSSM. TSSM is physio-chemical reaction diffusion equation in which firstly LSE equation get iterated and then regularize the level set function from the first step to ensure the stability and hence re-initialization is completely eliminated from LSE which also satisfy DRLSE.
Entropy computing via integration over fractal measures.
Słomczynski, Wojciech; Kwapien, Jarosław; Zyczkowski, Karol
2000-03-01
We discuss the properties of invariant measures corresponding to iterated function systems (IFSs) with place-dependent probabilities and compute their Renyi entropies, generalized dimensions, and multifractal spectra. It is shown that with certain dynamical systems, one can associate the corresponding IFSs in such a way that their generalized entropies are equal. This provides a new method of computing entropy for some classical and quantum dynamical systems. Numerical techniques are based on integration over the fractal measures. (c) 2000 American Institute of Physics.
Combinatorial fractal Brownian motion model
Institute of Scientific and Technical Information of China (English)
朱炬波; 梁甸农
2000-01-01
To solve the problem of how to determine the non-scaled interval when processing radar clutter using fractal Brownian motion (FBM) model, a concept of combinatorial FBM model is presented. Since the earth (or sea) surface varies diversely with space, a radar clutter contains several fractal structures, which coexist on all scales. Taking the combination of two FBMs into account, via theoretical derivation we establish a combinatorial FBM model and present a method to estimate its fractal parameters. The correctness of the model and the method is proved by simulation experiments and computation of practial data. Furthermore, we obtain the relationship between fractal parameters when processing combinatorial model with a single FBM model. Meanwhile, by theoretical analysis it is concluded that when combinatorial model is observed on different scales, one of the fractal structures is more obvious.
Requirements for effective functional breast imaging
Weinberg, I. N.; Zawarzin, V.; Adler, L. P.; Pani, R.; DeVincentis, G.; Khalkhali, I.; Vargas, H.; Venegas, R.; Kim, S. C.; Bakale, G.; Levine, E.; Perrier, N.; Freimanis, R. I.; Lesko, N. M.; Newman, D. P.; Geisinger, K. R.; Berg, W. A.; Masood, S.
2003-01-01
Most nuclear medicine physicists were trained on devices aimed at functional neuroimaging. The clinical goals of brain-centered devices differ dramatically from the parameters needed to be useful in the breast clinic. We will discuss similarities and differences that impact on design considerations, and describe our latest generation of positron emission mammography and intraoperative products. Source of physiologic contrast: Clinical neuroimaging depends on flow agents to detect the presence of breaks in the blood-brain barrier. Breast flow agents are nonspecific, and may miss preinvasive lesions. Resolution: Brain cancers are generally diagnosed at late stages, so resolution is not so critical. Detecting early breast cancers, and specifying margins for surgery requires 3 mm spatial resolution or better. Prevalence: Primary brain cancer is uncommon, and lesions mimicking brain cancer are rare. Primary breast cancer is common, and benign lesions are even more common, so specificity and biopsy capability are very important. Anatomic references: Brain structure is standard, while breast structure is highly variable, requiring immobilization/compression for physiologic imaging and biopsy. Surgery: Complete cancer resections for brain are very rare, but are possible for breast with appropriate imaging guidance, implying the need for rapid and reliable imaging. To summarize, the breast clinic needs a rapid and highly sensitive method of assessing breast physiology, compatible with biopsy and surgery. Positron emission mammography devices, in handheld and X-ray platform based configurations, are ideal for this mission.
Vialidad, conectividad y fractales
Pineda Paz, Eduardo; Guerrero Torrenegra, Alejandro
2014-01-01
La morfología urbana es posible analizarla mediante ecuaciones no lineales que aparentemente reflejan el comportamiento del hombre. La teoría del caos, la incertidumbre y los fractales, aportan nuevas posibilidades al planificador urbano. El estudio es descriptivo y analítico, siguiendo pautas fenomenológicas, combinando teoría y práctica urbanística, con matemática sencilla. La parroquia Olegario Villalobos de Maracaibo es el caso de estudio. La investigación abordó la dimensión ...
Directory of Open Access Journals (Sweden)
2006-01-01
Full Text Available The dynamics of complex cubic polynomials have been studied extensively in the recent years. The main interest in this work is to focus on the Julia sets in the dynamical plane, and then is consecrated to the study of several topics in more detail. Newton's method is considered since it is the main tool for finding solutions to equations, which leads to some fantastic images when it is applied to complex functions and gives rise to a chaotic sequence.
Clinical application of functional magnetic resonance imaging
Alwatban, A Z W
2002-01-01
The work described in this thesis was carried out at the Magnetic Resonance Centre of the University of Nottingham during the time from May 1998 to April 2001, and is the work of the except where indicated by reference. The main source of signal changes in functional magnetic resonance imaging (fMRJ) is the fluctuation of paramagnetic deoxyhaemoglobin in the venous blood during different states of functional performance. For the work of this thesis, fMRI studies were carried out using a 3 T MR system with an echo planar imaging (EPI) pulse sequence. Hearing research utilising fMRI has been previously reported in normal subjects. Hearing fMRI is normally performed by stimulating the auditory cortex via an acoustic task presentation such as music, tone, etc. However, performing the same research on deaf subjects requires special equipment to be designed to allow direct stimulation of the auditory nerve. In this thesis, a new method of direct electrical stimulation of the auditory nerve is described that uses a ...
Measuring border irregularities of skin lesions using fractal dimensions
Ng, Vincent T. Y.; Lee, Tim K.
1996-09-01
Malignant melanoma is the most common cancer in people less than 35 years of age and incident rates are increasing by approximately 5 percent per annum in many white populations, including British Columbia, Canada. In 1994, a clinical study has been established to digitize melanocytic lesions under a controlled environment. Lesions are digitized from patients who are referred to the Colored Pigment Lesion Clinic in the University of British Columbia. In this paper, we investigate how to use fractal dimensions (FDs) in measuring the irregularity of a skin lesion. In a previous project, we have experimented with 6 different methods to calculate fractal dimensions on a small number of images of skin lesions, and the simple box-counting method performed the best. However, the method did not exploit the intensity information of the images. With the new set of images which are digitized under the controlled environment, we utilize the differential box counting method to exploit such information. Four FD measures, including the direct FD, the horizontal and the vertical smoothing FDs, and the multi- fractal dimension of order two, are calculated based on the original color images. In addition, these 4 FD features are repeatedly calculate for the blue band of the images. This paper reports the different features through the calculations of the fractal dimensions and compares their differentiation power in the use of diagnosis of images of skin lesions.
Analysis of Fractional Flow for Transient Two-Phase Flow in Fractal Porous Medium
Lu, Ting; Duan, Yonggang; Fang, Quantang; Dai, Xiaolu; Wu, Jinsui
2016-03-01
Prediction of fractional flow in fractal porous medium is important for reservoir engineering and chemical engineering as well as hydrology. A physical conceptual fractional flow model of transient two-phase flow is developed in fractal porous medium based on the fractal characteristics of pore-size distribution and on the approximation that porous medium consist of a bundle of tortuous capillaries. The analytical expression for fractional flow for wetting phase is presented, and the proposed expression is the function of structural parameters (such as tortuosity fractal dimension, pore fractal dimension, maximum and minimum diameters of capillaries) and fluid properties (such as contact angle, viscosity and interfacial tension) in fractal porous medium. The sensitive parameters that influence fractional flow and its derivative are formulated, and their impacts on fractional flow are discussed.
Lin, Guoxing
2016-01-01
Pulsed field gradient (PFG) has been increasingly employed to study anomalous diffusions in Nuclear Magnetic Resonance (NMR) and Magnetic Resonance Imaging (MRI). However, the analysis of PFG anomalous diffusion is complicated. In this paper, a fractal derivative model based modified Gaussian phase distribution method is proposed to describe PFG anomalous diffusion. By using the phase distribution obtained from the effective phase shift diffusion method based on fractal derivatives, and employing some of the traditional Gaussian phase distribution approximation techniques, a general signal attenuation expression for free fractional diffusion is derived. This expression describes a stretched exponential function based attenuation, which is distinct from both the exponential attenuation for normal diffusion obtained from conventional Gaussian phase distribution approximation, and the Mittag-Leffler function based attenuation for anomalous diffusion obtained from fractional derivative. The obtained signal attenu...
Institute of Scientific and Technical Information of China (English)
CEN Wei; YANG ShiFeng; XUE Rong; XU RiWei; YU DingSheng
2007-01-01
Surface morphologies of supported polyethylene (PE) catalysts are investigated by an approach combining fractal with wavelet. The multiscale edge (detail) pictures of catalyst surface are extracted by wavelet transform modulus maxima (WTMM) method. And, the distribution of edge points on the edge image at every scale is studied with fractal and multifractal method. Furthermore, the singularity intensity distribution of edge points in the PE catalyst is analyzed by multifractal spectrum based on WTMM. The results reveal that the fractal dimension values and multifractal spectrums of edge images at small scales have a good relation with the activity and surface morphology of PE catalyst. Meanwhile the catalyst exhibiting the higher activity shows the wider singular strength span of multifractal spectrum based on WTMM, as well as the more edge points with the higher singular intensity. The research on catalyst surface morphology with hybrid fractal and wavelet method exerts the superiorities of wavelet and fractal theories and offers a thought for studying solid surfaces morphologies.
Patricio, Pedro; Duarte, Jorge; Januario, Cristina
2015-01-01
We investigate the rheology of a fractal network, in the framework of the linear theory of viscoelasticity. We identify each segment of the network with a simple Kelvin-Voigt element, with a well defined equilibrium length. The final structure retains the elastic characteristics of a solid or a gel. By considering a very simple regular self-similar structure of segments in series and in parallel, in 1, 2 or 3 dimensions, we are able to express the viscoelasticity of the network as an effective generalised Kelvin-Voigt model with a power law spectrum of retardation times, $\\phi\\sim\\tau^{\\alpha-1}$. We relate the parameter $\\alpha$ with the fractal dimension of the gel. In some regimes ($0<\\alpha<1$), we recover the weak power law behaviours of the elastic and viscous moduli with the angular frequencies, $G'\\sim G''\\sim w^\\alpha$, that occur in a variety of soft materials, including living cells. In other regimes, we find different and interesting power laws for $G'$ and $G''$.
A Fractal Perspective on Scale in Geography
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Bin Jiang
2016-06-01
Full Text Available Scale is a fundamental concept that has attracted persistent attention in geography literature over the past several decades. However, it creates enormous confusion and frustration, particularly in the context of geographic information science, because of scale-related issues such as image resolution and the modifiable areal unit problem (MAUP. This paper argues that the confusion and frustration arise from traditional Euclidean geometric thinking, in which locations, directions, and sizes are considered absolute, and it is now time to revise this conventional thinking. Hence, we review fractal geometry, together with its underlying way of thinking, and compare it to Euclidean geometry. Under the paradigm of Euclidean geometry, everything is measurable, no matter how big or small. However, most geographic features, due to their fractal nature, are essentially unmeasurable or their sizes depend on scale. For example, the length of a coastline, the area of a lake, and the slope of a topographic surface are all scale-dependent. Seen from the perspective of fractal geometry, many scale issues, such as the MAUP, are inevitable. They appear unsolvable, but can be dealt with. To effectively deal with scale-related issues, we present topological and scaling analyses illustrated by street-related concepts such as natural streets, street blocks, and natural cities. We further contend that one of the two spatial properties, spatial heterogeneity, is de facto the fractal nature of geographic features, and it should be considered the first effect among the two, because it is global and universal across all scales, which should receive more attention from practitioners of geography.
A Fractal Model for the Transverse Thermal Dispersion Conductivity in Porous Media
Institute of Scientific and Technical Information of China (English)
郁伯铭; 李建华
2004-01-01
A quasi-analytical model, i.e. the fractal model, for the transverse thermal dispersion conductivity in porous media is presented based on the fractal characteristics of tortuous flow paths/streamlines in porous media. The fractal dimension of tortuous flow paths, the spatial deviation velocity and the transverse thermal dispersion conductivity are derived. The proposed model is expressed as functions of the fractal dimension of tortuous flow paths/streamlines, Peclet number, porosity and structural parameters. The present results are compared with those from the existing correlation, and good agreement is found between the present model predictions and those from the existing correlation.
Fractal Structures Driven by Self-Gravity Molecular clouds and the Universe
Combes, F
1998-01-01
In the interstellar medium, as well as in the Universe, large density fluctuations are observed, that obey power-law density distributions and correlation functions. These structures are hierarchical, chaotic, turbulent, but are also self-organizing. The apparent disorder is not random noise, but can be described by a fractal, with a deterministic fractal dimension. We discuss the theories advanced to describe these fractal structures, and in particular a new theory of the self-gravity thermodynamics, that could explain their existence, and predict their fractal dimension. The media obeying scaling laws can be considered critical, as in second order phase transitions for instance.
Fractal characteristics for binary noise radar waveform
Li, Bing C.
2016-05-01
Noise radars have many advantages over conventional radars and receive great attentions recently. The performance of a noise radar is determined by its waveforms. Investigating characteristics of noise radar waveforms has significant value for evaluating noise radar performance. In this paper, we use binomial distribution theory to analyze general characteristics of binary phase coded (BPC) noise waveforms. Focusing on aperiodic autocorrelation function, we demonstrate that the probability distributions of sidelobes for a BPC noise waveform depend on the distances of these sidelobes to the mainlobe. The closer a sidelobe to the mainlobe, the higher the probability for this sidelobe to be a maximum sidelobe. We also develop Monte Carlo framework to explore the characteristics that are difficult to investigate analytically. Through Monte Carlo experiments, we reveal the Fractal relationship between the code length and the maximum sidelobe value for BPC waveforms, and propose using fractal dimension to measure noise waveform performance.
A TUTORIAL INTRODUCTION TO ADAPTIVE FRACTAL ANALYSIS
Directory of Open Access Journals (Sweden)
Michael A Riley
2012-09-01
Full Text Available The authors present a tutorial description of adaptive fractal analysis (AFA. AFA utilizes an adaptive detrending algorithm to extract globally smooth trend signals from the data and then analyzes the scaling of the residuals to the fit as a function of the time scale at which the fit is computed. The authors present applications to synthetic mathematical signals to verify the accuracy of AFA and demonstrate the basic steps of the analysis. The authors then present results from applying AFA to time series from a cognitive psychology experiment on repeated estimation of durations of time to illustrate some of the complexities of real-world data. AFA shows promise in dealing with many types of signals, but like any fractal analysis method there are special challenges and considerations to take into account, such as determining the presence of linear scaling regions.
The Fractal Dimensions of Complex Networks
Institute of Scientific and Technical Information of China (English)
GUO Long; CAI Xu
2009-01-01
It is shown that many real complex networks share distinctive features,such as the small-world effect and the heterogeneous property of connectivity of vertices,which are different from random networks and regular lattices.Although these features capture the important characteristics of complex networks,their applicability depends on the style of networks.To unravel the universal characteristics many complex networks have in common,we study the fractal dimensions of complex networks using the method introduced by Shanker.We lind that the average 'density' (p(r)) of complex networks follows a better power-law function as a function of distance r with the exponent df,which is defined as the fractal dimension,in some real complex networks.Furthermore,we study the relation between df and the shortcuts Nadd in small-world networks and the size N in regular lattices.Our present work provides a new perspective to understand the dependence of the fractal dimension df on the complex network structure.
Random-fractal Ansatz for the configurations of two-dimensional critical systems
Lee, Ching Hua; Ozaki, Dai; Matsueda, Hiroaki
2016-12-01
Critical systems have always intrigued physicists and precipitated the development of new techniques. Recently, there has been renewed interest in the information contained in the configurations of classical critical systems, whose computation do not require full knowledge of the wave function. Inspired by holographic duality, we investigated the entanglement properties of the classical configurations (snapshots) of the Potts model by introducing an Ansatz ensemble of random fractal images. By virtue of the central limit theorem, our Ansatz accurately reproduces the entanglement spectra of actual Potts snapshots without any fine tuning of parameters or artificial restrictions on ensemble choice. It provides a microscopic interpretation of the results of previous studies, which established a relation between the scaling behavior of snapshot entropy and the critical exponent. More importantly, it elucidates the role of ensemble disorder in restoring conformal invariance, an aspect previously ignored. Away from criticality, the breakdown of scale invariance leads to a renormalization of the parameter Σ in the random fractal Ansatz, whose variation can be used as an alternative determination of the critical exponent. We conclude by providing a recipe for the explicit construction of fractal unit cells consistent with a given scaling exponent.
Fractal analysis of sulphidic mineral
Directory of Open Access Journals (Sweden)
Miklúová Viera
2002-03-01
Full Text Available In this paper, the application of fractal theory in the characterization of fragmented surfaces, as well as the mass-size distributions are discussed. The investigated mineral-chalcopyrite of Slovak provenience is characterised after particle size reduction processes-crushing and grinding. The problem how the different size reduction methods influence the surface irregularities of obtained particles is solved. Mandelbrot (1983, introducing the fractal geometry, offered a new way of characterization of surface irregularities by the fractal dimension. The determination of the surface fractal dimension DS consists in measuring the specific surface by the BET method in several fractions into which the comminuted chalcopyrite is sieved. This investigation shows that the specific surface of individual fractions were higher for the crushed sample than for the short-term (3 min ground sample. The surface fractal dimension can give an information about the adsorption sites accessible to molecules of nitrogen and according to this, the value of the fractal dimension is higher for crushed sample.The effect of comminution processes on the mass distribution of particles crushed and ground in air as well as in polar liquids is also discussed. The estimation of fractal dimensions of particles mass distribution is done on the assumption that the particle size distribution is described by the power-law (1. The value of fractal dimension for the mass distribution in the crushed sample is lower than in the sample ground in air, because it is influenced by the energy required for comminution.The sample of chalcopyrite was ground (10min in ethanol and i-butanol [which according to Ikazaki (1991] are characterized by the parameter µ /V, where µ is its dipole moment and V is the molecular volume. The values of µ /V for the used polar liquids are of the same order. That is why the expressive differences in particle size distributions as well as in the values of
Tan, Wanyu; Li, Yongmei; Tan, Kaixuan; Duan, Xianzhe; Liu, Dong; Liu, Zehua
2016-12-01
Radon diffusion and transport through different media is a complex process affected by many factors. In this study, the fractal theories and field covering experiments were used to study the fractal characteristics of particle size distribution (PSD) of six kinds of geotechnical materials (e.g., waste rock, sand, laterite, kaolin, mixture of sand and laterite, and mixture of waste rock and laterite) and their effects on radon diffusion. In addition, the radon diffusion coefficient and diffusion length were calculated. Moreover, new formulas for estimating diffusion coefficient and diffusion length functional of fractal dimension d of PSD were proposed. These results demonstrate the following points: (1) the fractal dimension d of the PSD can be used to characterize the property of soils and rocks in the studies of radon diffusion behavior; (2) the diffusion coefficient and diffusion length decrease with increasing fractal dimension of PSD; and (3) the effectiveness of final covers in reducing radon exhalation of uranium tailings impoundments can be evaluated on the basis of the fractal dimension of PSD of materials.
Fractal texture analysis of the healing process after bone loss.
Borowska, Marta; Szarmach, Janusz; Oczeretko, Edward
2015-12-01
Radiological assessment of treatment effectiveness of guided bone regeneration (GBR) method in postresectal and postcystal bone loss cases, observed for one year. Group of 25 patients (17 females and 8 males) who underwent root resection with cystectomy were evaluated. The following combination therapy of intraosseous deficits was used, consisting of bone augmentation with xenogenic material together with covering regenerative membranes and tight wound closure. The bone regeneration process was estimated, comparing the images taken on the day of the surgery and 12 months later, by means of Kodak RVG 6100 digital radiography set. The interpretation of the radiovisiographic image depends on the evaluation ability of the eye looking at it, which leaves a large margin of uncertainty. So, several texture analysis techniques were developed and used sequentially on the radiographic image. For each method, the results were the mean from the 25 images. These methods compute the fractal dimension (D), each one having its own theoretic basis. We used five techniques for calculating fractal dimension: power spectral density method, triangular prism surface area method, blanket method, intensity difference scaling method and variogram analysis. Our study showed a decrease of fractal dimension during the healing process after bone loss. We also found evidence that various methods of calculating fractal dimension give different results. During the healing process after bone loss, the surfaces of radiographic images became smooth. The result obtained show that our findings may be of great importance for diagnostic purpose.
Teleseismic receiver functions imaging of Siberia
DEFF Research Database (Denmark)
Soliman, Mohammad Youssof Ahmad; Thybo, Hans; Artemieva, Irina
2014-01-01
be used for determining Moho depth, and are excellent for detecting relatively broad vertical gradients in velocity, such as expected for a thermally controlled LAB. The combination of both types of RFs allows for independent discontinuity models of the same area in different frequency bands using......We map the lithosphere in Siberia by using the available broadband seismic data for calculation of Ps- and Sp-wave receiver functions (RF). RFs show converted waves from discontinuities in the vicinity of the seismic stations. The main objective is to image the Moho and upper mantle discontinuities......, including the lithosphere-asthenosphere boundary (LAB) beneath the study area. We construct the RF using the LQT method (Vinnik, 1977; Kind et al. 1995) in the version by Yuan et al. (1997). Rotation of ray coordinates uses the incidence angles predicted by the AK135 velocity model. This decomposes the wave...
Institute of Scientific and Technical Information of China (English)
李彪; 许贵林; 卢远
2016-01-01
利用南流江流域30 m分辨率的DEM数据，介绍了ArcGIS中进行河网提取的一系列过程，并利用其图解建模工具，提取南流江流域的不同汇流累积面积的水系河网，实现了提取过程的流程化处理。分别统计河源密度和沟壑密度，并分别计算它们与汇流累积面积的几何函数关系，并对其进行二阶求导，确定其二阶导数关系，得到合适的汇流累积阈值，并借助分形分维理论对河网的分维值进行了验证。利用函数关系和分形分维确定汇流累积面积提取水系河网的方法有效地避免了人工选择汇流累积面积的主观性，提高了研究结果的准确性和可靠性，在知道研究流域河网分维值的前提下，可快速获取准确的汇流累计面积阈值。%Using Nanliu river basin 30 m resolution of DEM data, this paper introduces the ArcGIS for river network in extraction of a series of process, and use its graphical modeling tool, and extract the NanLiu river basins of different river confluence area of water system, realizes the extraction process routing process.Statistical heyuan density and gully density respectively, and calculate their geometric function relation with the accumulated flow area, and carries on the second order derivative calculation, determine its second derivative relationship, to get the right bus accumulation threshold, and with the help of fractal dimension fractal theory calculating fractal dimension value of the river network is verified.Function relation and the fractal dimension is used to determine the flow accu-mulation methods of extracting drainage river network area is effective to avoid the subjectivity of the convergence of artificial selection accumulation area and improve the veracity and reliability of the results of the study, under the premise that know river fractal dimen-sion is worth study basin, can quickly get accurate confluence area threshold.
Gray-Scale Image Colorization Using Various Affinity Functions
Directory of Open Access Journals (Sweden)
Imron Rosyadi
2012-02-01
Full Text Available In this paper, we have proposed, implemented, and compared some affinity functions for an image colorization algorithm. The colorization qualityof the proposed affinityfunctions was just slightly behind the original functions, while one of the proposed functions performed faster than the original affinity function. We also implemented the colorization algorithm for coloring an Indonesian historical image.
"General theory of a particle mechanics" arising from a fractal surface
Yefremov, Alexander P
2016-01-01
The logical line is traced of formulation of theory of mechanics founded on the basic correlations of mathematics of hypercomplex numbers and associated geometric images. Namely, it is shown that the physical equations of quantum, classical and relativistic mechanics can be regarded as mathematical consequences of a single condition of stability of exceptional algebras of real, complex and quaternion numbers under transformations of primitive constituents of their units and elements. In the course of the study a notion of basic fractal surface underlying the physical three-dimensional space is introduces, and an original geometric treatment (admitting visualization) of some formerly considered abstract functions (mechanical action, space-time interval) are suggested.
Fractal and Multifractal Time Series
Kantelhardt, Jan W
2008-01-01
Data series generated by complex systems exhibit fluctuations on many time scales and/or broad distributions of the values. In both equilibrium and non-equilibrium situations, the natural fluctuations are often found to follow a scaling relation over several orders of magnitude, allowing for a characterisation of the data and the generating complex system by fractal (or multifractal) scaling exponents. In addition, fractal and multifractal approaches can be used for modelling time series and deriving predictions regarding extreme events. This review article describes and exemplifies several methods originating from Statistical Physics and Applied Mathematics, which have been used for fractal and multifractal time series analysis.
Exterior dimension of fat fractals
Grebogi, C.; Mcdonald, S. W.; Ott, E.; Yorke, J. A.
1985-01-01
Geometric scaling properties of fat fractal sets (fractals with finite volume) are discussed and characterized via the introduction of a new dimension-like quantity which is called the exterior dimension. In addition, it is shown that the exterior dimension is related to the 'uncertainty exponent' previously used in studies of fractal basin boundaries, and it is shown how this connection can be exploited to determine the exterior dimension. Three illustrative applications are described, two in nonlinear dynamics and one dealing with blood flow in the body. Possible relevance to porous materials and ballistic driven aggregation is also noted.
Thermal collapse of snowflake fractals
Gallo, T.; Jurjiu, A.; Biscarini, F.; Volta, A.; Zerbetto, F.
2012-08-01
Snowflakes are thermodynamically unstable structures that would ultimately become ice balls. To investigate their dynamics, we mapped atomistic molecular dynamics simulations of small ice crystals - built as filled von Koch fractals - onto a discrete-time random walk model. Then the walkers explored the thermal evolution of high fractal generations. The in silico experiments showed that the evolution is not entirely random. The flakes step down one fractal generation before forfeiting their architecture. The effect may be used to trace the thermal history of snow.
Moghilevsky, Débora Estela
2011-01-01
A lo largo de los últimos años del siglo veinte se ha desarrollado la teoría de la complejidad. Este modelo relaciona las ciencias duras tales como la matemática, la teoría del caos, la física cuántica y la geometría fractal con las llamadas seudo ciencias. Dentro de este contexto podemos definir la Psicología Fractal como la ciencia que estudia los aspectos psíquicos como dinámicamente fractales.
Forthergillian Lecture. Imaging human brain function.
Frackowiak, R S
The non-invasive brain scanning techniques introduced a quarter of a century ago have become crucial for diagnosis in clinical neurology. They have also been used to investigate brain function and have provided information about normal activity and pathogenesis. They have been used to investigate functional specialization in the brain and how specialized areas communicate to generate complex integrated functions such as speech, memory, the emotions and so on. The phenomenon of brain plasticity is poorly understood and yet clinical neurologists are aware, from everyday observations, that spontaneous recovery from brain lesions is common. An improved understanding of the mechanisms of recovery may generate new therapeutic strategies and indicate ways of modulating mechanisms that promote plastic compensation for loss of function. The main methods used to investigate these issues are positron emission tomography and magnetic resonance imaging (M.R.I.). M.R.I. is also used to map brain structure. The techniques of functional brain mapping and computational morphometrics depend on high performance scanners and a validated set of analytic statistical procedures that generate reproducible data and meaningful inferences from brain scanning data. The motor system presents a good paradigm to illustrate advances made by scanning towards an understanding of plasticity at the level of brain areas. The normal motor system is organized in a nested hierarchy. Recovery from paralysis caused by internal capsule strokes involves functional reorganization manifesting itself as changed patterns of activity in the component brain areas of the normal motor system. The pattern of plastic modification depends in part on patterns of residual or disturbed connectivity after brain injury. Therapeutic manipulations in patients with Parkinson's disease using deep brain stimulation, dopaminergic agents or fetal mesencephalic transplantation provide a means to examine mechanisms underpinning
Clinical application of functional magnetic resonance imaging
Energy Technology Data Exchange (ETDEWEB)
Alwatban, Adnan Z.W
2002-07-01
The work described in this thesis was carried out at the Magnetic Resonance Centre of the University of Nottingham during the time from May 1998 to April 2001, and is the work of the author except where indicated by reference. The main source of signal changes in functional magnetic resonance imaging (fMRJ) is the fluctuation of paramagnetic deoxyhaemoglobin in the venous blood during different states of functional performance. For the work of this thesis, fMRI studies were carried out using a 3 T MR system with an echo planar imaging (EPI) pulse sequence. Hearing research utilising fMRI has been previously reported in normal subjects. Hearing fMRI is normally performed by stimulating the auditory cortex via an acoustic task presentation such as music, tone, etc. However, performing the same research on deaf subjects requires special equipment to be designed to allow direct stimulation of the auditory nerve. In this thesis, a new method of direct electrical stimulation of the auditory nerve is described that uses a transtympanic electrode implanted onto the surface of the cochlea. This approach would however, result in electromotive forces (EMFs) being induced by the time varying magnetic field, which would lead to current flow and heating, as well as deflection of the metallic electrode within the static magnetic field, and image distortion due to the magnetic susceptibility difference. A gold-plated tungsten electrode with a zero magnetic susceptibility was developed to avoid image distortion. Used with carbon leads and a carbon reference pad, it enabled safe, distortion-free fMRI studies of deaf subjects. The study revealed activation of the primary auditory cortex. This fMRI procedure can be used to demonstrate whether the auditory pathway is fully intact, and may provide a useful method for pre-operative assessment of candidates for cochlear implantation. Glucose is the energy source on which the function of the human brain is entirely dependent. Failure to
On the fractal morphology of combustion-generated soot aggregates
Energy Technology Data Exchange (ETDEWEB)
Koylu, U.O. [Yale Univ., New Haven, CT (United States)
1995-12-31
The fractal properties of soot aggregates were investigated using ex-situ and in-situ experimental methods as well as computer simulations. Ex-situ experiments involved thermophoretic sampling and analysis by transmission electron microscopy (TEM), while in-situ measurements employed angular static light scattering and data inversion based on Rayleigh-Debye-Gans (RDG) approximation. Computer simulations used a sequential algorithm which mimics mass fractal-like structures. So from a variety of hydrocarbon-fueled laminar and turbulent nonpremixed flame environments were considered in the present study. The TEM analysis of projected soot images sampled from fuel-rich conditions of buoyant and weakly-buoyant laminar flames indicated that the fractal dimension of soot was relatively independent of position in flames, fuel type and flame condition. These measurements yielded an average fractal dimension of 1.8, although other structure parameters such as the primary particle diameters and number of primary particles in aggregates had wide range of values. Fractal prefactor (lacunarity) was also measured for soot sampled from the fuel-lean conditions of turbulent flames, considering the actual morphology by tilting the samples during TEM analysis. These measurements yielded a fractal dimension of 1.65 and a lacunarity of 8.5, with experimental uncertainties (95% confidence) of 0.08 and 0.5, respectively. Relationships between the actual and projected structure properties of soot were also developed by combining TEM observations with numerical simulations. Practical approximate formulae were suggested to find radius of gyration of an aggregate from its maximum dimension, and number of primary particles in an aggregate from projected area. Finally, the fractal dimension and lacunarity of soot were obtained using light scattering for the same conditions of the above TEM measurements.
Three-dimensional reconstruction of functional brain images
Energy Technology Data Exchange (ETDEWEB)
Inoue, Masato; Shoji, Kazuhiko; Kojima, Hisayoshi; Hirano, Shigeru; Naito, Yasushi; Honjo, Iwao [Kyoto Univ. (Japan)
1999-08-01
We consider PET (positron emission tomography) measurement with SPM (Statistical Parametric Mapping) analysis to be one of the most useful methods to identify activated areas of the brain involved in language processing. SPM is an effective analytical method that detects markedly activated areas over the whole brain. However, with the conventional presentations of these functional brain images, such as horizontal slices, three directional projection, or brain surface coloring, makes understanding and interpreting the positional relationships among various brain areas difficult. Therefore, we developed three-dimensionally reconstructed images from these functional brain images to improve the interpretation. The subjects were 12 normal volunteers. The following three types of images were constructed: routine images by SPM, three-dimensional static images, and three-dimensional dynamic images, after PET images were analyzed by SPM during daily dialog listening. The creation of images of both the three-dimensional static and dynamic types employed the volume rendering method by VTK (The Visualization Toolkit). Since the functional brain images did not include original brain images, we synthesized SPM and MRI brain images by self-made C++ programs. The three-dimensional dynamic images were made by sequencing static images with available software. Images of both the three-dimensional static and dynamic types were processed by a personal computer system. Our newly created images showed clearer positional relationships among activated brain areas compared to the conventional method. To date, functional brain images have been employed in fields such as neurology or neurosurgery, however, these images may be useful even in the field of otorhinolaryngology, to assess hearing and speech. Exact three-dimensional images based on functional brain images are important for exact and intuitive interpretation, and may lead to new developments in brain science. Currently, the surface
Fractal structure and fractal dimension determination at nanometer scale
Institute of Scientific and Technical Information of China (English)
张跃; 李启楷; 褚武扬; 王琛; 白春礼
1999-01-01
Three-dimensional fractures of different fractal dimensions have been constructed with successive random addition algorithm, the applicability of various dimension determination methods at nanometer scale has been studied. As to the metallic fractures, owing to the limited number of slit islands in a slit plane or limited datum number at nanometer scale, it is difficult to use the area-perimeter method or power spectrum method to determine the fractal dimension. Simulation indicates that box-counting method can be used to determine the fractal dimension at nanometer scale. The dimensions of fractures of valve steel 5Cr21Mn9Ni4N have been determined with STM. Results confirmed that fractal dimension varies with direction at nanometer scale. Our study revealed that, as to theoretical profiles, the dependence of fractal dimension with direction is simply owing to the limited data set number, i.e. the effect of boundaries. However, the dependence of fractal dimension with direction at nanometer scale in rea
Functional hepatobiliary MR imaging in children
Energy Technology Data Exchange (ETDEWEB)
Tamrazi, Anobel; Vasanawala, Shreyas S. [Stanford University, Department of Radiology, Stanford, CA (United States)
2011-10-15
Clinical application efforts for the hepatocyte-specific MRI contrast agent gadolinium ethoxybenzyl diethylenetriamine pentaacetic acid (Gd-EOB-DTPA) have mainly been directed toward detection and characterization of various hepatic masses in the adult population. Here we report our initial experience with Gd-EOB-DTPA for evaluating congenital and acquired hepatobiliary pathologies in the pediatric population. Twenty-one consecutive children receiving Gd-EOB-DTPA for functional hepatobiliary evaluation at our institution were retrospectively identified with IRB approval. The use of Gd-EOB-DTPA was classified in each case as definite, potential, or no clinical utility, focusing on the clinical value gained beyond traditional noncontrast fluid-sensitive MR cholangiopancreatography (FS-MRCP) and other imaging modalities. Definite added value of Gd-EOB-DTPA was found in 12 patients, with potential value in 4 patients, and no value in 5 patients. Benefit was seen in cases of iatrogenic and non-iatrogenic biliary strictures, perihepatic fluid collections for biliary leak, hepatobiliary dysfunction in the absence of hyperbilirubinemia, and in the functional exclusion of cystic duct occlusion that can be seen in acute cholecystitis. This is the first reported series of children with Gd-EOB-DTPA and this early work suggests potential pediatric applications. (orig.)
Dynamic contact interactions of fractal surfaces
Jana, Tamonash; Mitra, Anirban; Sahoo, Prasanta
2017-01-01
Roughness parameters and material properties have significant influence on the static and dynamic properties of a rough surface. In the present paper, fractal surface is generated using the modified two-variable Weierstrass-Mandelbrot function in MATLAB and the same is imported to ANSYS to construct the finite element model of the rough surface. The force-deflection relationship between the deformable rough fractal surface and a contacting rigid flat is studied by finite element analysis. For the dynamic analysis, the contacting system is represented by a single degree of freedom spring mass-damper-system. The static force-normal displacement relationship obtained from FE analysis is used to determine the dynamic characteristics of the rough surface for free, as well as for forced damped vibration using numerical methods. The influence of fractal surface parameters and the material properties on the dynamics of the rough surface is also analyzed. The system exhibits softening property for linear elastic surface and the softening nature increases with rougher topography. The softening nature of the system increases with increase in tangent modulus value. Above a certain value of yield strength the nature of the frequency response curve is observed to change its nature from softening to hardening.
DEFF Research Database (Denmark)
Malureanu, Radu; Jepsen, Peter Uhd; Xiao, S.
2010-01-01
The concept of metamaterials (MTMs) is acknowledged for providing new horizons for controlling electromagnetic radiations thus their use in frequency ranges otherwise difficult to manage (e.g. THz radiation) broadens our possibility to better understand our world as well as opens the path for new...... frequency range as well as a clear differentiation between one polarisation and another. Based on theoretical predictions we fabricated and measured a fractal based THz metamaterial that shows more than 60% field transmission at around 1THz for TE polarized light while the TM waves have almost 80% field...... wavelength of THz radiation, the resolution requirements for fabrication of metamaterials are within the optical lithography range. However, the high aspect ratio of such structures as well as the substrate thickness pose challenges in the fabrication process. The measurements were made using terahertz time...
Eliazar, Iddo; Klafter, Joseph
2008-09-01
The Central Limit Theorem (CLT) and Extreme Value Theory (EVT) study, respectively, the stochastic limit-laws of sums and maxima of sequences of independent and identically distributed (i.i.d.) random variables via an affine scaling scheme. In this research we study the stochastic limit-laws of populations of i.i.d. random variables via nonlinear scaling schemes. The stochastic population-limits obtained are fractal Poisson processes which are statistically self-similar with respect to the scaling scheme applied, and which are characterized by two elemental structures: (i) a universal power-law structure common to all limits, and independent of the scaling scheme applied; (ii) a specific structure contingent on the scaling scheme applied. The sum-projection and the maximum-projection of the population-limits obtained are generalizations of the classic CLT and EVT results - extending them from affine to general nonlinear scaling schemes.
Diophantine approximations on fractals
Einsiedler, Manfred; Shapira, Uri
2009-01-01
We exploit dynamical properties of diagonal actions to derive results in Diophantine approximations. In particular, we prove that the continued fraction expansion of almost any point on the middle third Cantor set (with respect to the natural measure) contains all finite patterns (hence is well approximable). Similarly, we show that for a variety of fractals in [0,1]^2, possessing some symmetry, almost any point is not Dirichlet improvable (hence is well approximable) and has property C (after Cassels). We then settle by similar methods a conjecture of M. Boshernitzan saying that there are no irrational numbers x in the unit interval such that the continued fraction expansions of {nx mod1 : n is a natural number} are uniformly eventually bounded.
Three-Dimensional Surface Parameters and Multi-Fractal Spectrum of Corroded Steel.
Shanhua, Xu; Songbo, Ren; Youde, Wang
2015-01-01
To study multi-fractal behavior of corroded steel surface, a range of fractal surfaces of corroded surfaces of Q235 steel were constructed by using the Weierstrass-Mandelbrot method under a high total accuracy. The multi-fractal spectrum of fractal surface of corroded steel was calculated to study the multi-fractal characteristics of the W-M corroded surface. Based on the shape feature of the multi-fractal spectrum of corroded steel surface, the least squares method was applied to the quadratic fitting of the multi-fractal spectrum of corroded surface. The fitting function was quantitatively analyzed to simplify the calculation of multi-fractal characteristics of corroded surface. The results showed that the multi-fractal spectrum of corroded surface was fitted well with the method using quadratic curve fitting, and the evolution rules and trends were forecasted accurately. The findings can be applied to research on the mechanisms of corroded surface formation of steel and provide a new approach for the establishment of corrosion damage constitutive models of steel.
Three-Dimensional Surface Parameters and Multi-Fractal Spectrum of Corroded Steel.
Directory of Open Access Journals (Sweden)
Xu Shanhua
Full Text Available To study multi-fractal behavior of corroded steel surface, a range of fractal surfaces of corroded surfaces of Q235 steel were constructed by using the Weierstrass-Mandelbrot method under a high total accuracy. The multi-fractal spectrum of fractal surface of corroded steel was calculated to study the multi-fractal characteristics of the W-M corroded surface. Based on the shape feature of the multi-fractal spectrum of corroded steel surface, the least squares method was applied to the quadratic fitting of the multi-fractal spectrum of corroded surface. The fitting function was quantitatively analyzed to simplify the calculation of multi-fractal characteristics of corroded surface. The results showed that the multi-fractal spectrum of corroded surface was fitted well with the method using quadratic curve fitting, and the evolution rules and trends were forecasted accurately. The findings can be applied to research on the mechanisms of corroded surface formation of steel and provide a new approach for the establishment of corrosion damage constitutive models of steel.
Application of fractal dimensions to study the structure of flocs formed in lime softening process.
Vahedi, Arman; Gorczyca, Beata
2011-01-01
The use of fractal dimensions to study the internal structure and settling of flocs formed in lime softening process was investigated. Fractal dimensions of flocs were measured directly on floc images and indirectly from their settling velocity. An optical microscope with a motorized stage was used to measure the fractal dimensions of lime softening flocs directly on their images in 2 and 3D space. The directly determined fractal dimensions of the lime softening flocs were 1.11-1.25 for floc boundary, 1.82-1.99 for cross-sectional area and 2.6-2.99 for floc volume. The fractal dimension determined indirectly from the flocs settling rates was 1.87 that was different from the 3D fractal dimension determined directly on floc images. This discrepancy is due to the following incorrect assumptions used for fractal dimensions determined from floc settling rates: linear relationship between square settling velocity and floc size (Stokes' Law), Euclidean relationship between floc size and volume, constant fractal dimensions and one primary particle size describing entire population of flocs. Floc settling model incorporating variable floc fractal dimensions as well as variable primary particle size was found to describe the settling velocity of large (>50 μm) lime softening flocs better than Stokes' Law. Settling velocities of smaller flocs (lime floc size in this study indicated that two mechanisms are involved in the formation of these flocs: cluster-cluster aggregation for small flocs (50 μm). Therefore, the relationship between the floc fractal dimension and floc size appears to be determined by floc formation mechanisms.
Familial Essential Tremor Studied With Functional Magnetic Resonance Imaging
Hernandez, A.; Salgado, P.; Gil, A.; Barrios, F. A.
2003-09-01
Functional Magnetic Resonance Imaging has become an important analytical tool to study neurodegenerative diseases. We applied the EPI-BOLD functional Magnetic Resonance Imaging technique to acquire functional images of patients with familial essential tremor (FET) disorder and healthy control volunteers, during a motor task activity. Functional and anatomic images were used to produce the brain activation maps of the patients and volunteers. These functional maps of the primary somatosensorial and motor cortexes of patients and control subjects were compared for functional differences per subject. The averaged functional brain images of eight of each case were acquired were, it can be clearly observed the differences in active zones. The results presented in this work show that there are differences in the functional maps during motor task activation between control subjects and FET patients suggesting a cerebral functional reorganization that can be mapped with BOLD-fMRI.
Fractal geometry and computer graphics
Sakas, Georgios; Peitgen, Heinz-Otto; Englert, Gabriele
1992-01-01
Fractal geometry has become popular in the last 15 years, its applications can be found in technology, science, or even arts. Fractal methods and formalism are seen today as a general, abstract, but nevertheless practical instrument for the description of nature in a wide sense. But it was Computer Graphics which made possible the increasing popularity of fractals several years ago, and long after their mathematical formulation. The two disciplines are tightly linked. The book contains the scientificcontributions presented in an international workshop in the "Computer Graphics Center" in Darmstadt, Germany. The target of the workshop was to present the wide spectrum of interrelationships and interactions between Fractal Geometry and Computer Graphics. The topics vary from fundamentals and new theoretical results to various applications and systems development. All contributions are original, unpublished papers.The presentations have been discussed in two working groups; the discussion results, together with a...
Anomalous diffusion in fractal globules.
Tamm, M V; Nazarov, L I; Gavrilov, A A; Chertovich, A V
2015-05-01
The fractal globule state is a popular model for describing chromatin packing in eukaryotic nuclei. Here we provide a scaling theory and dissipative particle dynamics computer simulation for the thermal motion of monomers in the fractal globule state. Simulations starting from different entanglement-free initial states show good convergence which provides evidence supporting the existence of a unique metastable fractal globule state. We show monomer motion in this state to be subdiffusive described by ⟨X(2)(t)⟩∼t(αF) with αF close to 0.4. This result is in good agreement with existing experimental data on the chromatin dynamics, which makes an additional argument in support of the fractal globule model of chromatin packing.
Fractals endlessy repeated geometrical figures
Lauwerier, Hans
1991-01-01
Provides a basic mathematical introduction to fractal geometry, the mathematics that lie behind chaos theory. This book attempts to communicate the relatively simple understanding of the subject to an audience with a basic mathematical education.
[Modeling continuous scaling of NDVI based on fractal theory].
Luan, Hai-Jun; Tian, Qing-Jiu; Yu, Tao; Hu, Xin-Li; Huang, Yan; Du, Ling-Tong; Zhao, Li-Min; Wei, Xi; Han, Jie; Zhang, Zhou-Wei; Li, Shao-Peng
2013-07-01
Scale effect was one of the very important scientific problems of remote sensing. The scale effect of quantitative remote sensing can be used to study retrievals' relationship between different-resolution images, and its research became an effective way to confront the challenges, such as validation of quantitative remote sensing products et al. Traditional up-scaling methods cannot describe scale changing features of retrievals on entire series of scales; meanwhile, they are faced with serious parameters correction issues because of imaging parameters' variation of different sensors, such as geometrical correction, spectral correction, etc. Utilizing single sensor image, fractal methodology was utilized to solve these problems. Taking NDVI (computed by land surface radiance) as example and based on Enhanced Thematic Mapper Plus (ETM+) image, a scheme was proposed to model continuous scaling of retrievals. Then the experimental results indicated that: (a) For NDVI, scale effect existed, and it could be described by fractal model of continuous scaling; (2) The fractal method was suitable for validation of NDVI. All of these proved that fractal was an effective methodology of studying scaling of quantitative remote sensing.
Spatial Dynamics of Urban Growth Based on Entropy and Fractal Dimension
Chen, Yanguang
2016-01-01
The fractal dimension growth of urban form can be described with sigmoid functions such as logistic function due to squashing effect. The sigmoid curves of fractal dimension suggest a type of spatial replacement dynamics of urban evolution. How to understand the underlying rationale of the fractal dimension curves is a pending problem. This study is based on two previous findings. First, normalized fractal dimension proved to equal normalized spatial entropy; second, a sigmoid function proceeds from an urban-rural interaction model. Defining urban space-filling measurement by spatial entropy, and defining rural space-filling measurement by information gain, we can construct a new urban-rural interaction and coupling model. From this model, we can derive the logistic equation of fractal dimension growth strictly. This indicates that urban growth results from the unity of opposites between spatial entropy increase and information increase. In a city, an increase in spatial entropy is accompanied by a decrease i...
Use of fractal models in the Earth's remote sensing of the arctic zone
Berg, D. B.; Medvedev, A. N.; Manzhurov, I. L.; Taubaev, A. A.
2016-12-01
The development and practical application of new mathematical methods of processing, image analysis and pattern recognition has significant prospects for mapping the Earth from space. In the paper, it is proposed to use the fractal model of the surface contamination distribution, previously developed by the authors, for the analysis of color multispectral satellite images on the example of the territory of the Polar Urals. The research has shown the following: 1) The brightness distribution on remote sensing snapshot has a fractal character. 2) The values of fractal dimension of the territory images in different spectral ranges significantly differ. 3) The hierarchy of geomorphological structures in the range of 13-1700 m may be considered as self-similar. Thus, the proposed method of calculating the fractal dimension value of the snapshot may become one of the informative attributes for remote sensing images interpretation.
Directory of Open Access Journals (Sweden)
Chia-Hung Lin
2010-01-01
Full Text Available This paper proposes combining the biometric fractal pattern and particle swarm optimization (PSO-based classifier for fingerprint recognition. Fingerprints have arch, loop, whorl, and accidental morphologies, and embed singular points, resulting in the establishment of fingerprint individuality. An automatic fingerprint identification system consists of two stages: digital image processing (DIP and pattern recognition. DIP is used to convert to binary images, refine out noise, and locate the reference point. For binary images, Katz's algorithm is employed to estimate the fractal dimension (FD from a two-dimensional (2D image. Biometric features are extracted as fractal patterns using different FDs. Probabilistic neural network (PNN as a classifier performs to compare the fractal patterns among the small-scale database. A PSO algorithm is used to tune the optimal parameters and heighten the accuracy. For 30 subjects in the laboratory, the proposed classifier demonstrates greater efficiency and higher accuracy in fingerprint recognition.
基于子域对角和的快速分形图像编码算法%Fast Fractal Image Coding Algorithm Based on Subregion Diagonal Sum
Institute of Scientific and Technical Information of China (English)
王丽娜; 刘晓东; 贺兴华; 沈灿岭
2011-01-01
To reduce the long encoding time in fractal compression process which limits its various practical applications, the paper proposes a newly-defined subregion diagonal sum of normalized image block.After sorting the blocks in the codebook according to their subregion diagonal sum, the encoder finds out the nearest domain block in sorted codebook to each range block being encoded in the sense of subregion diagonal sum, then the encoder visits the codebook blocks in the vicinity of this nearest domain block to search out the best-matched block.Experimental results show that the proposed algorithm can significantly improve coding speed with the gurantee of decoded image's quality.%为了改进分形图像压缩编码过程耗时过长而影响实用的问题,新定义了子域对角和来描述图像块的特征.算法把码本按照子域对角和特征的大小排序,对每个待编码的Range块,仅在赋序码本中找到与Range块的子域对角和的数值最接近的Domain块,并在此Domain块的邻域内搜索最佳匹配块.实验结果表明,在保证解码图像质量的前提下,该算法较快地提高了编码速度.
Hydrophobicity classification of polymeric materials based on fractal dimension
Directory of Open Access Journals (Sweden)
Daniel Thomazini
2008-12-01
Full Text Available This study proposes a new method to obtain hydrophobicity classification (HC in high voltage polymer insulators. In the method mentioned, the HC was analyzed by fractal dimension (fd and its processing time was evaluated having as a goal the application in mobile devices. Texture images were created from spraying solutions produced of mixtures of isopropyl alcohol and distilled water in proportions, which ranged from 0 to 100% volume of alcohol (%AIA. Based on these solutions, the contact angles of the drops were measured and the textures were used as patterns for fractal dimension calculations.
Steady laminar flow of fractal fluids
Balankin, Alexander S.; Mena, Baltasar; Susarrey, Orlando; Samayoa, Didier
2017-02-01
We study laminar flow of a fractal fluid in a cylindrical tube. A flow of the fractal fluid is mapped into a homogeneous flow in a fractional dimensional space with metric induced by the fractal topology. The equations of motion for an incompressible Stokes flow of the Newtonian fractal fluid are derived. It is found that the radial distribution for the velocity in a steady Poiseuille flow of a fractal fluid is governed by the fractal metric of the flow, whereas the pressure distribution along the flow direction depends on the fractal topology of flow, as well as on the fractal metric. The radial distribution of the fractal fluid velocity in a steady Couette flow between two concentric cylinders is also derived.
Visible parts of fractal percolation
Arhosalo, I; Järvenpää, M; Rams, M; Shmerkin, P
2009-01-01
We study dimensional properties of visible parts of fractal percolation in the plane. Provided that the dimension of the fractal percolation is at least 1, we show that, conditioned on non-extinction, almost surely all visible parts from lines are 1-dimensional. Furthermore, almost all of them have positive and finite Hausdorff measure. We also verify analogous results for visible parts from points. These results are motivated by an open problem on the dimensions of visible parts.
Fractal Geometry of Particle Aggregates Formed in Calcium Sulfite Slurry
Institute of Scientific and Technical Information of China (English)
倪伟敏; 吴忠标; 官宝红; 赵伟荣; 郑平
2007-01-01
The solid-liquid separation is an important operation for the regenerated slurry of dual-alkali FGD system, and calcium sulfite could predominate in particle aggregates of the slurry. The settling velocity of calcium sulfite particles is a key parameter for the solid-liquid separation design. However, the settling velocity predicted by Stokes' Law could be suitable only for a spherical aggregate, but not for the irregular one. In this work, fractal geometry was introduced in order to characterize highly irregular geometric shapes. The sizes of calcium sulfite particle aggregates were analyzed using a metallographic phase microscope and image analysis. The results showed that particle aggregate had fractal features. The fractal dimensions could reveal the characteristics of the aggregates' geometry and aggregation process. An exponential relation between the fractal dimension D2 and the particle size l was determined as AμlD2. According to fractal theory, a parameter can be used to modify Stokes settling velocity close to actual settling velocity. The results could be valuable for the design of solid-liquid separation process.
Evolution of Fractal Parameters through Development Stage of Soil Crust
Ospina, Abelardo; Florentino, Adriana; Tarquis, Ana Maria
2016-04-01
Soil surface characteristics are subjected to changes driven by several interactions between water, air, biotic and abiotic components. One of the examples of such interactions is provided through biological soil crusts (BSC) in arid and semi-arid environments. BSC are communities composed of cyanobacteria, fungi, mosses, lichens, algae and liverworts covering the soil surface and play an important role in ecosystem functioning. The characteristics and formation of these BSC influence the soil hydrological balance, control the mass of eroded sediment, increase stability of soil surface, and influence plant productivity through the modification of nitrogen and carbon cycle. The site of this work is located at Quibor and Ojo de Agua (Lara state, Venezuela). The Quibor Depression in Venezuela is a major agricultural area being at semi-arid conditions and limited drainage favor the natural process of salinization. Additionally, the extension and intensification of agriculture has led to over-exploitation of groundwater in the past 30 years (Méndoza et al., 2013). The soil microbial crust develops initially on physical crusts which are mainly generated since wetting and drying, being a recurrent feature in the Quíbor arid zone. The microbiotic crust is organic, composed of macro organisms (bryophytes and lichens) and microorganisms (cyanobacteria, fungi algae, etc.); growing on the ground, forming a thickness no greater than 3 mm. For further details see Toledo and Florentino (2009). This study focus on characterize the development stage of the BSC based on image analysis. To this end, grayscale images of different types of biological soil crust at different stages where taken, each image corresponding to an area of 12.96 cm2 with a resolution of 1024x1024 pixels (Ospina et al., 2015). For each image lacunarity and fractal dimension through the differential box counting method were calculated. These were made with the software ImageJ/Fraclac (Karperien, 2013
Determining the Fractal Dimension of the Interstellar Medium
Sanchez, Nestor; Perez, Enrique
2008-01-01
The Interstellar Medium seems to have an underlying fractal structure, which can be characterized through its fractal dimension (Df). However, several factors may affect the determination of Df, such as distortions due to projection, low image resolution, opacity of the cloud, and low signal-to-noise ratio. Here we use both simulated clouds and real molecular cloud maps to study these effects in order to estimate Df in a reliable way. Our results indicate in a self-consistent way that the fractal dimension of the Interstellar Medium is in the range 2.6 < Df < 2.8, which is significantly higher than the value Df = 2.3 usually assumed in the literature.
The physiological and biochemical bases of functional brain imaging
2007-01-01
Functional brain imaging is based on the display of computer-derived images of changes in physiological and/or biochemical functions altered by activation or depression of local functional activities in the brain. This article reviews the physiological and biochemical mechanisms involved.
Functional cardiac imaging by random access microscopy
Directory of Open Access Journals (Sweden)
Claudia eCrocini
2014-10-01
Full Text Available Advances in the development of voltage sensitive dyes and Ca2+ sensors in combination with innovative microscopy techniques allowed researchers to perform functional measurements with an unprecedented spatial and temporal resolution. At the moment, one of the shortcomings of available technologies is their incapability of imaging multiple fast phenomena while controlling the biological determinants involved. In the near future, ultrafast deflectors can be used to rapidly scan laser beams across the sample, performing optical measurements of action potential and Ca2+ release from multiple sites within cardiac cells and tissues. The same scanning modality could also be used to control local Ca2+ release and membrane electrical activity by activation of caged compounds and light-gated ion channels. With this approach, local Ca2+ or voltage perturbations could be induced, simulating arrhythmogenic events, and their impact on physiological cell activity could be explored. The development of this optical methodology will provide fundamental insights in cardiac disease, boosting new therapeutic strategies, and, more generally, it will represent a new approach for the investigation of the physiology of excitable cells.
Application of fractal theory to unsaturated soil mechanics
Institute of Scientific and Technical Information of China (English)
XU Yongfu; TONG Lixin
2007-01-01
The mechanical properties of unsaturated soils are a function of the saturation degree or matric suction,and can be obtained based on currently available procedures.However,each procedure has its limitations and consequently,care should be taken in the selection of a proper procedure.The fractal approach seems to be a potentially useful tool to describe hierarchical systems and is suitable to model the structure and hydraulic properties of unsaturated soils.In this paper,the soil-water characteristics,unsaturated hydraulic conductivity function,unsaturated shear strength,swelling deformation and compression were derived from the fractal model for the pore-size distribution,and were expressed by only two independent physical parameters,the fractal dimension and the air entry value.The predictions of the proposed soil-water characteristics,unsaturated hydraulic conductivity,unsaturated shear strength,swelling deformation and compression were in good agreement with published experimental data.Comparisons between the experimental results of unsaturated hydraulic conductivity and the predictions of the both fractal model and the van Genuchten-Mualem model were also performed,and it was found that the predictions of the fractal model were better than that of the van Genuchten-Mualem model.
Institute of Scientific and Technical Information of China (English)
ZHAO Shi-wei; SU Jing; YANG Yong-hui; LIU Na-na; WU Jin-shui; SHANGGUAN Zhou-ping
2006-01-01
Fractal method is a new method to estimate soil structure. It has been shown to be a useful tool in studies related to physical properties of soil as well as erosion and other hydrological processes. Fractal dimension was used to study the soil structure in soil at different stages of vegetative succession on the Ziwuling Mountains. The land use and vegetation types included cultivated land, abandoned land, grassland, two types of shrub land, and three types of forests. The grassland, shrub land, and forested areas represented a continuum in vegetative succession that had occurred naturally,as the land was abandoned in 1862. Disturbed and undisturbed soil samples were collected from ten vegetation types from depths of 0-10, 10-20, and 20-30 cm on the Ziwuling Mountains, at a site with an elevation of about 1 500 m. Particle size distribution was determined by the pipette method and aggregate size distribution was determined by wet sieving. The results were used to calculate the particle and aggregate fractal dimension. The results showed that particle and aggregate fractal dimensions varied between vegetation types. There was a positive correlation between the particle fractal dimension and the weight of particles with diameter ＜ 0.001 mm, but no relationship between particle fractal dimension and the other particle size classes. Particle fractal dimension was lower in vegetated soils compared to cropland and there was no consistent relationship between fractal dimension and vegetation type. Aggregate fractal dimension was positively correlated with the weight of ＞ 0.25 mm aggregates. Aggregate fractal dimension was lower in vegetated soils compared with cropland. In contrast to particle fractal dimension, aggregate fractal dimension described changes in soil structure associated with vegetative succession. The results of this study indicate that aggregate fractal dimension is more effective in describing soil structure and function compared with particle
Fractal analysis of bone architecture at distal radius.
Tomomitsu, Tatsushi; Mimura, Hiroaki; Murase, Kenya; Sone, Teruki; Fukunaga, Masao
2005-12-20
Bone strength depends on bone quality (architecture, turnover, damage accumulation, and mineralization) as well as bone mass. In this study, human bone architecture was analyzed using fractal image analysis, and the clinical relevance of this method was evaluated. The subjects were 12 healthy female controls and 16 female patients suspected of having osteoporosis (age range, 22-70 years; mean age, 49.1 years). High-resolution CT images of the distal radius were acquired and analyzed using a peripheral quantitative computed tomography (pQCT) system. On the same day, bone mineral densities of the lumbar spine (L-BMD), proximal femur (F-BMD), and distal radius (R-BMD) were measured by dual-energy X-ray absorptiometry (DXA). We examined the correlation between the fractal dimension and six bone mass indices. Subjects diagnosed with osteopenia or osteoporosis were divided into two groups (with and without vertebral fracture), and we compared measured values between these two groups. The fractal dimension correlated most closely with L-BMD (r=0.744). The coefficient of correlation between the fractal dimension and L-BMD was very similar to the coefficient of correlation between L-BMD and F-BMD (r=0.783) and the coefficient of correlation between L-BMD and R-BMD (r=0.742). The fractal dimension was the only measured value that differed significantly between both the osteopenic and the osteoporotic subjects with and without vertebral fracture. The present results suggest that the fractal dimension of the distal radius can be reliably used as a bone strength index that reflects bone architecture as well as bone mass.
Synthetic turbulence, fractal interpolation, and large-eddy simulation.
Basu, Sukanta; Foufoula-Georgiou, Efi; Porté-Agel, Fernando
2004-08-01
Fractal interpolation has been proposed in the literature as an efficient way to construct closure models for the numerical solution of coarse-grained Navier-Stokes equations. It is based on synthetically generating a scale-invariant subgrid-scale field and analytically evaluating its effects on large resolved scales. In this paper, we propose an extension of previous work by developing a multiaffine fractal interpolation scheme and demonstrate that it preserves not only the fractal dimension but also the higher-order structure functions and the non-Gaussian probability density function of the velocity increments. Extensive a priori analyses of atmospheric boundary layer measurements further reveal that this multiaffine closure model has the potential for satisfactory performance in large-eddy simulations. The pertinence of this newly proposed methodology in the case of passive scalars is also discussed.