FRACTAL IMAGE FEATURE VECTORS WITH APPLICATIONS IN FRACTOGRAPHY

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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.

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.)

Fractal analysis in radiological and nuclear medicine perfusion imaging: a systematic review

International Nuclear Information System (INIS)

Michallek, Florian; Dewey, Marc

2014-01-01

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.)

Effect of exposure time and image resolution on fractal dimension

International Nuclear Information System (INIS)

An, Byung Mo; Heo, Min Suk; Lee, Seung Pyo; Lee, Sam Sun; Choi, Soon Chul; Park, Tae Won; Kim, Jong Dae

2002-01-01

To evaluate the effect of exposure time and image resolution on fractal dimension calculations for determining the optimal range of these two variances. Thirty-one radiographs of the mandibular angle area of sixteen human dry mandibles were taken at different exposure times (0.01, 0.08, 0.16, 0.25, 0.40, 0.64, and 0.80 s). Each radiograph was digitized at 1200 dpi, 8 bit, 256 gray level using a film scanner. We selected an Region of Interest (ROI) that corresponded to the same region as in each radiograph, but the resolution of ROI was degraded to 1000, 800, 600, 500, 400, 300, 200, and 100 dpi. The fractal dimension was calculated by using the tile-counting method for each image, and the calculated values were then compared statistically. As the exposure time and the image resolution increased, the mean value of the fractal dimension decreased, except the case where exposure time was set at 0.01 seconds (alpha = 0.05). The exposure time and image resolution affected the fractal dimension by interaction (p<0.001). When the exposure time was set to either 0.64 seconds or 0.80 seconds, the resulting fractal dimensions were lower, irrespective of image resolution, than at shorter exposure times (alpha = 0.05). The optimal range for exposure time and resolution was determined to be 0.08-0.40 seconds and from 400-1000 dpi, respectively. Adequate exposure time and image resolution is essential for acquiring the fractal dimension using tile-counting method for evaluation of the mandible.

Added soft tissue contrast using signal attenuation and the fractal dimension for optical coherence tomography images of porcine arterial tissue

International Nuclear Information System (INIS)

Flueraru, C; Mao, Y; Chang, S; Popescu, D P; Sowa, M G

2010-01-01

Optical coherence tomography (OCT) images of left-descending coronary tissues harvested from three porcine specimens were acquired with a home-build swept-source OCT setup. Despite the fact that OCT is capable of acquiring high resolution circumferential images of vessels, many distinct histological features of a vessel have comparable optical properties leading to poor contrast in OCT images. Two classification methods were tested in this report for the purpose of enhancing contrast between soft-tissue components of porcine coronary vessels. One method involved analyzing the attenuation of the OCT signal as a function of light penetration into the tissue. We demonstrated that by analyzing the signal attenuation in this manner we were able to differentiate two media sub-layers with different orientations of the smooth muscle cells. The other classification method used in our study was fractal analysis. Fractal analysis was implemented in a box-counting (fractal dimension) image-processing code and was used as a tool to differentiate and quantify variations in tissue texture at various locations in the OCT images. The calculated average fractal dimensions had different values in distinct regions of interest (ROI) within the imaged coronary samples. When compared to the results obtained by using the attenuation of the OCT signal, the method of fractal analysis demonstrated better classification potential for distinguishing amongst the tissue ROI.

Fast hybrid fractal image compression using an image feature and neural network

International Nuclear Information System (INIS)

Zhou Yiming; Zhang Chao; Zhang Zengke

2008-01-01

Since fractal image compression could maintain high-resolution reconstructed images at very high compression ratio, it has great potential to improve the efficiency of image storage and image transmission. On the other hand, fractal image encoding is time consuming for the best matching search between range blocks and domain blocks, which limits the algorithm to practical application greatly. In order to solve this problem, two strategies are adopted to improve the fractal image encoding algorithm in this paper. Firstly, based on the definition of an image feature, a necessary condition of the best matching search and FFC algorithm are proposed, and it could reduce the search space observably and exclude most inappropriate domain blocks according to each range block before the best matching search. Secondly, on the basis of FFC algorithm, in order to reduce the mapping error during the best matching search, a special neural network is constructed to modify the mapping scheme for the subblocks, in which the pixel values fluctuate greatly (FNFC algorithm). Experimental results show that the proposed algorithms could obtain good quality of the reconstructed images and need much less time than the baseline encoding algorithm

Tumor cells diagnostic through fractal dimensions

International Nuclear Information System (INIS)

Timbo, Christiano dos Santos

2004-01-01

This method relies on the application of an algorithm for the quantitative and statistic differentiation of a sample of cells stricken by a certain kind of pathology and a sample of healthy cells. This differentiation is made by applying the principles of fractal dimension to digital images of the cells. The algorithm was developed using the the concepts of Object- Oriented Programming, resulting in a simple code, divided in 5 distinct procedures, and a user-friendly interface. To obtain the fractal dimension of the images of the cells, the program processes the image, extracting its border, and uses it to characterize the complexity of the form of the cell in a quantitative way. In order to validate the code, it was used a digitalized image found in an article by W. Bauer, developer of an analog method. The result showed a difference of 6% between the value obtained by Bauer and the value obtained the algorithm developed in this work. (author)

Single-Image Super-Resolution Based on Rational Fractal Interpolation.

Science.gov (United States)

Zhang, Yunfeng; Fan, Qinglan; Bao, Fangxun; Liu, Yifang; Zhang, Caiming

2018-08-01

This paper presents a novel single-image super-resolution (SR) procedure, which upscales a given low-resolution (LR) input image to a high-resolution image while preserving the textural and structural information. First, we construct a new type of bivariate rational fractal interpolation model and investigate its analytical properties. This model has different forms of expression with various values of the scaling factors and shape parameters; thus, it can be employed to better describe image features than current interpolation schemes. Furthermore, this model combines the advantages of rational interpolation and fractal interpolation, and its effectiveness is validated through theoretical analysis. Second, we develop a single-image SR algorithm based on the proposed model. The LR input image is divided into texture and non-texture regions, and then, the image is interpolated according to the characteristics of the local structure. Specifically, in the texture region, the scaling factor calculation is the critical step. We present a method to accurately calculate scaling factors based on local fractal analysis. Extensive experiments and comparisons with the other state-of-the-art methods show that our algorithm achieves competitive performance, with finer details and sharper edges.

Modified Three-Step Search Block Matching Motion Estimation and Weighted Finite Automata based Fractal Video Compression

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Shailesh Kamble

2017-08-01

Full Text Available The major challenge with fractal image/video coding technique is that, it requires more encoding time. Therefore, how to reduce the encoding time is the research component remains in the fractal coding. Block matching motion estimation algorithms are used, to reduce the computations performed in the process of encoding. The objective of the proposed work is to develop an approach for video coding using modified three step search (MTSS block matching algorithm and weighted finite automata (WFA coding with a specific focus on reducing the encoding time. The MTSS block matching algorithm are used for computing motion vectors between the two frames i.e. displacement of pixels and WFA is used for the coding as it behaves like the Fractal Coding (FC. WFA represents an image (frame or motion compensated prediction error based on the idea of fractal that the image has self-similarity in itself. The self-similarity is sought from the symmetry of an image, so the encoding algorithm divides an image into multi-levels of quad-tree segmentations and creates an automaton from the sub-images. The proposed MTSS block matching algorithm is based on the combination of rectangular and hexagonal search pattern and compared with the existing New Three-Step Search (NTSS, Three-Step Search (TSS, and Efficient Three-Step Search (ETSS block matching estimation algorithm. The performance of the proposed MTSS block matching algorithm is evaluated on the basis of performance evaluation parameters i.e. mean absolute difference (MAD and average search points required per frame. Mean of absolute difference (MAD distortion function is used as the block distortion measure (BDM. Finally, developed approaches namely, MTSS and WFA, MTSS and FC, and Plane FC (applied on every frame are compared with each other. The experimentations are carried out on the standard uncompressed video databases, namely, akiyo, bus, mobile, suzie, traffic, football, soccer, ice etc. Developed

Novel prediction- and subblock-based algorithm for fractal image compression

International Nuclear Information System (INIS)

Chung, K.-L.; Hsu, C.-H.

2006-01-01

Fractal encoding is the most consuming part in fractal image compression. In this paper, a novel two-phase prediction- and subblock-based fractal encoding algorithm is presented. Initially the original gray image is partitioned into a set of variable-size blocks according to the S-tree- and interpolation-based decomposition principle. In the first phase, each current block of variable-size range block tries to find the best matched domain block based on the proposed prediction-based search strategy which utilizes the relevant neighboring variable-size domain blocks. The first phase leads to a significant computation-saving effect. If the domain block found within the predicted search space is unacceptable, in the second phase, a subblock strategy is employed to partition the current variable-size range block into smaller blocks to improve the image quality. Experimental results show that our proposed prediction- and subblock-based fractal encoding algorithm outperforms the conventional full search algorithm and the recently published spatial-correlation-based algorithm by Truong et al. in terms of encoding time and image quality. In addition, the performance comparison among our proposed algorithm and the other two algorithms, the no search-based algorithm and the quadtree-based algorithm, are also investigated

Study on fractal characteristics of remote sensing image in the typical volcanic uranium metallogenic areas

International Nuclear Information System (INIS)

Pan Wei; Ni Guoqiang; Li Hanbo

2010-01-01

Computing Methods of fractal dimension and multifractal spectrum about the remote sensing image are briefly introduced. The fractal method is used to study the characteristics of remote sensing images in Xiangshan and Yuhuashan volcanic uranium metallogenic areas in southern China. The research results indicate that the Xiangshan basin in which lots of volcanic uranium deposits occur,is of bigger fractal dimension based on remote sensing image texture than that of the Yuhuashan basin in which two uranium ore occurrences exist, and the multifractal spectrum in the Xiangshan basin obviously leans to less singularity index than in the Yuhuashan basin. The relation of the fractal dimension and multifractal singularity of remote sensing image to uranium metallogeny are discussed. The fractal dimension and multifractal singularity index of remote sensing image may be used to predict the volcanic uranium metallogenic areas. (authors)

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.

Interpolation decoding method with variable parameters for fractal image compression

International Nuclear Information System (INIS)

He Chuanjiang; Li Gaoping; Shen Xiaona

2007-01-01

The interpolation fractal decoding method, which is introduced by [He C, Yang SX, Huang X. Progressive decoding method for fractal image compression. IEE Proc Vis Image Signal Process 2004;3:207-13], involves generating progressively the decoded image by means of an interpolation iterative procedure with a constant parameter. It is well-known that the majority of image details are added at the first steps of iterations in the conventional fractal decoding; hence the constant parameter for the interpolation decoding method must be set as a smaller value in order to achieve a better progressive decoding. However, it needs to take an extremely large number of iterations to converge. It is thus reasonable for some applications to slow down the iterative process at the first stages of decoding and then to accelerate it afterwards (e.g., at some iteration as we need). To achieve the goal, this paper proposed an interpolation decoding scheme with variable (iteration-dependent) parameters and proved the convergence of the decoding process mathematically. Experimental results demonstrate that the proposed scheme has really achieved the above-mentioned goal

Infrared Image Segmentation by Combining Fractal Geometry with Wavelet Transformation

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Xionggang Tu

2014-11-01

Full Text Available An infrared image is decomposed into three levels by discrete stationary wavelet transform (DSWT. Noise is reduced by wiener filter in the high resolution levels in the DSWT domain. Nonlinear gray transformation operation is used to enhance details in the low resolution levels in the DSWT domain. Enhanced infrared image is obtained by inverse DSWT. The enhanced infrared image is divided into many small blocks. The fractal dimensions of all the blocks are computed. Region of interest (ROI is extracted by combining all the blocks, which have similar fractal dimensions. ROI is segmented by global threshold method. The man-made objects are efficiently separated from the infrared image by the proposed method.

Analysis of fractal dimensions of rat bones from film and digital images

Science.gov (United States)

Pornprasertsuk, S.; Ludlow, J. B.; Webber, R. L.; Tyndall, D. A.; Yamauchi, M.

2001-01-01

OBJECTIVES: (1) To compare the effect of two different intra-oral image receptors on estimates of fractal dimension; and (2) to determine the variations in fractal dimensions between the femur, tibia and humerus of the rat and between their proximal, middle and distal regions. METHODS: The left femur, tibia and humerus from 24 4-6-month-old Sprague-Dawley rats were radiographed using intra-oral film and a charge-coupled device (CCD). Films were digitized at a pixel density comparable to the CCD using a flat-bed scanner. Square regions of interest were selected from proximal, middle, and distal regions of each bone. Fractal dimensions were estimated from the slope of regression lines fitted to plots of log power against log spatial frequency. RESULTS: The fractal dimensions estimates from digitized films were significantly greater than those produced from the CCD (P=0.0008). Estimated fractal dimensions of three types of bone were not significantly different (P=0.0544); however, the three regions of bones were significantly different (P=0.0239). The fractal dimensions estimated from radiographs of the proximal and distal regions of the bones were lower than comparable estimates obtained from the middle region. CONCLUSIONS: Different types of image receptors significantly affect estimates of fractal dimension. There was no difference in the fractal dimensions of the different bones but the three regions differed significantly.

Measurement of heterogeneous distribution on technegas SPECT images by three-dimensional fractal analysis

International Nuclear Information System (INIS)

Nagao, Michinobu; Murase, Kenya

2002-01-01

This review article describes a method for quantifying heterogeneous distribution on Technegas ( 99m Tc-carbon particle radioaerosol) SPECT images by three-dimensional fractal analysis (3D-FA). Technegas SPECT was performed to quantify the severity of pulmonary emphysema. We delineated the SPECT images by using five cut-offs (15, 20, 25, 30 and 35% of the maximal voxel radioactivity), and measured the total number of voxels in the areas surrounded by the contours obtained with each cut-off level. We calculated fractal dimensions from the relationship between the total number of voxels and the cut-off levels transformed into natural logarithms. The fractal dimension derived from 3D-FA is the relative and objective measurement, which can assess the heterogeneous distribution on Technegas SPECT images. The fractal dimension strongly correlate pulmonary function in patients with emphysema and well documented the overall and regional severity of emphysema. (author)

Spatial correlation genetic algorithm for fractal image compression

International Nuclear Information System (INIS)

Wu, M.-S.; Teng, W.-C.; Jeng, J.-H.; Hsieh, J.-G.

2006-01-01

Fractal image compression explores the self-similarity property of a natural image and utilizes the partitioned iterated function system (PIFS) to encode it. This technique is of great interest both in theory and application. However, it is time-consuming in the encoding process and such drawback renders it impractical for real time applications. The time is mainly spent on the search for the best-match block in a large domain pool. In this paper, a spatial correlation genetic algorithm (SC-GA) is proposed to speed up the encoder. There are two stages for the SC-GA method. The first stage makes use of spatial correlations in images for both the domain pool and the range pool to exploit local optima. The second stage is operated on the whole image to explore more adequate similarities if the local optima are not satisfied. With the aid of spatial correlation in images, the encoding time is 1.5 times faster than that of traditional genetic algorithm method, while the quality of the retrieved image is almost the same. Moreover, about half of the matched blocks come from the correlated space, so fewer bits are required to represent the fractal transform and therefore the compression ratio is also improved

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...

Texture segmentation of non-cooperative spacecrafts images based on wavelet and fractal dimension

Science.gov (United States)

Wu, Kanzhi; Yue, Xiaokui

2011-06-01

With the increase of on-orbit manipulations and space conflictions, missions such as tracking and capturing the target spacecrafts are aroused. Unlike cooperative spacecrafts, fixing beacons or any other marks on the targets is impossible. Due to the unknown shape and geometry features of non-cooperative spacecraft, in order to localize the target and obtain the latitude, we need to segment the target image and recognize the target from the background. The data and errors during the following procedures such as feature extraction and matching can also be reduced. Multi-resolution analysis of wavelet theory reflects human beings' recognition towards images from low resolution to high resolution. In addition, spacecraft is the only man-made object in the image compared to the natural background and the differences will be certainly observed between the fractal dimensions of target and background. Combined wavelet transform and fractal dimension, in this paper, we proposed a new segmentation algorithm for the images which contains complicated background such as the universe and planet surfaces. At first, Daubechies wavelet basis is applied to decompose the image in both x axis and y axis, thus obtain four sub-images. Then, calculate the fractal dimensions in four sub-images using different methods; after analyzed the results of fractal dimensions in sub-images, we choose Differential Box Counting in low resolution image as the principle to segment the texture which has the greatest divergences between different sub-images. This paper also presents the results of experiments by using the algorithm above. It is demonstrated that an accurate texture segmentation result can be obtained using the proposed technique.

Plant Identification Based on Leaf Midrib Cross-Section Images Using Fractal Descriptors.

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Núbia Rosa da Silva

Full Text Available The correct identification of plants is a common necessity not only to researchers but also to the lay public. Recently, computational methods have been employed to facilitate this task, however, there are few studies front of the wide diversity of plants occurring in the world. This study proposes to analyse images obtained from cross-sections of leaf midrib using fractal descriptors. These descriptors are obtained from the fractal dimension of the object computed at a range of scales. In this way, they provide rich information regarding the spatial distribution of the analysed structure and, as a consequence, they measure the multiscale morphology of the object of interest. In Biology, such morphology is of great importance because it is related to evolutionary aspects and is successfully employed to characterize and discriminate among different biological structures. Here, the fractal descriptors are used to identify the species of plants based on the image of their leaves. A large number of samples are examined, being 606 leaf samples of 50 species from Brazilian flora. The results are compared to other imaging methods in the literature and demonstrate that fractal descriptors are precise and reliable in the taxonomic process of plant species identification.

Time Series Analysis OF SAR Image Fractal Maps: The Somma-Vesuvio Volcanic Complex Case Study

Science.gov (United States)

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

Fractal dimension and image statistics of anal intraepithelial neoplasia

International Nuclear Information System (INIS)

Ahammer, H.; Kroepfl, J.M.; Hackl, Ch.; Sedivy, R.

2011-01-01

Research Highlights: → Human papillomaviruses cause anal intraepithelial neoplasia (AIN). → Digital image processing was carried out to classify the grades of AIN quantitatively. → The fractal dimension as well as grey value statistics was calculated. → Higher grades of AIN yielded higher values of the fractal dimension. → An automatic detection system is feasible. - Abstract: It is well known that human papillomaviruses (HPV) induce a variety of tumorous lesions of the skin. HPV-subtypes also cause premalignant lesions which are termed anal intraepithelial neoplasia (AIN). The clinical classification of AIN is of growing interest in clinical practice, due to increasing HPV infection rates throughout human population. The common classification approach is based on subjective inspections of histological slices of anal tissues with all the drawbacks of depending on the status and individual variances of the trained pathologists. Therefore, a nonlinear quantitative classification method including the calculation of the fractal dimension and first order as well as second order image statistical parameters was developed. The absolute values of these quantitative parameters reflected the distinct grades of AIN very well. The quantitative approach has the potential to decrease classification errors significantly and it could be used as a widely applied screening technique.

Fractal analyses of osseous healing using Tuned Aperture Computed Tomography images

International Nuclear Information System (INIS)

Nair, M.K.; Nair, U.P.; Seyedain, A.; Webber, R.L.; Piesco, N.P.; Agarwal, S.; Mooney, M.P.; Groendahl, H.G.

2001-01-01

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.)

Tumor cells diagnostic through fractal dimensions; Diagnostico de celulas tumorais atraves de dimensoes fractais

Energy Technology Data Exchange (ETDEWEB)

Timbo, Christiano dos Santos

2004-07-01

This method relies on the application of an algorithm for the quantitative and statistic differentiation of a sample of cells stricken by a certain kind of pathology and a sample of healthy cells. This differentiation is made by applying the principles of fractal dimension to digital images of the cells. The algorithm was developed using the the concepts of Object- Oriented Programming, resulting in a simple code, divided in 5 distinct procedures, and a user-friendly interface. To obtain the fractal dimension of the images of the cells, the program processes the image, extracting its border, and uses it to characterize the complexity of the form of the cell in a quantitative way. In order to validate the code, it was used a digitalized image found in an article by W. Bauer, developer of an analog method. The result showed a difference of 6% between the value obtained by Bauer and the value obtained the algorithm developed in this work. (author)

Spatial and radiometric characterization of multi-spectrum satellite images through multi-fractal analysis

Science.gov (United States)

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.

A Double-Minded Fractal

Science.gov (United States)

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.)

Fractals everywhere

CERN Document Server

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

AFM imaging and fractal analysis of surface roughness of AlN epilayers on sapphire substrates

Energy Technology Data Exchange (ETDEWEB)

Dallaeva, Dinara, E-mail: dinara.dallaeva@yandex.ru [Brno University of Technology, Faculty of Electrical Engineering and Communication, Physics Department, Technická 8, 616 00 Brno (Czech Republic); Ţălu, Ştefan [Technical University of Cluj-Napoca, Faculty of Mechanical Engineering, Department of AET, Discipline of Descriptive Geometry and Engineering Graphics, 103-105 B-dul Muncii Street, Cluj-Napoca 400641, Cluj (Romania); Stach, Sebastian [University of Silesia, Faculty of Computer Science and Materials Science, Institute of Informatics, Department of Biomedical Computer Systems, ul. Będzińska 39, 41-205 Sosnowiec (Poland); Škarvada, Pavel; Tománek, Pavel; Grmela, Lubomír [Brno University of Technology, Faculty of Electrical Engineering and Communication, Physics Department, Technická 8, 616 00 Brno (Czech Republic)

2014-09-01

Graphical abstract: - Highlights: • We determined the complexity of 3D surface roughness of aluminum nitride layers. • We used atomic force microscopy and analyzed their fractal geometry. • We determined the fractal dimension of surface roughness of aluminum nitride layers. • We determined the dependence of layer morphology on substrate temperature. - Abstract: The paper deals with AFM imaging and characterization of 3D surface morphology of aluminum nitride (AlN) epilayers on sapphire substrates prepared by magnetron sputtering. Due to the effect of temperature changes on epilayer's surface during the fabrication, a surface morphology is studied by combination of atomic force microscopy (AFM) and fractal analysis methods. Both methods are useful tools that may assist manufacturers in developing and fabricating AlN thin films with optimal surface characteristics. Furthermore, they provide different yet complementary information to that offered by traditional surface statistical parameters. This combination is used for the first time for measurement on AlN epilayers on sapphire substrates, and provides the overall 3D morphology of the sample surfaces (by AFM imaging), and reveals fractal characteristics in the surface morphology (fractal analysis)

Determination of the fractal dimension surface of the fracture from SEM images with assistance of the computer image quantitative analysis system

International Nuclear Information System (INIS)

Wawszczak, J.

1999-01-01

This paper presents a procedure for quantitative image analysis for determination of the fractal dimension from SEM surface images of the fracture 0H14N5CuNb steel. Investigated quenched and tempered samples of the steel after impact tests (in room and -85 o C temperatures). This method can be useful for analysing local fractal dimension of any surface parts (not oriented) of the fracture with different topography of this surface. (author)

Fractal characteristics of an asphaltene deposited heterogeneous surface

International Nuclear Information System (INIS)

Amin, J. Sayyad; Ayatollahi, Sh.; Alamdari, A.

2009-01-01

Several methods have been employed in recent years to investigate homogeneous surface topography based on image analysis, such as AFM (atomic force microscopy) and SEM (scanning electron microscopy). Fractal analysis of the images provides fractal dimension of the surface which is used as one of the most common surface indices. Surface topography has generally been considered to be mono-fractal. On the other hand, precipitation of organic materials on a rough surface and its irregular growth result in morphology alteration and converts a homogeneous surface to a heterogeneous one. In this case a mono-fractal description of the surface does not completely describe the nature of the altered surface. This work aims to investigate the topography alteration of a glass surface as a result of asphaltene precipitation and its growth at various pressures using a bi-fractal approach. The experimental results of the deposited surfaces were clearly indicating two regions of micro- and macro-asperities namely, surface types I and II, respectively. The fractal plots were indicative of bi-fractal behavior and for each surface type one fractal dimension was calculated. The topography information of the surfaces was obtained by two image analyses, AFM and SEM imaging techniques. Results of the bi-fractal analysis demonstrated that topography alteration in surface type II (macro-asperities) is more evident than that in surface type I (micro-asperities). Compared to surface type II, a better correlation was observed between the fractal dimensions inferred from the AFM images (D A ) and those of the SEM images (D S ) in surface type I.

Classification of diabetic retinopathy using fractal dimension analysis of eye fundus image

Science.gov (United States)

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.

FRACTAL ANALYSIS OF TRABECULAR BONE: A STANDARDISED METHODOLOGY

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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.

Detecting abrupt dynamic change based on changes in the fractal properties of spatial images

Science.gov (United States)

Liu, Qunqun; He, Wenping; Gu, Bin; Jiang, Yundi

2017-10-01

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.

Zone specific fractal dimension of retinal images as predictor of stroke incidence.

Science.gov (United States)

Aliahmad, Behzad; Kumar, Dinesh Kant; Hao, Hao; Unnikrishnan, Premith; Che Azemin, Mohd Zulfaezal; Kawasaki, Ryo; Mitchell, Paul

2014-01-01

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.

Analysis of the fractal dimension of volcano geomorphology through Synthetic Aperture Radar (SAR) amplitude images acquired in C and X band.

Science.gov (United States)

Pepe, S.; Di Martino, G.; Iodice, A.; Manzo, M.; Pepe, A.; Riccio, D.; Ruello, G.; Sansosti, E.; Tizzani, P.; Zinno, I.

2012-04-01

In the last two decades several aspects relevant to volcanic activity have been analyzed in terms of fractal parameters that effectively describe natural objects geometry. More specifically, these researches have been aimed at the identification of (1) the power laws that governed the magma fragmentation processes, (2) the energy of explosive eruptions, and (3) the distribution of the associated earthquakes. In this paper, the study of volcano morphology via satellite images is dealt with; in particular, we use the complete forward model developed by some of the authors (Di Martino et al., 2012) that links the stochastic characterization of amplitude Synthetic Aperture Radar (SAR) images to the fractal dimension of the imaged surfaces, modelled via fractional Brownian motion (fBm) processes. Based on the inversion of such a model, a SAR image post-processing has been implemented (Di Martino et al., 2010), that allows retrieving the fractal dimension of the observed surfaces, dictating the distribution of the roughness over different spatial scales. The fractal dimension of volcanic structures has been related to the specific nature of materials and to the effects of active geodynamic processes. Hence, the possibility to estimate the fractal dimension from a single amplitude-only SAR image is of fundamental importance for the characterization of volcano structures and, moreover, can be very helpful for monitoring and crisis management activities in case of eruptions and other similar natural hazards. The implemented SAR image processing performs the extraction of the point-by-point fractal dimension of the scene observed by the sensor, providing - as an output product - the map of the fractal dimension of the area of interest. In this work, such an analysis is performed on Cosmo-SkyMed, ERS-1/2 and ENVISAT images relevant to active stratovolcanoes in different geodynamic contexts, such as Mt. Somma-Vesuvio, Mt. Etna, Vulcano and Stromboli in Southern Italy, Shinmoe

Characterisation of human non-proliferativediabetic retinopathy using the fractal analysis

Directory of Open Access Journals (Sweden)

Carmen Alina Lupaşcu

2015-08-01

Full Text Available 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 ImageJ. Statistical analyses were performed for these groups using Microsoft Office Excel 2003 and GraphPad InStat 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 lowest values 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 undeTrstanding 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

Recent advances in coding theory for near error-free communications

Science.gov (United States)

Cheung, K.-M.; Deutsch, L. J.; Dolinar, S. J.; Mceliece, R. J.; Pollara, F.; Shahshahani, M.; Swanson, L.

1991-01-01

Channel and source coding theories are discussed. The following subject areas are covered: large constraint length convolutional codes (the Galileo code); decoder design (the big Viterbi decoder); Voyager's and Galileo's data compression scheme; current research in data compression for images; neural networks for soft decoding; neural networks for source decoding; finite-state codes; and fractals for data compression.

Biomaterial porosity determined by fractal dimensions, succolarity and lacunarity on microcomputed tomographic images

International Nuclear Information System (INIS)

N'Diaye, Mambaye; Degeratu, Cristinel; Bouler, Jean-Michel; Chappard, Daniel

2013-01-01

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

2-D Fractal Wire Antenna Design and Performance

Science.gov (United States)

Tebbens, S. F.; Barton, C. C.; Peterman, D. J.; Ewing, J. J.; Abbott, C. S.; Rizki, M. M.

2017-12-01

A 2-D fractal wire antenna uses a fractal (self-similar) pattern to increase its length by iteration and can receive or transmit electromagnetic radiation. 2-D fractals are shapes that, at their mathematical limit (of infinite iterations) have an infinite length. The fractal dimension describes the degree of space filling. A fundamental property of fractal antennas lies in iteration (repetition) of a fractal pattern over a range of length scales. Iteration produces fractal antennas that can be very compact, wideband and multiband. As the number of iterations increases, the antenna tends to have additional frequencies that minimize far field return loss. This differs from traditional antenna designs in that a single fractal antenna can operate well at multiple frequencies. We have created a MATLAB code to generate deterministic and stochastic modes of fractal wire antennas with a range of fractal dimensions between 1 and 2. Variation in fractal dimension, stochasticity, and number of iterations have been computationally tested using COMSOL Multiphysics software to determine their effect on antenna performance.

A novel fractal image compression scheme with block classification and sorting based on Pearson's correlation coefficient.

Science.gov (United States)

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.

Investigation into How 8th Grade Students Define Fractals

Science.gov (United States)

Karakus, Fatih

2015-01-01

The analysis of 8th grade students' concept definitions and concept images can provide information about their mental schema of fractals. There is limited research on students' understanding and definitions of fractals. Therefore, this study aimed to investigate the elementary students' definitions of fractals based on concept image and concept…

2-D Fractal Carpet Antenna Design and Performance

Science.gov (United States)

Barton, C. C.; Tebbens, S. F.; Ewing, J. J.; Peterman, D. J.; Rizki, M. M.

2017-12-01

A 2-D fractal carpet antenna uses a fractal (self-similar) pattern to increase its perimeter by iteration and can receive or transmit electromagnetic radiation within its perimeter-bounded surface area. 2-D fractals are shapes that, at their mathematical limit (infinite iterations) have an infinite perimeter bounding a finite surface area. The fractal dimension describes the degree of space filling and lacunarity which quantifies the size and spatial distribution of open space bounded by a fractal shape. A key aspect of fractal antennas lies in iteration (repetition) of a fractal pattern over a range of length scales. Iteration produces fractal antennas that are very compact, wideband and multiband. As the number of iterations increases, the antenna operates at higher and higher frequencies. Manifestly different from traditional antenna designs, a fractal antenna can operate at multiple frequencies simultaneously. We have created a MATLAB code to generate deterministic and stochastic modes of Sierpinski carpet fractal antennas with a range of fractal dimensions between 1 and 2. Variation in fractal dimension, stochasticity, number of iterations, and lacunarities have been computationally tested using COMSOL Multiphysics software to determine their effect on antenna performance

Biometric feature extraction using local fractal auto-correlation

International Nuclear Information System (INIS)

Chen Xi; Zhang Jia-Shu

2014-01-01

Image texture feature extraction is a classical means for biometric recognition. To extract effective texture feature for matching, we utilize local fractal auto-correlation to construct an effective image texture descriptor. Three main steps are involved in the proposed scheme: (i) using two-dimensional Gabor filter to extract the texture features of biometric images; (ii) calculating the local fractal dimension of Gabor feature under different orientations and scales using fractal auto-correlation algorithm; and (iii) linking the local fractal dimension of Gabor feature under different orientations and scales into a big vector for matching. Experiments and analyses show our proposed scheme is an efficient biometric feature extraction approach. (condensed matter: structural, mechanical, and thermal properties)

Model to estimate fractal dimension for ion-bombarded materials

Energy Technology Data Exchange (ETDEWEB)

Hu, A., E-mail: hu77@purdue.edu; Hassanein, A.

2014-03-15

Comprehensive fractal Monte Carlo model ITMC-F (Hu and Hassanein, 2012 [1]) is developed based on the Monte Carlo ion bombardment simulation code, i.e., Ion Transport in Materials and Compounds (ITMC) code (Hassanein, 1985 [2]). The ITMC-F studies the impact of surface roughness on the angular dependence of sputtering yield. Instead of assuming material surfaces to be flat or composed of exact self-similar fractals in simulation, we developed a new method to describe the surface shapes. Random fractal surfaces which are generated by midpoint displacement algorithm and support vector machine algorithm are combined with ITMC. With this new fractal version of ITMC-F, we successfully simulated the angular dependence of sputtering yield for various ion-target combinations, with the input surface roughness exponent directly depicted from experimental data (Hu and Hassanein, 2012 [1]). The ITMC-F code showed good agreement with the experimental data. In advanced, we compare other experimental sputtering yield with the results from ITMC-F to estimate the surface roughness exponent for ion-bombarded material in this research.

The analysis of the influence of fractal structure of stimuli on fractal dynamics in fixational eye movements and EEG signal

Science.gov (United States)

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.

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%.

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.

FONT DISCRIMINATIO USING FRACTAL DIMENSIONS

Directory of Open Access Journals (Sweden)

S. Mozaffari

2014-09-01

Full Text Available One of the related problems of OCR systems is discrimination of fonts in machine printed document images. This task improves performance of general OCR systems. Proposed methods in this paper are based on various fractal dimensions for font discrimination. First, some predefined fractal dimensions were combined with directional methods to enhance font differentiation. Then, a novel fractal dimension was introduced in this paper for the first time. Our feature extraction methods which consider font recognition as texture identification are independent of document content. Experimental results on different pages written by several font types show that fractal geometry can overcome the complexities of font recognition problem.

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.

Contour fractal analysis of grains

Science.gov (United States)

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.

Intelligent fuzzy approach for fast fractal image compression

Science.gov (United States)

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.

Enhancing PIV image and fractal descriptor for velocity and shear stresses propagation around a circular pier

Directory of Open Access Journals (Sweden)

Alireza Keshavarzi

2017-07-01

Full Text Available In this study, the fractal dimensions of velocity fluctuations and the Reynolds shear stresses propagation for flow around a circular bridge pier are presented. In the study reported herein, the fractal dimension of velocity fluctuations (u′, v′, w′ and the Reynolds shear stresses (u′v′ and u′w′ of flow around a bridge pier were computed using a Fractal Interpolation Function (FIF algorithm. The velocity fluctuations of flow along a horizontal plane above the bed were measured using Acoustic Doppler Velocity meter (ADV and Particle Image Velocimetry (PIV. The PIV is a powerful technique which enables us to attain high resolution spatial and temporal information of turbulent flow using instantaneous time snapshots. In this study, PIV was used for detection of high resolution fractal scaling around a bridge pier. The results showed that the fractal dimension of flow fluctuated significantly in the longitudinal and transverse directions in the vicinity of the pier. It was also found that the fractal dimension of velocity fluctuations and shear stresses increased rapidly at vicinity of pier at downstream whereas it remained approximately unchanged far downstream of the pier. The higher value of fractal dimension was found at a distance equal to one times of the pier diameter in the back of the pier. Furthermore, the average fractal dimension for the streamwise and transverse velocity fluctuations decreased from the centreline to the side wall of the flume. Finally, the results from ADV measurement were consistent with the result from PIV, therefore, the ADV enables to detect turbulent characteristics of flow around a circular bridge pier.

Monitoring of dry sliding wear using fractal analysis

NARCIS (Netherlands)

Zhang, Jindang; Regtien, Paulus P.L.; Korsten, Maarten J.

2005-01-01

Reliable online monitoring of wear remains a challenge to tribology research as well as to the industry. This paper presents a new method for monitoring of dry sliding wear using digital imaging and fractal analysis. Fractal values, namely fractal dimension and intercept, computed from the power

Alzheimer's Disease Detection in Brain Magnetic Resonance Images Using Multiscale Fractal Analysis

International Nuclear Information System (INIS)

Lahmiri, Salim; Boukadoum, Mounir

2013-01-01

We present a new automated system for the detection of brain magnetic resonance images (MRI) affected by Alzheimer's disease (AD). The MRI is analyzed by means of multiscale analysis (MSA) to obtain its fractals at six different scales. The extracted fractals are used as features to differentiate healthy brain MRI from those of AD by a support vector machine (SVM) classifier. The result of classifying 93 brain MRIs consisting of 51 images of healthy brains and 42 of brains affected by AD, using leave-one-out cross-validation method, yielded 99.18% ± 0.01 classification accuracy, 100% sensitivity, and 98.20% ± 0.02 specificity. These results and a processing time of 5.64 seconds indicate that the proposed approach may be an efficient diagnostic aid for radiologists in the screening for AD

Fractal analysis for studying the evolution of forests

International Nuclear Information System (INIS)

Andronache, Ion C.; Ahammer, Helmut; Jelinek, Herbert F.; Peptenatu, Daniel; Ciobotaru, Ana-M.; Draghici, Cristian C.; Pintilii, Radu D.; Simion, Adrian G.

2016-01-01

Highlights: • Legal and illegal deforestation is investigated by fractal analysis. • A new fractal fragmentation index FFI is proposed. • Differences in shapes of forest areas indicate the type of deforestation. • Support of ecological management. - Abstract: Deforestation is an important phenomenon that may create major imbalances in ecosystems. In this study we propose a new mathematical analysis of the forest area dynamic, enabling qualitative as well as quantitative statements and results. Fractal dimensions of the area and the perimeter of a forest were determined using digital images. The difference between fractal dimensions of the area and the perimeter images turned out to be a crucial quantitative parameter. Accordingly, we propose a new fractal fragmentation index, FFI, which is based on this difference and which highlights the degree of compaction or non-compaction of the forest area in order to interpret geographic features. Particularly, this method was applied to forests, where large areas have been legally or illegally deforested. However, these methods can easily be used for other ecological or geographical investigations based on digital images, including deforestation of rainforests.

Fractals in DNA sequence analysis

Institute of Scientific and Technical Information of China (English)

Yu Zu-Guo(喻祖国); Vo Anh; Gong Zhi-Min(龚志民); Long Shun-Chao(龙顺潮)

2002-01-01

Fractal methods have been successfully used to study many problems in physics, mathematics, engineering, finance,and even in biology. There has been an increasing interest in unravelling the mysteries of DNA; for example, how can we distinguish coding and noncoding sequences, and the problems of classification and evolution relationship of organisms are key problems in bioinformatics. Although much research has been carried out by taking into consideration the long-range correlations in DNA sequences, and the global fractal dimension has been used in these works by other people, the models and methods are somewhat rough and the results are not satisfactory. In recent years, our group has introduced a time series model (statistical point of view) and a visual representation (geometrical point of view)to DNA sequence analysis. We have also used fractal dimension, correlation dimension, the Hurst exponent and the dimension spectrum (multifractal analysis) to discuss problems in this field. In this paper, we introduce these fractal models and methods and the results of DNA sequence analysis.

Conference on Fractals and Related Fields III

CERN Document Server

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.

Turbulence Enhancement by Fractal Square Grids: Effects of the Number of Fractal Scales

Science.gov (United States)

Omilion, Alexis; Ibrahim, Mounir; Zhang, Wei

2017-11-01

Fractal square grids offer a unique solution for passive flow control as they can produce wakes with a distinct turbulence intensity peak and a prolonged turbulence decay region at the expense of only minimal pressure drop. While previous studies have solidified this characteristic of fractal square grids, how the number of scales (or fractal iterations N) affect turbulence production and decay of the induced wake is still not well understood. The focus of this research is to determine the relationship between the fractal iteration N and the turbulence produced in the wake flow using well-controlled water-tunnel experiments. Particle Image Velocimetry (PIV) is used to measure the instantaneous velocity fields downstream of four different fractal grids with increasing number of scales (N = 1, 2, 3, and 4) and a conventional single-scale grid. By comparing the turbulent scales and statistics of the wake, we are able to determine how each iteration affects the peak turbulence intensity and the production/decay of turbulence from the grid. In light of the ability of these fractal grids to increase turbulence intensity with low pressure drop, this work can potentially benefit a wide variety of applications where energy efficient mixing or convective heat transfer is a key process.

Fractal Analysis of Elastographic Images for Automatic Detection of Diffuse Diseases of Salivary Glands: Preliminary Results

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.

Depth of focus enhancement of a modified imaging quasi-fractal zone plate.

Science.gov (United States)

Zhang, Qinqin; Wang, Jingang; Wang, Mingwei; Bu, Jing; Zhu, Siwei; Gao, Bruce Z; Yuan, Xiaocong

2012-10-01

We propose a new parameter w for optimization of foci distribution of conventional fractal zone plates (FZPs) with a greater depth of focus (DOF) in imaging. Numerical simulations of DOF distribution on axis directions indicate that the values of DOF can be extended by a factor of 1.5 or more by a modified quasi-FZP. In experiments, we employ a simple object-lens-image-plane arrangement to pick up images at various positions within the DOF of a conventional FZP and a quasi-FZP, respectively. Experimental results show that the parameter w improves foci distribution of FZPs in good agreement with theoretical predictions.

Image magnification based on similarity analogy

International Nuclear Information System (INIS)

Chen Zuoping; Ye Zhenglin; Wang Shuxun; Peng Guohua

2009-01-01

Aiming at the high time complexity of the decoding phase in the traditional image enlargement methods based on fractal coding, a novel image magnification algorithm is proposed in this paper, which has the advantage of iteration-free decoding, by using the similarity analogy between an image and its zoom-out and zoom-in. A new pixel selection technique is also presented to further improve the performance of the proposed method. Furthermore, by combining some existing fractal zooming techniques, an efficient image magnification algorithm is obtained, which can provides the image quality as good as the state of the art while greatly decrease the time complexity of the decoding phase.

Analysis and classification of commercial ham slice images using directional fractal dimension features.

Science.gov (United States)

Mendoza, Fernando; Valous, Nektarios A; Allen, Paul; Kenny, Tony A; Ward, Paddy; Sun, Da-Wen

2009-02-01

This paper presents a novel and non-destructive approach to the appearance characterization and classification of commercial pork, turkey and chicken ham slices. Ham slice images were modelled using directional fractal (DF(0°;45°;90°;135°)) dimensions and a minimum distance classifier was adopted to perform the classification task. Also, the role of different colour spaces and the resolution level of the images on DF analysis were investigated. This approach was applied to 480 wafer thin ham slices from four types of hams (120 slices per type): i.e., pork (cooked and smoked), turkey (smoked) and chicken (roasted). DF features were extracted from digitalized intensity images in greyscale, and R, G, B, L(∗), a(∗), b(∗), H, S, and V colour components for three image resolution levels (100%, 50%, and 25%). Simulation results show that in spite of the complexity and high variability in colour and texture appearance, the modelling of ham slice images with DF dimensions allows the capture of differentiating textural features between the four commercial ham types. Independent DF features entail better discrimination than that using the average of four directions. However, DF dimensions reveal a high sensitivity to colour channel, orientation and image resolution for the fractal analysis. The classification accuracy using six DF dimension features (a(90°)(∗),a(135°)(∗),H(0°),H(45°),S(0°),H(90°)) was 93.9% for training data and 82.2% for testing data.

Focusing behavior of the fractal vector optical fields designed by fractal lattice growth model.

Science.gov (United States)

Gao, Xu-Zhen; Pan, Yue; Zhao, Meng-Dan; Zhang, Guan-Lin; Zhang, Yu; Tu, Chenghou; Li, Yongnan; Wang, Hui-Tian

2018-01-22

We introduce a general fractal lattice growth model, significantly expanding the application scope of the fractal in the realm of optics. This model can be applied to construct various kinds of fractal "lattices" and then to achieve the design of a great diversity of fractal vector optical fields (F-VOFs) combinating with various "bases". We also experimentally generate the F-VOFs and explore their universal focusing behaviors. Multiple focal spots can be flexibly enginnered, and the optical tweezers experiment validates the simulated tight focusing fields, which means that this model allows the diversity of the focal patterns to flexibly trap and manipulate micrometer-sized particles. Furthermore, the recovery performance of the F-VOFs is also studied when the input fields and spatial frequency spectrum are obstructed, and the results confirm the robustness of the F-VOFs in both focusing and imaging processes, which is very useful in information transmission.

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.

FAST TRACK COMMUNICATION: Weyl law for fat fractals

Science.gov (United States)

Spina, María E.; García-Mata, Ignacio; Saraceno, Marcos

2010-10-01

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.

[Modeling continuous scaling of NDVI based on fractal theory].

Science.gov (United States)

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.

The fractal dimension of cell membrane correlates with its capacitance: A new fractal single-shell model

Science.gov (United States)

Wang, Xujing; Becker, Frederick F.; Gascoyne, Peter R. C.

2010-01-01

The scale-invariant property of the cytoplasmic membrane of biological cells is examined by applying the Minkowski–Bouligand method to digitized scanning electron microscopy images of the cell surface. The membrane is found to exhibit fractal behavior, and the derived fractal dimension gives a good description of its morphological complexity. Furthermore, we found that this fractal dimension correlates well with the specific membrane dielectric capacitance derived from the electrorotation measurements. Based on these findings, we propose a new fractal single-shell model to describe the dielectrics of mammalian cells, and compare it with the conventional single-shell model (SSM). We found that while both models fit with experimental data well, the new model is able to eliminate the discrepancy between the measured dielectric property of cells and that predicted by the SSM. PMID:21198103

The effects of voltage of x-ray tube on fractal dimension and anisotropy of diagnostic image

International Nuclear Information System (INIS)

Baik, Jee Seon; Lee, Sam Sun; Huh, Kyung Hoe; Yi, Won Jin; Heo, Min Suk; Choi, Soon Chul; Park, Kwan Soo

2007-01-01

The purpose of this study was to evaluate the effect of the kV on fractal dimension of trabecular bone in digital radiographs. 16 bone cores were obtained from patients who had taken partial resection of tibia due to accidents. Each bone core along with an aluminum step wedge was radiographed with an occlusal film at 0.08 sec and with the constant film-focus distance (32 cm). All radiographs were acquired at 60, 75, and 90 kV. A rectangular ROI was drawn at medial part, distal part, and the bone defect area of each bone core image according to each kV. The directional fractal dimension was measured using Fourier Transform spectrum, and the anisotropy was obtained using directional fractal dimension. The values were compared by the repeated measures ANOVA. The fractal dimensions increased along with kV increase (p<0.05). The anisotropy measurements did not show statistically significant difference according to kV change. The fractal dimensions of the bone defect areas of the bone cores have low values contrast to the non-defect areas of the bone cores. The anisotropy measurements of the bone defect areas were lower than those of the non-defect areas of the bone cores, but not statistically significant. Fractal analysis can notice a difference of a change of voltage of x-ray tube and bone defect or not. And anisotropy of a trabecular bone is coherent even with change of the voltage of x-ray tube or defecting off a part of bone

An investigation of fractal characteristics of mesoporous carbon electrodes with various pore structures

International Nuclear Information System (INIS)

Pyun, Su-Il; Rhee, Chang-Kyu

2004-01-01

Fractal characteristics of mesoporous carbon electrodes were investigated with various pore structures using the N 2 gas adsorption method and the transmission electron microscopy (TEM) image analysis method. The mesoporous carbons with various pore structures were prepared by imprinting mesophase pitch used as a carbonaceous precursor with different colloidal silica particles. All imprinted mesoporous carbons were composed of two groups of pores produced from the carbonisation of mesophase pitch and from the silica imprinting. The overall surface fractal dimensions of the carbon specimens were determined from the analyses of the N 2 gas adsorption isotherms. In order to distinguish the surface fractal dimension of the carbonisation-induced pore surface from that fractal dimension of the silica-imprinted pore surface, the individual surface fractal dimensions were determined from the image analyses of the TEM images. From the comparison of the overall surface fractal dimension with the individual surface fractal dimensions, it was recognised that the overall surface fractal dimension is crucially influenced by the individual surface fractal dimension of the silica-imprinted pore surface. Moreover, from the fact that the silica-imprinted pore surface with broad relative pore size distribution (PSD) gave lower value of the individual surface fractal dimension than that pore surface with narrow relative PSD, it is concluded that as the silica-imprinted pores comprising the carbon specimen agglomerate, the individual surface fractal dimension of that pore surface decreases

Fractal cosmology

International Nuclear Information System (INIS)

Dickau, Jonathan J.

2009-01-01

The use of fractals and fractal-like forms to describe or model the universe has had a long and varied history, which begins long before the word fractal was actually coined. Since the introduction of mathematical rigor to the subject of fractals, by Mandelbrot and others, there have been numerous cosmological theories and analyses of astronomical observations which suggest that the universe exhibits fractality or is by nature fractal. In recent years, the term fractal cosmology has come into usage, as a description for those theories and methods of analysis whereby a fractal nature of the cosmos is shown.

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.

Fractal analysis as a potential tool for surface morphology of thin films

Science.gov (United States)

Soumya, S.; Swapna, M. S.; Raj, Vimal; Mahadevan Pillai, V. P.; Sankararaman, S.

2017-12-01

Fractal geometry developed by Mandelbrot has emerged as a potential tool for analyzing complex systems in the diversified fields of science, social science, and technology. Self-similar objects having the same details in different scales are referred to as fractals and are analyzed using the mathematics of non-Euclidean geometry. The present work is an attempt to correlate fractal dimension for surface characterization by Atomic Force Microscopy (AFM). Taking the AFM images of zinc sulphide (ZnS) thin films prepared by pulsed laser deposition (PLD) technique, under different annealing temperatures, the effect of annealing temperature and surface roughness on fractal dimension is studied. The annealing temperature and surface roughness show a strong correlation with fractal dimension. From the regression equation set, the surface roughness at a given annealing temperature can be calculated from the fractal dimension. The AFM images are processed using Photoshop and fractal dimension is calculated by box-counting method. The fractal dimension decreases from 1.986 to 1.633 while the surface roughness increases from 1.110 to 3.427, for a change of annealing temperature 30 ° C to 600 ° C. The images are also analyzed by power spectrum method to find the fractal dimension. The study reveals that the box-counting method gives better results compared to the power spectrum method.

Fractal Image Filters for Specialized Image Recognition Tasks

Science.gov (United States)

2010-02-11

colorful than lines and circles drawn on papyrus: their depth and beauty are advertised to a broad audience via computer graphics represen- tations of... colours were obtained with the aid of a fractal transformation from the attractor to the small picture of the yellow �ower. as being the !-limit set of

Image encryption based on fractal-structured phase mask in fractional Fourier transform domain

Science.gov (United States)

Zhao, Meng-Dan; Gao, Xu-Zhen; Pan, Yue; Zhang, Guan-Lin; Tu, Chenghou; Li, Yongnan; Wang, Hui-Tian

2018-04-01

We present an optical encryption approach based on the combination of fractal Fresnel lens (FFL) and fractional Fourier transform (FrFT). Our encryption approach is in fact a four-fold encryption scheme, including the random phase encoding produced by the Gerchberg–Saxton algorithm, a FFL, and two FrFTs. A FFL is composed of a Sierpinski carpet fractal plate and a Fresnel zone plate. In our encryption approach, the security is enhanced due to the more expandable key spaces and the use of FFL overcomes the alignment problem of the optical axis in optical system. Only using the perfectly matched parameters of the FFL and the FrFT, the plaintext can be recovered well. We present an image encryption algorithm that from the ciphertext we can get two original images by the FrFT with two different phase distribution keys, obtained by performing 100 iterations between the two plaintext and ciphertext, respectively. We test the sensitivity of our approach to various parameters such as the wavelength of light, the focal length of FFL, and the fractional orders of FrFT. Our approach can resist various attacks.

Fractal characteristic in the wearing of cutting tool

Science.gov (United States)

Mei, Anhua; Wang, Jinghui

1995-11-01

This paper studies the cutting tool wear with fractal geometry. The wearing image of the flank has been collected by machine vision which consists of CCD camera and personal computer. After being processed by means of preserving smoothing, binary making and edge extracting, the clear boundary enclosing the worn area has been obtained. The fractal dimension of the worn surface is calculated by the methods called `Slit Island' and `Profile'. The experiments and calciating give the conclusion that the worn surface is enclosed by a irregular boundary curve with some fractal dimension and characteristics of self-similarity. Furthermore, the relation between the cutting velocity and the fractal dimension of the worn region has been submitted. This paper presents a series of methods for processing and analyzing the fractal information in the blank wear, which can be applied to research the projective relation between the fractal structure and the wear state, and establish the fractal model of the cutting tool wear.

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)

Hyper-Fractal Analysis: A visual tool for estimating the fractal dimension of 4D objects

Science.gov (United States)

Grossu, I. V.; Grossu, I.; Felea, D.; Besliu, C.; Jipa, Al.; Esanu, T.; Bordeianu, C. C.; Stan, E.

2013-04-01

This work presents a new version of a Visual Basic 6.0 application for estimating the fractal dimension of images and 3D objects (Grossu et al. (2010) [1]). The program was extended for working with four-dimensional objects stored in comma separated values files. This might be of interest in biomedicine, for analyzing the evolution in time of three-dimensional images. New version program summaryProgram title: Hyper-Fractal Analysis (Fractal Analysis v03) Catalogue identifier: AEEG_v3_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEEG_v3_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: Standard CPC license, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 745761 No. of bytes in distributed program, including test data, etc.: 12544491 Distribution format: tar.gz Programming language: MS Visual Basic 6.0 Computer: PC Operating system: MS Windows 98 or later RAM: 100M Classification: 14 Catalogue identifier of previous version: AEEG_v2_0 Journal reference of previous version: Comput. Phys. Comm. 181 (2010) 831-832 Does the new version supersede the previous version? Yes Nature of problem: Estimating the fractal dimension of 4D images. Solution method: Optimized implementation of the 4D box-counting algorithm. Reasons for new version: Inspired by existing applications of 3D fractals in biomedicine [3], we extended the optimized version of the box-counting algorithm [1, 2] to the four-dimensional case. This might be of interest in analyzing the evolution in time of 3D images. The box-counting algorithm was extended in order to support 4D objects, stored in comma separated values files. A new form was added for generating 2D, 3D, and 4D test data. The application was tested on 4D objects with known dimension, e.g. the Sierpinski hypertetrahedron gasket, Df=ln(5)/ln(2) (Fig. 1). The algorithm could be extended, with minimum effort, to

A fractal derivative model for the characterization of anomalous diffusion in magnetic resonance imaging

Science.gov (United States)

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

Fractal and digital image processing to determine the degree of dispersion of carbon nanotubes

International Nuclear Information System (INIS)

Liang, Xiao-ning; Li, Wei

2016-01-01

The degree of dispersion is an important parameter to quantitatively study properties of carbon nanotube composites. Among the many methods for studying dispersion, scanning electron microscopy, transmission electron microscopy, and atomic force microscopy are the most commonly used, intuitive, and convincing methods. However, they have the disadvantage of not being quantitative. To overcome this disadvantage, the fractal theory and digital image processing method can be used to provide a quantitative analysis of the morphology and properties of carbon nanotube composites. In this paper, the dispersion degree of carbon nanotubes was investigated using two fractal methods, namely, the box-counting method and the differential box-counting method. On the basis of the results, we propose a new method for the quantitative characterization of the degree of dispersion of carbon nanotubes. This hierarchical grid method can be used as a supplementary method, and can be combined with the fractal calculation method. Thus, the accuracy and effectiveness of the quantitative characterization of the dispersion degree of carbon nanotubes can be improved. (The outer diameter of the carbon nanotubes is about 50 nm; the length of the carbon nanotubes is 10–20 μm.)

Fractal and digital image processing to determine the degree of dispersion of carbon nanotubes

Energy Technology Data Exchange (ETDEWEB)

Liang, Xiao-ning, E-mail: xnliang0506@163.com; Li, Wei, E-mail: 1099006@mail.dhu.edu.cn, E-mail: liwei@dhu.edu.cn, E-mail: waiwentougao@outlook.com [Donghua University, College of Textiles (China)

2016-05-15

The degree of dispersion is an important parameter to quantitatively study properties of carbon nanotube composites. Among the many methods for studying dispersion, scanning electron microscopy, transmission electron microscopy, and atomic force microscopy are the most commonly used, intuitive, and convincing methods. However, they have the disadvantage of not being quantitative. To overcome this disadvantage, the fractal theory and digital image processing method can be used to provide a quantitative analysis of the morphology and properties of carbon nanotube composites. In this paper, the dispersion degree of carbon nanotubes was investigated using two fractal methods, namely, the box-counting method and the differential box-counting method. On the basis of the results, we propose a new method for the quantitative characterization of the degree of dispersion of carbon nanotubes. This hierarchical grid method can be used as a supplementary method, and can be combined with the fractal calculation method. Thus, the accuracy and effectiveness of the quantitative characterization of the dispersion degree of carbon nanotubes can be improved. (The outer diameter of the carbon nanotubes is about 50 nm; the length of the carbon nanotubes is 10–20 μm.)

Heterogeneity of Glucose Metabolism in Esophageal Cancer Measured by Fractal Analysis of Fluorodeoxyglucose Positron Emission Tomography Image: Correlation between Metabolic Heterogeneity and Survival.

Science.gov (United States)

Tochigi, Toru; Shuto, Kiyohiko; Kono, Tsuguaki; Ohira, Gaku; Tohma, Takayuki; Gunji, Hisashi; Hayano, Koichi; Narushima, Kazuo; Fujishiro, Takeshi; Hanaoka, Toshiharu; Akutsu, Yasunori; Okazumi, Shinichi; Matsubara, Hisahiro

2017-01-01

Intratumoral heterogeneity is a well-recognized characteristic feature of cancer. The purpose of this study is to assess the heterogeneity of the intratumoral glucose metabolism using fractal analysis, and evaluate its prognostic value in patients with esophageal squamous cell carcinoma (ESCC). 18F-fluorodeoxyglucose positron emission tomography (FDG-PET) studies of 79 patients who received curative surgery were evaluated. FDG-PET images were analyzed using fractal analysis software, where differential box-counting method was employed to calculate the fractal dimension (FD) of the tumor lesion. Maximum standardized uptake value (SUVmax) and FD were compared with overall survival (OS). The median SUVmax and FD of ESCCs in this cohort were 13.8 and 1.95, respectively. In univariate analysis performed using Cox's proportional hazard model, T stage and FD showed significant associations with OS (p = 0.04, p heterogeneity measured by fractal analysis can be a novel imaging biomarker for survival in patients with ESCC. © 2016 S. Karger AG, Basel.

Classification of radar echoes using fractal geometry

International Nuclear Information System (INIS)

Azzaz, Nafissa; Haddad, Boualem

2017-01-01

Highlights: • Implementation of two concepts of fractal geometry to classify two types of meteorological radar echoes. • A new approach, called a multi-scale fractal dimension is used for classification between fixed echoes and rain echoes. • An Automatic identification system of meteorological radar echoes was proposed using fractal geometry. - Abstract: This paper deals with the discrimination between the precipitation echoes and the ground echoes in meteorological radar images using fractal geometry. This study aims to improve the measurement of precipitations by weather radars. For this, we considered three radar sites: Bordeaux (France), Dakar (Senegal) and Me lbourne (USA). We showed that the fractal dimension based on contourlet and the fractal lacunarity are pertinent to discriminate between ground and precipitation echoes. We also demonstrated that the ground echoes have a multifractal structure but the precipitations are more homogeneous than ground echoes whatever the prevailing climate. Thereby, we developed an automatic classification system of radar using a graphic interface. This interface, based on the fractal geometry makes possible the identification of radar echoes type in real time. This system can be inserted in weather radar for the improvement of precipitation estimations.

Ultrasound imaging using coded signals

DEFF Research Database (Denmark)

Misaridis, Athanasios

Modulated (or coded) excitation signals can potentially improve the quality and increase the frame rate in medical ultrasound scanners. The aim of this dissertation is to investigate systematically the applicability of modulated signals in medical ultrasound imaging and to suggest appropriate...... methods for coded imaging, with the goal of making better anatomic and flow images and three-dimensional images. On the first stage, it investigates techniques for doing high-resolution coded imaging with improved signal-to-noise ratio compared to conventional imaging. Subsequently it investigates how...... coded excitation can be used for increasing the frame rate. The work includes both simulated results using Field II, and experimental results based on measurements on phantoms as well as clinical images. Initially a mathematical foundation of signal modulation is given. Pulse compression based...

High dynamic range coding imaging system

Science.gov (United States)

Wu, Renfan; Huang, Yifan; Hou, Guangqi

2014-10-01

We present a high dynamic range (HDR) imaging system design scheme based on coded aperture technique. This scheme can help us obtain HDR images which have extended depth of field. We adopt Sparse coding algorithm to design coded patterns. Then we utilize the sensor unit to acquire coded images under different exposure settings. With the guide of the multiple exposure parameters, a series of low dynamic range (LDR) coded images are reconstructed. We use some existing algorithms to fuse and display a HDR image by those LDR images. We build an optical simulation model and get some simulation images to verify the novel system.

Development of Fractal Pattern Making Application using L-System for Enhanced Machine Controller

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Gunawan Alexander A S

2014-03-01

Full Text Available One big issue facing the industry today is an automated machine lack of flexibility for customization because it is designed by the manufacturers based on certain standards. In this research, it is developed customized application software for CNC (Computer Numerically Controlled machines using open source platform. The application is enable us to create designs by means of fractal patterns using L-System, developed by turtle geometry interpretation and Python programming languages. The result of the application is the G-Code of fractal pattern formed by the method of L-System. In the experiment on the CNC machine, the G-Code of fractal pattern which involving the branching structure has been able to run well.

Fractal properties of fractured sandstones of the Guartela Canyon, Parana Basin - Brazil; Propriedades fractais de arenitos fraturados do Canyon Guartela, Formacao Furnas, Bacia do Parana

Energy Technology Data Exchange (ETDEWEB)

Souza, Jeferson de; Figueira, Isabela Francoso Rebutini; Santos, Thais Borba [Universidade Federal do Rio Grande do Norte (PPGG/DG/UFRN), Natal (Brazil). Dept. de Geologia. Programa de Pos-Graducao em Geologia; Rostirolla, Sidnei Pires [Universidade Federal do Rio Grande do Norte (DG/UFRN), Natal (Brazil). Dept. de Geologia; Pierin, Andre Ramiro; Spisila, Andre Luis [Universidade Federal do Rio Grande do Norte (DG/UFRN), Natal (Brazil). Dept. de Geologia. Programa de Iniciacao Cientifica

2008-03-15

The statistical and geometrical properties of fracture systems were obtained by analyzing remote sense images and outcrop data, in the Region of Guartela Canyon, in the central-eastern of Parana State. The probability distributions of fractures, with their parameters and attributes, were obtained through extensive statistical exploration of data. These parameters were used as input data for generating 3-D stochastic fractures models through the 'discrete fracture network - DFN' method. The modeling is performed by using the code FRED. To study the persistence of statistical parameters in multiple scales were used remote sensing images (SRTM, Landsat TM7 and aerial photos), covering a scale range from outcrops (few meters) to basin scales (hundreds of kilometers). The results indicated the presence of power-law (fractal) statistics for the spatial and size distributions. Fractals distributions were found for all sets studied, in some cases with different fractal exponents. The implications of fractal behavior for the generation of discrete fracture network, and consequently for the hydraulic properties, are briefly discussed. (author)

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.

Tree Coding of Bilevel Images

DEFF Research Database (Denmark)

Martins, Bo; Forchhammer, Søren

1998-01-01

Presently, sequential tree coders are the best general purpose bilevel image coders and the best coders of halftoned images. The current ISO standard, Joint Bilevel Image Experts Group (JBIG), is a good example. A sequential tree coder encodes the data by feeding estimates of conditional...... is one order of magnitude slower than JBIG, obtains excellent and highly robust compression performance. A multipass free tree coding scheme produces superior compression results for all test images. A multipass free template coding scheme produces significantly better results than JBIG for difficult...... images such as halftones. By utilizing randomized subsampling in the template selection, the speed becomes acceptable for practical image coding...

Survey Of Lossless Image Coding Techniques

Science.gov (United States)

Melnychuck, Paul W.; Rabbani, Majid

1989-04-01

Many image transmission/storage applications requiring some form of data compression additionally require that the decoded image be an exact replica of the original. Lossless image coding algorithms meet this requirement by generating a decoded image that is numerically identical to the original. Several lossless coding techniques are modifications of well-known lossy schemes, whereas others are new. Traditional Markov-based models and newer arithmetic coding techniques are applied to predictive coding, bit plane processing, and lossy plus residual coding. Generally speaking, the compression ratio offered by these techniques are in the area of 1.6:1 to 3:1 for 8-bit pictorial images. Compression ratios for 12-bit radiological images approach 3:1, as these images have less detailed structure, and hence, their higher pel correlation leads to a greater removal of image redundancy.

Applications of fractals in ecology.

Science.gov (United States)

Sugihara, G; M May, R

1990-03-01

Fractal models describe the geometry of a wide variety of natural objects such as coastlines, island chains, coral reefs, satellite ocean-color images and patches of vegetation. Cast in the form of modified diffusion models, they can mimic natural and artificial landscapes having different types of complexity of shape. This article provides a brief introduction to fractals and reports on how they can be used by ecologists to answer a variety of basic questions, about scale, measurement and hierarchy in, ecological systems. Copyright © 1990. Published by Elsevier Ltd.

Map of fluid flow in fractal porous medium into fractal continuum flow.

Science.gov (United States)

Balankin, Alexander S; Elizarraraz, Benjamin Espinoza

2012-05-01

This paper is devoted to fractal continuum hydrodynamics and its application to model fluid flows in fractally permeable reservoirs. Hydrodynamics of fractal continuum flow is developed on the basis of a self-consistent model of fractal continuum employing vector local fractional differential operators allied with the Hausdorff derivative. The generalized forms of Green-Gauss and Kelvin-Stokes theorems for fractional calculus are proved. The Hausdorff material derivative is defined and the form of Reynolds transport theorem for fractal continuum flow is obtained. The fundamental conservation laws for a fractal continuum flow are established. The Stokes law and the analog of Darcy's law for fractal continuum flow are suggested. The pressure-transient equation accounting the fractal metric of fractal continuum flow is derived. The generalization of the pressure-transient equation accounting the fractal topology of fractal continuum flow is proposed. The mapping of fluid flow in a fractally permeable medium into a fractal continuum flow is discussed. It is stated that the spectral dimension of the fractal continuum flow d(s) is equal to its mass fractal dimension D, even when the spectral dimension of the fractally porous or fissured medium is less than D. A comparison of the fractal continuum flow approach with other models of fluid flow in fractally permeable media and the experimental field data for reservoir tests are provided.

An Efficient Fractal Video Sequences Codec with Multiviews

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Shiping Zhu

2013-01-01

Full Text Available Multiview video consists of multiple views of the same scene. They require enormous amount of data to achieve high image quality, which makes it indispensable to compress multiview video. Therefore, data compression is a major issue for multiviews. In this paper, we explore an efficient fractal video codec to compress multiviews. The proposed scheme first compresses a view-dependent geometry of the base view using fractal video encoder with homogeneous region condition. With the extended fractional pel motion estimation algorithm and fast disparity estimation algorithm, it then generates prediction images of other views. The prediction image uses the image-based rendering techniques based on the decoded video. And the residual signals are obtained by the prediction image and the original image. Finally, it encodes residual signals by the fractal video encoder. The idea is also to exploit the statistical dependencies from both temporal and interview reference pictures for motion compensated prediction. Experimental results show that the proposed algorithm is consistently better than JMVC8.5, with 62.25% bit rate decrease and 0.37 dB PSNR increase based on the Bjontegaard metric, and the total encoding time (TET of the proposed algorithm is reduced by 92%.

FRACTAL DIMENSION OF URBAN EXPANSION BASED ON REMOTE SENSING IMAGES

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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.

An Evaluation of Fractal Surface Measurement Methods for Characterizing Landscape Complexity from Remote-Sensing Imagery

Science.gov (United States)

Lam, Nina Siu-Ngan; Qiu, Hong-Lie; Quattrochi, Dale A.; Emerson, Charles W.; Arnold, James E. (Technical Monitor)

2001-01-01

The rapid increase in digital data volumes from new and existing sensors necessitates the need for efficient analytical tools for extracting information. We developed an integrated software package called ICAMS (Image Characterization and Modeling System) to provide specialized spatial analytical functions for interpreting remote sensing data. This paper evaluates the three fractal dimension measurement methods: isarithm, variogram, and triangular prism, along with the spatial autocorrelation measurement methods Moran's I and Geary's C, that have been implemented in ICAMS. A modified triangular prism method was proposed and implemented. Results from analyzing 25 simulated surfaces having known fractal dimensions show that both the isarithm and triangular prism methods can accurately measure a range of fractal surfaces. The triangular prism method is most accurate at estimating the fractal dimension of higher spatial complexity, but it is sensitive to contrast stretching. The variogram method is a comparatively poor estimator for all of the surfaces, particularly those with higher fractal dimensions. Similar to the fractal techniques, the spatial autocorrelation techniques are found to be useful to measure complex images but not images with low dimensionality. These fractal measurement methods can be applied directly to unclassified images and could serve as a tool for change detection and data mining.

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...

Fractal Bread.

Science.gov (United States)

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)

Fractal analysis of bone architecture at distal radius

International Nuclear Information System (INIS)

Tomomitsu, Tatsushi; Mimura, Hiroaki; Murase, Kenya; Sone, Teruki; Fukunaga, Masao

2005-01-01

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. (author)

The Role of Resolution in the Estimation of Fractal Dimension Maps From SAR Data

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Gerardo Di Martino

2017-12-01

Full Text Available This work is aimed at investigating the role of resolution in fractal dimension map estimation, analyzing the role of the different surface spatial scales involved in the considered estimation process. The study is performed using a data set of actual Cosmo/SkyMed Synthetic Aperture Radar (SAR images relevant to two different areas, the region of Bidi in Burkina Faso and the city of Naples in Italy, acquired in stripmap and enhanced spotlight modes. The behavior of fractal dimension maps in the presence of areas with distinctive characteristics from the viewpoint of land-cover and surface features is discussed. Significant differences among the estimated maps are obtained in the presence of fine textural details, which significantly affect the fractal dimension estimation for the higher resolution spotlight images. The obtained results show that if we are interested in obtaining a reliable estimate of the fractal dimension of the observed natural scene, stripmap images should be chosen in view of both economic and computational considerations. In turn, the combination of fractal dimension maps obtained from stripmap and spotlight images can be used to identify areas on the scene presenting non-fractal behavior (e.g., urban areas. Along this guideline, a simple example of stripmap-spotlight data fusion is also presented.

Combining Biometric Fractal Pattern and Particle Swarm Optimization-Based Classifier for Fingerprint Recognition

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.

Fractal dimension analysis of malignant and benign endobronchial ultrasound nodes

International Nuclear Information System (INIS)

Fiz, José Antonio; Monte-Moreno, Enrique; Andreo, Felipe; Auteri, Santiago José; Sanz-Santos, José; Serra, Pere; Bonet, Gloria; Castellà, Eva; Manzano, Juan Ruiz

2014-01-01

Endobronchial ultrasonography (EBUS) has been applied as a routine procedure for the diagnostic of hiliar and mediastinal nodes. The authors assessed the relationship between the echographic appearance of mediastinal nodes, based on endobronchial ultrasound images, and the likelihood of malignancy. The images of twelve malignant and eleven benign nodes were evaluated. A previous processing method was applied to improve the quality of the images and to enhance the details. Texture and morphology parameters analyzed were: the image texture of the echographies and a fractal dimension that expressed the relationship between area and perimeter of the structures that appear in the image, and characterizes the convoluted inner structure of the hiliar and mediastinal nodes. Processed images showed that relationship between log perimeter and log area of hilar nodes was lineal (i.e. perimeter vs. area follow a power law). Fractal dimension was lower in the malignant nodes compared with non-malignant nodes (1.47(0.09), 1.53(0.10) mean(SD), Mann–Whitney U test p < 0.05)). Fractal dimension of ultrasonographic images of mediastinal nodes obtained through endobronchial ultrasound differ in malignant nodes from non-malignant. This parameter could differentiate malignat and non-malignat mediastinic and hiliar nodes

Bony change of apical lesion healing process using fractal analysis

International Nuclear Information System (INIS)

Lee, Ji Min; Park, Hyok; Jeong, Ho Gul; Kim, Kee Deog; Park, Chang Seo

2005-01-01

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 0 ) is 0.940 ± 0.361 and that of normal area (N 0 ) is 1.186 ± 0.727 (p 1 ) is 1.076 ± 0.069 and that of normal area (N 1 ) is 1.192 ± 0.055 (p 2 ) is 1.163 ± 0.074 and that of normal area (N 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.

Self-Similarity of Plasmon Edge Modes on Koch Fractal Antennas.

Science.gov (United States)

Bellido, Edson P; Bernasconi, Gabriel D; Rossouw, David; Butet, Jérémy; Martin, Olivier J F; Botton, Gianluigi A

2017-11-28

We investigate the plasmonic behavior of Koch snowflake fractal geometries and their possible application as broadband optical antennas. Lithographically defined planar silver Koch fractal antennas were fabricated and characterized with high spatial and spectral resolution using electron energy loss spectroscopy. The experimental data are supported by numerical calculations carried out with a surface integral equation method. Multiple surface plasmon edge modes supported by the fractal structures have been imaged and analyzed. Furthermore, by isolating and reproducing self-similar features in long silver strip antennas, the edge modes present in the Koch snowflake fractals are identified. We demonstrate that the fractal response can be obtained by the sum of basic self-similar segments called characteristic edge units. Interestingly, the plasmon edge modes follow a fractal-scaling rule that depends on these self-similar segments formed in the structure after a fractal iteration. As the size of a fractal structure is reduced, coupling of the modes in the characteristic edge units becomes relevant, and the symmetry of the fractal affects the formation of hybrid modes. This analysis can be utilized not only to understand the edge modes in other planar structures but also in the design and fabrication of fractal structures for nanophotonic applications.

Detection and classification of Breast Cancer in Wavelet Sub-bands of Fractal Segmented Cancerous Zones.

Science.gov (United States)

Shirazinodeh, Alireza; Noubari, Hossein Ahmadi; Rabbani, Hossein; Dehnavi, Alireza Mehri

2015-01-01

Recent studies on wavelet transform and fractal modeling applied on mammograms for the detection of cancerous tissues indicate that microcalcifications and masses can be utilized for the study of the morphology and diagnosis of cancerous cases. It is shown that the use of fractal modeling, as applied to a given image, can clearly discern cancerous zones from noncancerous areas. In this paper, for fractal modeling, the original image is first segmented into appropriate fractal boxes followed by identifying the fractal dimension of each windowed section using a computationally efficient two-dimensional box-counting algorithm. Furthermore, using appropriate wavelet sub-bands and image Reconstruction based on modified wavelet coefficients, it is shown that it is possible to arrive at enhanced features for detection of cancerous zones. In this paper, we have attempted to benefit from the advantages of both fractals and wavelets by introducing a new algorithm. By using a new algorithm named F1W2, the original image is first segmented into appropriate fractal boxes, and the fractal dimension of each windowed section is extracted. Following from that, by applying a maximum level threshold on fractal dimensions matrix, the best-segmented boxes are selected. In the next step, the segmented Cancerous zones which are candidates are then decomposed by utilizing standard orthogonal wavelet transform and db2 wavelet in three different resolution levels, and after nullifying wavelet coefficients of the image at the first scale and low frequency band of the third scale, the modified reconstructed image is successfully utilized for detection of breast cancer regions by applying an appropriate threshold. For detection of cancerous zones, our simulations indicate the accuracy of 90.9% for masses and 88.99% for microcalcifications detection results using the F1W2 method. For classification of detected mictocalcification into benign and malignant cases, eight features are identified and

Assessment of textural differentiations in forest resources in Romania using fractal analysis

DEFF Research Database (Denmark)

Andronache, Ion; Fensholt, Rasmus; Ahammer, Helmut

2017-01-01

regions in Romania affected by both deforestation and reforestation using a non-Euclidean method based on fractal analysis.We calculated four fractal dimensions of forest areas: the fractal box-counting dimension of the forest areas, the fractal box-counting dimension of the dilated forest areas......, the fractal dilation dimension and the box-counting dimension of the border of the dilated forest areas. Fractal analysis revealed morpho-structural and textural differentiations of forested, deforested and reforested areas in development regions with dominant mountain relief and high hills (more forested...... and compact organization) in comparison to the development regions dominated by plains or low hills (less forested, more fragmented with small and isolated clusters). Our analysis used the fractal analysis that has the advantage of analyzing the entire image, rather than studying local information, thereby...

Heterogeneity of cerebral blood flow: a fractal approach

International Nuclear Information System (INIS)

Kuikka, J.T.; Hartikainen, P.

2000-01-01

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.) [de

Ultrasound strain imaging using Barker code

Science.gov (United States)

Peng, Hui; Tie, Juhong; Guo, Dequan

2017-01-01

Ultrasound strain imaging is showing promise as a new way of imaging soft tissue elasticity in order to help clinicians detect lesions or cancers in tissues. In this paper, Barker code is applied to strain imaging to improve its quality. Barker code as a coded excitation signal can be used to improve the echo signal-to-noise ratio (eSNR) in ultrasound imaging system. For the Baker code of length 13, the sidelobe level of the matched filter output is -22dB, which is unacceptable for ultrasound strain imaging, because high sidelobe level will cause high decorrelation noise. Instead of using the conventional matched filter, we use the Wiener filter to decode the Barker-coded echo signal to suppress the range sidelobes. We also compare the performance of Barker code and the conventional short pulse in simulation method. The simulation results demonstrate that the performance of the Wiener filter is much better than the matched filter, and Baker code achieves higher elastographic signal-to-noise ratio (SNRe) than the short pulse in low eSNR or great depth conditions due to the increased eSNR with it.

Transmission imaging with a coded source

International Nuclear Information System (INIS)

Stoner, W.W.; Sage, J.P.; Braun, M.; Wilson, D.T.; Barrett, H.H.

1976-01-01

The conventional approach to transmission imaging is to use a rotating anode x-ray tube, which provides the small, brilliant x-ray source needed to cast sharp images of acceptable intensity. Stationary anode sources, although inherently less brilliant, are more compatible with the use of large area anodes, and so they can be made more powerful than rotating anode sources. Spatial modulation of the source distribution provides a way to introduce detailed structure in the transmission images cast by large area sources, and this permits the recovery of high resolution images, in spite of the source diameter. The spatial modulation is deliberately chosen to optimize recovery of image structure; the modulation pattern is therefore called a ''code.'' A variety of codes may be used; the essential mathematical property is that the code possess a sharply peaked autocorrelation function, because this property permits the decoding of the raw image cast by th coded source. Random point arrays, non-redundant point arrays, and the Fresnel zone pattern are examples of suitable codes. This paper is restricted to the case of the Fresnel zone pattern code, which has the unique additional property of generating raw images analogous to Fresnel holograms. Because the spatial frequency of these raw images are extremely coarse compared with actual holograms, a photoreduction step onto a holographic plate is necessary before the decoded image may be displayed with the aid of coherent illumination

Infrastructural Fractals

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....

Fractal analysis of Xylella fastidiosa biofilm formation

Science.gov (United States)

Moreau, A. L. D.; Lorite, G. S.; Rodrigues, C. M.; Souza, A. A.; Cotta, M. A.

2009-07-01

We have investigated the growth process of Xylella fastidiosa biofilms inoculated on a glass. The size and the distance between biofilms were analyzed by optical images; a fractal analysis was carried out using scaling concepts and atomic force microscopy images. We observed that different biofilms show similar fractal characteristics, although morphological variations can be identified for different biofilm stages. Two types of structural patterns are suggested from the observed fractal dimensions Df. In the initial and final stages of biofilm formation, Df is 2.73±0.06 and 2.68±0.06, respectively, while in the maturation stage, Df=2.57±0.08. These values suggest that the biofilm growth can be understood as an Eden model in the former case, while diffusion-limited aggregation (DLA) seems to dominate the maturation stage. Changes in the correlation length parallel to the surface were also observed; these results were correlated with the biofilm matrix formation, which can hinder nutrient diffusion and thus create conditions to drive DLA growth.

Iterons, fractals and computations of automata

Science.gov (United States)

Siwak, Paweł

1999-03-01

Processing of strings by some automata, when viewed on space-time (ST) diagrams, reveals characteristic soliton-like coherent periodic objects. They are inherently associated with iterations of automata mappings thus we call them the iterons. In the paper we present two classes of one-dimensional iterons: particles and filtrons. The particles are typical for parallel (cellular) processing, while filtrons, introduced in (32) are specific for serial processing of strings. In general, the images of iterated automata mappings exhibit not only coherent entities but also the fractals, and quasi-periodic and chaotic dynamics. We show typical images of such computations: fractals, multiplication by a number, and addition of binary numbers defined by a Turing machine. Then, the particles are presented as iterons generated by cellular automata in three computations: B/U code conversion (13, 29), majority classification (9), and in discrete version of the FPU (Fermi-Pasta-Ulam) dynamics (7, 23). We disclose particles by a technique of combinational recoding of ST diagrams (as opposed to sequential recoding). Subsequently, we recall the recursive filters based on FCA (filter cellular automata) window operators, and considered by Park (26), Ablowitz (1), Fokas (11), Fuchssteiner (12), Bruschi (5) and Jiang (20). We present the automata equivalents to these filters (33). Some of them belong to the class of filter automata introduced in (30). We also define and illustrate some properties of filtrons. Contrary to particles, the filtrons interact nonlocally in the sense that distant symbols may influence one another. Thus their interactions are very unusual. Some examples have been given in (32). Here we show new examples of filtron phenomena: multifiltron solitonic collisions, attracting and repelling filtrons, trapped bouncing filtrons (which behave like a resonance cavity) and quasi filtrons.

Balanced distributed coding of omnidirectional images

Science.gov (United States)

Thirumalai, Vijayaraghavan; Tosic, Ivana; Frossard, Pascal

2008-01-01

This paper presents a distributed coding scheme for the representation of 3D scenes captured by stereo omni-directional cameras. We consider a scenario where images captured from two different viewpoints are encoded independently, with a balanced rate distribution among the different cameras. The distributed coding is built on multiresolution representation and partitioning of the visual information in each camera. The encoder transmits one partition after entropy coding, as well as the syndrome bits resulting from the channel encoding of the other partition. The decoder exploits the intra-view correlation and attempts to reconstruct the source image by combination of the entropy-coded partition and the syndrome information. At the same time, it exploits the inter-view correlation using motion estimation between images from different cameras. Experiments demonstrate that the distributed coding solution performs better than a scheme where images are handled independently, and that the coding rate stays balanced between encoders.

An efficient adaptive arithmetic coding image compression technology

International Nuclear Information System (INIS)

Wang Xing-Yuan; Yun Jiao-Jiao; Zhang Yong-Lei

2011-01-01

This paper proposes an efficient lossless image compression scheme for still images based on an adaptive arithmetic coding compression algorithm. The algorithm increases the image coding compression rate and ensures the quality of the decoded image combined with the adaptive probability model and predictive coding. The use of adaptive models for each encoded image block dynamically estimates the probability of the relevant image block. The decoded image block can accurately recover the encoded image according to the code book information. We adopt an adaptive arithmetic coding algorithm for image compression that greatly improves the image compression rate. The results show that it is an effective compression technology. (electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics)

Evaluation of peri-implant bone using fractal analysis

International Nuclear Information System (INIS)

Jung, Yun Hoa

2005-01-01

The purpose of this study was to investigate whether the fractal dimension of successive panoramic radiographs of bone after implant placement is useful in the characterization of structural change in alveolar bone. Twelve subjects with thirty-five implants were retrospectively followed-up from one week to six months after implantation. Thirty-six panoramic radiographs from twelve patients were classified into 1 week. 1-2 months and 3-6 months after implantation and digitized. The windows of bone apical and mesial or distal to the implant were defined as peri apical region of interest (ROI) and inter dental ROI; the fractal dimension of the image was calculated. There was not a statistically significant difference in fractal dimensions during the period up to 6 months after implantation. The fractal dimensions were higher in 13 and 15 mm than 10 and 11.5 mm implant length at inter dental ROIs in 3-6 months after implantation (p<0.01). Longer fixtures showed the higher fractal dimension of bone around implant. This investigation needs further exploration with large numbers of implants for longer follow-up periods.

Fractal analysis of SEM images and mercury intrusion porosimetry data for the microstructural characterization of microcrystalline cellulose-based pellets

International Nuclear Information System (INIS)

Gomez-Carracedo, A.; Alvarez-Lorenzo, C.; Coca, R.; Martinez-Pacheco, R.; Concheiro, A.; Gomez-Amoza, J.L.

2009-01-01

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 μm 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

Advanced Imaging Optics Utilizing Wavefront Coding.

Energy Technology Data Exchange (ETDEWEB)

Scrymgeour, David [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Boye, Robert [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Adelsberger, Kathleen [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

2015-06-01

Image processing offers a potential to simplify an optical system by shifting some of the imaging burden from lenses to the more cost effective electronics. Wavefront coding using a cubic phase plate combined with image processing can extend the system's depth of focus, reducing many of the focus-related aberrations as well as material related chromatic aberrations. However, the optimal design process and physical limitations of wavefront coding systems with respect to first-order optical parameters and noise are not well documented. We examined image quality of simulated and experimental wavefront coded images before and after reconstruction in the presence of noise. Challenges in the implementation of cubic phase in an optical system are discussed. In particular, we found that limitations must be placed on system noise, aperture, field of view and bandwidth to develop a robust wavefront coded system.

Survey of coded aperture imaging

International Nuclear Information System (INIS)

Barrett, H.H.

1975-01-01

The basic principle and limitations of coded aperture imaging for x-ray and gamma cameras are discussed. Current trends include (1) use of time varying apertures, (2) use of ''dilute'' apertures with transmission much less than 50%, and (3) attempts to derive transverse tomographic sections, unblurred by other planes, from coded images

arXiv Generalized Fragmentation Functions for Fractal Jet Observables

CERN Document Server

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...

Fractal vector optical fields.

Science.gov (United States)

Pan, Yue; Gao, Xu-Zhen; Cai, Meng-Qiang; Zhang, Guan-Lin; Li, Yongnan; Tu, Chenghou; Wang, Hui-Tian

2016-07-15

We introduce the concept of a fractal, which provides an alternative approach for flexibly engineering the optical fields and their focal fields. We propose, design, and create a new family of optical fields-fractal vector optical fields, which build a bridge between the fractal and vector optical fields. The fractal vector optical fields have polarization states exhibiting fractal geometry, and may also involve the phase and/or amplitude simultaneously. The results reveal that the focal fields exhibit self-similarity, and the hierarchy of the fractal has the "weeding" role. The fractal can be used to engineer the focal field.

Fractals: Giant impurity nonlinearities in optics of fractal clusters

International Nuclear Information System (INIS)

Butenko, A.V.; Shalaev, V.M.; Stockman, M.I.

1988-01-01

A theory of nonlinear optical properties of fractals is developed. Giant enhancement of optical susceptibilities is predicted for impurities bound to a fractal. This enhancement occurs if the exciting radiation frequency lies within the absorption band of the fractal. The giant optical nonlinearities are due to existence of high local electric fields in the sites of impurity locations. Such fields are due to the inhomogeneously broadened character of a fractal spectrum, i.e. partial conservation of individuality of fractal-forming particles (monomers). The field enhancement is proportional to the Q-factor of the resonance of a monomer. The effects of coherent anti-Stokes Raman scattering (CARS) and phase conjugation (PC) of light waves are enhanced to a much greater degree than generation of higher harmonics. In a general case the susceptibility of a higher-order is enhanced in the maximum way if the process includes ''subtraction'' of photons (at least one of the strong field frequencies enters the susceptibility with the minus sign). Alternatively, enhancement for the highest-order harmonic generation (when all the photons are ''accumulated'') is minimal. The predicted phenomena bear information on spectral properties of both impurity molecules and a fractal. In particular, in the CARS spectra a narrow (with the natural width) resonant structure, which is proper to an isolated monomer of a fractal, is predicted to be observed. (orig.)

Inverted fractal analysis of TiO{sub x} thin layers grown by inverse pulsed laser deposition

Energy Technology Data Exchange (ETDEWEB)

Égerházi, L., E-mail: egerhazi.laszlo@gmail.com [University of Szeged, Faculty of Medicine, Department of Medical Physics and Informatics, Korányi fasor 9., H-6720 Szeged (Hungary); Smausz, T. [University of Szeged, Faculty of Science, Department of Optics and Quantum Electronics, Dóm tér 9., H-6720 Szeged (Hungary); Bari, F. [University of Szeged, Faculty of Medicine, Department of Medical Physics and Informatics, Korányi fasor 9., H-6720 Szeged (Hungary)

2013-08-01

Inverted fractal analysis (IFA), a method developed for fractal analysis of scanning electron microscopy images of cauliflower-like thin films is presented through the example of layers grown by inverse pulsed laser deposition (IPLD). IFA uses the integrated fractal analysis module (FracLac) of the image processing software ImageJ, and an objective thresholding routine that preserves the characteristic features of the images, independently of their brightness and contrast. IFA revealed f{sub D} = 1.83 ± 0.01 for TiO{sub x} layers grown at 5–50 Pa background pressures. For a series of images, this result was verified by evaluating the scaling of the number of still resolved features on the film, counted manually. The value of f{sub D} not only confirms the fractal structure of TiO{sub x} IPLD thin films, but also suggests that the aggregation of plasma species in the gas atmosphere may have only limited contribution to the deposition.

a New Method for Calculating Fractal Dimensions of Porous Media Based on Pore Size Distribution

Science.gov (United States)

Xia, Yuxuan; Cai, Jianchao; Wei, Wei; Hu, Xiangyun; Wang, Xin; Ge, Xinmin

Fractal theory has been widely used in petrophysical properties of porous rocks over several decades and determination of fractal dimensions is always the focus of researches and applications by means of fractal-based methods. In this work, a new method for calculating pore space fractal dimension and tortuosity fractal dimension of porous media is derived based on fractal capillary model assumption. The presented work establishes relationship between fractal dimensions and pore size distribution, which can be directly used to calculate the fractal dimensions. The published pore size distribution data for eight sandstone samples are used to calculate the fractal dimensions and simultaneously compared with prediction results from analytical expression. In addition, the proposed fractal dimension method is also tested through Micro-CT images of three sandstone cores, and are compared with fractal dimensions by box-counting algorithm. The test results also prove a self-similar fractal range in sandstone when excluding smaller pores.

Evolution of atomic-scale surface structures during ion bombardment: A fractal simulation

International Nuclear Information System (INIS)

Shaheen, M.A.; Ruzic, D.N.

1993-01-01

Surfaces of interest in microelectronics have been shown to exhibit fractal topographies on the atomic scale. A model utilizing self-similar fractals to simulate surface roughness has been added to the ion bombardment code TRIM. The model has successfully predicted experimental sputtering yields of low energy (less then 1000 eV) Ar on Si and D on C using experimentally determined fractal dimensions. Under ion bombardment the fractal surface structures evolve as the atoms in the collision cascade are displaced or sputtered. These atoms have been tracked and the evolution of the surface in steps of one monolayer of flux has been determined. The Ar--Si system has been studied for incidence energies of 100 and 500 eV, and incidence angles of 0 degree, 30 degree, and 60 degree. As expected, normally incident ion bombardment tends to reduce the roughness of the surface, whereas large angle ion bombardment increases the degree of surface roughness. Of particular interest though, the surfaces are still locally self-similar fractals after ion bombardment and a steady state fractal dimension is reached, except at large angles of incidence

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

: 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......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....... Retinal fractal analysis therefore is a potential tool for risk stratification in type 1 diabetes....

Fractal design concepts for stretchable electronics.

Science.gov (United States)

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

Science.gov (United States)

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.

Coding and transmission of subband coded images on the Internet

Science.gov (United States)

Wah, Benjamin W.; Su, Xiao

2001-09-01

Subband-coded images can be transmitted in the Internet using either the TCP or the UDP protocol. Delivery by TCP gives superior decoding quality but with very long delays when the network is unreliable, whereas delivery by UDP has negligible delays but with degraded quality when packets are lost. Although images are delivered currently over the Internet by TCP, we study in this paper the use of UDP to deliver multi-description reconstruction-based subband-coded images. First, in order to facilitate recovery from UDP packet losses, we propose a joint sender-receiver approach for designing optimized reconstruction-based subband transform (ORB-ST) in multi-description coding (MDC). Second, we carefully evaluate the delay-quality trade-offs between the TCP delivery of SDC images and the UDP and combined TCP/UDP delivery of MDC images. Experimental results show that our proposed ORB-ST performs well in real Internet tests, and UDP and combined TCP/UDP delivery of MDC images provide a range of attractive alternatives to TCP delivery.

Helicalised fractals

OpenAIRE

Saw, Vee-Liem; Chew, Lock Yue

2013-01-01

We formulate the helicaliser, which replaces a given smooth curve by another curve that winds around it. In our analysis, we relate this formulation to the geometrical properties of the self-similar circular fractal (the discrete version of the curved helical fractal). Iterative applications of the helicaliser to a given curve yields a set of helicalisations, with the infinitely helicalised object being a fractal. We derive the Hausdorff dimension for the infinitely helicalised straight line ...

Document image retrieval through word shape coding.

Science.gov (United States)

Lu, Shijian; Li, Linlin; Tan, Chew Lim

2008-11-01

This paper presents a document retrieval technique that is capable of searching document images without OCR (optical character recognition). The proposed technique retrieves document images by a new word shape coding scheme, which captures the document content through annotating each word image by a word shape code. In particular, we annotate word images by using a set of topological shape features including character ascenders/descenders, character holes, and character water reservoirs. With the annotated word shape codes, document images can be retrieved by either query keywords or a query document image. Experimental results show that the proposed document image retrieval technique is fast, efficient, and tolerant to various types of document degradation.

Bi-level image compression with tree coding

DEFF Research Database (Denmark)

Martins, Bo; Forchhammer, Søren

1996-01-01

Presently, tree coders are the best bi-level image coders. The current ISO standard, JBIG, is a good example. By organising code length calculations properly a vast number of possible models (trees) can be investigated within reasonable time prior to generating code. Three general-purpose coders...... are constructed by this principle. A multi-pass free tree coding scheme produces superior compression results for all test images. A multi-pass fast free template coding scheme produces much better results than JBIG for difficult images, such as halftonings. Rissanen's algorithm `Context' is presented in a new...

Content Progressive Coding of Limited Bits/pixel Images

DEFF Research Database (Denmark)

Jensen, Ole Riis; Forchhammer, Søren

1999-01-01

A new lossless context based method for content progressive coding of limited bits/pixel images is proposed. Progressive coding is achieved by separating the image into contelnt layers. Digital maps are compressed up to 3 times better than GIF.......A new lossless context based method for content progressive coding of limited bits/pixel images is proposed. Progressive coding is achieved by separating the image into contelnt layers. Digital maps are compressed up to 3 times better than GIF....

Fractal differential equations and fractal-time dynamical systems

Indian Academy of Sciences (India)

like fractal subsets of the real line may be termed as fractal-time dynamical systems. Formulation ... involving scaling and memory effects. But most of ..... begin by recalling the definition of the Riemann integral in ordinary calculus [33]. Let g: [a ...

A new set of wavelet- and fractals-based features for Gleason grading of prostate cancer histopathology images

Science.gov (United States)

Mosquera Lopez, Clara; Agaian, Sos

2013-02-01

Prostate cancer detection and staging is an important step towards patient treatment selection. Advancements in digital pathology allow the application of new quantitative image analysis algorithms for computer-assisted diagnosis (CAD) on digitized histopathology images. In this paper, we introduce a new set of features to automatically grade pathological images using the well-known Gleason grading system. The goal of this study is to classify biopsy images belonging to Gleason patterns 3, 4, and 5 by using a combination of wavelet and fractal features. For image classification we use pairwise coupling Support Vector Machine (SVM) classifiers. The accuracy of the system, which is close to 97%, is estimated through three different cross-validation schemes. The proposed system offers the potential for automating classification of histological images and supporting prostate cancer diagnosis.

Morphological Investigation and Fractal Properties of Realgar Nanoparticles

Directory of Open Access Journals (Sweden)

Amir Lashgari

2015-01-01

Full Text Available Some arsenic compounds can show extraordinary polymorphism. Realgar (As4S4 is among several minerals with various crystal forms and is one of the most important sources of arsenic for pharmaceutical use. Currently, realgar is used as an arsenic source in many industries, such as weaponry, publishing, textiles, cosmetics, and health products. In this paper, we used and reported new methods for the purification, nanonization, and structural morphological investigations of As4S4 by using planetary ball mills process for nanonization of the compound. The product was characterized using X-ray powder diffraction analysis, Fourier transform infrared spectrometry spectra, and field emission scanning electron microscope (FESEM imaging. We investigated the morphological properties of FESEM-imaged realgar nanoparticles by an image-processing technique that calculates fractal dimensions using values on a computer with MATLAB software. We applied the Statistical Package for the Social Sciences software for statistics data extracted from the FESEM image and obtained the statistics results of the fractal dimension and histogram plot for the FESEM image.

Fractal Dimension Analysis of Texture Formation of Whey Protein-Based Foods

Directory of Open Access Journals (Sweden)

Robi Andoyo

2018-01-01

Full Text Available Whey protein in the form of isolate or concentrate is widely used in food industries due to its functionality to form gel under certain condition and its nutritive value. Controlling or manipulating the formation of gel aggregates is used often to evaluate food texture. Many researchers made use of fractal analysis that provides the quantitative data (i.e., fractal dimension for fundamentally and rationally analyzing and designing whey protein-based food texture. This quantitative analysis is also done to better understand how the texture of whey protein-based food is formed. Two methods for fractal analysis were discussed in this review: image analysis (microscopy and rheology. These methods, however, have several limitations which greatly affect the accuracy of both fractal dimension values and types of aggregation obtained. This review therefore also discussed problem encountered and ways to reduce the potential errors during fractal analysis of each method.

Computing Challenges in Coded Mask Imaging

Science.gov (United States)

Skinner, Gerald

2009-01-01

This slide presaentation reviews the complications and challenges in developing computer systems for Coded Mask Imaging telescopes. The coded mask technique is used when there is no other way to create the telescope, (i.e., when there are wide fields of view, high energies for focusing or low energies for the Compton/Tracker Techniques and very good angular resolution.) The coded mask telescope is described, and the mask is reviewed. The coded Masks for the INTErnational Gamma-Ray Astrophysics Laboratory (INTEGRAL) instruments are shown, and a chart showing the types of position sensitive detectors used for the coded mask telescopes is also reviewed. Slides describe the mechanism of recovering an image from the masked pattern. The correlation with the mask pattern is described. The Matrix approach is reviewed, and other approaches to image reconstruction are described. Included in the presentation is a review of the Energetic X-ray Imaging Survey Telescope (EXIST) / High Energy Telescope (HET), with information about the mission, the operation of the telescope, comparison of the EXIST/HET with the SWIFT/BAT and details of the design of the EXIST/HET.

Fractal analysis of mandibular trabecular bone: optimal tile sizes for the tile counting method.

Science.gov (United States)

Huh, Kyung-Hoe; Baik, Jee-Seon; Yi, Won-Jin; Heo, Min-Suk; Lee, Sam-Sun; Choi, Soon-Chul; Lee, Sun-Bok; Lee, Seung-Pyo

2011-06-01

This study was performed to determine the optimal tile size for the fractal dimension of the mandibular trabecular bone using a tile counting method. Digital intraoral radiographic images were obtained at the mandibular angle, molar, premolar, and incisor regions of 29 human dry mandibles. After preprocessing, the parameters representing morphometric characteristics of the trabecular bone were calculated. The fractal dimensions of the processed images were analyzed in various tile sizes by the tile counting method. The optimal range of tile size was 0.132 mm to 0.396 mm for the fractal dimension using the tile counting method. The sizes were closely related to the morphometric parameters. The fractal dimension of mandibular trabecular bone, as calculated with the tile counting method, can be best characterized with a range of tile sizes from 0.132 to 0.396 mm.

Electromagnetic fields in fractal continua

Energy Technology Data Exchange (ETDEWEB)

Balankin, Alexander S., E-mail: abalankin@ipn.mx [Grupo “Mecánica Fractal”, Instituto Politécnico Nacional, México D.F., 07738 Mexico (Mexico); Mena, Baltasar [Instituto de Ingeniería, Universidad Nacional Autónoma de México, México D.F. (Mexico); Patiño, Julián [Grupo “Mecánica Fractal”, Instituto Politécnico Nacional, México D.F., 07738 Mexico (Mexico); Morales, Daniel [Instituto Mexicano del Petróleo, México D.F., 07730 Mexico (Mexico)

2013-04-01

Fractal continuum electrodynamics is developed on the basis of a model of three-dimensional continuum Φ{sub D}{sup 3}⊂E{sup 3} with a fractal metric. The generalized forms of Maxwell equations are derived employing the local fractional vector calculus related to the Hausdorff derivative. The difference between the fractal continuum electrodynamics based on the fractal metric of continua with Euclidean topology and the electrodynamics in fractional space F{sup α} accounting the fractal topology of continuum with the Euclidean metric is outlined. Some electromagnetic phenomena in fractal media associated with their fractal time and space metrics are discussed.

Fractals for Geoengineering

Science.gov (United States)

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

The global relationship between chromatin physical topology, fractal structure, and gene expression

DEFF Research Database (Denmark)

Almassalha, Luay M; Tiwari, A; Ruhoff, P T

2017-01-01

in an empty space, but in a highly complex, interrelated, and dense nanoenvironment that profoundly influences chemical interactions. We explored the relationship between the physical nanoenvironment of chromatin and gene transcription in vitro. We analytically show that changes in the fractal dimension, D...... show that the increased heterogeneity of physical structure of chromatin due to increase in fractal dimension correlates with increased heterogeneity of gene networks. These findings indicate that the higher order folding of chromatin topology may act as a molecular-pathway independent code regulating...

Image authentication using distributed source coding.

Science.gov (United States)

Lin, Yao-Chung; Varodayan, David; Girod, Bernd

2012-01-01

We present a novel approach using distributed source coding for image authentication. The key idea is to provide a Slepian-Wolf encoded quantized image projection as authentication data. This version can be correctly decoded with the help of an authentic image as side information. Distributed source coding provides the desired robustness against legitimate variations while detecting illegitimate modification. The decoder incorporating expectation maximization algorithms can authenticate images which have undergone contrast, brightness, and affine warping adjustments. Our authentication system also offers tampering localization by using the sum-product algorithm.

Future trends in image coding

Science.gov (United States)

Habibi, Ali

1993-01-01

The objective of this article is to present a discussion on the future of image data compression in the next two decades. It is virtually impossible to predict with any degree of certainty the breakthroughs in theory and developments, the milestones in advancement of technology and the success of the upcoming commercial products in the market place which will be the main factors in establishing the future stage to image coding. What we propose to do, instead, is look back at the progress in image coding during the last two decades and assess the state of the art in image coding today. Then, by observing the trends in developments of theory, software, and hardware coupled with the future needs for use and dissemination of imagery data and the constraints on the bandwidth and capacity of various networks, predict the future state of image coding. What seems to be certain today is the growing need for bandwidth compression. The television is using a technology which is half a century old and is ready to be replaced by high definition television with an extremely high digital bandwidth. Smart telephones coupled with personal computers and TV monitors accommodating both printed and video data will be common in homes and businesses within the next decade. Efficient and compact digital processing modules using developing technologies will make bandwidth compressed imagery the cheap and preferred alternative in satellite and on-board applications. In view of the above needs, we expect increased activities in development of theory, software, special purpose chips and hardware for image bandwidth compression in the next two decades. The following sections summarize the future trends in these areas.

Steady laminar flow of fractal fluids

Energy Technology Data Exchange (ETDEWEB)

Balankin, Alexander S., E-mail: abalankin@ipn.mx [Grupo Mecánica Fractal, ESIME, Instituto Politécnico Nacional, México D.F., 07738 (Mexico); Mena, Baltasar [Laboratorio de Ingeniería y Procesos Costeros, Instituto de Ingeniería, Universidad Nacional Autónoma de México, Sisal, Yucatán, 97355 (Mexico); Susarrey, Orlando; Samayoa, Didier [Grupo Mecánica Fractal, ESIME, Instituto Politécnico Nacional, México D.F., 07738 (Mexico)

2017-02-12

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. - Highlights: • Equations of Stokes flow of Newtonian fractal fluid are derived. • Pressure distribution in the Newtonian fractal fluid is derived. • Velocity distribution in Poiseuille flow of fractal fluid is found. • Velocity distribution in a steady Couette flow is established.

Mathematical diagnosis of pediatric echocardiograms with fractal dimension measures evaluated through intrinsic mathematical harmony

International Nuclear Information System (INIS)

Rodriguez V, Javier O; Prieto, Signed E; Ortiz, Liliana

2010-01-01

Geometry allows the objective mathematical characterization of forms. Fractal geometry characterizes irregular objects. The left ventricle dynamical states form observed through echocardiography can be objectively evaluated through fractal dimension measures. Methods: A measurement of fractal dimension was performed using the Box-counting method of three defined objects in 28 echocardiographic images, 16 from normal children (group A) and 12 ill children (group B), in order to establish differences between health and illness from its comparison with the fractal dimensions of 2 normality prototypes and 2 disease prototypes. Results: A new diagnostic, clinical application methodology was developed based in the intrinsic mathematical harmony (IMH) concept, and it was observed that the fractal dimensions of the defined objects for an abnormal echocardiogram show similarity to its fourth significant number, thus demonstrating the possibility of following up the evolution from normality towards disease. According to the performed calculations, 68.75% of the cases in group A could be better evaluated with the developed diagnostic methodology, and the ill ones could be diagnosed more effectively. Conclusions: The pediatric echocardiography images can be objectively characterized with fractal dimension measurements, thus enabling the development of a clinical diagnostic methodology of echocardiography in children from the IMH concept.

Coding aperture applied to X-ray imaging

International Nuclear Information System (INIS)

Brunol, J.; Sauneuf, R.; Gex, J.P.

1980-05-01

We present some X-ray images of grids and plasmas. These images were obtained by using a single circular slit (annular code) as coding aperture and a computer decoding process. The experimental resolution is better than 10μm and it is expected to be in the order of 2 or 3 μm with the same code and an improved decoding process

THE FRACTAL MARKET HYPOTHESIS

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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.

Use of digital image analysis combined with fractal theory to determine particle morphology and surface texture of quartz sands

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Georgia S. Araujo

2017-12-01

Full Text Available The particle morphology and surface texture play a major role in influencing mechanical and hydraulic behaviors of sandy soils. This paper presents the use of digital image analysis combined with fractal theory as a tool to quantify the particle morphology and surface texture of two types of quartz sands widely used in the region of Vitória, Espírito Santo, southeast of Brazil. The two investigated sands are sampled from different locations. The purpose of this paper is to present a simple, straightforward, reliable and reproducible methodology that can identify representative sandy soil texture parameters. The test results of the soil samples of the two sands separated by sieving into six size fractions are presented and discussed. The main advantages of the adopted methodology are its simplicity, reliability of the results, and relatively low cost. The results show that sands from the coastal spit (BS have a greater degree of roundness and a smoother surface texture than river sands (RS. The values obtained in the test are statistically analyzed, and again it is confirmed that the BS sand has a slightly greater degree of sphericity than that of the RS sand. Moreover, the RS sand with rough surface texture has larger specific surface area values than the similar BS sand, which agree with the obtained roughness fractal dimensions. The consistent experimental results demonstrate that image analysis combined with fractal theory is an accurate and efficient method to quantify the differences in particle morphology and surface texture of quartz sands.

Assessment of Textural Differentiations in Forest Resources in Romania Using Fractal Analysis

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Ion Andronache

2017-02-01

Full Text Available Deforestation and forest degradation have several negative effects on the environment including a loss of species habitats, disturbance of the water cycle and reduced ability to retain CO2, with consequences for global warming. We investigated the evolution of forest resources from development regions in Romania affected by both deforestation and reforestation using a non-Euclidean method based on fractal analysis. We calculated four fractal dimensions of forest areas: the fractal box-counting dimension of the forest areas, the fractal box-counting dimension of the dilated forest areas, the fractal dilation dimension and the box-counting dimension of the border of the dilated forest areas. Fractal analysis revealed morpho-structural and textural differentiations of forested, deforested and reforested areas in development regions with dominant mountain relief and high hills (more forested and compact organization in comparison to the development regions dominated by plains or low hills (less forested, more fragmented with small and isolated clusters. Our analysis used the fractal analysis that has the advantage of analyzing the entire image, rather than studying local information, thereby enabling quantification of the uniformity, fragmentation, heterogeneity and homogeneity of forests.

THE FRACTAL MARKET HYPOTHESIS

OpenAIRE

FELICIA RAMONA BIRAU

2012-01-01

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...

Image content authentication based on channel coding

Science.gov (United States)

Zhang, Fan; Xu, Lei

2008-03-01

The content authentication determines whether an image has been tampered or not, and if necessary, locate malicious alterations made on the image. Authentication on a still image or a video are motivated by recipient's interest, and its principle is that a receiver must be able to identify the source of this document reliably. Several techniques and concepts based on data hiding or steganography designed as a means for the image authentication. This paper presents a color image authentication algorithm based on convolution coding. The high bits of color digital image are coded by the convolution codes for the tamper detection and localization. The authentication messages are hidden in the low bits of image in order to keep the invisibility of authentication. All communications channels are subject to errors introduced because of additive Gaussian noise in their environment. Data perturbations cannot be eliminated but their effect can be minimized by the use of Forward Error Correction (FEC) techniques in the transmitted data stream and decoders in the receiving system that detect and correct bits in error. This paper presents a color image authentication algorithm based on convolution coding. The message of each pixel is convolution encoded with the encoder. After the process of parity check and block interleaving, the redundant bits are embedded in the image offset. The tamper can be detected and restored need not accessing the original image.

Do happy faces really modulate liking for Jackson Pollock art and statistical fractal noise images?

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Mundloch Katrin

2017-01-01

Full Text Available Flexas et al. (2013 demonstrated that happy faces increase preference for abstract art if seen in short succession. We could not replicate their findings. In our first experiment, we tested whether valence, saliency or arousal of facial primes can modulate liking of Jackson Pollock art crops. In the second experiment, the emphasis was on testing another type of abstract visual stimuli which possess similar low-level image features: statistical fractal noise images. Pollock crops were rated significantly higher when primed with happy faces in contrast to neutral faces, but not differently to the no-prime condition. Findings of our study suggest that affective priming with happy faces may be stimulus-specific and may have inadvertent effects on other abstract visual material.

A study of complexity of oral mucosa using fractal geometry

Directory of Open Access Journals (Sweden)

S R Shenoi

2017-01-01

Full Text Available Background: The oral mucosa lining the oral cavity is composed of epithelium supported by connective tissue. The shape of the epithelial-connective tissue interface has traditionally been used to describe physiological and pathological changes in the oral mucosa. Aim: The aim is to evaluate the morphometric complexity in normal, dysplastic, well-differentiated, and moderately differentiated squamous cell carcinoma (SCC of the oral mucosa using fractal geometry. Materials and Methods: A total of 80 periodic acid–Schiff stained histological images of four groups: normal mucosa, dysplasia, well-differentiated SCC, and moderately differentiated SCC were verified by the gold standard. These images were then subjected to fractal analysis. Statistical Analysis: ANOVA and post hoc test: Bonferroni was applied. Results: Fractal dimension (FD increases as the complexity increases from normal to dysplasia and then to SCC. Normal buccal mucosa was found to be significantly different from dysplasia and the two grades of SCC (P < 0.05. ANOVA of fractal scores of four morphometrically different groups of buccal mucosa was significantly different with F (3,76 = 23.720 and P< 0.01. However, FD of dysplasia was not significantly different from well-differentiated and moderately differentiated SCC (P = 1.000 and P = 0.382, respectively. Conclusion: This study establishes FD as a newer tool in differentiating normal tissue from dysplastic and neoplastic tissue. Fractal geometry is useful in the study of both physiological and pathological changes in the oral mucosa. A new grading system based on FD may emerge as an adjuvant aid in cancer diagnosis.

Image Coding Based on Address Vector Quantization.

Science.gov (United States)

Feng, Yushu

Image coding is finding increased application in teleconferencing, archiving, and remote sensing. This thesis investigates the potential of Vector Quantization (VQ), a relatively new source coding technique, for compression of monochromatic and color images. Extensions of the Vector Quantization technique to the Address Vector Quantization method have been investigated. In Vector Quantization, the image data to be encoded are first processed to yield a set of vectors. A codeword from the codebook which best matches the input image vector is then selected. Compression is achieved by replacing the image vector with the index of the code-word which produced the best match, the index is sent to the channel. Reconstruction of the image is done by using a table lookup technique, where the label is simply used as an address for a table containing the representative vectors. A code-book of representative vectors (codewords) is generated using an iterative clustering algorithm such as K-means, or the generalized Lloyd algorithm. A review of different Vector Quantization techniques are given in chapter 1. Chapter 2 gives an overview of codebook design methods including the Kohonen neural network to design codebook. During the encoding process, the correlation of the address is considered and Address Vector Quantization is developed for color image and monochrome image coding. Address VQ which includes static and dynamic processes is introduced in chapter 3. In order to overcome the problems in Hierarchical VQ, Multi-layer Address Vector Quantization is proposed in chapter 4. This approach gives the same performance as that of the normal VQ scheme but the bit rate is about 1/2 to 1/3 as that of the normal VQ method. In chapter 5, a Dynamic Finite State VQ based on a probability transition matrix to select the best subcodebook to encode the image is developed. In chapter 6, a new adaptive vector quantization scheme, suitable for color video coding, called "A Self -Organizing

Subband coding for image data archiving

Science.gov (United States)

Glover, Daniel; Kwatra, S. C.

1993-01-01

The use of subband coding on image data is discussed. An overview of subband coding is given. Advantages of subbanding for browsing and progressive resolution are presented. Implementations for lossless and lossy coding are discussed. Algorithm considerations and simple implementations of subband systems are given.

Quantitative assessment of the influence of anatomic noise on the detection of subtle lung nodule in digital chest radiography using fractal-feature distance

International Nuclear Information System (INIS)

Imai, Kuniharu; Ikeda, Mitsuru; Enchi, Yukihiro; Niimi, Takanaga

2008-01-01

Purpose: To confirm whether or not the influence of anatomic noise on the detection of nodules in digital chest radiography can be evaluated by the fractal-feature distance. Materials and methods: We used the square images with and without a simulated nodule which were generated in our previous observer performance study; the simulated nodule was located on the upper margin of a rib, the inside of a rib, the lower margin of a rib, or the central region between two adjoining ribs. For the square chest images, fractal analysis was conducted using the virtual volume method. The fractal-feature distances between the considered and the reference images were calculated using the pseudo-fractal dimension and complexity, and the square images without the simulated nodule were employed as the reference images. We compared the fractal-feature distances with the observer's confidence level regarding the presence of a nodule in plain chest radiograph. Results: For all square chest images, the relationships between the length of the square boxes and the mean of the virtual volumes were linear on a log-log scale. For all types of the simulated nodules, the fractal-feature distance was the highest for the simulated nodules located on the central region between two adjoining ribs and was the lowest for those located in the inside of a rib. The fractal-feature distance showed a linear relation to an observer's confidence level. Conclusion: The fractal-feature distance would be useful for evaluating the influence of anatomic noise on the detection of nodules in digital chest radiography

Fractal Metrology for biogeosystems analysis

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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.

A Novel High Efficiency Fractal Multiview Video Codec

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Shiping Zhu

2015-01-01

Full Text Available Multiview video which is one of the main types of three-dimensional (3D video signals, captured by a set of video cameras from various viewpoints, has attracted much interest recently. Data compression for multiview video has become a major issue. In this paper, a novel high efficiency fractal multiview video codec is proposed. Firstly, intraframe algorithm based on the H.264/AVC intraprediction modes and combining fractal and motion compensation (CFMC algorithm in which range blocks are predicted by domain blocks in the previously decoded frame using translational motion with gray value transformation is proposed for compressing the anchor viewpoint video. Then temporal-spatial prediction structure and fast disparity estimation algorithm exploiting parallax distribution constraints are designed to compress the multiview video data. The proposed fractal multiview video codec can exploit temporal and spatial correlations adequately. Experimental results show that it can obtain about 0.36 dB increase in the decoding quality and 36.21% decrease in encoding bitrate compared with JMVC8.5, and the encoding time is saved by 95.71%. The rate-distortion comparisons with other multiview video coding methods also demonstrate the superiority of the proposed scheme.

Coding of Depth Images for 3DTV

DEFF Research Database (Denmark)

Zamarin, Marco; Forchhammer, Søren

In this short paper a brief overview of the topic of coding and compression of depth images for multi-view image and video coding is provided. Depth images represent a convenient way to describe distances in the 3D scene, useful for 3D video processing purposes. Standard approaches...... for the compression of depth images are described and compared against some recent specialized algorithms able to achieve higher compression performances. Future research directions close the paper....

Fractal description of fractures

International Nuclear Information System (INIS)

Lung, C.W.

1991-06-01

Recent studies on the fractal description of fractures are reviewed. Some problems on this subject are discussed. It seems hopeful to use the fractal dimension as a parameter for quantitative fractography and to apply fractal structures to the development of high toughness materials. (author). 28 refs, 7 figs

Fractals and foods.

Science.gov (United States)

Peleg, M

1993-01-01

Fractal geometry and related concepts have had only a very minor impact on food research. The very few reported food applications deal mainly with the characterization of the contours of agglomerated instant coffee particles, the surface morphology of treated starch particles, the microstructure of casein gels viewed as a product limited diffusion aggregation, and the jagged mechanical signatures of crunchy dry foods. Fractal geometry describes objects having morphological features that are scale invariant. A demonstration of the self-similarity of fractal objects can be found in the familiar morphology of cauliflower and broccoli, both foods. Processes regulated by nonlinear dynamics can exhibit a chaotic behavior that has fractal characteristics. Examples are mixing of viscous fluids, turbulence, crystallization, agglomeration, diffusion, and possibly food spoilage.

X-ray image coding

International Nuclear Information System (INIS)

1974-01-01

The invention aims at decreasing the effect of stray radiation in X-ray images. This is achieved by putting a plate between source and object with parallel zones of alternating high and low absorption coefficients for X-radiation. The image is scanned with the help of electronic circuits which decode the signal space coded by the plate, thus removing the stray radiation

Flames in fractal grid generated turbulence

Energy Technology Data Exchange (ETDEWEB)

Goh, K H H; Hampp, F; Lindstedt, R P [Department of Mechanical Engineering, Imperial College, London SW7 2AZ (United Kingdom); Geipel, P, E-mail: p.lindstedt@imperial.ac.uk [Siemens Industrial Turbomachinery AB, SE-612 83 Finspong (Sweden)

2013-12-15

Twin premixed turbulent opposed jet flames were stabilized for lean mixtures of air with methane and propane in fractal grid generated turbulence. A density segregation method was applied alongside particle image velocimetry to obtain velocity and scalar statistics. It is shown that the current fractal grids increase the turbulence levels by around a factor of 2. Proper orthogonal decomposition (POD) was applied to show that the fractal grids produce slightly larger turbulent structures that decay at a slower rate as compared to conventional perforated plates. Conditional POD (CPOD) was also implemented using the density segregation technique and the results show that CPOD is essential to segregate the relative structures and turbulent kinetic energy distributions in each stream. The Kolmogorov length scales were also estimated providing values {approx}0.1 and {approx}0.5 mm in the reactants and products, respectively. Resolved profiles of flame surface density indicate that a thin flame assumption leading to bimodal statistics is not perfectly valid under the current conditions and it is expected that the data obtained will be of significant value to the development of computational methods that can provide information on the conditional structure of turbulence. It is concluded that the increase in the turbulent Reynolds number is without any negative impact on other parameters and that fractal grids provide a route towards removing the classical problem of a relatively low ratio of turbulent to bulk strain associated with the opposed jet configuration. (paper)

Fractal Analysis of Mobile Social Networks

International Nuclear Information System (INIS)

Zheng Wei; Pan Qian; Sun Chen; Deng Yu-Fan; Zhao Xiao-Kang; Kang Zhao

2016-01-01

Fractal and self similarity of complex networks have attracted much attention in recent years. The fractal dimension is a useful method to describe the fractal property of networks. However, the fractal features of mobile social networks (MSNs) are inadequately investigated. In this work, a box-covering method based on the ratio of excluded mass to closeness centrality is presented to investigate the fractal feature of MSNs. Using this method, we find that some MSNs are fractal at different time intervals. Our simulation results indicate that the proposed method is available for analyzing the fractal property of MSNs. (paper)

A progressive data compression scheme based upon adaptive transform coding: Mixture block coding of natural images

Science.gov (United States)

Rost, Martin C.; Sayood, Khalid

1991-01-01

A method for efficiently coding natural images using a vector-quantized variable-blocksized transform source coder is presented. The method, mixture block coding (MBC), incorporates variable-rate coding by using a mixture of discrete cosine transform (DCT) source coders. Which coders are selected to code any given image region is made through a threshold driven distortion criterion. In this paper, MBC is used in two different applications. The base method is concerned with single-pass low-rate image data compression. The second is a natural extension of the base method which allows for low-rate progressive transmission (PT). Since the base method adapts easily to progressive coding, it offers the aesthetic advantage of progressive coding without incorporating extensive channel overhead. Image compression rates of approximately 0.5 bit/pel are demonstrated for both monochrome and color images.

Predicting beauty: fractal dimension and visual complexity in art.

Science.gov (United States)

Forsythe, A; Nadal, M; Sheehy, N; Cela-Conde, C J; Sawey, M

2011-02-01

Visual complexity has been known to be a significant predictor of preference for artistic works for some time. The first study reported here examines the extent to which perceived visual complexity in art can be successfully predicted using automated measures of complexity. Contrary to previous findings the most successful predictor of visual complexity was Gif compression. The second study examined the extent to which fractal dimension could account for judgments of perceived beauty. The fractal dimension measure accounts for more of the variance in judgments of perceived beauty in visual art than measures of visual complexity alone, particularly for abstract and natural images. Results also suggest that when colour is removed from an artistic image observers are unable to make meaningful judgments as to its beauty. ©2010 The British Psychological Society.

Fractal dust grains in plasma

International Nuclear Information System (INIS)

Huang, F.; Peng, R. D.; Liu, Y. H.; Chen, Z. Y.; Ye, M. F.; Wang, L.

2012-01-01

Fractal dust grains of different shapes are observed in a radially confined magnetized radio frequency plasma. The fractal dimensions of the dust structures in two-dimensional (2D) horizontal dust layers are calculated, and their evolution in the dust growth process is investigated. It is found that as the dust grains grow the fractal dimension of the dust structure decreases. In addition, the fractal dimension of the center region is larger than that of the entire region in the 2D dust layer. In the initial growth stage, the small dust particulates at a high number density in a 2D layer tend to fill space as a normal surface with fractal dimension D = 2. The mechanism of the formation of fractal dust grains is discussed.

Assessment of disintegrant efficacy with fractal dimensions from real-time MRI.

Science.gov (United States)

Quodbach, Julian; Moussavi, Amir; Tammer, Roland; Frahm, Jens; Kleinebudde, Peter

2014-11-20

An efficient disintegrant is capable of breaking up a tablet in the smallest possible particles in the shortest time. Until now, comparative data on the efficacy of different disintegrants is based on dissolution studies or the disintegration time. Extending these approaches, this study introduces a method, which defines the evolution of fractal dimensions of tablets as surrogate parameter for the available surface area. Fractal dimensions are a measure for the tortuosity of a line, in this case the upper surface of a disintegrating tablet. High-resolution real-time MRI was used to record videos of disintegrating tablets. The acquired video images were processed to depict the upper surface of the tablets and a box-counting algorithm was used to estimate the fractal dimensions. The influence of six different disintegrants, of different relative tablet density, and increasing disintegrant concentration was investigated to evaluate the performance of the novel method. Changing relative densities hardly affect the progression of fractal dimensions, whereas an increase in disintegrant concentration causes increasing fractal dimensions during disintegration, which are also reached quicker. Different disintegrants display only minor differences in the maximal fractal dimension, yet the kinetic in which the maximum is reached allows a differentiation and classification of disintegrants. Copyright © 2014 Elsevier B.V. All rights reserved.

Fast-neutron, coded-aperture imager

International Nuclear Information System (INIS)

Woolf, Richard S.; Phlips, Bernard F.; Hutcheson, Anthony L.; Wulf, Eric A.

2015-01-01

This work discusses a large-scale, coded-aperture imager for fast neutrons, building off a proof-of concept instrument developed at the U.S. Naval Research Laboratory (NRL). The Space Science Division at the NRL has a heritage of developing large-scale, mobile systems, using coded-aperture imaging, for long-range γ-ray detection and localization. The fast-neutron, coded-aperture imaging instrument, designed for a mobile unit (20 ft. ISO container), consists of a 32-element array of 15 cm×15 cm×15 cm liquid scintillation detectors (EJ-309) mounted behind a 12×12 pseudorandom coded aperture. The elements of the aperture are composed of 15 cm×15 cm×10 cm blocks of high-density polyethylene (HDPE). The arrangement of the aperture elements produces a shadow pattern on the detector array behind the mask. By measuring of the number of neutron counts per masked and unmasked detector, and with knowledge of the mask pattern, a source image can be deconvolved to obtain a 2-d location. The number of neutrons per detector was obtained by processing the fast signal from each PMT in flash digitizing electronics. Digital pulse shape discrimination (PSD) was performed to filter out the fast-neutron signal from the γ background. The prototype instrument was tested at an indoor facility at the NRL with a 1.8-μCi and 13-μCi 252Cf neutron/γ source at three standoff distances of 9, 15 and 26 m (maximum allowed in the facility) over a 15-min integration time. The imaging and detection capabilities of the instrument were tested by moving the source in half- and one-pixel increments across the image plane. We show a representative sample of the results obtained at one-pixel increments for a standoff distance of 9 m. The 1.8-μCi source was not detected at the 26-m standoff. In order to increase the sensitivity of the instrument, we reduced the fastneutron background by shielding the top, sides and back of the detector array with 10-cm-thick HDPE. This shielding configuration led

Fast-neutron, coded-aperture imager

Energy Technology Data Exchange (ETDEWEB)

Woolf, Richard S., E-mail: richard.woolf@nrl.navy.mil; Phlips, Bernard F., E-mail: bernard.phlips@nrl.navy.mil; Hutcheson, Anthony L., E-mail: anthony.hutcheson@nrl.navy.mil; Wulf, Eric A., E-mail: eric.wulf@nrl.navy.mil

2015-06-01

This work discusses a large-scale, coded-aperture imager for fast neutrons, building off a proof-of concept instrument developed at the U.S. Naval Research Laboratory (NRL). The Space Science Division at the NRL has a heritage of developing large-scale, mobile systems, using coded-aperture imaging, for long-range γ-ray detection and localization. The fast-neutron, coded-aperture imaging instrument, designed for a mobile unit (20 ft. ISO container), consists of a 32-element array of 15 cm×15 cm×15 cm liquid scintillation detectors (EJ-309) mounted behind a 12×12 pseudorandom coded aperture. The elements of the aperture are composed of 15 cm×15 cm×10 cm blocks of high-density polyethylene (HDPE). The arrangement of the aperture elements produces a shadow pattern on the detector array behind the mask. By measuring of the number of neutron counts per masked and unmasked detector, and with knowledge of the mask pattern, a source image can be deconvolved to obtain a 2-d location. The number of neutrons per detector was obtained by processing the fast signal from each PMT in flash digitizing electronics. Digital pulse shape discrimination (PSD) was performed to filter out the fast-neutron signal from the γ background. The prototype instrument was tested at an indoor facility at the NRL with a 1.8-μCi and 13-μCi 252Cf neutron/γ source at three standoff distances of 9, 15 and 26 m (maximum allowed in the facility) over a 15-min integration time. The imaging and detection capabilities of the instrument were tested by moving the source in half- and one-pixel increments across the image plane. We show a representative sample of the results obtained at one-pixel increments for a standoff distance of 9 m. The 1.8-μCi source was not detected at the 26-m standoff. In order to increase the sensitivity of the instrument, we reduced the fastneutron background by shielding the top, sides and back of the detector array with 10-cm-thick HDPE. This shielding configuration led

Fractality and growth of He bubbles in metals

Science.gov (United States)

Kajita, Shin; Ito, Atsushi M.; Ohno, Noriyasu

2017-08-01

Pinholes are formed on surfaces of metals by the exposure to helium plasmas, and they are regarded as the initial process of the growth of fuzzy nanostructures. In this study, number density of the pinholes is investigated in detail from the scanning electron microscope (SEM) micrographs of tungsten and tantalum exposed to the helium plasmas. A power law relation was identified between the number density and the size of pinholes. From the slope and the region where the power law was satisfied, the fractal dimension D and smin, which characterize the SEM images, are deduced. Parametric dependences and material dependence of D and smin are revealed. To explain the fractality, simple Monte-Carlo simulations including random walks of He atoms and absorption on bubble was introduced. It is shown that the initial position of the random walk is one of the key factors to deduce the fractality. The results indicated that new nucleations of bubbles are necessary to reproduce the number-density distribution of bubbles.

Discovery of cosmic fractals

CERN Document Server

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

Proliferative diabetic retinopathy characterization based on fractal features: Evaluation on a publicly available dataset.

Science.gov (United States)

Orlando, José Ignacio; van Keer, Karel; Barbosa Breda, João; Manterola, Hugo Luis; Blaschko, Matthew B; Clausse, Alejandro

2017-12-01

Diabetic retinopathy (DR) is one of the most widespread causes of preventable blindness in the world. The most dangerous stage of this condition is proliferative DR (PDR), in which the risk of vision loss is high and treatments are less effective. Fractal features of the retinal vasculature have been previously explored as potential biomarkers of DR, yet the current literature is inconclusive with respect to their correlation with PDR. In this study, we experimentally assess their discrimination ability to recognize PDR cases. A statistical analysis of the viability of using three reference fractal characterization schemes - namely box, information, and correlation dimensions - to identify patients with PDR is presented. These descriptors are also evaluated as input features for training ℓ1 and ℓ2 regularized logistic regression classifiers, to estimate their performance. Our results on MESSIDOR, a public dataset of 1200 fundus photographs, indicate that patients with PDR are more likely to exhibit a higher fractal dimension than healthy subjects or patients with mild levels of DR (P≤1.3×10-2). Moreover, a supervised classifier trained with both fractal measurements and red lesion-based features reports an area under the ROC curve of 0.93 for PDR screening and 0.96 for detecting patients with optic disc neovascularizations. The fractal dimension of the vasculature increases with the level of DR. Furthermore, PDR screening using multiscale fractal measurements is more feasible than using their derived fractal dimensions. Code and further resources are provided at https://github.com/ignaciorlando/fundus-fractal-analysis. © 2017 American Association of Physicists in Medicine.

Fractal zeta functions and fractal drums higher-dimensional theory of complex dimensions

CERN Document Server

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...

Using Fractal And Morphological Criteria For Automatic Classification Of Lung Diseases

Science.gov (United States)

Vehel, Jacques Levy

1989-11-01

Medical Images are difficult to analyze by means of classical image processing tools because they are very complex and irregular. Such shapes are obtained for instance in Nuclear Medecine with the spatial distribution of activity for organs such as lungs, liver, and heart. We have tried to apply two different theories to these signals: - Fractal Geometry deals with the analysis of complex irregular shapes which cannot well be described by the classical Euclidean geometry. - Integral Geometry treats sets globally and allows to introduce robust measures. We have computed three parameters on three kinds of Lung's SPECT images: normal, pulmonary embolism and chronic desease: - The commonly used fractal dimension (FD), that gives a measurement of the irregularity of the 3D shape. - The generalized lacunarity dimension (GLD), defined as the variance of the ratio of the local activity by the mean activity, which is only sensitive to the distribution and the size of gaps in the surface. - The Favard length that gives an approximation of the surface of a 3-D shape. The results show that each slice of the lung, considered as a 3D surface, is fractal and that the fractal dimension is the same for each slice and for the three kind of lungs; as for the lacunarity and Favard length, they are clearly different for normal lungs, pulmonary embolisms and chronic diseases. These results indicate that automatic classification of Lung's SPECT can be achieved, and that a quantitative measurement of the evolution of the disease could be made.

Fractal geometry and number theory complex dimensions of fractal strings and zeros of zeta functions

CERN Document Server

Lapidus, Michael L

1999-01-01

A fractal drum is a bounded open subset of R. m with a fractal boundary. A difficult problem is to describe the relationship between the shape (geo­ metry) of the drum and its sound (its spectrum). In this book, we restrict ourselves to the one-dimensional case of fractal strings, and their higher dimensional analogues, fractal sprays. We develop a theory of complex di­ mensions of a fractal string, and we study how these complex dimensions relate the geometry with the spectrum of the fractal string. We refer the reader to [Berrl-2, Lapl-4, LapPol-3, LapMal-2, HeLapl-2] and the ref­ erences therein for further physical and mathematical motivations of this work. (Also see, in particular, Sections 7. 1, 10. 3 and 10. 4, along with Ap­ pendix B. ) In Chapter 1, we introduce the basic object of our research, fractal strings (see [Lapl-3, LapPol-3, LapMal-2, HeLapl-2]). A 'standard fractal string' is a bounded open subset of the real line. Such a set is a disjoint union of open intervals, the lengths of which ...

Quantum Fractal Eigenstates

OpenAIRE

Casati, Giulio; Maspero, Giulio; Shepelyansky, Dima L.

1997-01-01

We study quantum chaos in open dynamical systems and show that it is characterized by quantum fractal eigenstates located on the underlying classical strange repeller. The states with longest life times typically reveal a scars structure on the classical fractal set.

Electromagnetism on anisotropic fractal media

Science.gov (United States)

Ostoja-Starzewski, Martin

2013-04-01

Basic equations of electromagnetic fields in anisotropic fractal media are obtained using a dimensional regularization approach. First, a formulation based on product measures is shown to satisfy the four basic identities of the vector calculus. This allows a generalization of the Green-Gauss and Stokes theorems as well as the charge conservation equation on anisotropic fractals. Then, pursuing the conceptual approach, we derive the Faraday and Ampère laws for such fractal media, which, along with two auxiliary null-divergence conditions, effectively give the modified Maxwell equations. Proceeding on a separate track, we employ a variational principle for electromagnetic fields, appropriately adapted to fractal media, so as to independently derive the same forms of these two laws. It is next found that the parabolic (for a conducting medium) and the hyperbolic (for a dielectric medium) equations involve modified gradient operators, while the Poynting vector has the same form as in the non-fractal case. Finally, Maxwell's electromagnetic stress tensor is reformulated for fractal systems. In all the cases, the derived equations for fractal media depend explicitly on fractal dimensions in three different directions and reduce to conventional forms for continuous media with Euclidean geometries upon setting these each of dimensions equal to unity.

Pseudo color ghost coding imaging with pseudo thermal light

Science.gov (United States)

Duan, De-yang; Xia, Yun-jie

2018-04-01

We present a new pseudo color imaging scheme named pseudo color ghost coding imaging based on ghost imaging but with multiwavelength source modulated by a spatial light modulator. Compared with conventional pseudo color imaging where there is no nondegenerate wavelength spatial correlations resulting in extra monochromatic images, the degenerate wavelength and nondegenerate wavelength spatial correlations between the idle beam and signal beam can be obtained simultaneously. This scheme can obtain more colorful image with higher quality than that in conventional pseudo color coding techniques. More importantly, a significant advantage of the scheme compared to the conventional pseudo color coding imaging techniques is the image with different colors can be obtained without changing the light source and spatial filter.

Inkjet-Printed Ultra Wide Band Fractal Antennas

KAUST Repository

Maza, Armando Rodriguez

2012-05-01

In this work, Paper-based inkjet-printed Ultra-wide band (UWB) fractal antennas are presented. Three new designs, a combined UWB fractal monopole based on the fourth order Koch Snowflake fractal which utilizes a Sierpinski Gasket fractal for ink reduction, a Cantor-based fractal antenna which performs a larger bandwidth compared to previously published UWB Cantor fractal monopole antenna, and a 3D loop fractal antenna which attains miniaturization, impedance matching and multiband characteristics. It is shown that fractals prove to be a successful method of reducing fabrication cost in inkjet printed antennas while retaining or enhancing printed antenna performance.

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.

Alpha-spectrometry and fractal analysis of surface micro-images for characterisation of porous materials used in manufacture of targets for laser plasma experiments

Energy Technology Data Exchange (ETDEWEB)

Aushev, A A; Barinov, S P; Vasin, M G; Drozdov, Yu M; Ignat' ev, Yu V; Izgorodin, V M; Kovshov, D K; Lakhtikov, A E; Lukovkina, D D; Markelov, V V; Morovov, A P; Shishlov, V V [Russian Federal Nuclear Center ' All-Russian Research Institute of Experimental Physics' , Sarov, Nizhnii Novgorod region (Russian Federation)

2015-06-30

We present the results of employing the alpha-spectrometry method to determine the characteristics of porous materials used in targets for laser plasma experiments. It is shown that the energy spectrum of alpha-particles, after their passage through porous samples, allows one to determine the distribution of their path length in the foam skeleton. We describe the procedure of deriving such a distribution, excluding both the distribution broadening due to statistical nature of the alpha-particle interaction with an atomic structure (straggling) and hardware effects. The fractal analysis of micro-images is applied to the same porous surface samples that have been studied by alpha-spectrometry. The fractal dimension and size distribution of the number of the foam skeleton grains are obtained. Using the data obtained, a distribution of the total foam skeleton thickness along a chosen direction is constructed. It roughly coincides with the path length distribution of alpha-particles within a range of larger path lengths. It is concluded that the combined use of the alpha-spectrometry method and fractal analysis of images will make it possible to determine the size distribution of foam skeleton grains (or pores). The results can be used as initial data in theoretical studies on propagation of the laser and X-ray radiation in specific porous samples. (laser plasma)

Random walk through fractal environments

OpenAIRE

Isliker, H.; Vlahos, L.

2002-01-01

We analyze random walk through fractal environments, embedded in 3-dimensional, permeable space. Particles travel freely and are scattered off into random directions when they hit the fractal. The statistical distribution of the flight increments (i.e. of the displacements between two consecutive hittings) is analytically derived from a common, practical definition of fractal dimension, and it turns out to approximate quite well a power-law in the case where the dimension D of the fractal is ...

Fractals via iterated functions and multifunctions

International Nuclear Information System (INIS)

Singh, S.L.; Prasad, Bhagwati; Kumar, Ashish

2009-01-01

Fractals have wide applications in biology, computer graphics, quantum physics and several other areas of applied sciences (see, for instance [Daya Sagar BS, Rangarajan Govindan, Veneziano Daniele. Preface - fractals in geophysics. Chaos, Solitons and Fractals 2004;19:237-39; El Naschie MS. Young double-split experiment Heisenberg uncertainty principles and cantorian space-time. Chaos, Solitons and Fractals 1994;4(3):403-09; El Naschie MS. Quantum measurement, information, diffusion and cantorian geodesics. In: El Naschie MS, Rossler OE, Prigogine I, editors. Quantum mechanics, diffusion and Chaotic fractals. Oxford: Elsevier Science Ltd; 1995. p. 191-205; El Naschie MS. Iterated function systems, information and the two-slit experiment of quantum mechanics. In: El Naschie MS, Rossler OE, Prigogine I, editors. Quantum mechanics, diffusion and Chaotic fractals. Oxford: Elsevier Science Ltd; 1995. p. 185-9; El Naschie MS, Rossler OE, Prigogine I. Forward. In: El Naschie MS, Rossler OE, Prigogine I, editors. Quantum mechanics, diffusion and Chaotic fractals. Oxford: Elsevier Science Ltd; 1995; El Naschie MS. A review of E-infinity theory and the mass spectrum of high energy particle physics. Chaos, Solitons and Fractals 2004;19:209-36; El Naschie MS. Fractal black holes and information. Chaos, Solitons and Fractals 2006;29:23-35; El Naschie MS. Superstring theory: what it cannot do but E-infinity could. Chaos, Solitons and Fractals 2006;29:65-8). Especially, the study of iterated functions has been found very useful in the theory of black holes, two-slit experiment in quantum mechanics (cf. El Naschie, as mentioned above). The intent of this paper is to give a brief account of recent developments of fractals arising from IFS. We also discuss iterated multifunctions.

Fractal Electrochemical Microsupercapacitors

KAUST Repository

Hota, Mrinal Kanti

2017-08-17

The first successful fabrication of microsupercapacitors (μ-SCs) using fractal electrode designs is reported. Using sputtered anhydrous RuO thin-film electrodes as prototypes, μ-SCs are fabricated using Hilbert, Peano, and Moore fractal designs, and their performance is compared to conventional interdigital electrode structures. Microsupercapacitor performance, including energy density, areal and volumetric capacitances, changes with fractal electrode geometry. Specifically, the μ-SCs based on the Moore design show a 32% enhancement in energy density compared to conventional interdigital structures, when compared at the same power density and using the same thin-film RuO electrodes. The energy density of the Moore design is 23.2 mWh cm at a volumetric power density of 769 mW cm. In contrast, the interdigital design shows an energy density of only 17.5 mWh cm at the same power density. We show that active electrode surface area cannot alone explain the increase in capacitance and energy density. We propose that the increase in electrical lines of force, due to edging effects in the fractal electrodes, also contribute to the higher capacitance. This study shows that electrode fractal design is a viable strategy for improving the performance of integrated μ-SCs that use thin-film electrodes at no extra processing or fabrication cost.

Fractal Electrochemical Microsupercapacitors

KAUST Repository

Hota, Mrinal Kanti; Jiang, Qiu; Mashraei, Yousof; Salama, Khaled N.; Alshareef, Husam N.

2017-01-01

The first successful fabrication of microsupercapacitors (μ-SCs) using fractal electrode designs is reported. Using sputtered anhydrous RuO thin-film electrodes as prototypes, μ-SCs are fabricated using Hilbert, Peano, and Moore fractal designs, and their performance is compared to conventional interdigital electrode structures. Microsupercapacitor performance, including energy density, areal and volumetric capacitances, changes with fractal electrode geometry. Specifically, the μ-SCs based on the Moore design show a 32% enhancement in energy density compared to conventional interdigital structures, when compared at the same power density and using the same thin-film RuO electrodes. The energy density of the Moore design is 23.2 mWh cm at a volumetric power density of 769 mW cm. In contrast, the interdigital design shows an energy density of only 17.5 mWh cm at the same power density. We show that active electrode surface area cannot alone explain the increase in capacitance and energy density. We propose that the increase in electrical lines of force, due to edging effects in the fractal electrodes, also contribute to the higher capacitance. This study shows that electrode fractal design is a viable strategy for improving the performance of integrated μ-SCs that use thin-film electrodes at no extra processing or fabrication cost.

Fractal analysis reveals reduced complexity of retinal vessels in CADASIL.

Directory of Open Access Journals (Sweden)

Michele Cavallari

2011-04-01

Full Text Available The Cerebral Autosomal Dominant Arteriopathy with Subcortical Infarcts and Leukoencephalopathy (CADASIL affects mainly small cerebral arteries and leads to disability and dementia. The relationship between clinical expression of the disease and progression of the microvessel pathology is, however, uncertain as we lack tools for imaging brain vessels in vivo. Ophthalmoscopy is regarded as a window into the cerebral microcirculation. In this study we carried out an ophthalmoscopic examination in subjects with CADASIL. Specifically, we performed fractal analysis of digital retinal photographs. Data are expressed as mean fractal dimension (mean-D, a parameter that reflects complexity of the retinal vessel branching. Ten subjects with genetically confirmed diagnosis of CADASIL and 10 sex and age-matched control subjects were enrolled. Fractal analysis of retinal digital images was performed by means of a computer-based program, and the data expressed as mean-D. Brain MRI lesion volume in FLAIR and T1-weighted images was assessed using MIPAV software. Paired t-test was used to disclose differences in mean-D between CADASIL and control groups. Spearman rank analysis was performed to evaluate potential associations between mean-D values and both disease duration and disease severity, the latter expressed as brain MRI lesion volumes, in the subjects with CADASIL. The results showed that mean-D value of patients (1.42±0.05; mean±SD was lower than control (1.50±0.04; p = 0.002. Mean-D did not correlate with disease duration nor with MRI lesion volumes of the subjects with CADASIL. The findings suggest that fractal analysis is a sensitive tool to assess changes of retinal vessel branching, likely reflecting early brain microvessel alterations, in CADASIL patients.

Fractals and chaos

CERN Document Server

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...

Comparison of two fractal interpolation methods

Science.gov (United States)

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

Microstructure and fractal characteristics of the solid-liquid interface forming during directional solidification of Inconel 718

Directory of Open Access Journals (Sweden)

WANG Ling

2007-08-01

Full Text Available The solidification microstructure and fractal characteristics of the solid-liquid interfaces of Inconel 718, under different cooling rates during directional solidification, were investigated by using SEM. Results showed that 5 μm/s was the cellular-dendrite transient rate. The prime dendrite arm spacing (PDAS was measured by Image Tool and it decreased with the cooling rate increased. The fractal dimension of the interfaces was calculated and it changes from 1.204310 to 1.517265 with the withdrawal rate ranging from 10 to 100 μm/s. The physical significance of the fractal dimension was analyzed by using fractal theory. It was found that the fractal dimension of the dendrites can be used to describe the solidification microstructure and parameters at low cooling rate, but both the fractal dimension and the dendrite arm spacing are needed in order to integrally describe the evaluation of the solidification microstructure completely.

Fractal analysis of MRI data for the characterization of patients with schizophrenia and bipolar disorder

Science.gov (United States)

Squarcina, Letizia; De Luca, Alberto; Bellani, Marcella; Brambilla, Paolo; Turkheimer, Federico E.; Bertoldo, Alessandra

2015-02-01

Fractal geometry can be used to analyze shape and patterns in brain images. With this study we use fractals to analyze T1 data of patients affected by schizophrenia or bipolar disorder, with the aim of distinguishing between healthy and pathological brains using the complexity of brain structure, in particular of grey matter, as a marker of disease. 39 healthy volunteers, 25 subjects affected by schizophrenia and 11 patients affected by bipolar disorder underwent an MRI session. We evaluated fractal dimension of the brain cortex and its substructures, calculated with an algorithm based on the box-count algorithm. We modified this algorithm, with the aim of avoiding the segmentation processing step and using all the information stored in the image grey levels. Moreover, to increase sensitivity to local structural changes, we computed a value of fractal dimension for each slice of the brain or of the particular structure. To have reference values in comparing healthy subjects with patients, we built a template by averaging fractal dimension values of the healthy volunteers data. Standard deviation was evaluated and used to create a confidence interval. We also performed a slice by slice t-test to assess the difference at slice level between the three groups. Consistent average fractal dimension values were found across all the structures in healthy controls, while in the pathological groups we found consistent differences, indicating a change in brain and structures complexity induced by these disorders.

Fractal analysis of MRI data for the characterization of patients with schizophrenia and bipolar disorder

International Nuclear Information System (INIS)

Squarcina, Letizia; Bellani, Marcella; De Luca, Alberto; Bertoldo, Alessandra; Brambilla, Paolo; Turkheimer, Federico E

2015-01-01

Fractal geometry can be used to analyze shape and patterns in brain images. With this study we use fractals to analyze T1 data of patients affected by schizophrenia or bipolar disorder, with the aim of distinguishing between healthy and pathological brains using the complexity of brain structure, in particular of grey matter, as a marker of disease. 39 healthy volunteers, 25 subjects affected by schizophrenia and 11 patients affected by bipolar disorder underwent an MRI session. We evaluated fractal dimension of the brain cortex and its substructures, calculated with an algorithm based on the box-count algorithm. We modified this algorithm, with the aim of avoiding the segmentation processing step and using all the information stored in the image grey levels. Moreover, to increase sensitivity to local structural changes, we computed a value of fractal dimension for each slice of the brain or of the particular structure. To have reference values in comparing healthy subjects with patients, we built a template by averaging fractal dimension values of the healthy volunteers data. Standard deviation was evaluated and used to create a confidence interval. We also performed a slice by slice t-test to assess the difference at slice level between the three groups. Consistent average fractal dimension values were found across all the structures in healthy controls, while in the pathological groups we found consistent differences, indicating a change in brain and structures complexity induced by these disorders. (paper)

Automatic generation of aesthetic patterns on fractal tilings by means of dynamical systems

International Nuclear Information System (INIS)

Chung, K.W.; Ma, H.M.

2005-01-01

A fractal tiling or f-tiling is a tiling which possesses self-similarity and the boundary of which is a fractal. In this paper, we investigate the classification of fractal tilings with kite-shaped and dart-shaped prototiles from which three new f-tilings are found. Invariant mappings are constructed for the creation of aesthetic patterns on such tilings. A modified convergence time scheme is described, which reflects the rate of convergence of various orbits and at the same time, enhances the artistic appeal of a generated image. A scheme based on the frequency of visit at a pixel is used to generate chaotic attractors

Towards a physics on fractals: Differential vector calculus in three-dimensional continuum with fractal metric

Science.gov (United States)

Balankin, Alexander S.; Bory-Reyes, Juan; Shapiro, Michael

2016-02-01

One way to deal with physical problems on nowhere differentiable fractals is the mapping of these problems into the corresponding problems for continuum with a proper fractal metric. On this way different definitions of the fractal metric were suggested to account for the essential fractal features. In this work we develop the metric differential vector calculus in a three-dimensional continuum with a non-Euclidean metric. The metric differential forms and Laplacian are introduced, fundamental identities for metric differential operators are established and integral theorems are proved by employing the metric version of the quaternionic analysis for the Moisil-Teodoresco operator, which has been introduced and partially developed in this paper. The relations between the metric and conventional operators are revealed. It should be emphasized that the metric vector calculus developed in this work provides a comprehensive mathematical formalism for the continuum with any suitable definition of fractal metric. This offers a novel tool to study physics on fractals.

SU-D-BRA-04: Fractal Dimension Analysis of Edge-Detected Rectal Cancer CTs for Outcome Prediction

International Nuclear Information System (INIS)

Zhong, H; Wang, J; Hu, W; Shen, L; Wan, J; Zhou, Z; Zhang, Z

2015-01-01

Purpose: To extract the fractal dimension features from edge-detected rectal cancer CTs, and to examine the predictability of fractal dimensions to outcomes of primary rectal cancer patients. Methods: Ninety-seven rectal cancer patients treated with neo-adjuvant chemoradiation were enrolled in this study. CT images were obtained before chemoradiotherapy. The primary lesions of the rectal cancer were delineated by experienced radiation oncologists. These images were extracted and filtered by six different Laplacian of Gaussian (LoG) filters with different filter values (0.5–3.0: from fine to coarse) to achieve primary lesions in different anatomical scales. Edges of the original images were found at zero-crossings of the filtered images. Three different fractal dimensions (box-counting dimension, Minkowski dimension, mass dimension) were calculated upon the image slice with the largest cross-section of the primary lesion. The significance of these fractal dimensions in survival, recurrence and metastasis were examined by Student’s t-test. Results: For a follow-up time of two years, 18 of 97 patients had experienced recurrence, 24 had metastasis, and 18 were dead. Minkowski dimensions under large filter values (2.0, 2.5, 3.0) were significantly larger (p=0.014, 0.006, 0.015) in patients with recurrence than those without. For metastasis, only box-counting dimensions under a single filter value (2.5) showed differences (p=0.016) between patients with and without. For overall survival, box-counting dimensions (filter values = 0.5, 1.0, 1.5), Minkowski dimensions (filter values = 0.5, 1.5, 2.0, 2,5) and mass dimensions (filter values = 1.5, 2.0) were all significant (p<0.05). Conclusion: It is feasible to extract shape information by edge detection and fractal dimensions analysis in neo-adjuvant rectal cancer patients. This information can be used to prognosis prediction

Medical image compression based on vector quantization with variable block sizes in wavelet domain.

Science.gov (United States)

Jiang, Huiyan; Ma, Zhiyuan; Hu, Yang; Yang, Benqiang; Zhang, Libo

2012-01-01

An optimized medical image compression algorithm based on wavelet transform and improved vector quantization is introduced. The goal of the proposed method is to maintain the diagnostic-related information of the medical image at a high compression ratio. Wavelet transformation was first applied to the image. For the lowest-frequency subband of wavelet coefficients, a lossless compression method was exploited; for each of the high-frequency subbands, an optimized vector quantization with variable block size was implemented. In the novel vector quantization method, local fractal dimension (LFD) was used to analyze the local complexity of each wavelet coefficients, subband. Then an optimal quadtree method was employed to partition each wavelet coefficients, subband into several sizes of subblocks. After that, a modified K-means approach which is based on energy function was used in the codebook training phase. At last, vector quantization coding was implemented in different types of sub-blocks. In order to verify the effectiveness of the proposed algorithm, JPEG, JPEG2000, and fractal coding approach were chosen as contrast algorithms. Experimental results show that the proposed method can improve the compression performance and can achieve a balance between the compression ratio and the image visual quality.

Order-fractal transitions in abstract paintings

Energy Technology Data Exchange (ETDEWEB)

Calleja, E.M. de la, E-mail: elsama79@gmail.com [Instituto de Física, Universidade Federal do Rio Grande do Sul, Caixa Postal 15051, 91501-970, Porto Alegre, RS (Brazil); Cervantes, F. [Department of Applied Physics, CINVESTAV-IPN, Carr. Antigua a Progreso km.6, Cordemex, C.P.97310, Mérida, Yucatán (Mexico); Calleja, J. de la [Department of Informatics, Universidad Politécnica de Puebla, 72640 (Mexico)

2016-08-15

In this study, we determined the degree of order for 22 Jackson Pollock paintings using the Hausdorff–Besicovitch fractal dimension. Based on the maximum value of each multi-fractal spectrum, the artworks were classified according to the year in which they were painted. It has been reported that Pollock’s paintings are fractal and that this feature was more evident in his later works. However, our results show that the fractal dimension of these paintings ranges among values close to two. We characterize this behavior as a fractal-order transition. Based on the study of disorder-order transition in physical systems, we interpreted the fractal-order transition via the dark paint strokes in Pollock’s paintings as structured lines that follow a power law measured by the fractal dimension. We determined self-similarity in specific paintings, thereby demonstrating an important dependence on the scale of observations. We also characterized the fractal spectrum for the painting entitled Teri’s Find. We obtained similar spectra for Teri’s Find and Number 5, thereby suggesting that the fractal dimension cannot be rejected completely as a quantitative parameter for authenticating these artworks. -- Highlights: •We determined the degree of order in Jackson Pollock paintings using the Hausdorff–Besicovitch dimension. •We detected a fractal-order transition from Pollock’s paintings between 1947 and 1951. •We suggest that Jackson Pollock could have painted Teri’s Find.

Results from the coded aperture neutron imaging system

International Nuclear Information System (INIS)

Brubaker, Erik; Steele, John T.; Brennan, James S.; Marleau, Peter

2010-01-01

Because of their penetrating power, energetic neutrons and gamma rays (∼1 MeV) offer the best possibility of detecting highly shielded or distant special nuclear material (SNM). Of these, fast neutrons offer the greatest advantage due to their very low and well understood natural background. We are investigating a new approach to fast-neutron imaging - a coded aperture neutron imaging system (CANIS). Coded aperture neutron imaging should offer a highly efficient solution for improved detection speed, range, and sensitivity. We have demonstrated fast neutron and gamma ray imaging with several different configurations of coded masks patterns and detectors including an 'active' mask that is composed of neutron detectors. Here we describe our prototype detector and present some initial results from laboratory tests and demonstrations.

Entrainment to a real time fractal visual stimulus modulates fractal gait dynamics.

Science.gov (United States)

Rhea, Christopher K; Kiefer, Adam W; D'Andrea, Susan E; Warren, William H; Aaron, Roy K

2014-08-01

Fractal patterns characterize healthy biological systems and are considered to reflect the ability of the system to adapt to varying environmental conditions. Previous research has shown that fractal patterns in gait are altered following natural aging or disease, and this has potential negative consequences for gait adaptability that can lead to increased risk of injury. However, the flexibility of a healthy neurological system to exhibit different fractal patterns in gait has yet to be explored, and this is a necessary step toward understanding human locomotor control. Fifteen participants walked for 15min on a treadmill, either in the absence of a visual stimulus or while they attempted to couple the timing of their gait with a visual metronome that exhibited a persistent fractal pattern (contained long-range correlations) or a random pattern (contained no long-range correlations). The stride-to-stride intervals of the participants were recorded via analog foot pressure switches and submitted to detrended fluctuation analysis (DFA) to determine if the fractal patterns during the visual metronome conditions differed from the baseline (no metronome) condition. DFA α in the baseline condition was 0.77±0.09. The fractal patterns in the stride-to-stride intervals were significantly altered when walking to the fractal metronome (DFA α=0.87±0.06) and to the random metronome (DFA α=0.61±0.10) (both p<.05 when compared to the baseline condition), indicating that a global change in gait dynamics was observed. A variety of strategies were identified at the local level with a cross-correlation analysis, indicating that local behavior did not account for the consistent global changes. Collectively, the results show that a gait dynamics can be shifted in a prescribed manner using a visual stimulus and the shift appears to be a global phenomenon. Copyright © 2014 Elsevier B.V. All rights reserved.

Positron annihilation near fractal surfaces

International Nuclear Information System (INIS)

Lung, C.W.; Deng, K.M.; Xiong, L.Y.

1991-07-01

A model for positron annihilation in the sub-surface region near a fractal surface is proposed. It is found that the power law relationship between the mean positron implantation depth and incident positron energy can be used to measure the fractal dimension of the fractal surface in materials. (author). 10 refs, 2 figs

2-Step scalar deadzone quantization for bitplane image coding.

Science.gov (United States)

Auli-Llinas, Francesc

2013-12-01

Modern lossy image coding systems generate a quality progressive codestream that, truncated at increasing rates, produces an image with decreasing distortion. Quality progressivity is commonly provided by an embedded quantizer that employs uniform scalar deadzone quantization (USDQ) together with a bitplane coding strategy. This paper introduces a 2-step scalar deadzone quantization (2SDQ) scheme that achieves same coding performance as that of USDQ while reducing the coding passes and the emitted symbols of the bitplane coding engine. This serves to reduce the computational costs of the codec and/or to code high dynamic range images. The main insights behind 2SDQ are the use of two quantization step sizes that approximate wavelet coefficients with more or less precision depending on their density, and a rate-distortion optimization technique that adjusts the distortion decreases produced when coding 2SDQ indexes. The integration of 2SDQ in current codecs is straightforward. The applicability and efficiency of 2SDQ are demonstrated within the framework of JPEG2000.

Statistical and Fractal Processing of Phase Images of Human Biological Fluids

Directory of Open Access Journals (Sweden)

MARCHUK, Y. I.

2010-11-01

Full Text Available Performed in this work are complex statistical and fractal analyses of phase properties inherent to birefringence networks of liquid crystals consisting of optically-thin layers prepared from human bile. Within the framework of a statistical approach, the authors have investigated values and ranges for changes of statistical moments of the 1-st to 4-th orders that characterize coordinate distributions for phase shifts between orthogonal components of amplitudes inherent to laser radiation transformed by human bile with various pathologies. Using the Gramm-Charlie method, ascertained are correlation criteria for differentiation of phase maps describing pathologically changed liquid-crystal networks. In the framework of the fractal approach, determined are dimensionalities of self-similar coordinate phase distributions as well as features of transformation of logarithmic dependences for power spectra of these distributions for various types of human pathologies.

Feature extraction algorithm for space targets based on fractal theory

Science.gov (United States)

Tian, Balin; Yuan, Jianping; Yue, Xiaokui; Ning, Xin

2007-11-01

In order to offer a potential for extending the life of satellites and reducing the launch and operating costs, satellite servicing including conducting repairs, upgrading and refueling spacecraft on-orbit become much more frequently. Future space operations can be more economically and reliably executed using machine vision systems, which can meet real time and tracking reliability requirements for image tracking of space surveillance system. Machine vision was applied to the research of relative pose for spacecrafts, the feature extraction algorithm was the basis of relative pose. In this paper fractal geometry based edge extraction algorithm which can be used in determining and tracking the relative pose of an observed satellite during proximity operations in machine vision system was presented. The method gets the gray-level image distributed by fractal dimension used the Differential Box-Counting (DBC) approach of the fractal theory to restrain the noise. After this, we detect the consecutive edge using Mathematical Morphology. The validity of the proposed method is examined by processing and analyzing images of space targets. The edge extraction method not only extracts the outline of the target, but also keeps the inner details. Meanwhile, edge extraction is only processed in moving area to reduce computation greatly. Simulation results compared edge detection using the method which presented by us with other detection methods. The results indicate that the presented algorithm is a valid method to solve the problems of relative pose for spacecrafts.

A Complex Story: Universal Preference vs. Individual Differences Shaping Aesthetic Response to Fractals Patterns

Science.gov (United States)

Street, Nichola; Forsythe, Alexandra M.; Reilly, Ronan; Taylor, Richard; Helmy, Mai S.

2016-01-01

Fractal patterns offer one way to represent the rough complexity of the natural world. Whilst they dominate many of our visual experiences in nature, little large-scale perceptual research has been done to explore how we respond aesthetically to these patterns. Previous research (Taylor et al., 2011) suggests that the fractal patterns with mid-range fractal dimensions (FDs) have universal aesthetic appeal. Perceptual and aesthetic responses to visual complexity have been more varied with findings suggesting both linear (Forsythe et al., 2011) and curvilinear (Berlyne, 1970) relationships. Individual differences have been found to account for many of the differences we see in aesthetic responses but some, such as culture, have received little attention within the fractal and complexity research fields. This two-study article aims to test preference responses to FD and visual complexity, using a large cohort (N = 443) of participants from around the world to allow universality claims to be tested. It explores the extent to which age, culture and gender can predict our preferences for fractally complex patterns. Following exploratory analysis that found strong correlations between FD and visual complexity, a series of linear mixed-effect models were implemented to explore if each of the individual variables could predict preference. The first tested a linear complexity model (likelihood of selecting the more complex image from the pair of images) and the second a mid-range FD model (likelihood of selecting an image within mid-range). Results show that individual differences can reliably predict preferences for complexity across culture, gender and age. However, in fitting with current findings the mid-range models show greater consistency in preference not mediated by gender, age or culture. This article supports the established theory that the mid-range fractal patterns appear to be a universal construct underlying preference but also highlights the fragility of

Low-Rank Sparse Coding for Image Classification

KAUST Repository

Zhang, Tianzhu; Ghanem, Bernard; Liu, Si; Xu, Changsheng; Ahuja, Narendra

2013-01-01

In this paper, we propose a low-rank sparse coding (LRSC) method that exploits local structure information among features in an image for the purpose of image-level classification. LRSC represents densely sampled SIFT descriptors, in a spatial neighborhood, collectively as low-rank, sparse linear combinations of code words. As such, it casts the feature coding problem as a low-rank matrix learning problem, which is different from previous methods that encode features independently. This LRSC has a number of attractive properties. (1) It encourages sparsity in feature codes, locality in codebook construction, and low-rankness for spatial consistency. (2) LRSC encodes local features jointly by considering their low-rank structure information, and is computationally attractive. We evaluate the LRSC by comparing its performance on a set of challenging benchmarks with that of 7 popular coding and other state-of-the-art methods. Our experiments show that by representing local features jointly, LRSC not only outperforms the state-of-the-art in classification accuracy but also improves the time complexity of methods that use a similar sparse linear representation model for feature coding.

Low-Rank Sparse Coding for Image Classification

KAUST Repository

Zhang, Tianzhu

2013-12-01

In this paper, we propose a low-rank sparse coding (LRSC) method that exploits local structure information among features in an image for the purpose of image-level classification. LRSC represents densely sampled SIFT descriptors, in a spatial neighborhood, collectively as low-rank, sparse linear combinations of code words. As such, it casts the feature coding problem as a low-rank matrix learning problem, which is different from previous methods that encode features independently. This LRSC has a number of attractive properties. (1) It encourages sparsity in feature codes, locality in codebook construction, and low-rankness for spatial consistency. (2) LRSC encodes local features jointly by considering their low-rank structure information, and is computationally attractive. We evaluate the LRSC by comparing its performance on a set of challenging benchmarks with that of 7 popular coding and other state-of-the-art methods. Our experiments show that by representing local features jointly, LRSC not only outperforms the state-of-the-art in classification accuracy but also improves the time complexity of methods that use a similar sparse linear representation model for feature coding.

Pseudo real-time coded aperture imaging system with intensified vidicon cameras

International Nuclear Information System (INIS)

Han, K.S.; Berzins, G.J.

1977-01-01

A coded image displayed on a TV monitor was used to directly reconstruct a decoded image. Both the coded and the decoded images were viewed with intensified vidicon cameras. The coded aperture was a 15-element nonredundant pinhole array. The coding and decoding were accomplished simultaneously during the scanning of a single 16-msec TV frame

Fast-neutron, coded-aperture imager

Science.gov (United States)

Woolf, Richard S.; Phlips, Bernard F.; Hutcheson, Anthony L.; Wulf, Eric A.

2015-06-01

This work discusses a large-scale, coded-aperture imager for fast neutrons, building off a proof-of concept instrument developed at the U.S. Naval Research Laboratory (NRL). The Space Science Division at the NRL has a heritage of developing large-scale, mobile systems, using coded-aperture imaging, for long-range γ-ray detection and localization. The fast-neutron, coded-aperture imaging instrument, designed for a mobile unit (20 ft. ISO container), consists of a 32-element array of 15 cm×15 cm×15 cm liquid scintillation detectors (EJ-309) mounted behind a 12×12 pseudorandom coded aperture. The elements of the aperture are composed of 15 cm×15 cm×10 cm blocks of high-density polyethylene (HDPE). The arrangement of the aperture elements produces a shadow pattern on the detector array behind the mask. By measuring of the number of neutron counts per masked and unmasked detector, and with knowledge of the mask pattern, a source image can be deconvolved to obtain a 2-d location. The number of neutrons per detector was obtained by processing the fast signal from each PMT in flash digitizing electronics. Digital pulse shape discrimination (PSD) was performed to filter out the fast-neutron signal from the γ background. The prototype instrument was tested at an indoor facility at the NRL with a 1.8-μCi and 13-μCi 252Cf neutron/γ source at three standoff distances of 9, 15 and 26 m (maximum allowed in the facility) over a 15-min integration time. The imaging and detection capabilities of the instrument were tested by moving the source in half- and one-pixel increments across the image plane. We show a representative sample of the results obtained at one-pixel increments for a standoff distance of 9 m. The 1.8-μCi source was not detected at the 26-m standoff. In order to increase the sensitivity of the instrument, we reduced the fastneutron background by shielding the top, sides and back of the detector array with 10-cm-thick HDPE. This shielding configuration led

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.

Encounters with chaos and fractals

CERN Document Server

Gulick, Denny

2012-01-01

Periodic Points Iterates of Functions Fixed Points Periodic Points Families of Functions The Quadratic Family Bifurcations Period-3 Points The Schwarzian Derivative One-Dimensional Chaos Chaos Transitivity and Strong Chaos Conjugacy Cantor Sets Two-Dimensional Chaos Review of Matrices Dynamics of Linear FunctionsNonlinear Maps The Hénon Map The Horseshoe Map Systems of Differential Equations Review of Systems of Differential Equations Almost Linearity The Pendulum The Lorenz System Introduction to Fractals Self-Similarity The Sierpiński Gasket and Other "Monsters"Space-Filling Curves Similarity and Capacity DimensionsLyapunov Dimension Calculating Fractal Dimensions of Objects Creating Fractals Sets Metric Spaces The Hausdorff Metric Contractions and Affine Functions Iterated Function SystemsAlgorithms for Drawing Fractals Complex Fractals: Julia Sets and the Mandelbrot Set Complex Numbers and Functions Julia Sets The Mandelbrot Set Computer Programs Answers to Selected Exercises References Index.

Fractal Structures For Fixed Mems Capacitors

KAUST Repository

Elshurafa, Amro M.

2014-08-28

An embodiment of a fractal fixed capacitor comprises a capacitor body in a microelectromechanical system (MEMS) structure. The capacitor body has a first plate with a fractal shape separated by a horizontal distance from a second plate with a fractal shape. The first plate and the second plate are within the same plane. Such a fractal fixed capacitor further comprises a substrate above which the capacitor body is positioned.

Enhanced Graphene Photodetector with Fractal Metasurface

DEFF Research Database (Denmark)

Fan, Jieran; Wang, Di; DeVault, Clayton

2016-01-01

We designed and fabricated a broadband, polarization-independent photodetector by integrating graphene with a fractal Cayley tree metasurface. Our measurements show an almost uniform, tenfold enhancement in photocurrent generation due to the fractal metasurface structure.......We designed and fabricated a broadband, polarization-independent photodetector by integrating graphene with a fractal Cayley tree metasurface. Our measurements show an almost uniform, tenfold enhancement in photocurrent generation due to the fractal metasurface structure....

Fractal Structures For Fixed Mems Capacitors

KAUST Repository

Elshurafa, Amro M.; Radwan, Ahmed Gomaa Ahmed; Emira, Ahmed A.; Salama, Khaled N.

2014-01-01

An embodiment of a fractal fixed capacitor comprises a capacitor body in a microelectromechanical system (MEMS) structure. The capacitor body has a first plate with a fractal shape separated by a horizontal distance from a second plate with a fractal shape. The first plate and the second plate are within the same plane. Such a fractal fixed capacitor further comprises a substrate above which the capacitor body is positioned.

Psicodiagnóstico fractal

OpenAIRE

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.

Code-modulated interferometric imaging system using phased arrays

Science.gov (United States)

Chauhan, Vikas; Greene, Kevin; Floyd, Brian

2016-05-01

Millimeter-wave (mm-wave) imaging provides compelling capabilities for security screening, navigation, and bio- medical applications. Traditional scanned or focal-plane mm-wave imagers are bulky and costly. In contrast, phased-array hardware developed for mass-market wireless communications and automotive radar promise to be extremely low cost. In this work, we present techniques which can allow low-cost phased-array receivers to be reconfigured or re-purposed as interferometric imagers, removing the need for custom hardware and thereby reducing cost. Since traditional phased arrays power combine incoming signals prior to digitization, orthogonal code-modulation is applied to each incoming signal using phase shifters within each front-end and two-bit codes. These code-modulated signals can then be combined and processed coherently through a shared hardware path. Once digitized, visibility functions can be recovered through squaring and code-demultiplexing operations. Pro- vided that codes are selected such that the product of two orthogonal codes is a third unique and orthogonal code, it is possible to demultiplex complex visibility functions directly. As such, the proposed system modulates incoming signals but demodulates desired correlations. In this work, we present the operation of the system, a validation of its operation using behavioral models of a traditional phased array, and a benchmarking of the code-modulated interferometer against traditional interferometer and focal-plane arrays.

A Fractal Perspective on Scale in Geography

Directory of Open Access Journals (Sweden)

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.

Design of LTCC Based Fractal Antenna

KAUST Repository

AdbulGhaffar, Farhan

2010-09-01

The thesis presents a Sierpinski Carpet fractal antenna array designed at 24 GHz for automotive radar applications. Miniaturized, high performance and low cost antennas are required for this application. To meet these specifications a fractal array has been designed for the first time on Low Temperature Co-fired Ceramic (LTCC) based substrate. LTCC provides a suitable platform for the development of these antennas due to its properties of vertical stack up and embedded passives. The complete antenna concept involves integration of this fractal antenna array with a Fresnel lens antenna providing a total gain of 15dB which is appropriate for medium range radar applications. The thesis also presents a comparison between the designed fractal antenna and a conventional patch antenna outlining the advantages of fractal antenna over the later one. The fractal antenna has a bandwidth of 1.8 GHz which is 7.5% of the centre frequency (24GHz) as compared to 1.9% of the conventional patch antenna. Furthermore the fractal design exhibits a size reduction of 53% as compared to the patch antenna. In the end a sensitivity analysis is carried out for the fractal antenna design depicting the robustness of the proposed design against the typical LTCC fabrication tolerances.

Variable Rate, Adaptive Transform Tree Coding Of Images

Science.gov (United States)

Pearlman, William A.

1988-10-01

A tree code, asymptotically optimal for stationary Gaussian sources and squared error distortion [2], is used to encode transforms of image sub-blocks. The variance spectrum of each sub-block is estimated and specified uniquely by a set of one-dimensional auto-regressive parameters. The expected distortion is set to a constant for each block and the rate is allowed to vary to meet the given level of distortion. Since the spectrum and rate are different for every block, the code tree differs for every block. Coding simulations for target block distortion of 15 and average block rate of 0.99 bits per pel (bpp) show that very good results can be obtained at high search intensities at the expense of high computational complexity. The results at the higher search intensities outperform a parallel simulation with quantization replacing tree coding. Comparative coding simulations also show that the reproduced image with variable block rate and average rate of 0.99 bpp has 2.5 dB less distortion than a similarly reproduced image with a constant block rate equal to 1.0 bpp.

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...

Optical image encryption based on real-valued coding and subtracting with the help of QR code

Science.gov (United States)

Deng, Xiaopeng

2015-08-01

A novel optical image encryption based on real-valued coding and subtracting is proposed with the help of quick response (QR) code. In the encryption process, the original image to be encoded is firstly transformed into the corresponding QR code, and then the corresponding QR code is encoded into two phase-only masks (POMs) by using basic vector operations. Finally, the absolute values of the real or imaginary parts of the two POMs are chosen as the ciphertexts. In decryption process, the QR code can be approximately restored by recording the intensity of the subtraction between the ciphertexts, and hence the original image can be retrieved without any quality loss by scanning the restored QR code with a smartphone. Simulation results and actual smartphone collected results show that the method is feasible and has strong tolerance to noise, phase difference and ratio between intensities of the two decryption light beams.

Fractal analysis of sulphidic mineral

Directory of Open Access Journals (Sweden)

Miklúšová 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

Improvement of Secret Image Invisibility in Circulation Image with Dyadic Wavelet Based Data Hiding with Run-Length Coded Secret Images of Which Location of Codes are Determined with Random Number

OpenAIRE

Kohei Arai; Yuji Yamada

2011-01-01

An attempt is made for improvement of secret image invisibility in circulation images with dyadic wavelet based data hiding with run-length coded secret images of which location of codes are determined by random number. Through experiments, it is confirmed that secret images are almost invisible in circulation images. Also robustness of the proposed data hiding method against data compression of circulation images is discussed. Data hiding performance in terms of invisibility of secret images...

Variability of the fractal dimension of the left coronary tree in-patient with disease arterial severe occlusive

International Nuclear Information System (INIS)

Rodriguez, Javier; Alvarez, Luisa F; Marino, Martha E and others

2004-01-01

Fractal geometry is a chapter of mathematics that allows the measurement of irregularity in natural objects. The adequate measures in order to characterize the forms of the human body are the fractal dimensions. Coronary ramification is a fractal object, which enables the diagnosis of occlusive arterial disease by the measurement of an arterial segment obtained by coronary angiography, without measuring the impact of the obstruction in the whole ramification. Fractal dimension evaluates the irregularity of the whole coronary ramification. The right anterior oblique projection (RAO) of the left coronary ramifications (LCR) obtained through arteriography is evaluated with fractal dimensions, using the box counting method. Images of the ramification between systole and diastole were measured in 14 patients, 7 of them without occlusive arterial disease, group 1, and 7 with severe occlusive arterial disease, group 2. Patients without occlusive arterial disease showed a greater variability in the fractal dimensions sequence evaluated with the net difference, being in general this difference other than zero

Variable code gamma ray imaging system

International Nuclear Information System (INIS)

Macovski, A.; Rosenfeld, D.

1979-01-01

A gamma-ray source distribution in the body is imaged onto a detector using an array of apertures. The transmission of each aperture is modulated using a code such that the individual views of the source through each aperture can be decoded and separated. The codes are chosen to maximize the signal to noise ratio for each source distribution. These codes determine the photon collection efficiency of the aperture array. Planar arrays are used for volumetric reconstructions and circular arrays for cross-sectional reconstructions. 14 claims

Collaborative Image Coding and Transmission over Wireless Sensor Networks

Directory of Open Access Journals (Sweden)

Min Wu

2007-01-01

Full Text Available The imaging sensors are able to provide intuitive visual information for quick recognition and decision. However, imaging sensors usually generate vast amount of data. Therefore, processing and coding of image data collected in a sensor network for the purpose of energy efficient transmission poses a significant technical challenge. In particular, multiple sensors may be collecting similar visual information simultaneously. We propose in this paper a novel collaborative image coding and transmission scheme to minimize the energy for data transmission. First, we apply a shape matching method to coarsely register images to find out maximal overlap to exploit the spatial correlation between images acquired from neighboring sensors. For a given image sequence, we transmit background image only once. A lightweight and efficient background subtraction method is employed to detect targets. Only the regions of target and their spatial locations are transmitted to the monitoring center. The whole image can then be reconstructed by fusing the background and the target images as well as their spatial locations. Experimental results show that the energy for image transmission can indeed be greatly reduced with collaborative image coding and transmission.

Fractal analysis of phasic laser images of the myocardium for the purpose of diagnostics of acute coronary insufficiency

Science.gov (United States)

Wanchuliak, O. Y.; Bachinskyi, V. T.

2011-09-01

In this work on the base of Mueller-matrix description of optical anisotropy, the possibility of monitoring of time changes of myocardium tissue birefringence, has been considered. The optical model of polycrystalline networks of myocardium is suggested. The results of investigating the interrelation between the values correlation (correlation area, asymmetry coefficient and autocorrelation function excess) and fractal (dispersion of logarithmic dependencies of power spectra) parameters are presented. They characterize the distributions of Mueller matrix elements in the points of laser images of myocardium histological sections. The criteria of differentiation of death coming reasons are determined.

Radiologic assessment of bone healing after orthognathic surgery using fractal analysis

Energy Technology Data Exchange (ETDEWEB)

Park, Kwang Soo; Heo, Min Suk; Lee, Sam Sun; Choi, Soon Chul; Park, Tae Won [College of Dentistry, Seoul National University, Seoul (Korea, Republic of); Jeon, In Seong [Department of Dentistry, Inje University Sanggyepaik Hospital, Seoul (Korea, Republic of); Kim, Jong Dae [Division of Information and Communication Engineering, Hallym university, Chuncheon (Korea, Republic of)

2002-12-15

To evaluate the radiographic change of operation sites after orthognathic surgery using the digital image processing and fractal analysis. A series of panoramic radiographs of thirty-five randomly selected patients who had undergone mandibular orthognathic surgery (bilateral sagittal split ramus osteotomy) without clinical complication for osseous healing, were taken. The panoramic radiographs of each selected patient were taken at pre-operation (stage 0), 1 or 2 days after operation (stage 1), 1 month after operation (stage 2), 6 months after operation (stage 3), and 12 months after operation (stage 4). The radiographs were digitized at 600 dpi, 8 bit, and 256 gray levels. The region of interest, centered on the bony gap area of the operation site, was selected and the fractal dimension was calculated by using the tile-counting method. The mean values and standard deviations of fractal dimension for each stage were calculated and the differences among stage 0, 1, 2, 3, and 4 were evaluated through repeated measures of the ANOVA and paired t-test. The mean values and standard deviations of the fractal dimensions obtained from stage 0, 1, 2, 3, and 4 were 1.658 {+-} 0.048, 1.580 {+-} 0.050, 1.607 {+-} 0.046, 1.624 {+-} 0.049, and 1.641 {+-} 0.061, respectively. The fractal dimensions from stage 1 to stage 4 were shown to have a tendency to increase (p<0.05). The tendency of the fractal dimesion to increase relative to healing time may be a useful means of evaluating post-operative bony healing of the osteotomy site.

Radiologic assessment of bone healing after orthognathic surgery using fractal analysis

International Nuclear Information System (INIS)

Park, Kwang Soo; Heo, Min Suk; Lee, Sam Sun; Choi, Soon Chul; Park, Tae Won; Jeon, In Seong; Kim, Jong Dae

2002-01-01

To evaluate the radiographic change of operation sites after orthognathic surgery using the digital image processing and fractal analysis. A series of panoramic radiographs of thirty-five randomly selected patients who had undergone mandibular orthognathic surgery (bilateral sagittal split ramus osteotomy) without clinical complication for osseous healing, were taken. The panoramic radiographs of each selected patient were taken at pre-operation (stage 0), 1 or 2 days after operation (stage 1), 1 month after operation (stage 2), 6 months after operation (stage 3), and 12 months after operation (stage 4). The radiographs were digitized at 600 dpi, 8 bit, and 256 gray levels. The region of interest, centered on the bony gap area of the operation site, was selected and the fractal dimension was calculated by using the tile-counting method. The mean values and standard deviations of fractal dimension for each stage were calculated and the differences among stage 0, 1, 2, 3, and 4 were evaluated through repeated measures of the ANOVA and paired t-test. The mean values and standard deviations of the fractal dimensions obtained from stage 0, 1, 2, 3, and 4 were 1.658 ± 0.048, 1.580 ± 0.050, 1.607 ± 0.046, 1.624 ± 0.049, and 1.641 ± 0.061, respectively. The fractal dimensions from stage 1 to stage 4 were shown to have a tendency to increase (p<0.05). The tendency of the fractal dimesion to increase relative to healing time may be a useful means of evaluating post-operative bony healing of the osteotomy site.

Bilipschitz embedding of homogeneous fractals

OpenAIRE

Lü, Fan; Lou, Man-Li; Wen, Zhi-Ying; Xi, Li-Feng

2014-01-01

In this paper, we introduce a class of fractals named homogeneous sets based on some measure versions of homogeneity, uniform perfectness and doubling. This fractal class includes all Ahlfors-David regular sets, but most of them are irregular in the sense that they may have different Hausdorff dimensions and packing dimensions. Using Moran sets as main tool, we study the dimensions, bilipschitz embedding and quasi-Lipschitz equivalence of homogeneous fractals.

Fractal Communication System Using Digital Signal Processing Starter Kit (DSK TMS320c6713

Directory of Open Access Journals (Sweden)

Arsyad Ramadhan Darlis

2015-12-01

Full Text Available In 1992, Wornell and Oppenheim did research on a modulation which is formed by using wavelet theory. In some other studies, proved that this modulation can survive on a few channels and has reliability in some applications. Because of this modulation using the concept of fractal, then it is called as fractalmodulation. Fractal modulation is formed by inserting information signal into fractal signals that are selffractal similary. This modulation technique has the potential to replace the OFDM (Orthogonal Frequency Division Multiplexing, which is currently used on some of the latest telecommunication technologies. The purpose of this research is to implement the fractal communication system using Digital Signal Processing Starter Kit (DSK TMS320C6713 without using AWGN and Rayleigh channel in order to obtain the ideal performance of the system. From the simulation results using MATLAB7.4. it appears that this communication system has good performance on some channels than any other communication systems. While in terms of implementation by using (DSK via TMS320C6713 Code Composer Studio (CCS, it can be concluded that thefractal communication system has a better execution time on some tests.

Coded aperture imaging system for nuclear fuel motion detection

International Nuclear Information System (INIS)

Stalker, K.T.; Kelly, J.G.

1980-01-01

A Coded Aperature Imaging System (CAIS) has been developed at Sandia National Laboratories to image the motion of nuclear fuel rods undergoing tests simulating accident conditions within a liquid metal fast breeder reactor. The tests require that the motion of the test fuel be monitored while it is immersed in a liquid sodium coolant precluding the use of normal optical means of imaging. However, using the fission gamma rays emitted by the fuel itself and coded aperture techniques, images with 1.5 mm radial and 5 mm axial resolution have been attained. Using an electro-optical detection system coupled to a high speed motion picture camera a time resolution of one millisecond can be achieved. This paper will discuss the application of coded aperture imaging to the problem, including the design of the one-dimensional Fresnel zone plate apertures used and the special problems arising from the reactor environment and use of high energy gamma ray photons to form the coded image. Also to be discussed will be the reconstruction techniques employed and the effect of various noise sources on system performance. Finally, some experimental results obtained using the system will be presented

Recognition of fractal graphs

NARCIS (Netherlands)

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

Electromagnetic backscattering from one-dimensional drifting fractal sea surface II: Electromagnetic backscattering model

International Nuclear Information System (INIS)

Xie Tao; Zhao Shang-Zhuo; Fang He; Yu Wen-Jin; He Yi-Jun; Perrie, William

2016-01-01

Sea surface current has a significant influence on electromagnetic (EM) backscattering signals and may constitute a dominant synthetic aperture radar (SAR) imaging mechanism. An effective EM backscattering model for a one-dimensional drifting fractal sea surface is presented in this paper. This model is used to simulate EM backscattering signals from the drifting sea surface. Numerical results show that ocean currents have a significant influence on EM backscattering signals from the sea surface. The normalized radar cross section (NRCS) discrepancies between the model for a coupled wave-current fractal sea surface and the model for an uncoupled fractal sea surface increase with the increase of incidence angle, as well as with increasing ocean currents. Ocean currents that are parallel to the direction of the wave can weaken the EM backscattering signal intensity, while the EM backscattering signal is intensified by ocean currents propagating oppositely to the wave direction. The model presented in this paper can be used to study the SAR imaging mechanism for a drifting sea surface. (paper)

Random walk through fractal environments

International Nuclear Information System (INIS)

Isliker, H.; Vlahos, L.

2003-01-01

We analyze random walk through fractal environments, embedded in three-dimensional, permeable space. Particles travel freely and are scattered off into random directions when they hit the fractal. The statistical distribution of the flight increments (i.e., of the displacements between two consecutive hittings) is analytically derived from a common, practical definition of fractal dimension, and it turns out to approximate quite well a power-law in the case where the dimension D F of the fractal is less than 2, there is though, always a finite rate of unaffected escape. Random walks through fractal sets with D F ≤2 can thus be considered as defective Levy walks. The distribution of jump increments for D F >2 is decaying exponentially. The diffusive behavior of the random walk is analyzed in the frame of continuous time random walk, which we generalize to include the case of defective distributions of walk increments. It is shown that the particles undergo anomalous, enhanced diffusion for D F F >2 is normal for large times, enhanced though for small and intermediate times. In particular, it follows that fractals generated by a particular class of self-organized criticality models give rise to enhanced diffusion. The analytical results are illustrated by Monte Carlo simulations

Rheological and fractal characteristics of unconditioned and conditioned water treatment residuals.

Science.gov (United States)

Dong, Y J; Wang, Y L; Feng, J

2011-07-01

The rheological and fractal characteristics of raw (unconditioned) and conditioned water treatment residuals (WTRs) were investigated in this study. Variations in morphology, size, and image fractal dimensions of the flocs/aggregates in these WTR systems with increasing polymer doses were analyzed. The results showed that when the raw WTRs were conditioned with the polymer CZ8688, the optimum polymer dosage was observed at 24 kg/ton dry sludge. The average diameter of irregularly shaped flocs/aggregates in the WTR suspensions increased from 42.54 μm to several hundred micrometers with increasing polymer doses. Furthermore, the aggregates in the conditioned WTR system displayed boundary/surface and mass fractals. At the optimum polymer dosage, the aggregates formed had a volumetric average diameter of about 820.7 μm, with a one-dimensional fractal dimension of 1.01 and a mass fractal dimension of 2.74 on the basis of the image analysis. Rheological tests indicated that the conditioned WTRs at the optimum polymer dosage showed higher levels of shear-thinning behavior than the raw WTRs. Variations in the limiting viscosity (η(∞)) of conditioned WTRs with sludge content could be described by a linear equation, which were different from the often-observed empirical exponential relationship for most municipal sludge. With increasing temperature, the η(∞) of the raw WTRs decreased more rapidly than that of the raw WTRs. Good fitting results for the relationships between lgη(∞)∼T using the Arrhenius equation indicate that the WTRs had a much higher activation energy for viscosity of about 17.86-26.91 J/mol compared with that of anaerobic granular sludge (2.51 J/mol) (Mu and Yu, 2006). In addition, the Bingham plastic model adequately described the rheological behavior of the conditioned WTRs, whereas the rheology of the raw WTRs fit the Herschel-Bulkley model well at only certain sludge contents. Considering the good power-law relationships between the

A fractal image analysis methodology for heat damage inspection in carbon fiber reinforced composites

Science.gov (United States)

Haridas, Aswin; Crivoi, Alexandru; Prabhathan, P.; Chan, Kelvin; Murukeshan, V. M.

2017-06-01

The use of carbon fiber-reinforced polymer (CFRP) composite materials in the aerospace industry have far improved the load carrying properties and the design flexibility of aircraft structures. A high strength to weight ratio, low thermal conductivity, and a low thermal expansion coefficient gives it an edge for applications demanding stringent loading conditions. Specifically, this paper focuses on the behavior of CFRP composites under stringent thermal loads. The properties of composites are largely affected by external thermal loads, especially when the loads are beyond the glass temperature, Tg, of the composite. Beyond this, the composites are subject to prominent changes in mechanical and thermal properties which may further lead to material decomposition. Furthermore, thermal damage formation being chaotic, a strict dimension cannot be associated with the formed damage. In this context, this paper focuses on comparing multiple speckle image analysis algorithms to effectively characterize the formed thermal damages on the CFRP specimen. This would provide us with a fast method for quantifying the extent of heat damage in carbon composites, thus reducing the required time for inspection. The image analysis methods used for the comparison include fractal dimensional analysis of the formed speckle pattern and analysis of number and size of various connecting elements in the binary image.

Chaos and fractals. Applications to nuclear engineering; Caos y fractales. Aplicaciones en ingenieria nuclear

Energy Technology Data Exchange (ETDEWEB)

Clausse, A; Delmastro, D F

1991-12-31

This work presents a description of the research lines carried out by the authors on chaos and fractal theories, oriented to the nuclear field. The possibilities that appear in the nuclear security branch where the information deriving from chaos and fractal techniques may help to the development of better criteria and more reliable designs, are of special importance. (Author). [Espanol] En este trabajo se presenta una descripcion de las lineas de investigacion que los autores estan llevando a cabo en teoria de caos y fractales orientadas al campo nuclear. Es de especial importancia las posibilidades que se abren en el area de la seguridad nuclear, en donde la informacion proveniente de las tecnicas de caos y fractales pueden ayudar al desarrollo de mejores criterios y disenos mas confiables. (Autor).

Multispectral code excited linear prediction coding and its application in magnetic resonance images.

Science.gov (United States)

Hu, J H; Wang, Y; Cahill, P T

1997-01-01

This paper reports a multispectral code excited linear prediction (MCELP) method for the compression of multispectral images. Different linear prediction models and adaptation schemes have been compared. The method that uses a forward adaptive autoregressive (AR) model has been proven to achieve a good compromise between performance, complexity, and robustness. This approach is referred to as the MFCELP method. Given a set of multispectral images, the linear predictive coefficients are updated over nonoverlapping three-dimensional (3-D) macroblocks. Each macroblock is further divided into several 3-D micro-blocks, and the best excitation signal for each microblock is determined through an analysis-by-synthesis procedure. The MFCELP method has been applied to multispectral magnetic resonance (MR) images. To satisfy the high quality requirement for medical images, the error between the original image set and the synthesized one is further specified using a vector quantizer. This method has been applied to images from 26 clinical MR neuro studies (20 slices/study, three spectral bands/slice, 256x256 pixels/band, 12 b/pixel). The MFCELP method provides a significant visual improvement over the discrete cosine transform (DCT) based Joint Photographers Expert Group (JPEG) method, the wavelet transform based embedded zero-tree wavelet (EZW) coding method, and the vector tree (VT) coding method, as well as the multispectral segmented autoregressive moving average (MSARMA) method we developed previously.

Fractal analysis of fractures and microstructures in rocks

International Nuclear Information System (INIS)

Merceron, T.; Nakashima, S.; Velde, B.; Badri, A.

1991-01-01

Fractal geometry was used to characterize the distribution of fracture fields in rocks, which represent main pathways for material migration such as groundwater flow. Fractal investigations of fracture distribution were performed on granite along Auriat and Shikoku boreholes. Fractal dimensions range between 0.3 and 0.5 according to the different sets of fracture planes selected for the analyses. Shear, tension and compressional modes exhibit different fractal values while the composite fracture patterns are also fractal but with a different, median, fractal value. These observations indicate that the fractal method can be used to distinguish fracture types of different origins in a complex system. Fractal results for Shikoku borehole also correlate with geophysical parameters recorded along, drill-holes such as resistivity and possibly permeability. These results represent the first steps of the fractal investigation along drill-holes. Future studies will be conducted to verify relationships between fractal dimensions and permeability by using available geophysical data. Microstructures and microcracks were analysed in the Inada granite. Microcrack patterns are fractal but fractal dimensions values vary according to both mineral type and orientations of measurement within the mineral. Microcracks in quartz are characterized by more irregular distribution (average D = 0.40) than those in feldspars (D = 0.50) suggesting a different mode of rupture. Highest values of D are reported along main cleavage planes for feldspars or C axis for quartz. Further fractal investigations of microstructure in granite will be used to characterize the potential pathways for fluid migration and diffusion in the rock matrix. (author)

Performance of JPEG Image Transmission Using Proposed Asymmetric Turbo Code

Directory of Open Access Journals (Sweden)

Siddiqi Mohammad Umar

2007-01-01

Full Text Available This paper gives the results of a simulation study on the performance of JPEG image transmission over AWGN and Rayleigh fading channels using typical and proposed asymmetric turbo codes for error control coding. The baseline JPEG algorithm is used to compress a QCIF ( "Suzie" image. The recursive systematic convolutional (RSC encoder with generator polynomials , that is, (13/11 in decimal, and 3G interleaver are used for the typical WCDMA and CDMA2000 turbo codes. The proposed asymmetric turbo code uses generator polynomials , that is, (13/11; 13/9 in decimal, and a code-matched interleaver. The effect of interleaver in the proposed asymmetric turbo code is studied using weight distribution and simulation. The simulation results and performance bound for proposed asymmetric turbo code for the frame length , code rate with Log-MAP decoder over AWGN channel are compared with the typical system. From the simulation results, it is observed that the image transmission using proposed asymmetric turbo code performs better than that with the typical system.

Results from the Coded Aperture Neutron Imaging System (CANIS)

International Nuclear Information System (INIS)

Brubaker, Erik; Steele, John T.; Brennan, James S.; Hilton, Nathan R.; Marleau, Peter

2010-01-01

Because of their penetrating power, energetic neutrons and gamma rays (∼1 MeV) offer the best possibility of detecting highly shielded or distant special nuclear material (SNM). Of these, fast neutrons offer the greatest advantage due to their very low and well understood natural background. We are investigating a new approach to fast-neutron imaging- a coded aperture neutron imaging system (CANIS). Coded aperture neutron imaging should offer a highly efficient solution for improved detection speed, range, and sensitivity. We have demonstrated fast neutron and gamma ray imaging with several different configurations of coded masks patterns and detectors including an 'active' mask that is composed of neutron detectors. Here we describe our prototype detector and present some initial results from laboratory tests and demonstrations.

Comparison of surface fractal dimensions of chromizing coating and P110 steel for corrosion resistance estimation

International Nuclear Information System (INIS)

Lin, Naiming; Guo, Junwen; Xie, Faqin; Zou, Jiaojuan; Tian, Wei; Yao, Xiaofei; Zhang, Hongyan; Tang, Bin

2014-01-01

Highlights: • Continuous chromizing coating was synthesized on P110 steel by pack cementation. • The chromizing coating showed better corrosion resistance. • Comparison of surface fractal dimensions can estimate corrosion resistance. - Abstract: In the field of corrosion research, mass gain/loss, electrochemical tests and comparing the surface elemental distributions, phase constitutions as well as surface morphologies before and after corrosion are extensively applied to investigate the corrosion behavior or estimate the corrosion resistance of materials that operated in various environments. Most of the above methods are problem oriented, complex and longer-period time-consuming. However from an object oriented point of view, the corroded surfaces of materials often have self-similar characterization: fractal property which can be employed to efficiently achieve damaged surface analysis. The present work describes a strategy of comparison of the surface fractal dimensions for corrosion resistance estimation: chromizing coating was synthesized on P110 steel surface to improve its performance via pack cementation. Scanning electron microscope (SEM) was used to investigate the surface morphologies of the original and corroded samples. Surface fractal dimensions of the detected samples were calculated by binary images related to SEM images of surface morphologies with box counting algorithm method. The results showed that both surface morphologies and surface fractal dimensions of P110 steel varied greatly before and after corrosion test, but the chromizing coating changed slightly. The chromizing coating indicated better corrosion resistance than P110 steel. Comparison of surface fractal dimensions of original and corroded samples can rapidly and exactly realize the estimation of corrosion resistance

Comparison of surface fractal dimensions of chromizing coating and P110 steel for corrosion resistance estimation

Energy Technology Data Exchange (ETDEWEB)

Lin, Naiming, E-mail: lnmlz33@163.com [Research Institute of Surface Engineering, Taiyuan University of Technology, Taiyuan 030024 (China); Guo, Junwen [Research Institute of Surface Engineering, Taiyuan University of Technology, Taiyuan 030024 (China); Xie, Faqin [School of Aeronautics, Northwestern Polytechnical University, Xi’an 710072 (China); Zou, Jiaojuan; Tian, Wei [Research Institute of Surface Engineering, Taiyuan University of Technology, Taiyuan 030024 (China); Yao, Xiaofei [School of Materials and Chemical Engineering, Xi’an Technological University, Xi’an 710032 (China); Zhang, Hongyan; Tang, Bin [Research Institute of Surface Engineering, Taiyuan University of Technology, Taiyuan 030024 (China)

2014-08-30

Highlights: • Continuous chromizing coating was synthesized on P110 steel by pack cementation. • The chromizing coating showed better corrosion resistance. • Comparison of surface fractal dimensions can estimate corrosion resistance. - Abstract: In the field of corrosion research, mass gain/loss, electrochemical tests and comparing the surface elemental distributions, phase constitutions as well as surface morphologies before and after corrosion are extensively applied to investigate the corrosion behavior or estimate the corrosion resistance of materials that operated in various environments. Most of the above methods are problem oriented, complex and longer-period time-consuming. However from an object oriented point of view, the corroded surfaces of materials often have self-similar characterization: fractal property which can be employed to efficiently achieve damaged surface analysis. The present work describes a strategy of comparison of the surface fractal dimensions for corrosion resistance estimation: chromizing coating was synthesized on P110 steel surface to improve its performance via pack cementation. Scanning electron microscope (SEM) was used to investigate the surface morphologies of the original and corroded samples. Surface fractal dimensions of the detected samples were calculated by binary images related to SEM images of surface morphologies with box counting algorithm method. The results showed that both surface morphologies and surface fractal dimensions of P110 steel varied greatly before and after corrosion test, but the chromizing coating changed slightly. The chromizing coating indicated better corrosion resistance than P110 steel. Comparison of surface fractal dimensions of original and corroded samples can rapidly and exactly realize the estimation of corrosion resistance.

Probability- and curve-based fractal reconstruction on 2D DEM terrain profile

International Nuclear Information System (INIS)

Lai, F.-J.; Huang, Y.M.

2009-01-01

Data compression and reconstruction has been playing important roles in information science and engineering. As part of them, image compression and reconstruction that mainly deal with image data set reduction for storage or transmission and data set restoration with least loss is still a topic deserved a great deal of works to focus on. In this paper we propose a new scheme in comparison with the well-known Improved Douglas-Peucker (IDP) method to extract characteristic or feature points of two-dimensional digital elevation model (2D DEM) terrain profile to compress data set. As for reconstruction in use of fractal interpolation, we propose a probability-based method to speed up the fractal interpolation execution to a rate as high as triple or even ninefold of the regular. In addition, a curve-based method is proposed in the study to determine the vertical scaling factor that much affects the generation of the interpolated data points to significantly improve the reconstruction performance. Finally, an evaluation is made to show the advantage of employing the proposed new method to extract characteristic points associated with our novel fractal interpolation scheme.

Fractal structures and fractal functions as disease indicators

Science.gov (United States)

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.

Medical Image Compression Based on Vector Quantization with Variable Block Sizes in Wavelet Domain

Directory of Open Access Journals (Sweden)

Huiyan Jiang

2012-01-01

Full Text Available An optimized medical image compression algorithm based on wavelet transform and improved vector quantization is introduced. The goal of the proposed method is to maintain the diagnostic-related information of the medical image at a high compression ratio. Wavelet transformation was first applied to the image. For the lowest-frequency subband of wavelet coefficients, a lossless compression method was exploited; for each of the high-frequency subbands, an optimized vector quantization with variable block size was implemented. In the novel vector quantization method, local fractal dimension (LFD was used to analyze the local complexity of each wavelet coefficients, subband. Then an optimal quadtree method was employed to partition each wavelet coefficients, subband into several sizes of subblocks. After that, a modified K-means approach which is based on energy function was used in the codebook training phase. At last, vector quantization coding was implemented in different types of sub-blocks. In order to verify the effectiveness of the proposed algorithm, JPEG, JPEG2000, and fractal coding approach were chosen as contrast algorithms. Experimental results show that the proposed method can improve the compression performance and can achieve a balance between the compression ratio and the image visual quality.

Fractal geometry mathematical foundations and applications

CERN Document Server

Falconer, Kenneth

2013-01-01

The seminal text on fractal geometry for students and researchers: extensively revised and updated with new material, notes and references that reflect recent directions. Interest in fractal geometry continues to grow rapidly, both as a subject that is fascinating in its own right and as a concept that is central to many areas of mathematics, science and scientific research. Since its initial publication in 1990 Fractal Geometry: Mathematical Foundations and Applications has become a seminal text on the mathematics of fractals.  The book introduces and develops the general theory and applica

Fractal nature of hydrocarbon deposits. 2. Spatial distribution

International Nuclear Information System (INIS)

Barton, C.C.; Schutter, T.A; Herring, P.R.; Thomas, W.J.; Scholz, C.H.

1991-01-01

Hydrocarbons are unevenly distributed within reservoirs and are found in patches whose size distribution is a fractal over a wide range of scales. The spatial distribution of the patches is also fractal and this can be used to constrain the design of drilling strategies also defined by a fractal dimension. Fractal distributions are scale independent and are characterized by a power-law scaling exponent termed the fractal dimension. The authors have performed fractal analyses on the spatial distribution of producing and showing wells combined and of dry wells in 1,600-mi 2 portions of the Denver and Powder River basins that were nearly completely drilled on quarter-mile square-grid spacings. They have limited their analyses to wells drilled to single stratigraphic intervals so that the map pattern revealed by drilling is representative of the spatial patchiness of hydrocarbons at depth. The fractal dimensions for the spatial patchiness of hydrocarbons in the two basins are 1.5 and 1.4, respectively. The fractal dimension for the pattern of all wells drilled is 1.8 for both basins, which suggests a drilling strategy with a fractal dimension significantly higher than the dimensions 1.5 and 1.4 sufficient to efficiently and economically explore these reservoirs. In fact, the fractal analysis reveals that the drilling strategy used in these basins approaches a fractal dimension of 2.0, which is equivalent to random drilling with no geologic input. Knowledge of the fractal dimension of a reservoir prior to drilling would provide a basis for selecting and a criterion for halting a drilling strategy for exploration whose fractal dimension closely matches that of the spatial fractal dimension of the reservoir, such a strategy should prove more efficient and economical than current practice

Lossless Image Compression Based on Multiple-Tables Arithmetic Coding

Directory of Open Access Journals (Sweden)

Rung-Ching Chen

2009-01-01

Full Text Available This paper is intended to present a lossless image compression method based on multiple-tables arithmetic coding (MTAC method to encode a gray-level image f. First, the MTAC method employs a median edge detector (MED to reduce the entropy rate of f. The gray levels of two adjacent pixels in an image are usually similar. A base-switching transformation approach is then used to reduce the spatial redundancy of the image. The gray levels of some pixels in an image are more common than those of others. Finally, the arithmetic encoding method is applied to reduce the coding redundancy of the image. To promote high performance of the arithmetic encoding method, the MTAC method first classifies the data and then encodes each cluster of data using a distinct code table. The experimental results show that, in most cases, the MTAC method provides a higher efficiency in use of storage space than the lossless JPEG2000 does.

Fractal electrodynamics via non-integer dimensional space approach

Science.gov (United States)

Tarasov, Vasily E.

2015-09-01

Using the recently suggested vector calculus for non-integer dimensional space, we consider electrodynamics problems in isotropic case. This calculus allows us to describe fractal media in the framework of continuum models with non-integer dimensional space. We consider electric and magnetic fields of fractal media with charges and currents in the framework of continuum models with non-integer dimensional spaces. An application of the fractal Gauss's law, the fractal Ampere's circuital law, the fractal Poisson equation for electric potential, and equation for fractal stream of charges are suggested. Lorentz invariance and speed of light in fractal electrodynamics are discussed. An expression for effective refractive index of non-integer dimensional space is suggested.

Correlated statistical uncertainties in coded-aperture imaging

International Nuclear Information System (INIS)

Fleenor, Matthew C.; Blackston, Matthew A.; Ziock, Klaus P.

2015-01-01

In nuclear security applications, coded-aperture imagers can provide a wealth of information regarding the attributes of both the radioactive and nonradioactive components of the objects being imaged. However, for optimum benefit to the community, spatial attributes need to be determined in a quantitative and statistically meaningful manner. To address a deficiency of quantifiable errors in coded-aperture imaging, we present uncertainty matrices containing covariance terms between image pixels for MURA mask patterns. We calculated these correlated uncertainties as functions of variation in mask rank, mask pattern over-sampling, and whether or not anti-mask data are included. Utilizing simulated point source data, we found that correlations arose when two or more image pixels were summed. Furthermore, we found that the presence of correlations was heightened by the process of over-sampling, while correlations were suppressed by the inclusion of anti-mask data and with increased mask rank. As an application of this result, we explored how statistics-based alarming is impacted in a radiological search scenario

Long-Range Order and Fractality in the Structure and Organization of Eukaryotic Genomes

Science.gov (United States)

Polychronopoulos, Dimitris; Tsiagkas, Giannis; Athanasopoulou, Labrini; Sellis, Diamantis; Almirantis, Yannis

2014-12-01

The late Professor J.S. Nicolis always emphasized, both in his writings and in presentations and discussions with students and friends, the relevance of a dynamical systems approach to biology. In particular, viewing the genome as a "biological text" captures the dynamical character of both the evolution and function of the organisms in the form of correlations indicating the presence of a long-range order. This genomic structure can be expressed in forms reminiscent of natural languages and several temporal and spatial traces l by the functioning of dynamical systems: Zipf laws, self-similarity and fractality. Here we review several works of our group and recent unpublished results, focusing on the chromosomal distribution of biologically active genomic components: Genes and protein-coding segments, CpG islands, transposable elements belonging to all major classes and several types of conserved non-coding genomic elements. We report the systematic appearance of power-laws in the size distribution of the distances between elements belonging to each of these types of functional genomic elements. Moreover, fractality is also found in several cases, using box-counting and entropic scaling.We present here, for the first time in a unified way, an aggregative model of the genomic dynamics which can explain the observed patterns on the grounds of known phenomena accompanying genome evolution. Our results comply with recent findings about a "fractal globule" geometry of chromatin in the eukaryotic nucleus.

Lossy/lossless coding of bi-level images

DEFF Research Database (Denmark)

Martins, Bo; Forchhammer, Søren

1997-01-01

Summary form only given. We present improvements to a general type of lossless, lossy, and refinement coding of bi-level images (Martins and Forchhammer, 1996). Loss is introduced by flipping pixels. The pixels are coded using arithmetic coding of conditional probabilities obtained using a template...... as is known from JBIG and proposed in JBIG-2 (Martins and Forchhammer). Our new state-of-the-art results are obtained using the more general free tree instead of a template. Also we introduce multiple refinement template coding. The lossy algorithm is analogous to the greedy `rate...

Inkjet-Printed Ultra Wide Band Fractal Antennas

KAUST Repository

Maza, Armando Rodriguez

2012-01-01

reduction, a Cantor-based fractal antenna which performs a larger bandwidth compared to previously published UWB Cantor fractal monopole antenna, and a 3D loop fractal antenna which attains miniaturization, impedance matching and multiband characteristics

Categorization of new fractal carpets

International Nuclear Information System (INIS)

Rani, Mamta; Goel, Saurabh

2009-01-01

Sierpinski carpet is one of the very beautiful fractals from the historic gallery of classical fractals. Carpet designing is not only a fascinating activity in computer graphics, but it has real applications in carpet industry as well. One may find illusionary delighted carpets designed here, which are useful in real designing of carpets. In this paper, we attempt to systematize their generation and put them into categories. Each next category leads to a more generalized form of the fractal carpet.

On the Lipschitz condition in the fractal calculus

International Nuclear Information System (INIS)

Golmankhaneh, Alireza K.; Tunc, Cemil

2017-01-01

In this paper, the existence and uniqueness theorems are proved for the linear and non-linear fractal differential equations. The fractal Lipschitz condition is given on the F"α-calculus which applies for the non-differentiable function in the sense of the standard calculus. More, the metric spaces associated with fractal sets and about functions with fractal supports are defined to build fractal Cauchy sequence. Furthermore, Picard iterative process in the F"α-calculus which have important role in the numerical and approximate solution of fractal differential equations is explored. We clarify the results using the illustrative examples.

Decoding using back-project algorithm from coded image in ICF

International Nuclear Information System (INIS)

Jiang shaoen; Liu Zhongli; Zheng Zhijian; Tang Daoyuan

1999-01-01

The principle of the coded imaging and its decoding in inertial confinement fusion is described simply. The authors take ring aperture microscope for example and use back-project (BP) algorithm to decode the coded image. The decoding program has been performed for numerical simulation. Simulations of two models are made, and the results show that the accuracy of BP algorithm is high and effect of reconstruction is good. Thus, it indicates that BP algorithm is applicable to decoding for coded image in ICF experiments

Integrated quantitative fractal polarimetric analysis of monolayer lung cancer cells

Science.gov (United States)

Shrestha, Suman; Zhang, Lin; Quang, Tri; Farrahi, Tannaz; Narayan, Chaya; Deshpande, Aditi; Na, Ying; Blinzler, Adam; Ma, Junyu; Liu, Bo; Giakos, George C.

2014-05-01

Digital diagnostic pathology has become one of the most valuable and convenient advancements in technology over the past years. It allows us to acquire, store and analyze pathological information from the images of histological and immunohistochemical glass slides which are scanned to create digital slides. In this study, efficient fractal, wavelet-based polarimetric techniques for histological analysis of monolayer lung cancer cells will be introduced and different monolayer cancer lines will be studied. The outcome of this study indicates that application of fractal, wavelet polarimetric principles towards the analysis of squamous carcinoma and adenocarcinoma cancer cell lines may be proved extremely useful in discriminating among healthy and lung cancer cells as well as differentiating among different lung cancer cells.

Fractal dimension of turbulent black holes

Science.gov (United States)

Westernacher-Schneider, John Ryan

2017-11-01

We present measurements of the fractal dimension of a turbulent asymptotically anti-de Sitter black brane reconstructed from simulated boundary fluid data at the perfect fluid order using the fluid-gravity duality. We argue that the boundary fluid energy spectrum scaling as E (k )˜k-2 is a more natural setting for the fluid-gravity duality than the Kraichnan-Kolmogorov scaling of E (k )˜k-5 /3, but we obtain fractal dimensions D for spatial sections of the horizon H ∩Σ in both cases: D =2.584 (1 ) and D =2.645 (4 ), respectively. These results are consistent with the upper bound of D =3 , thereby resolving the tension with the recent claim in Adams et al. [Phys. Rev. Lett. 112, 151602 (2014), 10.1103/PhysRevLett.112.151602] that D =3 +1 /3 . We offer a critical examination of the calculation which led to their result, and show that their proposed definition of the fractal dimension performs poorly as a fractal dimension estimator on one-dimensional curves with known fractal dimension. Finally, we describe how to define and in principle calculate the fractal dimension of spatial sections of the horizon H ∩Σ in a covariant manner, and we speculate on assigning a "bootstrapped" value of fractal dimension to the entire horizon H when it is in a statistically quasisteady turbulent state.

Fractals as objects with nontrivial structures at all scales

International Nuclear Information System (INIS)

Lacan, Francis; Tresser, Charles

2015-01-01

Toward the middle of 2001, the authors started arguing that fractals are important when discussing the operational resilience of information systems and related computer sciences issues such as artificial intelligence. But in order to argue along these lines it turned out to be indispensable to define fractals so as to let one recognize as fractals some sets that are very far from being self similar in the (usual) metric sense. This paper is devoted to define (in a loose sense at least) fractals in ways that allow for instance all the Cantor sets to be fractals and that permit to recognize fractality (the property of being fractal) in the context of the information technology issues that we had tried to comprehend. Starting from the meta-definition of a fractal as an “object with non-trivial structure at all scales” that we had used for long, we ended up taking these words seriously. Accordingly we define fractals in manners that depend both on the structures that the fractals are endowed with and the chosen sets of structure compatible maps, i.e., we approach fractals in a category-dependent manner. We expect that this new approach to fractals will contribute to the understanding of more of the fractals that appear in exact and other sciences than what can be handled presently

Information retrieval based on single-pixel optical imaging with quick-response code

Science.gov (United States)

Xiao, Yin; Chen, Wen

2018-04-01

Quick-response (QR) code technique is combined with ghost imaging (GI) to recover original information with high quality. An image is first transformed into a QR code. Then the QR code is treated as an input image in the input plane of a ghost imaging setup. After measurements, traditional correlation algorithm of ghost imaging is utilized to reconstruct an image (QR code form) with low quality. With this low-quality image as an initial guess, a Gerchberg-Saxton-like algorithm is used to improve its contrast, which is actually a post processing. Taking advantage of high error correction capability of QR code, original information can be recovered with high quality. Compared to the previous method, our method can obtain a high-quality image with comparatively fewer measurements, which means that the time-consuming postprocessing procedure can be avoided to some extent. In addition, for conventional ghost imaging, the larger the image size is, the more measurements are needed. However, for our method, images with different sizes can be converted into QR code with the same small size by using a QR generator. Hence, for the larger-size images, the time required to recover original information with high quality will be dramatically reduced. Our method makes it easy to recover a color image in a ghost imaging setup, because it is not necessary to divide the color image into three channels and respectively recover them.

Fractal Structures For Mems Variable Capacitors

KAUST Repository

Elshurafa, Amro M.

2014-08-28

In accordance with the present disclosure, one embodiment of a fractal variable capacitor comprises a capacitor body in a microelectromechanical system (MEMS) structure, wherein the capacitor body has an upper first metal plate with a fractal shape separated by a vertical distance from a lower first metal plate with a complementary fractal shape; and a substrate above which the capacitor body is suspended.

Fractal THz metamaterials

DEFF Research Database (Denmark)

Malureanu, Radu; Jepsen, Peter Uhd; Xiao, S.

2010-01-01

applications. THz radiation can be employed for various purposes, among them the study of vibrations in biological molecules, motion of electrons in semiconductors and propagation of acoustic shock waves in crystals. We propose here a new THz fractal MTM design that shows very high transmission in the desired...... 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...... transmission peak at 0.6THz. One of the main characteristics of this design is its tunability by design: by simply changing the length of the fractal elements one can choose the operating frequency window. The modelling, fabrication and characterisation results will be presented in this paper. Due to the long...

Categorization of fractal plants

International Nuclear Information System (INIS)

Chandra, Munesh; Rani, Mamta

2009-01-01

Fractals in nature are always a result of some growth process. The language of fractals which has been created specifically for the description of natural growth process is called L-systems. Recently, superior iterations (essentially, investigated by Mann [Mann WR. Mean value methods in iteration. Proc Am Math Soc 1953;4:506-10 [MR0054846 (14,988f)

Fractal and multifractal analysis of LiF thin film surface

International Nuclear Information System (INIS)

Yadav, R.P.; Dwivedi, S.; Mittal, A.K.; Kumar, M.; Pandey, A.C.

2012-01-01

Highlights: ► Fractal and multifractal analysis of surface morphologies of the LiF thin films. ► Complexity and roughness of the LiF thin films increases as thickness increases. ► LiF thin films are multifractal in nature. ► Strength of the multifractality increases with thickness of the film. - Abstract: Fractal and multifractal analysis is performed on the atomic force microscopy (AFM) images of the surface morphologies of the LiF thin films of thickness 10 nm, 20 nm, and 40 nm, respectively. Autocorrelation function, height–height correlation function, and two-dimensional multifractal detrended fluctuation analysis (MFDFA) are used for characterizing the surface. It is found that the interface width, average roughness, lateral correlation length, and fractal dimension of the LiF thin film increase with the thickness of the film, whereas the roughness exponent decreases with thickness. Thus, the complexity and roughness of the LiF thin films increases as thickness increases. It is also demonstrated that the LiF thin films are multifractal in nature. Strength of the multifractality increases with thickness of the film.

Morphometric relations of fractal-skeletal based channel network model

Directory of Open Access Journals (Sweden)

B. S. Daya Sagar

1998-01-01

Full Text Available A fractal-skeletal based channel network (F-SCN model is proposed. Four regular sided initiator-basins are transformed as second order fractal basins by following a specific generating mechanism with non-random rule. The morphological skeletons, hereafter referred to as channel networks, are extracted from these fractal basins. The morphometric and fractal relationships of these F-SCNs are shown. The fractal dimensions of these fractal basins, channel networks, and main channel lengths (computed through box counting method are compared with those of estimated length–area measures. Certain morphometric order ratios to show fractal relations are also highlighted.

Fractal Analysis of Rock Joint Profiles

Science.gov (United States)

Audy, Ondřej; Ficker, Tomáš

2017-10-01

Surface reliefs of rock joints are analyzed in geotechnics when shear strength of rocky slopes is estimated. The rock joint profiles actually are self-affine fractal curves and computations of their fractal dimensions require special methods. Many papers devoted to the fractal properties of these profiles were published in the past but only a few of those papers employed a convenient computational method that would have guaranteed a sound value of that dimension. As a consequence, anomalously low dimensions were presented. This contribution deals with two computational modifications that lead to sound fractal dimensions of the self-affine rock joint profiles. These are the modified box-counting method and the modified yard-stick method sometimes called the compass method. Both these methods are frequently applied to self-similar fractal curves but the self-affine profile curves due to their self-affine nature require modified computational procedures implemented in computer programs.

A random walk through fractal dimensions

CERN Document Server

Kaye, Brian H

2008-01-01

Fractal geometry is revolutionizing the descriptive mathematics of applied materials systems. Rather than presenting a mathematical treatise, Brian Kaye demonstrates the power of fractal geometry in describing materials ranging from Swiss cheese to pyrolytic graphite. Written from a practical point of view, the author assiduously avoids the use of equations while introducing the reader to numerous interesting and challenging problems in subject areas ranging from geography to fine particle science. The second edition of this successful book provides up-to-date literature coverage of the use of fractal geometry in all areas of science.From reviews of the first edition:''...no stone is left unturned in the quest for applications of fractal geometry to fine particle problems....This book should provide hours of enjoyable reading to those wishing to become acquainted with the ideas of fractal geometry as applied to practical materials problems.'' MRS Bulletin

Effects of fractal pore on coal devolatilization

Energy Technology Data Exchange (ETDEWEB)

Chen, Yongli; He, Rong [Tsinghua Univ., Beijing (China). Dept. of Thermal Engineering; Wang, Xiaoliang; Cao, Liyong [Dongfang Electric Corporation, Chengdu (China). Centre New Energy Inst.

2013-07-01

Coal devolatilization is numerically investigated by drop tube furnace and a coal pyrolysis model (Fragmentation and Diffusion Model). The fractal characteristics of coal and char pores are investigated. Gas diffusion and secondary reactions in fractal pores are considered in the numerical simulations of coal devolatilization, and the results show that the fractal dimension is increased firstly and then decreased later with increased coal conversions during devolatilization. The mechanisms of effects of fractal pores on coal devolatilization are analyzed.

Fractal dimension and turbulence in Giant HII Regions

International Nuclear Information System (INIS)

Caicedo-Ortiz, H E; Santiago-Cortes, E; López-Bonilla, J; er piso, CP 07738, México D.F (Mexico))" data-affiliation=" (ESFM, Instituto Politécnico Nacional, Edif. 9, 1er piso, CP 07738, México D.F (Mexico))" >Castañeda, H O

2015-01-01

We have measured the fractal dimensions of the Giant HII Regions Hubble X and Hubble V in NGC6822 using images obtained with the Hubble's Wide Field Planetary Camera 2 (WFPC2). These measures are associated with the turbulence observed in these regions, which is quantified through the velocity dispersion of emission lines in the visible. Our results suggest low turbulence behaviour

Closed contour fractal dimension estimation by the Fourier transform

International Nuclear Information System (INIS)

Florindo, J.B.; Bruno, O.M.

2011-01-01

Highlights: → A novel fractal dimension concept, based on Fourier spectrum, is proposed. → Computationally simple. Computational time smaller than conventional fractal methods. → Results are closer to Hausdorff-Besicovitch than conventional methods. → The method is more accurate and robustness to geometric operations and noise addition. - Abstract: This work proposes a novel technique for the numerical calculus of the fractal dimension of fractal objects which can be represented as a closed contour. The proposed method maps the fractal contour onto a complex signal and calculates its fractal dimension using the Fourier transform. The Fourier power spectrum is obtained and an exponential relation is verified between the power and the frequency. From the parameter (exponent) of the relation, is obtained the fractal dimension. The method is compared to other classical fractal dimension estimation methods in the literature, e.g., Bouligand-Minkowski, box-counting and classical Fourier. The comparison is achieved by the calculus of the fractal dimension of fractal contours whose dimensions are well-known analytically. The results showed the high precision and robustness of the proposed technique.

Band structures in fractal grading porous phononic crystals

Science.gov (United States)

Wang, Kai; Liu, Ying; Liang, Tianshu; Wang, Bin

2018-05-01

In this paper, a new grading porous structure is introduced based on a Sierpinski triangle routine, and wave propagation in this fractal grading porous phononic crystal is investigated. The influences of fractal hierarchy and porosity on the band structures in fractal graidng porous phononic crystals are clarified. Vibration modes of unit cell at absolute band gap edges are given to manifest formation mechanism of absolute band gaps. The results show that absolute band gaps are easy to form in fractal structures comparatively to the normal ones with the same porosity. Structures with higher fractal hierarchies benefit multiple wider absolute band gaps. This work provides useful guidance in design of fractal porous phononic crystals.

Zone-plate coded imaging of thermonuclear burn

International Nuclear Information System (INIS)

Ceglio, N.M.

1978-01-01

The first high-resolution, direct images of the region of thermonuclear burn in laser fusion experiments have been produced using a novel, two-step imaging technique called zone-plate coded imaging. This technique is extremely versatile and well suited for the microscopy of laser fusion targets. It has a tomographic capability, which provides three-dimensional images of the source distribution. It is equally useful for imaging x-ray and particle emissions. Since this technique is much more sensitive than competing imaging techniques, it permits us to investigate low-intensity sources

Slow Motion and Zoom in HD Digital Videos Using Fractals

Directory of Open Access Journals (Sweden)

Maurizio Murroni

2009-01-01

Full Text Available Slow motion replay and spatial zooming are special effects used in digital video rendering. At present, most techniques to perform digital spatial zoom and slow motion are based on interpolation for both enlarging the size of the original pictures and generating additional intermediate frames. Mainly, interpolation is done either by linear or cubic spline functions or by motion estimation/compensation which both can be applied pixel by pixel, or by partitioning frames into blocks. Purpose of this paper is to present an alternative technique combining fractals theory and wavelet decomposition to achieve spatial zoom and slow motion replay of HD digital color video sequences. Fast scene change detection, active scene detection, wavelet subband analysis, and color fractal coding based on Earth Mover's Distance (EMD measure are used to reduce computational load and to improve visual quality. Experiments show that the proposed scheme achieves better results in terms of overall visual quality compared to the state-of-the-art techniques.

Thermodynamics for Fractal Statistics

OpenAIRE

da Cruz, Wellington

1998-01-01

We consider for an anyon gas its termodynamics properties taking into account the fractal statistics obtained by us recently. This approach describes the anyonic excitations in terms of equivalence classes labeled by fractal parameter or Hausdorff dimension $h$. An exact equation of state is obtained in the high-temperature and low-temperature limits, for gases with a constant density of states.

Turbulent wakes of fractal objects

NARCIS (Netherlands)

Staicu, A.D.; Mazzi, B.; Vassilicos, J.C.; Water, van de W.

2003-01-01

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

Fractal geometry and computer graphics

CERN Document Server

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...

Compressive Sampling based Image Coding for Resource-deficient Visual Communication.

Science.gov (United States)

Liu, Xianming; Zhai, Deming; Zhou, Jiantao; Zhang, Xinfeng; Zhao, Debin; Gao, Wen

2016-04-14

In this paper, a new compressive sampling based image coding scheme is developed to achieve competitive coding efficiency at lower encoder computational complexity, while supporting error resilience. This technique is particularly suitable for visual communication with resource-deficient devices. At the encoder, compact image representation is produced, which is a polyphase down-sampled version of the input image; but the conventional low-pass filter prior to down-sampling is replaced by a local random binary convolution kernel. The pixels of the resulting down-sampled pre-filtered image are local random measurements and placed in the original spatial configuration. The advantages of local random measurements are two folds: 1) preserve high-frequency image features that are otherwise discarded by low-pass filtering; 2) remain a conventional image and can therefore be coded by any standardized codec to remove statistical redundancy of larger scales. Moreover, measurements generated by different kernels can be considered as multiple descriptions of the original image and therefore the proposed scheme has the advantage of multiple description coding. At the decoder, a unified sparsity-based soft-decoding technique is developed to recover the original image from received measurements in a framework of compressive sensing. Experimental results demonstrate that the proposed scheme is competitive compared with existing methods, with a unique strength of recovering fine details and sharp edges at low bit-rates.

Surface morphology analysis of nanostructured (Ba sub x , Sr sub 1 sub - sub x)TiO sub 3 thin films using fractal method

CERN Document Server

Hong, K J; Choi, W K; Cho, J C

2003-01-01

Based on the fractal theory, this paper uses scanning electron microscopy images to investigate the roughness characteristics of nanostructured (Ba Sr)TiO sub 3 thin films by sol-gel methods. The percentage grain area, surface fractal dimensions and 3D image are evaluated using image analysis methods. The thickness of the (Ba Sr)TiO sub 3 thin films was 260-280 nm. The surface fractal dimensions were increased with strontium doping, and grain area, were decreased with it. The fractal dimension and the grain areas of the (Ba sub 0 sub . sub 7 Sr sub 0 sub . sub 3)TiO sub 3 thin films were 1.81 and 81%. Based on the image analysis, the roughness height of 3D images as 256 levels was about 3 nm and its distribution was about 35-40% for the (Ba sub 0 sub . sub 8 Sr sub 0 sub . sub 2)TiO sub 3 and (Ba sub 0 sub . sub 7 Sr sub 0 sub . sub 3)TiO sub 3 thin films. The roughness height of the BST thin films was distributed from 35% to 40% ranging from 3 nm to 4 nm. By increasing the strontium doping, the roughness hei...

Ag nanoparticles formed by femtosecond pulse laser ablation in water: self-assembled fractal structures

Energy Technology Data Exchange (ETDEWEB)

Santillán, Jesica M. J. [CONICET La Plata-CIC, Centro de Investigaciones Ópticas (CIOp) (Argentina); Fernández van Raap, Marcela B., E-mail: raap@fisica.unlp.edu.ar; Mendoza Zélis, Pedro; Coral, Diego [CONICET, Instituto de Física La Plata (IFLP) (Argentina); Muraca, Diego [Universidade Estadual de Campinas, Instituto de Física “Gleb Wataghin” (IFGW) (Brazil); Schinca, Daniel C.; Scaffardi, Lucía B., E-mail: lucias@ciop.unlp.edu.ar [CONICET La Plata-CIC, Centro de Investigaciones Ópticas (CIOp) (Argentina)

2015-02-15

We report for the first time on the formation of self-assembled fractals of spherical Ag nanoparticles (Nps) fabricated by femtosecond pulse laser ablation of a solid silver target in water. Fractal structures grew both in two and three Euclidean dimensions (d). Ramified-fractal assemblies of 2 nm height and 5–14 μm large, decorated with Ag Nps of 3 nm size, were obtained in a 2d geometry when highly diluted drops of colloidal suspension were dried at a fast heating rate over a mica substrate. When less-diluted drops were dried at slow heating rate, isolated single Nps or rosette-like structures were formed. Fractal aggregates about 31 nm size in 3d geometry were observed in the as-prepared colloidal suspension. Electron diffraction and optical extinction spectroscopy (OES) analyses performed on the samples confirmed the presence of Ag and Ag{sub 2}O. The analysis of the optical extinction spectrum, using the electrostatic approximation of Mie theory for small spheres, showed the existence of Ag bare core, Ag–Ag{sub 2}O and air–Ag core–shell Nps, Ag–Ag{sub 2}O being the most frequent type [69 % relative abundance (r.a.)]. Core-size and shell-thickness distribution was derived from OES. In situ scattering measurements of the Ag colloidal suspension, carried out by small-angle X-ray scattering, indicate a mass fractal composed of packaged 〈D{sub SAXS}〉 = (5 ± 1) nm particles and fractal dimension d{sub f} = 2.5. Ex situ atomic force microscopy imaging displayed well-ramified structures, which, analyzed with box-counting method, yield a fractal dimension d{sub f} = 1.67. The growing behavior of these 2d and 3d self-assembled fractals is consistent with the diffusion-limited aggregation model.

Symmetric intersections of Rauzy fractals | Sellami | Quaestiones ...

African Journals Online (AJOL)

In this article we study symmetric subsets of Rauzy fractals of unimodular irreducible Pisot substitutions. The symmetry considered is re ection through the origin. Given an unimodular irreducible Pisot substitution, we consider the intersection of its Rauzy fractal with the Rauzy fractal of the reverse substitution. This set is ...

Scintillator Based Coded-Aperture Imaging for Neutron Detection

International Nuclear Information System (INIS)

Hayes, Sean-C.; Gamage, Kelum-A-A.

2013-06-01

In this paper we are going to assess the variations of neutron images using a series of Monte Carlo simulations. We are going to study neutron images of the same neutron source with different source locations, using a scintillator based coded-aperture system. The Monte Carlo simulations have been conducted making use of the EJ-426 neutron scintillator detector. This type of detector has a low sensitivity to gamma rays and is therefore of particular use in a system with a source that emits a mixed radiation field. From the use of different source locations, several neutron images have been produced, compared both qualitatively and quantitatively for each case. This allows conclusions to be drawn on how suited the scintillator based coded-aperture neutron imaging system is to detecting various neutron source locations. This type of neutron imaging system can be easily used to identify and locate nuclear materials precisely. (authors)

Synthetic Minority Oversampling Technique and Fractal Dimension for Identifying Multiple Sclerosis

Science.gov (United States)

Zhang, Yu-Dong; Zhang, Yin; Phillips, Preetha; Dong, Zhengchao; Wang, Shuihua

Multiple sclerosis (MS) is a severe brain disease. Early detection can provide timely treatment. Fractal dimension can provide statistical index of pattern changes with scale at a given brain image. In this study, our team used susceptibility weighted imaging technique to obtain 676 MS slices and 880 healthy slices. We used synthetic minority oversampling technique to process the unbalanced dataset. Then, we used Canny edge detector to extract distinguishing edges. The Minkowski-Bouligand dimension was a fractal dimension estimation method and used to extract features from edges. Single hidden layer neural network was used as the classifier. Finally, we proposed a three-segment representation biogeography-based optimization to train the classifier. Our method achieved a sensitivity of 97.78±1.29%, a specificity of 97.82±1.60% and an accuracy of 97.80±1.40%. The proposed method is superior to seven state-of-the-art methods in terms of sensitivity and accuracy.

Lossless, Near-Lossless, and Refinement Coding of Bi-level Images

DEFF Research Database (Denmark)

Martins, Bo; Forchhammer, Søren Otto

1999-01-01

We present general and unified algorithms for lossy/lossless coding of bi-level images. The compression is realized by applying arithmetic coding to conditional probabilities. As in the current JBIG standard the conditioning may be specified by a template.For better compression, the more general...... to the specialized soft pattern matching techniques which work better for text. Template based refinement coding is applied for lossy-to-lossless refinement. Introducing only a small amount of loss in halftoned test images, compression is increased by up to a factor of four compared with JBIG. Lossy, lossless......, and refinement decoding speed and lossless encoding speed are less than a factor of two slower than JBIG. The (de)coding method is proposed as part of JBIG2, an emerging international standard for lossless/lossy compression of bi-level images....

Poiseuille equation for steady flow of fractal fluid

Science.gov (United States)

Tarasov, Vasily E.

2016-07-01

Fractal fluid is considered in the framework of continuous models with noninteger dimensional spaces (NIDS). A recently proposed vector calculus in NIDS is used to get a description of fractal fluid flow in pipes with circular cross-sections. The Navier-Stokes equations of fractal incompressible viscous fluids are used to derive a generalization of the Poiseuille equation of steady flow of fractal media in pipe.

Hybrid coded aperture and Compton imaging using an active mask

International Nuclear Information System (INIS)

Schultz, L.J.; Wallace, M.S.; Galassi, M.C.; Hoover, A.S.; Mocko, M.; Palmer, D.M.; Tornga, S.R.; Kippen, R.M.; Hynes, M.V.; Toolin, M.J.; Harris, B.; McElroy, J.E.; Wakeford, D.; Lanza, R.C.; Horn, B.K.P.; Wehe, D.K.

2009-01-01

The trimodal imager (TMI) images gamma-ray sources from a mobile platform using both coded aperture (CA) and Compton imaging (CI) modalities. In this paper we will discuss development and performance of image reconstruction algorithms for the TMI. In order to develop algorithms in parallel with detector hardware we are using a GEANT4 [J. Allison, K. Amako, J. Apostolakis, H. Araujo, P.A. Dubois, M. Asai, G. Barrand, R. Capra, S. Chauvie, R. Chytracek, G. Cirrone, G. Cooperman, G. Cosmo, G. Cuttone, G. Daquino, et al., IEEE Trans. Nucl. Sci. NS-53 (1) (2006) 270] based simulation package to produce realistic data sets for code development. The simulation code incorporates detailed detector modeling, contributions from natural background radiation, and validation of simulation results against measured data. Maximum likelihood algorithms for both imaging methods are discussed, as well as a hybrid imaging algorithm wherein CA and CI information is fused to generate a higher fidelity reconstruction.

Fractal dimensions the digital art of Eric Hammel

CERN Document Server

Hammel, Eric

2014-01-01

The concept behind fractal geometry is extremely difficult to explain . . . but easy to see and enjoy. Eric Hammel, a professional author of military history books, is unable to explain fractals in a way that will be clear to anyone else, but most mathematicians can't explain fractals in language most people can understand. The simplest explanation is that fractals are graphic representations of high-order mathematical formulas that repeat patterns to infinity.Don't get hung up on the math. It's really all in the seeing. Like Volume 1 of Eric Hammel's Fractal Dimensions, Volume 2 is filled wit

Fractal dimensions the digital art of Eric Hammel

CERN Document Server

Hammel, Eric

2014-01-01

The concept behind fractal geometry is extremely difficult to explain . . . but easy to see and enjoy. Eric Hammel, a professional author of military history books, is unable to explain fractals in a way that will be clear to anyone else, but most mathematicians can't explain fractals in language most people can understand. The simplest explanation is that fractals are graphic representations of high-order mathematical formulas that repeat patterns to infinity.Don't get hung up on the math. It's really all in the seeing. Like Volumes 1, 2, and 3 of Eric Hammel's Fractal Dimensions, Volume 4 is

Fractal dimensions the digital art of Eric Hammel

CERN Document Server

Hammel, Eric

2014-01-01

The concept behind fractal geometry is extremely difficult to explain . . . but easy to see and enjoy. Eric Hammel, a professional author of military history books, is unable to explain fractals in a way that will be clear to anyone else, but most mathematicians can't explain fractals in language most people can understand. The simplest explanation is that fractals are graphic representations of high-order mathematical formulas that repeat patterns to infinity.Don't get hung up on the math. It's really all in the seeing. Like Volumes 1 and 2 of Eric Hammel's Fractal Dimensions, Volume 3 is fil

Fractal analysis in oral leukoplakia

Directory of Open Access Journals (Sweden)

Prashant Bhai Pandey

2015-01-01

Full Text Available Introduction: Fractal analysis (FA quantifies complex geometric structures by generating a fractal dimension (FD, which can measure the complexity of mucosa. FA is a quantitative tool used to measure the complexity of self-similar or semi-self-similar structures. Aim and Objective: The study was done to perform the FA of oral mucosa with keratotic changes, as it is also made up of self-similar tissues, and thus, its FD can be calculated. Results: In oral leukoplakia, keratinization increases the complexity of mucosa, which denotes fractal geometry. We evaluated and compared pretreated and post-treated oral leukoplakia in 50 patients with clinically proven oral leukoplakia and analyzed the normal oral mucosa and lesional or keratinized mucosa in oral leukoplakia patients through FA using box counting method. Conclusion: FA using the fractal geometry is an efficient, noninvasive prediction tool for early detection of oral leukoplakia and other premalignant conditions in patients.

Practicing the Code of Ethics, finding the image of God.

Science.gov (United States)

Hoglund, Barbara A

2013-01-01

The Code of Ethics for Nurses gives a professional obligation to practice in a compassionate and respectful way that is unaffected by the attributes of the patient. This article explores the concept "made in the image of God" and the complexities inherent in caring for those perceived as exhibiting distorted images of God. While the Code provides a professional standard consistent with a biblical worldview, human nature impacts the ability to consistently act congruently with the Code. Strategies and nursing interventions that support development of practice from a biblical worldview and the Code of Ethics for Nurses are presented.

Fractal-based exponential distribution of urban density and self-affine fractal forms of cities

International Nuclear Information System (INIS)

Chen Yanguang; Feng Jian

2012-01-01

Highlights: ► The model of urban population density differs from the common exponential function. ► Fractal landscape influences the exponential distribution of urban density. ► The exponential distribution of urban population suggests a self-affine fractal. ► Urban space can be divided into three layers with scaling and non-scaling regions. ► The dimension of urban form with characteristic scale can be treated as 2. - Abstract: 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 verify the theoretical inference. Based on the empirical analysis, a three-ring model of cities is presented and a city is conceptually divided into three layers from core to periphery. The scaling region and non-scaling region appear alternately in the city. This model may be helpful for future urban studies and city planning.

Fractional hydrodynamic equations for fractal media

International Nuclear Information System (INIS)

Tarasov, Vasily E.

2005-01-01

We use the fractional integrals in order to describe dynamical processes in the fractal medium. We consider the 'fractional' continuous medium model for the fractal media and derive the fractional generalization of the equations of balance of mass density, momentum density, and internal energy. The fractional generalization of Navier-Stokes and Euler equations are considered. We derive the equilibrium equation for fractal media. The sound waves in the continuous medium model for fractional media are considered

Ghost quintessence in fractal gravity

Indian Academy of Sciences (India)

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.

Coded aperture imaging of alpha source spatial distribution

International Nuclear Information System (INIS)

Talebitaher, Alireza; Shutler, Paul M.E.; Springham, Stuart V.; Rawat, Rajdeep S.; Lee, Paul

2012-01-01

The Coded Aperture Imaging (CAI) technique has been applied with CR-39 nuclear track detectors to image alpha particle source spatial distributions. The experimental setup comprised: a 226 Ra source of alpha particles, a laser-machined CAI mask, and CR-39 detectors, arranged inside a vacuum enclosure. Three different alpha particle source shapes were synthesized by using a linear translator to move the 226 Ra source within the vacuum enclosure. The coded mask pattern used is based on a Singer Cyclic Difference Set, with 400 pixels and 57 open square holes (representing ρ = 1/7 = 14.3% open fraction). After etching of the CR-39 detectors, the area, circularity, mean optical density and positions of all candidate tracks were measured by an automated scanning system. Appropriate criteria were used to select alpha particle tracks, and a decoding algorithm applied to the (x, y) data produced the de-coded image of the source. Signal to Noise Ratio (SNR) values obtained for alpha particle CAI images were found to be substantially better than those for corresponding pinhole images, although the CAI-SNR values were below the predictions of theoretical formulae. Monte Carlo simulations of CAI and pinhole imaging were performed in order to validate the theoretical SNR formulae and also our CAI decoding algorithm. There was found to be good agreement between the theoretical formulae and SNR values obtained from simulations. Possible reasons for the lower SNR obtained for the experimental CAI study are discussed.

High-dynamic range compressive spectral imaging by grayscale coded aperture adaptive filtering

Directory of Open Access Journals (Sweden)

Nelson Eduardo Diaz

2015-09-01

Full Text Available The coded aperture snapshot spectral imaging system (CASSI is an imaging architecture which senses the three dimensional informa-tion of a scene with two dimensional (2D focal plane array (FPA coded projection measurements. A reconstruction algorithm takes advantage of the compressive measurements sparsity to recover the underlying 3D data cube. Traditionally, CASSI uses block-un-block coded apertures (BCA to spatially modulate the light. In CASSI the quality of the reconstructed images depends on the design of these coded apertures and the FPA dynamic range. This work presents a new CASSI architecture based on grayscaled coded apertu-res (GCA which reduce the FPA saturation and increase the dynamic range of the reconstructed images. The set of GCA is calculated in a real-time adaptive manner exploiting the information from the FPA compressive measurements. Extensive simulations show the attained improvement in the quality of the reconstructed images when GCA are employed.  In addition, a comparison between traditional coded apertures and GCA is realized with respect to noise tolerance.

The fractal nature of vacuum arc cathode spots

International Nuclear Information System (INIS)

Anders, Andre

2005-01-01

Cathode spot phenomena show many features of fractals, for example self-similar patterns in the emitted light and arc erosion traces. Although there have been hints on the fractal nature of cathode spots in the literature, the fractal approach to spot interpretation is underutilized. In this work, a brief review of spot properties is given, touching the differences between spot type 1 (on cathodes surfaces with dielectric layers) and spot type 2 (on metallic, clean surfaces) as well as the known spot fragment or cell structure. The basic properties of self-similarity, power laws, random colored noise, and fractals are introduced. Several points of evidence for the fractal nature of spots are provided. Specifically power laws are identified as signature of fractal properties, such as spectral power of noisy arc parameters (ion current, arc voltage, etc) obtained by fast Fourier transform. It is shown that fractal properties can be observed down to the cutoff by measurement resolution or occurrence of elementary steps in physical processes. Random walk models of cathode spot motion are well established: they go asymptotically to Brownian motion for infinitesimal step width. The power spectrum of the arc voltage noise falls as 1/f 2 , where f is frequency, supporting a fractal spot model associated with Brownian motion

Variability of fractal dimension of solar radio flux

Science.gov (United States)

Bhatt, Hitaishi; Sharma, Som Kumar; Trivedi, Rupal; Vats, Hari Om

2018-04-01

In the present communication, the variation of the fractal dimension of solar radio flux is reported. Solar radio flux observations on a day to day basis at 410, 1415, 2695, 4995, and 8800 MHz are used in this study. The data were recorded at Learmonth Solar Observatory, Australia from 1988 to 2009 covering an epoch of two solar activity cycles (22 yr). The fractal dimension is calculated for the listed frequencies for this period. The fractal dimension, being a measure of randomness, represents variability of solar radio flux at shorter time-scales. The contour plot of fractal dimension on a grid of years versus radio frequency suggests high correlation with solar activity. Fractal dimension increases with increasing frequency suggests randomness increases towards the inner corona. This study also shows that the low frequency is more affected by solar activity (at low frequency fractal dimension difference between solar maximum and solar minimum is 0.42) whereas, the higher frequency is less affected by solar activity (here fractal dimension difference between solar maximum and solar minimum is 0.07). A good positive correlation is found between fractal dimension averaged over all frequencies and yearly averaged sunspot number (Pearson's coefficient is 0.87).

Fractal dimension determined through optical and scanning electron microscopy on FeCrAl alloy after polishing, erosion, and oxidizing processes

Energy Technology Data Exchange (ETDEWEB)

Guzman-Castaneda, J.I.; Garcia-Borquez, A. [Instituto Politecnico Nacional, ESFM, 07738 Mexico D.F. (Mexico); Arizabalo-Salas, R.D. [Instituto Mexicano del Petroleo, Direccion de Investigacion y Posgrado, 07730 Mexico D.F. (Mexico)

2012-06-15

Optical and scanning electron microscopy (OM and SEM) are techniques that are normally used for 2D-analysis of surface features. By fractal dimension analysis of the gray-scale OM and SEM images, it is possible to get quantitative topographical measurements. In this work, three different surface topographies (polished, eroded, and oxidized) were analyzed on FeCrAl alloy by OM and SEM. Clear surface topographical changes can be qualitatively observed. In order to quantify such changes, two steps were followed: (i) a gray-scale digitalization from each image was used to reproduce topographical features on the analyzed surface, and (ii) from this information, the fractal dimension (D) was determined using fractal3e software. The fractal dimension determined in this form follows coherently the topographical changes produced on the FeCrAl alloy after polishing, erosion, and oxidizing processes. The variations of fractal dimension values against the temperature of the oxidizing processes reflect well the oxide growth changes. Moreover, a minimum D-value is registered at 750 C, which corresponds to the {delta}-{theta} alumina phase transition temperature as determined by differential thermal analysis (DTA) on the same alloy. (Copyright copyright 2012 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)

Undergraduate experiment with fractal diffraction gratings

International Nuclear Information System (INIS)

Monsoriu, Juan A; Furlan, Walter D; Pons, Amparo; Barreiro, Juan C; Gimenez, Marcos H

2011-01-01

We present a simple diffraction experiment with fractal gratings based on the triadic Cantor set. Diffraction by fractals is proposed as a motivating strategy for students of optics in the potential applications of optical processing. Fraunhofer diffraction patterns are obtained using standard equipment present in most undergraduate physics laboratories and compared with those obtained with conventional periodic gratings. It is shown that fractal gratings produce self-similar diffraction patterns which can be evaluated analytically. Good agreement is obtained between experimental and numerical results.

On the arithmetic of fractal dimension using hyperhelices

International Nuclear Information System (INIS)

Toledo-Suarez, Carlos D.

2009-01-01

A hyperhelix is a fractal curve generated by coiling a helix around a rect line, then another helix around the first one, a third around the second... an infinite number of times. A way to generate hyperhelices with any desired fractal dimension is presented, leading to the result that they have embedded an algebraic structure that allows making arithmetic with fractal dimensions and to the idea of an infinitesimal of fractal dimension

A Method for Improving the Progressive Image Coding Algorithms

Directory of Open Access Journals (Sweden)

Ovidiu COSMA

2014-12-01

Full Text Available This article presents a method for increasing the performance of the progressive coding algorithms for the subbands of images, by representing the coefficients with a code that reduces the truncation error.

A fractal nature for polymerized laminin.

Directory of Open Access Journals (Sweden)

Camila Hochman-Mendez

Full Text Available Polylaminin (polyLM is a non-covalent acid-induced nano- and micro-structured polymer of the protein laminin displaying distinguished biological properties. Polylaminin stimulates neuritogenesis beyond the levels achieved by ordinary laminin and has been shown to promote axonal regeneration in animal models of spinal cord injury. Here we used confocal fluorescence microscopy (CFM, scanning electron microscopy (SEM and atomic force microscopy (AFM to characterize its three-dimensional structure. Renderization of confocal optical slices of immunostained polyLM revealed the aspect of a loose flocculated meshwork, which was homogeneously stained by the antibody. On the other hand, an ordinary matrix obtained upon adsorption of laminin in neutral pH (LM was constituted of bulky protein aggregates whose interior was not accessible to the same anti-laminin antibody. SEM and AFM analyses revealed that the seed unit of polyLM was a flat polygon formed in solution whereas the seed structure of LM was highly heterogeneous, intercalating rod-like, spherical and thin spread lamellar deposits. As polyLM was visualized at progressively increasing magnifications, we observed that the morphology of the polymer was alike independently of the magnification used for the observation. A search for the Hausdorff dimension in images of the two matrices showed that polyLM, but not LM, presented fractal dimensions of 1.55, 1.62 and 1.70 after 1, 8 and 12 hours of adsorption, respectively. Data in the present work suggest that the intrinsic fractal nature of polymerized laminin can be the structural basis for the fractal-like organization of basement membranes in the neurogenic niches of the central nervous system.

A fractal nature for polymerized laminin.

Science.gov (United States)

Hochman-Mendez, Camila; Cantini, Marco; Moratal, David; Salmeron-Sanchez, Manuel; Coelho-Sampaio, Tatiana

2014-01-01

Polylaminin (polyLM) is a non-covalent acid-induced nano- and micro-structured polymer of the protein laminin displaying distinguished biological properties. Polylaminin stimulates neuritogenesis beyond the levels achieved by ordinary laminin and has been shown to promote axonal regeneration in animal models of spinal cord injury. Here we used confocal fluorescence microscopy (CFM), scanning electron microscopy (SEM) and atomic force microscopy (AFM) to characterize its three-dimensional structure. Renderization of confocal optical slices of immunostained polyLM revealed the aspect of a loose flocculated meshwork, which was homogeneously stained by the antibody. On the other hand, an ordinary matrix obtained upon adsorption of laminin in neutral pH (LM) was constituted of bulky protein aggregates whose interior was not accessible to the same anti-laminin antibody. SEM and AFM analyses revealed that the seed unit of polyLM was a flat polygon formed in solution whereas the seed structure of LM was highly heterogeneous, intercalating rod-like, spherical and thin spread lamellar deposits. As polyLM was visualized at progressively increasing magnifications, we observed that the morphology of the polymer was alike independently of the magnification used for the observation. A search for the Hausdorff dimension in images of the two matrices showed that polyLM, but not LM, presented fractal dimensions of 1.55, 1.62 and 1.70 after 1, 8 and 12 hours of adsorption, respectively. Data in the present work suggest that the intrinsic fractal nature of polymerized laminin can be the structural basis for the fractal-like organization of basement membranes in the neurogenic niches of the central nervous system.

Progressive Coding of Palette Images and Digital Maps

DEFF Research Database (Denmark)

Forchhammer, Søren; Salinas, J. Martin

2002-01-01

image layer. The resolution is increased by a factor of 2 in each step. The 2D PPM coding is applied to palette images and street maps. The sequential results are comparable to PWC. The PPM results are a little better for the palette images with few colors (up to 4-5 bpp) and a little worse...

Design of LTCC Based Fractal Antenna

KAUST Repository

AdbulGhaffar, Farhan

2010-01-01

The thesis presents a Sierpinski Carpet fractal antenna array designed at 24 GHz for automotive radar applications. Miniaturized, high performance and low cost antennas are required for this application. To meet these specifications a fractal array

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.

JJ1017 committee report: image examination order codes--standardized codes for imaging modality, region, and direction with local expansion: an extension of DICOM.

Science.gov (United States)

Kimura, Michio; Kuranishi, Makoto; Sukenobu, Yoshiharu; Watanabe, Hiroki; Tani, Shigeki; Sakusabe, Takaya; Nakajima, Takashi; Morimura, Shinya; Kabata, Shun

2002-06-01

The digital imaging and communications in medicine (DICOM) standard includes parts regarding nonimage data information, such as image study ordering data and performed procedure data, and is used for sharing information between HIS/RIS and modality systems, which is essential for IHE. To bring such parts of the DICOM standard into force in Japan, a joint committee of JIRA and JAHIS established the JJ1017 management guideline, specifying, for example, which items are legally required in Japan, while remaining optional in the DICOM standard. In Japan, the contents of orders from referring physicians for radiographic examinations include details of the examination. Such details are not used typically by referring physicians requesting radiographic examinations in the United States, because radiologists in the United States often determine the examination protocol. The DICOM standard has code tables for examination type, region, and direction for image examination orders. However, this investigation found that it does not include items that are detailed sufficiently for use in Japan, because of the above-mentioned reason. To overcome these drawbacks, we have generated the JJ1017 code for these 3 codes for use based on the JJ1017 guidelines. This report introduces the JJ1017 code. These codes (the study type codes in particular) must be expandable to keep up with technical advances in equipment. Expansion has 2 directions: width for covering more categories and depth for specifying the information in more detail (finer categories). The JJ1017 code takes these requirements into consideration and clearly distinguishes between the stem part as the common term and the expansion. The stem part of the JJ1017 code partially utilizes the DICOM codes to remain in line with the DICOM standard. This work is an example of how local requirements can be met by using the DICOM standard and extending it.

Fractal Geometry Enables Classification of Different Lung Morphologies in a Model of Experimental Asthma

Science.gov (United States)

Obert, Martin; Hagner, Stefanie; Krombach, Gabriele A.; Inan, Selcuk; Renz, Harald

2015-06-01

Animal models represent the basis of our current understanding of the pathophysiology of asthma and are of central importance in the preclinical development of drug therapies. The characterization of irregular lung shapes is a major issue in radiological imaging of mice in these models. The aim of this study was to find out whether differences in lung morphology can be described by fractal geometry. Healthy and asthmatic mouse groups, before and after an acute asthma attack induced by methacholine, were studied. In vivo flat-panel-based high-resolution Computed Tomography (CT) was used for mice's thorax imaging. The digital image data of the mice's lungs were segmented from the surrounding tissue. After that, the lungs were divided by image gray-level thresholds into two additional subsets. One subset contained basically the air transporting bronchial system. The other subset corresponds mainly to the blood vessel system. We estimated the fractal dimension of all sets of the different mouse groups using the mass radius relation (mrr). We found that the air transporting subset of the bronchial lung tissue enables a complete and significant differentiation between all four mouse groups (mean D of control mice before methacholine treatment: 2.64 ± 0.06; after treatment: 2.76 ± 0.03; asthma mice before methacholine treatment: 2.37 ± 0.16; after treatment: 2.71 ± 0.03; p < 0.05). We conclude that the concept of fractal geometry allows a well-defined, quantitative numerical and objective differentiation of lung shapes — applicable most likely also in human asthma diagnostics.

Fractal Structures For Mems Variable Capacitors

KAUST Repository

Elshurafa, Amro M.; Radwan, Ahmed Gomaa Ahmed; Emira, Ahmed A.; Salama, Khaled N.

2014-01-01

In accordance with the present disclosure, one embodiment of a fractal variable capacitor comprises a capacitor body in a microelectromechanical system (MEMS) structure, wherein the capacitor body has an upper first metal plate with a fractal shape

Model of fractal aggregates induced by shear

Directory of Open Access Journals (Sweden)

Wan Zhanhong

2013-01-01

Full Text Available It is an undoubted fact that particle aggregates from marine, aerosol, and engineering systems have fractal structures. In this study, fractal geometry is used to describe the morphology of irregular aggregates. The mean-field theory is employed to solve coagulation kinetic equation of aggregates. The Taylor-expansion method of moments in conjunction with the self-similar fractal characteristics is used to represent the particulate field. The effect of the target fractal dimensions on zeroth-order moment, second-order moment, and geometric standard deviation of the aggregates is explored. Results show that the developed moment method is an efficient and powerful approach to solving such evolution equations.

Fractal Structure and Entropy Production within the Central Nervous System

Directory of Open Access Journals (Sweden)

Andrew J. E. Seely

2014-08-01

Full Text Available Our goal is to explore the relationship between two traditionally unrelated concepts, fractal structure and entropy production, evaluating both within the central nervous system (CNS. Fractals are temporal or spatial structures with self-similarity across scales of measurement; whereas entropy production represents the necessary exportation of entropy to our environment that comes with metabolism and life. Fractals may be measured by their fractal dimension; and human entropy production may be estimated by oxygen and glucose metabolism. In this paper, we observe fractal structures ubiquitously present in the CNS, and explore a hypothetical and unexplored link between fractal structure and entropy production, as measured by oxygen and glucose metabolism. Rapid increase in both fractal structures and metabolism occur with childhood and adolescent growth, followed by slow decrease during aging. Concomitant increases and decreases in fractal structure and metabolism occur with cancer vs. Alzheimer’s and multiple sclerosis, respectively. In addition to fractals being related to entropy production, we hypothesize that the emergence of fractal structures spontaneously occurs because a fractal is more efficient at dissipating energy gradients, thus maximizing entropy production. Experimental evaluation and further understanding of limitations and necessary conditions are indicated to address broad scientific and clinical implications of this work.

a Fractal Network Model for Fractured Porous Media

Science.gov (United States)

Xu, Peng; Li, Cuihong; Qiu, Shuxia; Sasmito, Agus Pulung

2016-04-01

The transport properties and mechanisms of fractured porous media are very important for oil and gas reservoir engineering, hydraulics, environmental science, chemical engineering, etc. In this paper, a fractal dual-porosity model is developed to estimate the equivalent hydraulic properties of fractured porous media, where a fractal tree-like network model is used to characterize the fracture system according to its fractal scaling laws and topological structures. The analytical expressions for the effective permeability of fracture system and fractured porous media, tortuosity, fracture density and fraction are derived. The proposed fractal model has been validated by comparisons with available experimental data and numerical simulation. It has been shown that fractal dimensions for fracture length and aperture have significant effect on the equivalent hydraulic properties of fractured porous media. The effective permeability of fracture system can be increased with the increase of fractal dimensions for fracture length and aperture, while it can be remarkably lowered by introducing tortuosity at large branching angle. Also, a scaling law between the fracture density and fractal dimension for fracture length has been found, where the scaling exponent depends on the fracture number. The present fractal dual-porosity model may shed light on the transport physics of fractured porous media and provide theoretical basis for oil and gas exploitation, underground water, nuclear waste disposal and geothermal energy extraction as well as chemical engineering, etc.

Fractal analysis of the surgical treatment of ligature-induced peri-implantitis in dogs

International Nuclear Information System (INIS)

Kim, Hak Kun; Kim, Jin Soo

2010-01-01

To evaluate the effect of surgical treatment of ligature-induced peri-implantitis in dogs using fractal analysis. Also, the capabilities of fractal analysis as bone analysis techniques were compared with those of histomorphometric analysis. A total of 24 implants were inserted in 6 dogs. After a 3-months, experimental periimplantitis characterized by a bone loss of about 3 mm was established by inducing with wires. Surgical treatment involving flap procedure, debridement of implants surface with chlorhexidine and saline (group 1), guided bone regeneration (GBR) with absorbable collagen membrane and mineralized bone graft (group 2), and CO2 laser application with GBR (group 3) were performed. After animals were sacrificed in 8 and 16 weeks respectively, bone sections including implants were made. Fractal dimensions were calculated by box-counting method on the skeletonized images, made from each region of interest, including five screws at medial and distal aspects of implant, were selected. Statistically significant differences in the fractal dimensions between the group 1 (0.9340 ± 0.0126) and group 3 (0.9783 ± 0.0118) at 16 weeks were found (P<0.05). The fractal dimension was statistically significant different between 8 (0.9395 ± 0.0283) and 16 weeks in group 3 (P<0.05). These results were similar with the result of the evaluation of new bone formation in histomorphometric analysis. Treatment of experimental peri-implantitis by using CO2 laser with GBR is more useful than other treatments in the formation of new bone and also the tendency of fractal dimension to increase relative to healing time may be a useful means of evaluating.

Fractal analysis of the surgical treatment of ligature-induced peri-implantitis in dogs

Energy Technology Data Exchange (ETDEWEB)

Kim, Hak Kun; Kim, Jin Soo [School of Dentisity, Chosun University, Gwangju (Korea, Republic of)

2010-09-15

To evaluate the effect of surgical treatment of ligature-induced peri-implantitis in dogs using fractal analysis. Also, the capabilities of fractal analysis as bone analysis techniques were compared with those of histomorphometric analysis. A total of 24 implants were inserted in 6 dogs. After a 3-months, experimental periimplantitis characterized by a bone loss of about 3 mm was established by inducing with wires. Surgical treatment involving flap procedure, debridement of implants surface with chlorhexidine and saline (group 1), guided bone regeneration (GBR) with absorbable collagen membrane and mineralized bone graft (group 2), and CO2 laser application with GBR (group 3) were performed. After animals were sacrificed in 8 and 16 weeks respectively, bone sections including implants were made. Fractal dimensions were calculated by box-counting method on the skeletonized images, made from each region of interest, including five screws at medial and distal aspects of implant, were selected. Statistically significant differences in the fractal dimensions between the group 1 (0.9340 {+-} 0.0126) and group 3 (0.9783 {+-} 0.0118) at 16 weeks were found (P<0.05). The fractal dimension was statistically significant different between 8 (0.9395 {+-} 0.0283) and 16 weeks in group 3 (P<0.05). These results were similar with the result of the evaluation of new bone formation in histomorphometric analysis. Treatment of experimental peri-implantitis by using CO2 laser with GBR is more useful than other treatments in the formation of new bone and also the tendency of fractal dimension to increase relative to healing time may be a useful means of evaluating.

Semiflexible crossing-avoiding trails on plane-filling fractals

International Nuclear Information System (INIS)

Živić, I.; Elezović-Hadžić, S.; Milošević, S.

2015-01-01

We have studied the statistics of semiflexible polymer chains modeled by crossing-avoiding trails (CAT) situated on the family of plane-filling (PF) fractals. The fractals are compact, that is, their fractal dimension d_f is equal to 2 for all members of the fractal family. By applying the exact and Monte Carlo real-space renormalization group method we have calculated the critical exponent ν, which governs the scaling behavior of the end-to-end distance of the polymer, as well as the entropic critical exponent γ, for a large set of fractals, and various values of polymer flexibility. Our results, obtained for CAT model on PF fractals, show that both critical exponents depend on the polymer flexibility, in such a way that less flexible polymer chains display enlarged values of ν, and diminished values of γ. We have compared the obtained results for CAT model with the known results for the self-avoiding walk and self-avoiding trail models and discussed the influence of excluded volume effect on the values of semiflexible polymer critical exponents, for a large set of studied compact fractals.

Mathematica® for Theoretical Physics Electrodynamics, Quantum Mechanics, General Relativity and Fractals

CERN Document Server

Baumann, Gerd

2005-01-01

Mathematica for Theoretical Physics: Electrodynamics, Quantum Mechanics, General Relativity, and Fractals This second edition of Baumann's Mathematica® in Theoretical Physics shows readers how to solve physical problems and deal with their underlying theoretical concepts while using Mathematica® to derive numeric and symbolic solutions. Each example and calculation can be evaluated by the reader, and the reader can change the example calculations and adopt the given code to related or similar problems. The second edition has been completely revised and expanded into two volumes: The first volume covers classical mechanics and nonlinear dynamics. Both topics are the basis of a regular mechanics course. The second volume covers electrodynamics, quantum mechanics, relativity, and fractals and fractional calculus. New examples have been added and the representation has been reworked to provide a more interactive problem-solving presentation. This book can be used as a textbook or as a reference work, by student...

Generalized Warburg impedance on realistic self-affine fractals ...

Indian Academy of Sciences (India)

2016-08-26

Aug 26, 2016 ... We analyse the problem of impedance for a diffusion controlled charge transfer process across an irregular interface. These interfacial irregularities are characterized as two class of random fractals: (i) a statistically isotropic self-affine fractals and (ii) a statistically corrugated self-affine fractals.

Fractals and multifractals in physics

International Nuclear Information System (INIS)

Arcangelis, L. de.

1987-01-01

We present a general introduction to the world of fractals. The attention is mainly devoted to stress how fractals do indeed appear in the real world and to find quantitative methods for characterizing their properties. The idea of multifractality is also introduced and it is presented in more details within the framework of the percolation problem

A novel approach to correct the coded aperture misalignment for fast neutron imaging

Energy Technology Data Exchange (ETDEWEB)

Zhang, F. N.; Hu, H. S., E-mail: huasi-hu@mail.xjtu.edu.cn; Wang, D. M.; Jia, J. [School of Energy and Power Engineering, Xi’an Jiaotong University, Xi’an 710049 (China); Zhang, T. K. [Laser Fusion Research Center, CAEP, Mianyang, 621900 Sichuan (China); Jia, Q. G. [Institute of Applied Physics and Computational Mathematics, Beijing 100094 (China)

2015-12-15

Aperture alignment is crucial for the diagnosis of neutron imaging because it has significant impact on the coding imaging and the understanding of the neutron source. In our previous studies on the neutron imaging system with coded aperture for large field of view, “residual watermark,” certain extra information that overlies reconstructed image and has nothing to do with the source is discovered if the peak normalization is employed in genetic algorithms (GA) to reconstruct the source image. Some studies on basic properties of residual watermark indicate that the residual watermark can characterize coded aperture and can thus be used to determine the location of coded aperture relative to the system axis. In this paper, we have further analyzed the essential conditions for the existence of residual watermark and the requirements of the reconstruction algorithm for the emergence of residual watermark. A gamma coded imaging experiment has been performed to verify the existence of residual watermark. Based on the residual watermark, a correction method for the aperture misalignment has been studied. A multiple linear regression model of the position of coded aperture axis, the position of residual watermark center, and the gray barycenter of neutron source with twenty training samples has been set up. Using the regression model and verification samples, we have found the position of the coded aperture axis relative to the system axis with an accuracy of approximately 20 μm. Conclusively, a novel approach has been established to correct the coded aperture misalignment for fast neutron coded imaging.

Fractal Image Compression Based on High Entropy Values Technique

Directory of Open Access Journals (Sweden)

Douaa Younis Abbaas

2018-04-01

Full Text Available There are many attempts tried to improve the encoding stage of FIC because it consumed time. These attempts worked by reducing size of the search pool for pair range-domain matching but most of them led to get a bad quality, or a lower compression ratio of reconstructed image. This paper aims to present a method to improve performance of the full search algorithm by combining FIC (lossy compression and another lossless technique (in this case entropy coding is used. The entropy technique will reduce size of the domain pool (i. e., number of domain blocks based on the entropy value of each range block and domain block and then comparing the results of full search algorithm and proposed algorithm based on entropy technique to see each of which give best results (such as reduced the encoding time with acceptable values in both compression quali-ty parameters which are C. R (Compression Ratio and PSNR (Image Quality. The experimental results of the proposed algorithm proven that using the proposed entropy technique reduces the encoding time while keeping compression rates and reconstruction image quality good as soon as possible.

Generalized Warburg impedance on realistic self-affine fractals

Indian Academy of Sciences (India)

We analyse the problem of impedance for a diffusion controlled charge transfer process across an irregular interface. These interfacial irregularities are characterized as two class of random fractals: (i) a statistically isotropic self-affine fractals and (ii) a statistically corrugated self-affine fractals. The information about the ...

Fractal analytical approach of urban form based on spatial correlation function

International Nuclear Information System (INIS)

Chen, Yanguang

2013-01-01

Highlights: ► Many fractal parameter relations of cities can be derived by scaling analysis. ► The area-radius scaling of cities suggests a spatial correlation function. ► Spectral analysis can be used to estimate fractal dimension values of urban form. ► The valid range of fractal dimension of urban form comes between 1.5 and 2. ► The traditional scale concept will be replaced by scaling concept in geography. -- Abstract: Urban form has been empirically demonstrated to be of scaling invariance and can be described with fractal geometry. However, the rational range of fractal dimension value and the relationships between various fractal indicators of cities are not yet revealed in theory. By mathematical deduction and transform (e.g., Fourier transform), I find that scaling analysis, spectral analysis, and spatial correlation analysis are all associated with fractal concepts and can be integrated into a new approach to fractal analysis of cities. This method can be termed ‘3S analyses’ of urban form. Using the 3S analysis, I derived a set of fractal parameter equations, by which different fractal parameters of cities can be linked up with one another. Each fractal parameter has its own reasonable extent of values. According to the fractal parameter equations, the intersection of the rational ranges of different fractal parameters suggests the proper scale of the fractal dimension of urban patterns, which varies from 1.5 to 2. The fractal dimension equations based on the 3S analysis and the numerical relationships between different fractal parameters are useful for geographers to understand urban evolution and potentially helpful for future city planning

International Conference and Workshop on Fractals and Wavelets

CERN Document Server

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.

Fractal physiology and the fractional calculus: a perspective.

Science.gov (United States)

West, Bruce J

2010-01-01

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. Not only are anatomical structures (Grizzi and Chiriva-Internati, 2005), such as the convoluted surface of the brain, the lining of the bowel, neural networks and placenta, fractal, but the output of dynamical physiologic networks are fractal as well (Bassingthwaighte et al., 1994). The time series for the inter-beat intervals of the heart, inter-breath intervals and inter-stride intervals have all been shown to be fractal and/or multifractal statistical phenomena. Consequently, the fractal dimension turns out to be a significantly better indicator of organismic functions in health and disease than the traditional average measures, such as heart rate, breathing rate, and stride rate. The observation that human physiology is primarily fractal was first made in the 1980s, based on the analysis of a limited number of datasets. We review some of these phenomena herein by applying an allometric aggregation approach to the processing of physiologic time series. 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. A fractional operator (derivative or integral) acting on a fractal function, yields another fractal function, allowing us to construct a fractional Langevin equation to describe the evolution of a

Convergence of trajectories in fractal interpolation of stochastic processes

International Nuclear Information System (INIS)

MaIysz, Robert

2006-01-01

The notion of fractal interpolation functions (FIFs) can be applied to stochastic processes. Such construction is especially useful for the class of α-self-similar processes with stationary increments and for the class of α-fractional Brownian motions. For these classes, convergence of the Minkowski dimension of the graphs in fractal interpolation of the Hausdorff dimension of the graph of original process was studied in [Herburt I, MaIysz R. On convergence of box dimensions of fractal interpolation stochastic processes. Demonstratio Math 2000;4:873-88.], [MaIysz R. A generalization of fractal interpolation stochastic processes to higher dimension. Fractals 2001;9:415-28.], and [Herburt I. Box dimension of interpolations of self-similar processes with stationary increments. Probab Math Statist 2001;21:171-8.]. We prove that trajectories of fractal interpolation stochastic processes converge to the trajectory of the original process. We also show that convergence of the trajectories in fractal interpolation of stochastic processes is equivalent to the convergence of trajectories in linear interpolation

Probabilistic hypergraph based hash codes for social image search

Institute of Scientific and Technical Information of China (English)

Yi XIE; Hui-min YU; Roland HU

2014-01-01

With the rapid development of the Internet, recent years have seen the explosive growth of social media. This brings great challenges in performing efficient and accurate image retrieval on a large scale. Recent work shows that using hashing methods to embed high-dimensional image features and tag information into Hamming space provides a powerful way to index large collections of social images. By learning hash codes through a spectral graph partitioning algorithm, spectral hashing (SH) has shown promising performance among various hashing approaches. However, it is incomplete to model the relations among images only by pairwise simple graphs which ignore the relationship in a higher order. In this paper, we utilize a probabilistic hypergraph model to learn hash codes for social image retrieval. A probabilistic hypergraph model offers a higher order repre-sentation among social images by connecting more than two images in one hyperedge. Unlike a normal hypergraph model, a probabilistic hypergraph model considers not only the grouping information, but also the similarities between vertices in hy-peredges. Experiments on Flickr image datasets verify the performance of our proposed approach.

Chaos and fractals an elementary introduction

CERN Document Server

Feldman, David P

2012-01-01

For students with a background in elementary algebra, this text provides a vivid introduction to the key phenomena and ideas of chaos and fractals, including the butterfly effect, strange attractors, fractal dimensions, Julia sets and the Mandelbrot set, power laws, and cellular automata.

Evaluación de la dimensión fractal reactiva de los glicinatos de magnesio, manganeso y zinc Evaluation of the reactive fractal dimension of magnesium, manganese and zinc glycinates

Directory of Open Access Journals (Sweden)

Julie Fernanda Benavides Arevalo

2012-03-01

Full Text Available Introducción: complejos de glicina con los cationes magnesio, manganeso y zinc podrían ser parte de una formulación de un suplemento nutricional que proporcione una adecuada absorción de los metales en el organismo sin generar molestias gastrointestinales. Objetivo: realizar una aproximación a la solubilidad de los complejos de glicina con los cationes magnesio, manganeso y zinc. Métodos: se efectuaron estudios de disolución y análisis de imagen. Se realizó la síntesis y la verificación de formación de los complejos por espectroscopia infrarroja, calorimetría de barrido diferencial, análisis termogravimétrico y difracción de rayos X de polvos. Resultados: se obtuvieron por análisis de imagen los descriptores: circularidad, diámetro de Feret y dimensión fractal; esta última se relacionó con el proceso de disolución en agua, para obtener dos propiedades relacionadas: la dimensión fractal superficial y la dimensión fractal reactiva. Conclusiones: los resultados muestran que el proceso de disolución de los glicinatos, se realiza a través de los poros o grietas de la superficie de las partículas de estos y que son aptos para su empleo en formulaciones nutricionales como fuentes de magnesio, manganeso y zinc.Introduction: Complexes of glycine and cations magnesium, manganese and zinc, could be included in the formulation of a nutritional supplement that provides adequate absorption of these metals into the body without gastrointestinal disturbances. Objective: to study the solubility of complexes of glycine and cations manganese, zinc and magnesium. Methods: dissolution and image analysis studies were performed. The synthesis and verification of the formation of complexes were carried out by infrared spectroscopy, differential scanning calorimetry, thermal gravimetric analysis, and X-ray diffraction of dust. Results: the image analysis showed some descriptors such as circularity, the Ferret diameter and the fractal dimension

Fractal characterization of the silicon surfaces produced by ion beam irradiation of varying fluences

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.

A fractal-like resistive network

International Nuclear Information System (INIS)

Saggese, A; De Luca, R

2014-01-01

The equivalent resistance of a fractal-like network is calculated by means of approaches similar to those employed in defining the equivalent resistance of an infinite ladder. Starting from an elementary triangular circuit, a fractal-like network, named after Saggese, is developed. The equivalent resistance of finite approximations of this network is measured, and the didactical implications of the model are highlighted. (paper)

Electro-chemical manifestation of nanoplasmonics in fractal media

Science.gov (United States)

Baskin, Emmanuel; Iomin, Alexander

2013-06-01

Electrodynamics of composite materials with fractal geometry is studied in the framework of fractional calculus. This consideration establishes a link between fractal geometry of the media and fractional integrodifferentiation. The photoconductivity in the vicinity of the electrode-electrolyte fractal interface is studied. The methods of fractional calculus are employed to obtain an analytical expression for the giant local enhancement of the optical electric field inside the fractal composite structure at the condition of the surface plasmon excitation. This approach makes it possible to explain experimental data on photoconductivity in the nano-electrochemistry.

Paper-based inkjet-printed ultra-wideband fractal antennas

KAUST Repository

Maza, Armando Rodriguez

2012-01-01

For the first time, paper-based inkjet-printed ultra-wideband (UWB) fractal antennas are presented. Two new designs, a miniaturised UWB monopole, which utilises a fractal matching network and is the smallest reported inkjet-printed UWB printed antenna to date, and a fourth-order Koch Snowflake monopole, which utilises a Sierpinski gasket fractal for ink reduction, are demonstrated. It is shown that fractals prove to be a successful method of reducing fabrication costs in inkjet-printed antennas, while retaining or enhancing printed antenna performance. © 2012 The Institution of Engineering and Technology.

Effective degrees of freedom of a random walk on a fractal

Science.gov (United States)

Balankin, Alexander S.

2015-12-01

We argue that a non-Markovian random walk on a fractal can be treated as a Markovian process in a fractional dimensional space with a suitable metric. This allows us to define the fractional dimensional space allied to the fractal as the ν -dimensional space Fν equipped with the metric induced by the fractal topology. The relation between the number of effective spatial degrees of freedom of walkers on the fractal (ν ) and fractal dimensionalities is deduced. The intrinsic time of random walk in Fν is inferred. The Laplacian operator in Fν is constructed. This allows us to map physical problems on fractals into the corresponding problems in Fν. In this way, essential features of physics on fractals are revealed. Particularly, subdiffusion on path-connected fractals is elucidated. The Coulomb potential of a point charge on a fractal embedded in the Euclidean space is derived. Intriguing attributes of some types of fractals are highlighted.

A new coding concept for fast ultrasound imaging using pulse trains

DEFF Research Database (Denmark)

Misaridis, T.; Jensen, Jørgen Arendt

2002-01-01

Frame rate in ultrasound imaging can he increased by simultaneous transmission of multiple beams using coded waveforms. However, the achievable degree of orthogonality among coded waveforms is limited in ultrasound, and the image quality degrades unacceptably due to interbeam interference....... In this paper, an alternative combined time-space coding approach is undertaken. In the new method all transducer elements are excited with short pulses and the high time-bandwidth (TB) product waveforms are generated acoustically. Each element transmits a short pulse spherical wave with a constant transmit...... delay from element to element, long enough to assure no pulse overlapping for all depths in the image. Frequency shift keying is used for "per element" coding. The received signals from a point scatterer are staggered pulse trains which are beamformed for all beam directions and further processed...

Power Load Prediction Based on Fractal Theory

OpenAIRE

Jian-Kai, Liang; Cattani, Carlo; Wan-Qing, Song

2015-01-01

The basic theories of load forecasting on the power system are summarized. Fractal theory, which is a new algorithm applied to load forecasting, is introduced. Based on the fractal dimension and fractal interpolation function theories, the correlation algorithms are applied to the model of short-term load forecasting. According to the process of load forecasting, the steps of every process are designed, including load data preprocessing, similar day selecting, short-term load forecasting, and...

Naturaleza fractal en redes de cristales de grasas

Directory of Open Access Journals (Sweden)

Gómez Herrera, C.

2004-06-01

Full Text Available The determination of the mechanical and rheological characteris­tics of several plastic fats requires a detailed understanding of the microstructure of the fat crystal network aggregates. The (or A fractal approach is useful for the characterization of this micros­tructure. This review begins with information on fractality and statistical self-similar structure. Estimations for fractal dimension by means of equations relating the volume fraction of solid fat to shear elastic modulus G' in linear region are described. The influence of interesterification on fractal dimension decrease (from 2, 46 to 2 ,15 for butterfat-canola oil blends is notable . This influence is not significant for fat blends without butterfat. The need for an increase in research concerning the relationship between fractality and rheology in plastic fats is emphasized.La determinación de las características mecánicas y reológicas de ciertas grasas plásticas requiere conocimientos detallados sobre las microestructuras de los agregados que forman la red de cristales grasos. El estudio de la naturaleza fractal de estas microestructuras resulta útil para su carac­terización. Este artículo de información se inicia con descripciones de la dimensión fractal y de la "autosimilitud estadística". A continuación se describe el cálculo de la dimensión fractal mediante ecuaciones que relacionan la fracción en volumen de grasa sólida con el módulo de recuperación (G' dentro de un comportamiento viscoelástico lineal. Se destaca la influencia que la interesterificación ejerce sobre la dimensión fractal de una mezcla de grasa láctea y aceite de canola (que pasa de 2,64 a 2,15. Esta influencia no se presenta en mezclas sin grasa láctea. Se insiste sobre la necesidad de incrementar las investi­gaciones sobre la relación entre reología y estructura fractal en grasas plásticas.

Fractal analysis of visual search activity for mass detection during mammographic screening.

Science.gov (United States)

Alamudun, Folami; Yoon, Hong-Jun; Hudson, Kathleen B; Morin-Ducote, Garnetta; Hammond, Tracy; Tourassi, Georgia D

2017-03-01

The objective of this study was to assess the complexity of human visual search activity during mammographic screening using fractal analysis and to investigate its relationship with case and reader characteristics. The study was performed for the task of mammographic screening with simultaneous viewing of four coordinated breast views as typically done in clinical practice. Eye-tracking data and diagnostic decisions collected for 100 mammographic cases (25 normal, 25 benign, 50 malignant) from 10 readers (three board certified radiologists and seven Radiology residents), formed the corpus for this study. The fractal dimension of the readers' visual scanning pattern was computed with the Minkowski-Bouligand box-counting method and used as a measure of gaze complexity. Individual factor and group-based interaction ANOVA analysis was performed to study the association between fractal dimension, case pathology, breast density, and reader experience level. The consistency of the observed trends depending on gaze data representation was also examined. Case pathology, breast density, reader experience level, and individual reader differences are all independent predictors of the complexity of visual scanning pattern when screening for breast cancer. No higher order effects were found to be significant. Fractal characterization of visual search behavior during mammographic screening is dependent on case properties and image reader characteristics. © 2017 American Association of Physicists in Medicine.

Connotations of pixel-based scale effect in remote sensing and the modified fractal-based analysis method

Science.gov (United States)

Feng, Guixiang; Ming, Dongping; Wang, Min; Yang, Jianyu

2017-06-01

Scale problems are a major source of concern in the field of remote sensing. Since the remote sensing is a complex technology system, there is a lack of enough cognition on the connotation of scale and scale effect in remote sensing. Thus, this paper first introduces the connotations of pixel-based scale and summarizes the general understanding of pixel-based scale effect. Pixel-based scale effect analysis is essentially important for choosing the appropriate remote sensing data and the proper processing parameters. Fractal dimension is a useful measurement to analysis pixel-based scale. However in traditional fractal dimension calculation, the impact of spatial resolution is not considered, which leads that the scale effect change with spatial resolution can't be clearly reflected. Therefore, this paper proposes to use spatial resolution as the modified scale parameter of two fractal methods to further analyze the pixel-based scale effect. To verify the results of two modified methods (MFBM (Modified Windowed Fractal Brownian Motion Based on the Surface Area) and MDBM (Modified Windowed Double Blanket Method)); the existing scale effect analysis method (information entropy method) is used to evaluate. And six sub-regions of building areas and farmland areas were cut out from QuickBird images to be used as the experimental data. The results of the experiment show that both the fractal dimension and information entropy present the same trend with the decrease of spatial resolution, and some inflection points appear at the same feature scales. Further analysis shows that these feature scales (corresponding to the inflection points) are related to the actual sizes of the geo-object, which results in fewer mixed pixels in the image, and these inflection points are significantly indicative of the observed features. Therefore, the experiment results indicate that the modified fractal methods are effective to reflect the pixel-based scale effect existing in remote sensing

Graphics with Mathematica fractals, Julia sets, patterns and natural forms

CERN Document Server

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

Fractal Analysis of Radiologists Visual Scanning Pattern in Screening Mammography

Energy Technology Data Exchange (ETDEWEB)

Alamudun, Folami T [ORNL; Yoon, Hong-Jun [ORNL; Hudson, Kathy [University of Tennessee, Knoxville (UTK); Morin-Ducote, Garnetta [University of Tennessee, Knoxville (UTK); Tourassi, Georgia [ORNL

2015-01-01

Several investigators have investigated radiologists visual scanning patterns with respect to features such as total time examining a case, time to initially hit true lesions, number of hits, etc. The purpose of this study was to examine the complexity of the radiologists visual scanning pattern when viewing 4-view mammographic cases, as they typically do in clinical practice. Gaze data were collected from 10 readers (3 breast imaging experts and 7 radiology residents) while reviewing 100 screening mammograms (24 normal, 26 benign, 50 malignant). The radiologists scanpaths across the 4 mammographic views were mapped to a single 2-D image plane. Then, fractal analysis was applied on the derived scanpaths using the box counting method. For each case, the complexity of each radiologist s scanpath was estimated using fractal dimension. The association between gaze complexity, case pathology, case density, and radiologist experience was evaluated using 3 factor fixed effects ANOVA. ANOVA showed that case pathology, breast density, and experience level are all independent predictors of the visual scanning pattern complexity. Visual scanning patterns are significantly different for benign and malignant cases than for normal cases as well as when breast parenchyma density changes.

Random-fractal Ansatz for the configurations of two-dimensional critical systems.

Science.gov (United States)

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 nature of humic materials

International Nuclear Information System (INIS)

Rice, J.A.

1992-01-01

Fractals are geometric representatives of strongly disordered systems whose structure is described by nonintegral dimensions. A fundamental tenet of fractal geometry is that disorder persists at any characterization scale-length used to describe the system. The nonintegral nature of these fractal dimensions is the result of the realization that a disordered system must possess more structural detail than an ordered system with classical dimensions of 1, 2, or 3 in order to accommodate this ''disorder within disorder.'' Thus from a fractal perspective, disorder is seen as an inherent characteristic of the system rather than as a perturbative phenomena forced upon it. Humic materials are organic substances that are formed by the profound alteration of organic matter in a natural environment. They can be operationally divided into 3 fractions; humic acid (soluble in base), fulvic acid (soluble in acid or base), and humin (insoluble in acid or base). Each of these fraction has been shown to be an extremely heterogeneous mixture. These mixtures have proven so intractable that they may represent the ultimate in molecular disorder. In fact, based on the characteristics that humic materials must possess in order to perform their functions in natural systems, it has been proposed that the fundamental chemical characteristic of a humic material is not a discrete chemical structure but a pronounced lack of order on a molecular level. If the fundamental chemical characteristic of a humic material is a strongly disordered nature, as has been proposed, then humic materials should be amenable to characterization by fractal geometry. The purpose of this paper is to test this hypothesis

110 °C range athermalization of wavefront coding infrared imaging systems

Science.gov (United States)

Feng, Bin; Shi, Zelin; Chang, Zheng; Liu, Haizheng; Zhao, Yaohong

2017-09-01

110 °C range athermalization is significant but difficult for designing infrared imaging systems. Our wavefront coding athermalized infrared imaging system adopts an optical phase mask with less manufacturing errors and a decoding method based on shrinkage function. The qualitative experiments prove that our wavefront coding athermalized infrared imaging system has three prominent merits: (1) working well over a temperature range of 110 °C; (2) extending the focal depth up to 15.2 times; (3) achieving a decoded image being approximate to its corresponding in-focus infrared image, with a mean structural similarity index (MSSIM) value greater than 0.85.

Node insertion in Coalescence Fractal Interpolation Function

International Nuclear Information System (INIS)

Prasad, Srijanani Anurag

2013-01-01

The Iterated Function System (IFS) used in the construction of Coalescence Hidden-variable Fractal Interpolation Function (CHFIF) depends on the interpolation data. The insertion of a new point in a given set of interpolation data is called the problem of node insertion. In this paper, the effect of insertion of new point on the related IFS and the Coalescence Fractal Interpolation Function is studied. Smoothness and Fractal Dimension of a CHFIF obtained with a node are also discussed

Fractals in Power Reactor Noise

International Nuclear Information System (INIS)

Aguilar Martinez, O.

1994-01-01

In this work the non- lineal dynamic problem of power reactor is analyzed using classic concepts of fractal analysis as: attractors, Hausdorff-Besikovics dimension, phase space, etc. A new non-linear problem is also analyzed: the discrimination of chaotic signals from random neutron noise signals and processing for diagnosis purposes. The advantages of a fractal analysis approach in the power reactor noise are commented in details

Adaptive coded aperture imaging in the infrared: towards a practical implementation

Science.gov (United States)

Slinger, Chris W.; Gilholm, Kevin; Gordon, Neil; McNie, Mark; Payne, Doug; Ridley, Kevin; Strens, Malcolm; Todd, Mike; De Villiers, Geoff; Watson, Philip; Wilson, Rebecca; Dyer, Gavin; Eismann, Mike; Meola, Joe; Rogers, Stanley

2008-08-01

An earlier paper [1] discussed the merits of adaptive coded apertures for use as lensless imaging systems in the thermal infrared and visible. It was shown how diffractive (rather than the more conventional geometric) coding could be used, and that 2D intensity measurements from multiple mask patterns could be combined and decoded to yield enhanced imagery. Initial experimental results in the visible band were presented. Unfortunately, radiosity calculations, also presented in that paper, indicated that the signal to noise performance of systems using this approach was likely to be compromised, especially in the infrared. This paper will discuss how such limitations can be overcome, and some of the tradeoffs involved. Experimental results showing tracking and imaging performance of these modified, diffractive, adaptive coded aperture systems in the visible and infrared will be presented. The subpixel imaging and tracking performance is compared to that of conventional imaging systems and shown to be superior. System size, weight and cost calculations indicate that the coded aperture approach, employing novel photonic MOEMS micro-shutter architectures, has significant merits for a given level of performance in the MWIR when compared to more conventional imaging approaches.

Transport properties of electrons in fractal magnetic-barrier structures

Science.gov (United States)

Sun, Lifeng; Fang, Chao; Guo, Yong

2010-09-01

Quantum transport properties in fractal magnetically modulated structures are studied by the transfer-matrix method. It is found that the transmission spectra depend sensitively not only on the incident energy and the direction of the wave vector but also on the stage of the fractal structures. Resonance splitting, enhancement, and position shift of the resonance peaks under different magnetic modulation are observed at four different fractal stages, and the relationship between the conductance in the fractal structure and magnetic modulation is also revealed. The results indicate the spectra of the transmission can be considered as fingerprints for the fractal structures, which show the subtle correspondence between magnetic structures and transport behaviors.

Radionuclide imaging with coded apertures and three-dimensional image reconstruction from focal-plane tomography

International Nuclear Information System (INIS)

Chang, L.T.

1976-05-01

Two techniques for radionuclide imaging and reconstruction have been studied;; both are used for improvement of depth resolution. The first technique is called coded aperture imaging, which is a technique of tomographic imaging. The second technique is a special 3-D image reconstruction method which is introduced as an improvement to the so called focal-plane tomography

Towards thermomechanics of fractal media

Science.gov (United States)

Ostoja-Starzewski, Martin

2007-11-01

Hans Ziegler’s thermomechanics [1,2,3], established half a century ago, is extended to fractal media on the basis of a recently introduced continuum mechanics due to Tarasov [14,15]. Employing the concept of internal (kinematic) variables and internal stresses, as well as the quasiconservative and dissipative stresses, a field form of the second law of thermodynamics is derived. In contradistinction to the conventional Clausius Duhem inequality, it involves generalized rates of strain and internal variables. Upon introducing a dissipation function and postulating the thermodynamic orthogonality on any lengthscale, constitutive laws of elastic-dissipative fractal media naturally involving generalized derivatives of strain and stress can then be derived. This is illustrated on a model viscoelastic material. Also generalized to fractal bodies is the Hill condition necessary for homogenization of their constitutive responses.

Dimensional analysis, scaling and fractals

International Nuclear Information System (INIS)

Timm, L.C.; Reichardt, K.; Oliveira Santos Bacchi, O.

2004-01-01

Dimensional analysis refers to the study of the dimensions that characterize physical entities, like mass, force and energy. Classical mechanics is based on three fundamental entities, with dimensions MLT, the mass M, the length L and the time T. The combination of these entities gives rise to derived entities, like volume, speed and force, of dimensions L 3 , LT -1 , MLT -2 , respectively. In other areas of physics, four other fundamental entities are defined, among them the temperature θ and the electrical current I. The parameters that characterize physical phenomena are related among themselves by laws, in general of quantitative nature, in which they appear as measures of the considered physical entities. The measure of an entity is the result of its comparison with another one, of the same type, called unit. Maps are also drawn in scale, for example, in a scale of 1:10,000, 1 cm 2 of paper can represent 10,000 m 2 in the field. Entities that differ in scale cannot be compared in a simple way. Fractal geometry, in contrast to the Euclidean geometry, admits fractional dimensions. The term fractal is defined in Mandelbrot (1982) as coming from the Latin fractus, derived from frangere which signifies to break, to form irregular fragments. The term fractal is opposite to the term algebra (from the Arabic: jabara) which means to join, to put together the parts. For Mandelbrot, fractals are non topologic objects, that is, objects which have as their dimension a real, non integer number, which exceeds the topologic dimension. For the topologic objects, or Euclidean forms, the dimension is an integer (0 for the point, 1 for a line, 2 for a surface, and 3 for a volume). The fractal dimension of Mandelbrot is a measure of the degree of irregularity of the object under consideration. It is related to the speed by which the estimate of the measure of an object increases as the measurement scale decreases. An object normally taken as uni-dimensional, like a piece of a

Undergraduate Experiment with Fractal Diffraction Gratings

Science.gov (United States)

Monsoriu, Juan A.; Furlan, Walter D.; Pons, Amparo; Barreiro, Juan C.; Gimenez, Marcos H.

2011-01-01

We present a simple diffraction experiment with fractal gratings based on the triadic Cantor set. Diffraction by fractals is proposed as a motivating strategy for students of optics in the potential applications of optical processing. Fraunhofer diffraction patterns are obtained using standard equipment present in most undergraduate physics…

Pore Structure and Fractal Characteristics of Niutitang Shale from China

Directory of Open Access Journals (Sweden)

Zhaodong Xi

2018-04-01

Full Text Available A suite of shale samples from the Lower Cambrian Niutitang Formation in northwestern Hunan Province, China, were investigated to better understand the pore structure and fractal characteristics of marine shale. Organic geochemistry, mineralogy by X-ray diffraction, porosity, permeability, mercury intrusion and nitrogen adsorption and methane adsorption experiments were conducted for each sample. Fractal dimension D was obtained from the nitrogen adsorption data using the fractal Frenkel-Halsey-Hill (FHH model. The relationships between total organic carbon (TOC content, mineral compositions, pore structure parameters and fractal dimension are discussed, along with the contributions of fractal dimension to shale gas reservoir evaluation. Analysis of the results showed that Niutitang shale samples featured high TOC content (2.51% on average, high thermal maturity (3.0% on average, low permeability and complex pore structures, which are highly fractal. TOC content and mineral compositions are two major factors affecting pore structure but they have different impacts on the fractal dimension. Shale samples with higher TOC content had a larger specific surface area (SSA, pore volume (PV and fractal dimension, which enhanced the heterogeneity of the pore structure. Quartz content had a relatively weak influence on shale pore structure, whereas SSA, PV and fractal dimension decreased with increasing clay mineral content. Shale with a higher clay content weakened pore structure heterogeneity. The permeability and Langmuir volume of methane adsorption were affected by fractal dimension. Shale samples with higher fractal dimension had higher adsorption capacity but lower permeability, which is favorable for shale gas adsorption but adverse to shale gas seepage and diffusion.

The Application of Fractal and Multifractal Theory in Hydraulic-Flow-Unit Characterization and Permeability Estimation

Science.gov (United States)

Chen, X.; Yao, G.; Cai, J.

2017-12-01

Pore structure characteristics are important factors in influencing the fluid transport behavior of porous media, such as pore-throat ratio, pore connectivity and size distribution, moreover, wettability. To accurately characterize the diversity of pore structure among HFUs, five samples selected from different HFUs (porosities are approximately equal, however permeability varies widely) were chosen to conduct micro-computerized tomography test to acquire direct 3D images of pore geometries and to perform mercury injection experiments to obtain the pore volume-radii distribution. To characterize complex and high nonlinear pore structure of all samples, three classic fractal geometry models were applied. Results showed that each HFU has similar box-counting fractal dimension and generalized fractal dimension in the number-area model, but there are significant differences in multifractal spectrums. In the radius-volume model, there are three obvious linear segments, corresponding to three fractal dimension values, and the middle one is proved as the actual fractal dimension according to the maximum radius. In the number-radius model, the spherical-pore size distribution extracted by maximum ball algorithm exist a decrease in the number of small pores compared with the fractal power rate rather than the traditional linear law. Among the three models, only multifractal analysis can classify the HFUs accurately. Additionally, due to the tightness and low-permeability in reservoir rocks, connate water film existing in the inner surface of pore channels commonly forms bound water. The conventional model which is known as Yu-Cheng's model has been proved to be typically not applicable. Considering the effect of irreducible water saturation, an improved fractal permeability model was also deduced theoretically. The comparison results showed that the improved model can be applied to calculate permeability directly and accurately in such unconventional rocks.

Highly parallel line-based image coding for many cores.

Science.gov (United States)

Peng, Xiulian; Xu, Jizheng; Zhou, You; Wu, Feng

2012-01-01

Computers are developing along with a new trend from the dual-core and quad-core processors to ones with tens or even hundreds of cores. Multimedia, as one of the most important applications in computers, has an urgent need to design parallel coding algorithms for compression. Taking intraframe/image coding as a start point, this paper proposes a pure line-by-line coding scheme (LBLC) to meet the need. In LBLC, an input image is processed line by line sequentially, and each line is divided into small fixed-length segments. The compression of all segments from prediction to entropy coding is completely independent and concurrent at many cores. Results on a general-purpose computer show that our scheme can get a 13.9 times speedup with 15 cores at the encoder and a 10.3 times speedup at the decoder. Ideally, such near-linear speeding relation with the number of cores can be kept for more than 100 cores. In addition to the high parallelism, the proposed scheme can perform comparatively or even better than the H.264 high profile above middle bit rates. At near-lossless coding, it outperforms H.264 more than 10 dB. At lossless coding, up to 14% bit-rate reduction is observed compared with H.264 lossless coding at the high 4:4:4 profile.

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....

Fractal dimension analysis of complexity in Ligeti piano pieces

Science.gov (United States)

Bader, Rolf

2005-04-01

Fractal correlation dimensional analysis has been performed with whole solo piano pieces by Gyrgy Ligeti at every 50ms interval of the pieces. The resulting curves of development of complexity represented by the fractal dimension showed up a very reasonable correlation with the perceptional density of events during these pieces. The seventh piece of Ligeti's ``Musica ricercata'' was used as a test case. Here, each new part of the piece was followed by an increase of the fractal dimension because of the increase of information at the part changes. The second piece ``Galamb borong,'' number seven of the piano Etudes was used, because Ligeti wrote these Etudes after studying fractal geometry. Although the piece is not fractal in the strict mathematical sense, the overall structure of the psychoacoustic event-density as well as the detailed event development is represented by the fractal dimension plot.

Comparisons of coded aperture imaging using various apertures and decoding methods

International Nuclear Information System (INIS)

Chang, L.T.; Macdonald, B.; Perez-Mendez, V.

1976-07-01

The utility of coded aperture γ camera imaging of radioisotope distributions in Nuclear Medicine is in its ability to give depth information about a three dimensional source. We have calculated imaging with Fresnel zone plate and multiple pinhole apertures to produce coded shadows and reconstruction of these shadows using correlation, Fresnel diffraction, and Fourier transform deconvolution. Comparisons of the coded apertures and decoding methods are made by evaluating their point response functions both for in-focus and out-of-focus image planes. Background averages and standard deviations were calculated. In some cases, background subtraction was made using combinations of two complementary apertures. Results using deconvolution reconstruction for finite numbers of events are also given

Random walks of oriented particles on fractals

International Nuclear Information System (INIS)

Haber, René; Prehl, Janett; Hoffmann, Karl Heinz; Herrmann, Heiko

2014-01-01

Random walks of point particles on fractals exhibit subdiffusive behavior, where the anomalous diffusion exponent is smaller than one, and the corresponding random walk dimension is larger than two. This is due to the limited space available in fractal structures. Here, we endow the particles with an orientation and analyze their dynamics on fractal structures. In particular, we focus on the dynamical consequences of the interactions between the local surrounding fractal structure and the particle orientation, which are modeled using an appropriate move class. These interactions can lead to particles becoming temporarily or permanently stuck in parts of the structure. A surprising finding is that the random walk dimension is not affected by the orientation while the diffusion constant shows a variety of interesting and surprising features. (paper)

FDG uptake heterogeneity evaluated by fractal analysis improves the differential diagnosis of pulmonary nodules

Energy Technology Data Exchange (ETDEWEB)

Miwa, Kenta, E-mail: kenta5710@gmail.com [Department of Nuclear Medicine, Cancer Institute Hospital of Japanese Foundation for Cancer Research, 3-8-31 Ariake, Koto-ku, Tokyo 135-8550 (Japan); Division of Medical Quantum Science, Department of Health Sciences, Graduate School of Medical Sciences, Kyushu University, 3-1-1 Maidashi, Higashi-ku, Fukuoka 812-8582 (Japan); Inubushi, Masayuki, E-mail: inubushi@med.kawasaki-m.ac.jp [Department of Nuclear Medicine, Kawasaki Medical School, 577 Matsushima Kurashiki, Okayama 701-0192 (Japan); Wagatsuma, Kei, E-mail: kei1192@hotmail.co.jp [Department of Nuclear Medicine, Cancer Institute Hospital of Japanese Foundation for Cancer Research, 3-8-31 Ariake, Koto-ku, Tokyo 135-8550 (Japan); Nagao, Michinobu, E-mail: minagao@radiol.med.kyushu-u.ac.jp [Department of Molecular Imaging and Diagnosis, Graduate School of Medical Sciences, Kyushu University, 3-1-1 Maidashi, Higashi-ku, Fukuoka 812-8582 (Japan); Murata, Taisuke, E-mail: taisuke113@gmail.com [Department of Nuclear Medicine, Cancer Institute Hospital of Japanese Foundation for Cancer Research, 3-8-31 Ariake, Koto-ku, Tokyo 135-8550 (Japan); Koyama, Masamichi, E-mail: masamichi.koyama@jfcr.or.jp [Department of Nuclear Medicine, Cancer Institute Hospital of Japanese Foundation for Cancer Research, 3-8-31 Ariake, Koto-ku, Tokyo 135-8550 (Japan); Koizumi, Mitsuru, E-mail: mitsuru@jfcr.or.jp [Department of Nuclear Medicine, Cancer Institute Hospital of Japanese Foundation for Cancer Research, 3-8-31 Ariake, Koto-ku, Tokyo 135-8550 (Japan); Sasaki, Masayuki, E-mail: msasaki@hs.med.kyushu-u.ac.jp [Division of Medical Quantum Science, Department of Health Sciences, Graduate School of Medical Sciences, Kyushu University, 3-1-1 Maidashi, Higashi-ku, Fukuoka 812-8582 (Japan)

2014-04-15

Purpose: The present study aimed to determine whether fractal analysis of morphological complexity and intratumoral heterogeneity of FDG uptake can help to differentiate malignant from benign pulmonary nodules. Materials and methods: We retrospectively analyzed data from 54 patients with suspected non-small cell lung cancer (NSCLC) who were examined by FDG PET/CT. Pathological assessments of biopsy specimens confirmed 35 and 19 nodules as NSCLC and inflammatory lesions, respectively. The morphological fractal dimension (m-FD), maximum standardized uptake value (SUV{sub max}) and density fractal dimension (d-FD) of target nodules were calculated from CT and PET images. Fractal dimension is a quantitative index of morphological complexity and tracer uptake heterogeneity; higher values indicate increased complexity and heterogeneity. Results: The m-FD, SUV{sub max} and d-FD significantly differed between malignant and benign pulmonary nodules (p < 0.05). Although the diagnostic ability was better for d-FD than m-FD and SUV{sub max}, the difference did not reach statistical significance. Tumor size correlated significantly with SUV{sub max} (r = 0.51, p < 0.05), but not with either m-FD or d-FD. Furthermore, m-FD combined with either SUV{sub max} or d-FD improved diagnostic accuracy to 92.6% and 94.4%, respectively. Conclusion: The d-FD of intratumoral heterogeneity of FDG uptake can help to differentially diagnose malignant and benign pulmonary nodules. The SUV{sub max} and d-FD obtained from FDG-PET images provide different types of information that are equally useful for differential diagnoses. Furthermore, the morphological complexity determined by CT combined with heterogeneous FDG uptake determined by PET improved diagnostic accuracy.

Quantitative assessment of early diabetic retinopathy using fractal analysis.

Science.gov (United States)

Cheung, Ning; Donaghue, Kim C; Liew, Gerald; Rogers, Sophie L; Wang, Jie Jin; Lim, Shueh-Wen; Jenkins, Alicia J; Hsu, Wynne; Li Lee, Mong; Wong, Tien Y

2009-01-01

Fractal analysis can quantify the geometric complexity of the retinal vascular branching pattern and may therefore offer a new method to quantify early diabetic microvascular damage. In this study, we examined the relationship between retinal fractal dimension and retinopathy in young individuals with type 1 diabetes. We conducted a cross-sectional study of 729 patients with type 1 diabetes (aged 12-20 years) who had seven-field stereoscopic retinal photographs taken of both eyes. From these photographs, retinopathy was graded according to the modified Airlie House classification, and fractal dimension was quantified using a computer-based program following a standardized protocol. In this study, 137 patients (18.8%) had diabetic retinopathy signs; of these, 105 had mild retinopathy. Median (interquartile range) retinal fractal dimension was 1.46214 (1.45023-1.47217). After adjustment for age, sex, diabetes duration, A1C, blood pressure, and total cholesterol, increasing retinal vascular fractal dimension was significantly associated with increasing odds of retinopathy (odds ratio 3.92 [95% CI 2.02-7.61] for fourth versus first quartile of fractal dimension). In multivariate analysis, each 0.01 increase in retinal vascular fractal dimension was associated with a nearly 40% increased odds of retinopathy (1.37 [1.21-1.56]). This association remained after additional adjustment for retinal vascular caliber. Greater retinal fractal dimension, representing increased geometric complexity of the retinal vasculature, is independently associated with early diabetic retinopathy signs in type 1 diabetes. Fractal analysis of fundus photographs may allow quantitative measurement of early diabetic microvascular damage.

Warped Discrete Cosine Transform-Based Low Bit-Rate Block Coding Using Image Downsampling

Directory of Open Access Journals (Sweden)

Ertürk Sarp

2007-01-01

Full Text Available This paper presents warped discrete cosine transform (WDCT-based low bit-rate block coding using image downsampling. While WDCT aims to improve the performance of conventional DCT by frequency warping, the WDCT has only been applicable to high bit-rate coding applications because of the overhead required to define the parameters of the warping filter. Recently, low bit-rate block coding based on image downsampling prior to block coding followed by upsampling after the decoding process is proposed to improve the compression performance for low bit-rate block coders. This paper demonstrates that a superior performance can be achieved if WDCT is used in conjunction with image downsampling-based block coding for low bit-rate applications.

A multiplex coding imaging spectrometer for X-ray astronomy

International Nuclear Information System (INIS)

Rocchia, R.; Deschamps, J.Y.; Koch-Miramond, L.; Tarrius, A.

1985-06-01

The paper describes a multiplex coding system associated with a solid state spectrometer Si(Li) designed to be placed at the focus of a grazing incidence telescope. In this instrument the spectrometric and imaging functions are separated. The coding system consists in a movable mask with pseudo randomly distributed holes, located in the focal plane of the telescope. The pixel size lies in the range 100-200 microns. The close association of the coding system with a Si(Li) detector gives an imaging spectrometer combining the good efficiency (50% between 0,5 and 10 keV) and energy resolution (ΔE approximately 90 to 160 eV) of solid state spectrometers with the spatial resolution of the mask. Simulations and results obtained with a laboratory model are presented

Fractals and spectra related to fourier analysis and function spaces

CERN Document Server

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 (…) ...

Usefulness of fractal analysis for the diagnosis of periodontitis

Energy Technology Data Exchange (ETDEWEB)

Cha, Sang Yun; Han, Won Jeong; Kim, Eun Kyung [Dankook Univ. School of Dentistry, Seoul (Korea, Republic of)

2001-03-15

To evaluate the usefulness of fractal analysis for diagnosis of periodontitis. Each 30 cases of periapical films of male mandibular molar were selected in normal group and patient group which had complete furcation involvement. They were digitized at 300 dpi, 256 gray levels and saved with gif format. Rectangular ROIs (10 X 20 pixel) were selected at furcation, interdental crest, and interdental middle 1/3 area. Fractal dimensions were calculated three times at each area by mass radius method and were determined using a mean of three measurements. We computed fractal dimensions at furcation and interdental crest area of normal group with those of patient group. And then we compared ratio of fractal dimensions at furcation area, interdental crest area to interdental middle 1/3 area. Fractal dimension at interdental crest area of normal group was 1.979{+-}0.018 (p<0.05). The radio of fractal dimension at furcation area to interdental middle 1/3 of normal group was 1.006{+-}0.018 and that of patient group 0.9940.018 (p<0.05). The radio of fractal dimension at interdental crest and furcation area to interdental middle 1/3 area showed a statistically significant difference between normal and patient group. In conclusion, it is thought that fractal analysis might be useful for the diagnosis of periodontitis.

Using Peano Curves to Construct Laplacians on Fractals

Science.gov (United States)

Molitor, Denali; Ott, Nadia; Strichartz, Robert

2015-12-01

We describe a new method to construct Laplacians on fractals using a Peano curve from the circle onto the fractal, extending an idea that has been used in the case of certain Julia sets. The Peano curve allows us to visualize eigenfunctions of the Laplacian by graphing the pullback to the circle. We study in detail three fractals: the pentagasket, the octagasket and the magic carpet. We also use the method for two nonfractal self-similar sets, the torus and the equilateral triangle, obtaining appealing new visualizations of eigenfunctions on the triangle. In contrast to the many familiar pictures of approximations to standard Peano curves, that do no show self-intersections, our descriptions of approximations to the Peano curves have self-intersections that play a vital role in constructing graph approximations to the fractal with explicit graph Laplacians that give the fractal Laplacian in the limit.

ABC of multi-fractal spacetimes and fractional sea turtles

Energy Technology Data Exchange (ETDEWEB)

Calcagni, Gianluca [Instituto de Estructura de la Materia, CSIC, Madrid (Spain)

2016-04-15

We clarify what it means to have a spacetime fractal geometry in quantum gravity and show that its properties differ from those of usual fractals. A weak and a strong definition of multi-scale and multi-fractal spacetimes are given together with a sketch of the landscape of multi-scale theories of gravitation. Then, in the context of the fractional theory with q-derivatives, we explore the consequences of living in a multi-fractal spacetime. To illustrate the behavior of a non-relativistic body, we take the entertaining example of a sea turtle. We show that, when only the time direction is fractal, sea turtles swim at a faster speed than in an ordinary world, while they swim at a slower speed if only the spatial directions are fractal. The latter type of geometry is the one most commonly found in quantum gravity. For time-like fractals, relativistic objects can exceed the speed of light, but strongly so only if their size is smaller than the range of particle-physics interactions. We also find new results about log-oscillating measures, the measure presentation and their role in physical observations and in future extensions to nowhere-differentiable stochastic spacetimes. (orig.)

ABC of multi-fractal spacetimes and fractional sea turtles

International Nuclear Information System (INIS)

Calcagni, Gianluca

2016-01-01

We clarify what it means to have a spacetime fractal geometry in quantum gravity and show that its properties differ from those of usual fractals. A weak and a strong definition of multi-scale and multi-fractal spacetimes are given together with a sketch of the landscape of multi-scale theories of gravitation. Then, in the context of the fractional theory with q-derivatives, we explore the consequences of living in a multi-fractal spacetime. To illustrate the behavior of a non-relativistic body, we take the entertaining example of a sea turtle. We show that, when only the time direction is fractal, sea turtles swim at a faster speed than in an ordinary world, while they swim at a slower speed if only the spatial directions are fractal. The latter type of geometry is the one most commonly found in quantum gravity. For time-like fractals, relativistic objects can exceed the speed of light, but strongly so only if their size is smaller than the range of particle-physics interactions. We also find new results about log-oscillating measures, the measure presentation and their role in physical observations and in future extensions to nowhere-differentiable stochastic spacetimes. (orig.)

ABC of multi-fractal spacetimes and fractional sea turtles

Science.gov (United States)

Calcagni, Gianluca

2016-04-01

We clarify what it means to have a spacetime fractal geometry in quantum gravity and show that its properties differ from those of usual fractals. A weak and a strong definition of multi-scale and multi-fractal spacetimes are given together with a sketch of the landscape of multi-scale theories of gravitation. Then, in the context of the fractional theory with q-derivatives, we explore the consequences of living in a multi-fractal spacetime. To illustrate the behavior of a non-relativistic body, we take the entertaining example of a sea turtle. We show that, when only the time direction is fractal, sea turtles swim at a faster speed than in an ordinary world, while they swim at a slower speed if only the spatial directions are fractal. The latter type of geometry is the one most commonly found in quantum gravity. For time-like fractals, relativistic objects can exceed the speed of light, but strongly so only if their size is smaller than the range of particle-physics interactions. We also find new results about log-oscillating measures, the measure presentation and their role in physical observations and in future extensions to nowhere-differentiable stochastic spacetimes.

Heritability of Retinal Vascular Fractals

DEFF Research Database (Denmark)

Vergmann, Anna Stage; Broe, Rebecca; Kessel, Line

2017-01-01

Purpose: To determine the genetic contribution to the pattern of retinal vascular branching expressed by its fractal dimension. Methods: This was a cross-sectional study of 50 monozygotic and 49 dizygotic, same-sex twin pairs aged 20 to 46 years. In 50°, disc-centered fundus photographs, the reti...... fractal dimension did not differ statistically significantly between monozygotic and dizygotic twin pairs (1.505 vs. 1.495, P = 0.06), supporting that the study population was suitable for quantitative analysis of heritability. The intrapair correlation was markedly higher (0.505, P = 0.......0002) in monozygotic twins than in dizygotic twins (0.108, P = 0.46), corresponding to a heritability h2 for the fractal dimension of 0.79. In quantitative genetic models, dominant genetic effects explained 54% of the variation and 46% was individually environmentally determined. Conclusions: In young adult twins...

Product code optimization for determinate state LDPC decoding in robust image transmission.

Science.gov (United States)

Thomos, Nikolaos; Boulgouris, Nikolaos V; Strintzis, Michael G

2006-08-01

We propose a novel scheme for error-resilient image transmission. The proposed scheme employs a product coder consisting of low-density parity check (LDPC) codes and Reed-Solomon codes in order to deal effectively with bit errors. The efficiency of the proposed scheme is based on the exploitation of determinate symbols in Tanner graph decoding of LDPC codes and a novel product code optimization technique based on error estimation. Experimental evaluation demonstrates the superiority of the proposed system in comparison to recent state-of-the-art techniques for image transmission.

Pulse regime in formation of fractal fibers

Energy Technology Data Exchange (ETDEWEB)

Smirnov, B. M., E-mail: bmsmirnov@gmail.com [Joint Institute for High Temperatures (Russian Federation)

2016-11-15

The pulse regime of vaporization of a bulk metal located in a buffer gas is analyzed as a method of generation of metal atoms under the action of a plasma torch or a laser beam. Subsequently these atoms are transformed into solid nanoclusters, fractal aggregates and then into fractal fibers if the growth process proceeds in an external electric field. We are guided by metals in which transitions between s and d-electrons of their atoms are possible, since these metals are used as catalysts and filters in interaction with gas flows. The resistance of metal fractal structures to a gas flow is evaluated that allows one to find optimal parameters of a fractal structure for gas flow propagation through it. The thermal regime of interaction between a plasma pulse or a laser beam and a metal surface is analyzed. It is shown that the basic energy from an external source is consumed on a bulk metal heating, and the efficiency of atom evaporation from the metal surface, that is the ratio of energy fluxes for vaporization and heating, is 10{sup –3}–10{sup –4} for transient metals under consideration. A typical energy flux (~10{sup 6} W/cm{sup 2}), a typical surface temperature (~3000 K), and a typical pulse duration (~1 μs) provide a sufficient amount of evaporated atoms to generate fractal fibers such that each molecule of a gas flow collides with the skeleton of fractal fibers many times.

Fractal characterization of the compaction and sintering of ferrites

NARCIS (Netherlands)

Glass, H.J.; With, de G.

2001-01-01

A novel parameter, the fractal exponent DE, is derived using the concept of fractal scaling. The fractal exponent DE relates the development of a feature within a material to the development of the size of the material. As an application, structural changes during the compaction and sintering of

A Tutorial Review on Fractal Spacetime and Fractional Calculus

Science.gov (United States)

He, Ji-Huan

2014-11-01

This tutorial review of fractal-Cantorian spacetime and fractional calculus begins with Leibniz's notation for derivative without limits which can be generalized to discontinuous media like fractal derivative and q-derivative of quantum calculus. Fractal spacetime is used to elucidate some basic properties of fractal which is the foundation of fractional calculus, and El Naschie's mass-energy equation for the dark energy. The variational iteration method is used to introduce the definition of fractional derivatives. Fractal derivative is explained geometrically and q-derivative is motivated by quantum mechanics. Some effective analytical approaches to fractional differential equations, e.g., the variational iteration method, the homotopy perturbation method, the exp-function method, the fractional complex transform, and Yang-Laplace transform, are outlined and the main solution processes are given.

Alignment effects on a neutron imaging system using coded apertures

International Nuclear Information System (INIS)

Thfoin, Isabelle; Landoas, Olivier; Caillaud, Tony; Vincent, Maxime; Bourgade, Jean-Luc; Rosse, Bertrand; Disdier, Laurent; Sangster, Thomas C.; Glebov, Vladimir Yu.; Pien, Greg; Armstrong, William

2010-01-01

A high resolution neutron imaging system is being developed and tested on the OMEGA laser facility for inertial confinement fusion experiments. This diagnostic uses a coded imaging technique with a penumbral or an annular aperture. The sensitiveness of these techniques to misalignment was pointed out with both experiments and simulations. Results obtained during OMEGA shots are in good agreement with calculations performed with the Monte Carlo code GEANT4. Both techniques are sensitive to the relative position of the source in the field of view. The penumbral imaging technique then demonstrates to be less sensitive to misalignment compared to the ring. These results show the necessity to develop a neutron imaging diagnostic for megajoule class lasers taking into account our alignment capabilities on such facilities.

Fractal analysis for heat extraction in geothermal system

Directory of Open Access Journals (Sweden)

Shang Xiaoji

2017-01-01

Full Text Available Heat conduction and convection play a key role in geothermal development. These two processes are coupled and influenced by fluid seepage in hot porous rock. A number of integer dimension thermal fluid models have been proposed to describe this coupling mechanism. However, fluid flow, heat conduction and convection in porous rock are usually non-linear, tortuous and fractal, thus the integer dimension thermal fluid flow models can not well describe these phenomena. In this study, a fractal thermal fluid coupling model is proposed to describe the heat conduction and flow behaviors in fractal hot porous rock in terms of local fractional time and space derivatives. This coupling equation is analytically solved through the fractal travelling wave transformation method. Analytical solutions of Darcy’s velocity, fluid temperature with fractal time and space are obtained. The solutions show that the introduction of fractional parameters is essential to describe the mechanism of heat conduction and convection.

Study on 3D gamma-ray imaging for medical diagnosis with coded aperture

International Nuclear Information System (INIS)

Horiki, Kazunari; Shimazoe, Kenji; Ohno, Masashi; Takahashi, Hiroyuki; Kobashi, Keiji; Moro, Eiji

2014-01-01

The conventional methods for medical imaging have several disadvantages such as restriction on the energy and detection efficiency. Coded aperture imaging can be used for medical imagings without restriction on the energy, which makes it possible to use multiple tracers in diagnosis. The detection efficiency of Coded aperture imaging is ten times better than that of the pinhole collimator. First, simulations of the coded aperture imaging have been done to confirm M-array's effectiveness. Second, two experiments have been done with low-energy gamma-ray (122 keV( 57 Co)) and with high-energy gamma-ray (662 keV( 137 Cs)). In both cases reconstructed image was successfully acquired. The measured spatial resolution in the experiment using 57 Co is 4.3 mm (FWHM). (author)

Investigation of changes in fractal dimension from layered retinal structures of healthy and diabetic eyes with optical coherence tomography

Science.gov (United States)

Gao, Wei; Zakharov, Valery P.; Myakinin, Oleg O.; Bratchenko, Ivan A.; Artemyev, Dmitry N.; Kornilin, Dmitry V.

2015-07-01

Optical coherence tomography (OCT) is usually employed for the measurement of retinal thickness characterizing the structural changes of tissue. However, fractal dimension (FD) could also character the structural changes of tissue. Therefore, fractal dimension changes may provide further information regarding cellular layers and early damage in ocular diseases. We investigated the possibility of OCT in detecting changes in fractal dimension from layered retinal structures. OCT images were obtained from diabetic patients without retinopathy (DM, n = 38 eyes) or mild diabetic retinopathy (MDR, n = 43 eyes) and normal healthy subjects (Controls, n = 74 eyes). Fractal dimension was calculated using the differentiate box counting methodology. We evaluated the usefulness of quantifying fractal dimension of layered structures in the detection of retinal damage. Generalized estimating equations considering within-subject intereye relations were used to test for differences between the groups. A modified p value of <0.001 was considered statistically significant. Receiver operating characteristic (ROC) curves were constructed to describe the ability of fractal dimension to discriminate between the eyes of DM, MDR and healthy eyes. Significant decreases of fractal dimension were observed in all layers in the MDR eyes compared with controls except in the inner nuclear layer (INL). Significant decreases of fractal dimension were also observed in all layers in the MDR eyes compared with DM eyes. The highest area under receiver operating characteristic curve (AUROC) values estimated for fractal dimension were observed for the outer plexiform layer (OPL) and outer segment photoreceptors (OS) when comparing MDR eyes with controls. The highest AUROC value estimated for fractal dimension were also observed for the retinal nerve fiber layer (RNFL) and OS when comparing MDR eyes with DM eyes. Our results suggest that fractal dimension of the intraretinal layers may provide useful

Adaptive bit plane quadtree-based block truncation coding for image compression

Science.gov (United States)

Li, Shenda; Wang, Jin; Zhu, Qing

2018-04-01

Block truncation coding (BTC) is a fast image compression technique applied in spatial domain. Traditional BTC and its variants mainly focus on reducing computational complexity for low bit rate compression, at the cost of lower quality of decoded images, especially for images with rich texture. To solve this problem, in this paper, a quadtree-based block truncation coding algorithm combined with adaptive bit plane transmission is proposed. First, the direction of edge in each block is detected using Sobel operator. For the block with minimal size, adaptive bit plane is utilized to optimize the BTC, which depends on its MSE loss encoded by absolute moment block truncation coding (AMBTC). Extensive experimental results show that our method gains 0.85 dB PSNR on average compare to some other state-of-the-art BTC variants. So it is desirable for real time image compression applications.

Three-Dimensional Terahertz Coded-Aperture Imaging Based on Single Input Multiple Output Technology

Directory of Open Access Journals (Sweden)

Shuo Chen

2018-01-01

Full Text Available As a promising radar imaging technique, terahertz coded-aperture imaging (TCAI can achieve high-resolution, forward-looking, and staring imaging by producing spatiotemporal independent signals with coded apertures. In this paper, we propose a three-dimensional (3D TCAI architecture based on single input multiple output (SIMO technology, which can reduce the coding and sampling times sharply. The coded aperture applied in the proposed TCAI architecture loads either purposive or random phase modulation factor. In the transmitting process, the purposive phase modulation factor drives the terahertz beam to scan the divided 3D imaging cells. In the receiving process, the random phase modulation factor is adopted to modulate the terahertz wave to be spatiotemporally independent for high resolution. Considering human-scale targets, images of each 3D imaging cell are reconstructed one by one to decompose the global computational complexity, and then are synthesized together to obtain the complete high-resolution image. As for each imaging cell, the multi-resolution imaging method helps to reduce the computational burden on a large-scale reference-signal matrix. The experimental results demonstrate that the proposed architecture can achieve high-resolution imaging with much less time for 3D targets and has great potential in applications such as security screening, nondestructive detection, medical diagnosis, etc.

Fractal dimension of cantori

International Nuclear Information System (INIS)

Li, W.; Bak, P.

1986-01-01

At a critical point the golden-mean Kolmogorov-Arnol'd-Moser trajectory of Chirikov's standard map breaks up into a fractal orbit called a cantorus. The transition describes a pinning of the incommensurate phase of the Frenkel-Kontorowa model. We find that the fractal dimension of the cantorus is D = 0 and that the transition from the Kolmogorov-Arnol'd-Moser trajectory with dimension D = 1 to the cantorus is governed by an exponent ν = 0.98. . . and a universal scaling function. It is argued that the exponent is equal to that of the Lyapunov exponent

Error Concealment using Neural Networks for Block-Based Image Coding

Directory of Open Access Journals (Sweden)

M. Mokos

2006-06-01

Full Text Available In this paper, a novel adaptive error concealment (EC algorithm, which lowers the requirements for channel coding, is proposed. It conceals errors in block-based image coding systems by using neural network. In this proposed algorithm, only the intra-frame information is used for reconstruction of the image with separated damaged blocks. The information of pixels surrounding a damaged block is used to recover the errors using the neural network models. Computer simulation results show that the visual quality and the MSE evaluation of a reconstructed image are significantly improved using the proposed EC algorithm. We propose also a simple non-neural approach for comparison.

Lossless, Near-Lossless, and Refinement Coding of Bi-level Images

DEFF Research Database (Denmark)

Martins, Bo; Forchhammer, Søren Otto

1997-01-01

We present general and unified algorithms for lossy/lossless codingof bi-level images. The compression is realized by applying arithmetic coding to conditional probabilities. As in the current JBIG standard the conditioning may be specified by a template.For better compression, the more general....... Introducing only a small amount of loss in halftoned test images, compression is increased by up to a factor of four compared with JBIG. Lossy, lossless, and refinement decoding speed and lossless encoding speed are less than a factor of two slower than JBIG. The (de)coding method is proposed as part of JBIG......-2, an emerging international standard for lossless/lossy compression of bi-level images....

Bridging Three Orders of Magnitude: Multiple Scattered Waves Sense Fractal Microscopic Structures via Dispersion

Science.gov (United States)

Lambert, Simon A.; Näsholm, Sven Peter; Nordsletten, David; Michler, Christian; Juge, Lauriane; Serfaty, Jean-Michel; Bilston, Lynne; Guzina, Bojan; Holm, Sverre; Sinkus, Ralph

2015-08-01

Wave scattering provides profound insight into the structure of matter. Typically, the ability to sense microstructure is determined by the ratio of scatterer size to probing wavelength. Here, we address the question of whether macroscopic waves can report back the presence and distribution of microscopic scatterers despite several orders of magnitude difference in scale between wavelength and scatterer size. In our analysis, monosized hard scatterers 5 μ m in radius are immersed in lossless gelatin phantoms to investigate the effect of multiple reflections on the propagation of shear waves with millimeter wavelength. Steady-state monochromatic waves are imaged in situ via magnetic resonance imaging, enabling quantification of the phase velocity at a voxel size big enough to contain thousands of individual scatterers, but small enough to resolve the wavelength. We show in theory, experiments, and simulations that the resulting coherent superposition of multiple reflections gives rise to power-law dispersion at the macroscopic scale if the scatterer distribution exhibits apparent fractality over an effective length scale that is comparable to the probing wavelength. Since apparent fractality is naturally present in any random medium, microstructure can thereby leave its fingerprint on the macroscopically quantifiable power-law exponent. Our results are generic to wave phenomena and carry great potential for sensing microstructure that exhibits intrinsic fractality, such as, for instance, vasculature.

Fractal characteristic study of shearer cutter cutting resistance curves

Energy Technology Data Exchange (ETDEWEB)

Liu, C. [Heilongjiang Scientific and Technical Institute, Haerbin (China). Dept of Mechanical Engineering

2004-02-01

The cutting resistance curve is the most useful tool for reflecting the overall cutting performance of a cutting machine. The cutting resistance curve is influenced by many factors such as the pick structure and arrangement, the cutter operation parameters, coal quality and geologic conditions. This paper discusses the use of fractal geometry to study the properties of the cutting resistance curve, and the use of fractal dimensions to evaluate cutting performance. On the basis of fractal theory, the general form and calculation method of fractal characteristics are given. 4 refs., 3 figs., 1 tab.

Solving inverse two-point boundary value problems using collage coding

Science.gov (United States)

Kunze, H.; Murdock, S.

2006-08-01

The method of collage coding, with its roots in fractal imaging, is the central tool in a recently established rigorous framework for solving inverse initial value problems for ordinary differential equations (Kunze and Vrscay 1999 Inverse Problems 15 745-70). We extend these ideas to solve the following inverse problem: given a function u(x) on [A, B] (which may be the interpolation of data points), determine a two-point boundary value problem on [A, B] which admits u(x) as a solution as closely as desired. The solution of such inverse problems may be useful in parameter estimation or determination of potential functional forms of the underlying differential equation. We discuss ways to improve results, including the development of a partitioning scheme. Several examples are considered.

Interactive QR code beautification with full background image embedding

Science.gov (United States)

Lin, Lijian; Wu, Song; Liu, Sijiang; Jiang, Bo

2017-06-01

QR (Quick Response) code is a kind of two dimensional barcode that was first developed in automotive industry. Nowadays, QR code has been widely used in commercial applications like product promotion, mobile payment, product information management, etc. Traditional QR codes in accordance with the international standard are reliable and fast to decode, but are lack of aesthetic appearance to demonstrate visual information to customers. In this work, we present a novel interactive method to generate aesthetic QR code. By given information to be encoded and an image to be decorated as full QR code background, our method accepts interactive user's strokes as hints to remove undesired parts of QR code modules based on the support of QR code error correction mechanism and background color thresholds. Compared to previous approaches, our method follows the intention of the QR code designer, thus can achieve more user pleasant result, while keeping high machine readability.

Constructing and applying the fractal pied de poule (houndstooth)

NARCIS (Netherlands)

Feijs, L.M.G.; Toeters, M.J.; Hart, G.; Sarhangi, R.

2013-01-01

Time is ready for a fractal version of pied de poule; it is almost "in the air". Taking inspiration from the Cantor set, and using the analysis of the classical pattern, we obtain a family of elegant new fractal Pied de Poules. We calculate the fractal dimension and develop an attractive fashion

Multirate diversity strategy of fractal modulation

International Nuclear Information System (INIS)

Yuan Yong; Shi Si-Hong; Luo Mao-Kang

2011-01-01

Previous analyses of fractal modulation were carried out mostly from a signle perspective or a subband, but the analyses from the perspective of multiscale synthesis have not been found yet; while multiscale synthesis is just the essence of the mutlirate diversity which is the most important characteristic of fractal modulation. As for the mutlirate diversity of fractal modulation, previous studies only dealt with the general outspread of its concept, lacked the thorough and intensive quantitative comparison and analysis. In light of the above fact, from the perspective of multiscale synthesis, in this paper we provide a comprehensive analysis of the multirate diversity of fractal modulation and corresponding quantitative analysis. The results show that mutlirate diversity, which is a fusion of frequency diversity and time diversity, pays an acceptable price in spectral efficiency in exchange for a significant improvement in bit error rate. It makes fractal modulation particularly suitable for the channels whose bandwidth and duration parameters are unknown or cannot be predicted to the transmitter. Surely it is clearly of great significance for reliable communications. Moreover, we also attain the ability to flexibly make various rate-bandwidth tradeoffs between the transmitter and the receiver, to freely select the reception time and to expediently control the total bandwidth. Furthermore, the acquisitions or improvements of these fine features could provide support of the technical feasibility for the electromagnetic spectrum control technology in a complex electromagnetic environment. (general)

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.

Implementational Aspects of the Contourlet Filter Bank and Application in Image Coding

Directory of Open Access Journals (Sweden)

Truong T. Nguyen

2009-02-01

Full Text Available This paper analyzed the implementational aspects of the contourlet filter bank (or the pyramidal directional filter bank (PDFB, and considered its application in image coding. First, details of the binary tree-structured directional filter bank (DFB are presented, including a modification to minimize the phase delay factor and necessary steps for handling rectangular images. The PDFB is viewed as an overcomplete filter bank, and the directional filters are expressed in terms of polyphase components of the pyramidal filter bank and the conventional DFB. The aliasing effect of the conventional DFB and the Laplacian pyramid to the directional filters is then considered, and the conditions for reducing this effect are presented. The new filters obtained by redesigning the PDFBs satisfying these requirements have much better frequency responses. A hybrid multiscale filter bank consisting of the PDFB at higher scales and the traditional maximally decimated wavelet filter bank at lower scales is constructed to provide a sparse image representation. A novel embedded image coding system based on the image decomposition and a morphological dilation algorithm is then presented. The coding algorithm efficiently clusters the significant coefficients using progressive morphological operations. Context models for arithmetic coding are designed to exploit the intraband dependency and the correlation existing among the neighboring directional subbands. Experimental results show that the proposed coding algorithm outperforms the current state-of-the-art wavelet-based coders, such as JPEG2000, for images with directional features.

Optical diffraction from fractals with a structural transition

International Nuclear Information System (INIS)

Perez Rodriguez, F.; Canessa, E.

1994-04-01

A macroscopic characterization of fractals showing up a structural transition from dense to multibranched growth is made using optical diffraction theory. Such fractals are generated via the numerical solution of the 2D Poisson and biharmonic equations and are compared to more 'regular' irreversible clusters such as diffusion limited and Laplacian aggregates. The optical diffraction method enables to identify a decrease of the fractal dimension above the structural point. (author). 19 refs, 6 figs

Statistical properties and fractals of nucleotide clusters in DNA sequences

International Nuclear Information System (INIS)

Sun Tingting; Zhang Linxi; Chen Jin; Jiang Zhouting

2004-01-01

Statistical properties of nucleotide clusters in DNA sequences and their fractals are investigated in this paper. The average size of nucleotide clusters in non-coding sequence is larger than that in coding sequence. We investigate the cluster-size distribution P(S) for human chromosomes 21 and 22, and the results are different from previous works. The cluster-size distribution P(S 1 +S 2 ) with the total size of sequential Pu-cluster and Py-cluster S 1 +S 2 is studied. We observe that P(S 1 +S 2 ) follows an exponential decay both in coding and non-coding sequences. However, we get different results for human chromosomes 21 and 22. The probability distribution P(S 1 ,S 2 ) of nucleotide clusters with the size of sequential Pu-cluster and Py-cluster S 1 and S 2 respectively, is also examined. In the meantime, some of the linear correlations are obtained in the double logarithmic plots of the fluctuation F(l) versus nucleotide cluster distance l along the DNA chain. The power spectrums of nucleotide clusters are also discussed, and it is concluded that the curves are flat and hardly changed and the 1/3 frequency is neither observed in coding sequence nor in non-coding sequence. These investigations can provide some insights into the nucleotide clusters of DNA sequences

Fractal analysis of polar bear hairs

Directory of Open Access Journals (Sweden)

Wang Qing-Li