Flux Tensor Constrained Geodesic Active Contours with Sensor Fusion for Persistent Object Tracking
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Filiz Bunyak
2007-08-01
Full Text Available This paper makes new contributions in motion detection, object segmentation and trajectory estimation to create a successful object tracking system. A new efficient motion detection algorithm referred to as the flux tensor is used to detect moving objects in infrared video without requiring background modeling or contour extraction. The flux tensor-based motion detector when applied to infrared video is more accurate than thresholding ”hot-spots”, and is insensitive to shadows as well as illumination changes in the visible channel. In real world monitoring tasks fusing scene information from multiple sensors and sources is a useful core mechanism to deal with complex scenes, lighting conditions and environmental variables. The object segmentation algorithm uses level set-based geodesic active contour evolution that incorporates the fusion of visible color and infrared edge informations in a novel manner. Touching or overlapping objects are further refined during the segmentation process using an appropriate shapebased model. Multiple object tracking using correspondence graphs is extended to handle groups of objects and occlusion events by Kalman filter-based cluster trajectory analysis and watershed segmentation. The proposed object tracking algorithm was successfully tested on several difficult outdoor multispectral videos from stationary sensors and is not confounded by shadows or illumination variations.
Jurcak, V; Fripp, J; Engstrom, C; Walker, D; Salvado, O; Ourselin, S; Crozier, S
2008-01-01
This study presents a novel method for the automatic segmentation of the quadratus lumborum (QL) muscle from axial magnetic resonance (MR) images using a hybrid scheme incorporating the use of non-rigid registration with probabilistic atlases (PAs) and geodesic active contours (GACs). The scheme was evaluated on an MR database of 7mm axial images of the lumbar spine from 20 subjects (fast bowlers and athletic controls). This scheme involved several steps, including (i) image pre-processing, (ii) generation of PAs for the QL, psoas (PS) and erector spinae+multifidus (ES+MT) muscles and (iii) segmentation, using 3D GACs initialized and constrained by the propagation of the PAs using non-rigid registration. Pre-processing of the images involved bias field correction based on local entropy minimization with a bicubic spline model and a reverse diffusion interpolation algorithm to increase the slice resolution to 0.98 x 0.98 x 1.75mm. The processed images were then registered (affine and non-rigid) and used to generate an average atlas. The PAs for the QL, PS and ES+MT were then generated by propagation of manual segmentations. These atlases were further analysed with specialised filtering to constrain the QL segmentation from adjacent non-muscle tissues (kidney, fat). This information was then used in 3D GACs to obtain the final segmentation of the QL. The automatic segmentation results were compared with the manual segmentations using the Dice similarity metric (DSC), with a median DSC for the right and left QL muscles of 0.78 (mean = 0.77, sd=0.07) and 0.75 (mean =0.74, sd=0.07), respectively.
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Fritscher, Karl D., E-mail: Karl.Fritscher@umit.at; Sharp, Gregory [Department for Radiation Oncology, Massachusetts General Hospital, Boston, Massachusetts 02114 (United States); Peroni, Marta [Paul Scherrer Institut, Villigen 5232 (Switzerland); Zaffino, Paolo; Spadea, Maria Francesca [Department of Experimental and Clinical Medicine, Magna Graecia University, Catanzaro 88100 (Italy); Schubert, Rainer [Institute for Biomedical Image Analysis, Private University of Health Sciences, Medical Informatics and Technology, Hall in Tirol 6060 (Austria)
2014-05-15
Purpose: Accurate delineation of organs at risk (OARs) is a precondition for intensity modulated radiation therapy. However, manual delineation of OARs is time consuming and prone to high interobserver variability. Because of image artifacts and low image contrast between different structures, however, the number of available approaches for autosegmentation of structures in the head-neck area is still rather low. In this project, a new approach for automated segmentation of head-neck CT images that combine the robustness of multiatlas-based segmentation with the flexibility of geodesic active contours and the prior knowledge provided by statistical appearance models is presented. Methods: The presented approach is using an atlas-based segmentation approach in combination with label fusion in order to initialize a segmentation pipeline that is based on using statistical appearance models and geodesic active contours. An anatomically correct approximation of the segmentation result provided by atlas-based segmentation acts as a starting point for an iterative refinement of this approximation. The final segmentation result is based on using model to image registration and geodesic active contours, which are mutually influencing each other. Results: 18 CT images in combination with manually segmented labels of parotid glands and brainstem were used in a leave-one-out cross validation scheme in order to evaluate the presented approach. For this purpose, 50 different statistical appearance models have been created and used for segmentation. Dice coefficient (DC), mean absolute distance and max. Hausdorff distance between the autosegmentation results and expert segmentations were calculated. An average Dice coefficient of DC = 0.81 (right parotid gland), DC = 0.84 (left parotid gland), and DC = 0.86 (brainstem) could be achieved. Conclusions: The presented framework provides accurate segmentation results for three important structures in the head neck area. Compared to a
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Suzuki, Kenji; Kohlbrenner, Ryan; Epstein, Mark L.; Obajuluwa, Ademola M.; Xu Jianwu; Hori, Masatoshi [Department of Radiology, University of Chicago, 5841 South Maryland Avenue, Chicago, Illinois 60637 (United States)
2010-05-15
Purpose: Computerized liver extraction from hepatic CT images is challenging because the liver often abuts other organs of a similar density. The purpose of this study was to develop a computer-aided measurement of liver volumes in hepatic CT. Methods: The authors developed a computerized liver extraction scheme based on geodesic active contour segmentation coupled with level-set contour evolution. First, an anisotropic diffusion filter was applied to portal-venous-phase CT images for noise reduction while preserving the liver structure, followed by a scale-specific gradient magnitude filter to enhance the liver boundaries. Then, a nonlinear grayscale converter enhanced the contrast of the liver parenchyma. By using the liver-parenchyma-enhanced image as a speed function, a fast-marching level-set algorithm generated an initial contour that roughly estimated the liver shape. A geodesic active contour segmentation algorithm coupled with level-set contour evolution refined the initial contour to define the liver boundaries more precisely. The liver volume was then calculated using these refined boundaries. Hepatic CT scans of 15 prospective liver donors were obtained under a liver transplant protocol with a multidetector CT system. The liver volumes extracted by the computerized scheme were compared to those traced manually by a radiologist, used as ''gold standard.''Results: The mean liver volume obtained with our scheme was 1504 cc, whereas the mean gold standard manual volume was 1457 cc, resulting in a mean absolute difference of 105 cc (7.2%). The computer-estimated liver volumetrics agreed excellently with the gold-standard manual volumetrics (intraclass correlation coefficient was 0.95) with no statistically significant difference (F=0.77; p(F{<=}f)=0.32). The average accuracy, sensitivity, specificity, and percent volume error were 98.4%, 91.1%, 99.1%, and 7.2%, respectively. Computerized CT liver volumetry would require substantially less
Active Contour with A Tangential Component
Wang, Junyan
2012-01-01
Conventional edge-based active contours often require the normal component of an edge indicator function on the optimal contours to approximate zero, while the tangential component can still be significant. In real images, the full gradients of the edge indicator function along the object boundaries are often small. Hence, the curve evolution of edge-based active contours can terminate early before converging to the object boundaries with a careless contour initialization. We propose a novel Geodesic Snakes (GeoSnakes) active contour that requires the full gradients of the edge indicator to vanish at the optimal solution. Besides, the conventional curve evolution approach for minimizing active contour energy cannot fully solve the Euler-Lagrange (EL) equation of our GeoSnakes active contour, causing a Pseudo Stationary Phenomenon (PSP). To address the PSP problem, we propose an auxiliary curve evolution equation, named the equilibrium flow (EF) equation. Based on the EF and the conventional curve evolution, w...
Dynamic Active Contours for Visual Tracking.
Niethammer, Marc; Tannenbaum, Allen; Angenent, Sigurd
2006-01-01
Visual tracking using active contours is usually set in a static framework. The active contour tracks the object of interest in a given frame of an image sequence. A subsequent prediction step ensures good initial placement for the next frame. This approach is unnatural; the curve evolution gets decoupled from the actual dynamics of the objects to be tracked. True dynamical approaches exist, all being marker particle based and thus prone to the shortcomings of such particle-based implementations. In particular, topological changes are not handled naturally in this framework. The now classical level set approach is tailored for evolutions of manifolds of codimension one. However, dynamic curve evolution is at least a codimension two problem. We propose an efficient, level set based approach for dynamic curve evolution, which addresses the artificial separation of segmentation and prediction while retaining all the desirable properties of the level set formulation. It is based on a new energy minimization functional which, for the first time, puts dynamics into the geodesic active contour framework.
Geodesic active fields--a geometric framework for image registration.
Zosso, Dominique; Bresson, Xavier; Thiran, Jean-Philippe
2011-05-01
In this paper we present a novel geometric framework called geodesic active fields for general image registration. In image registration, one looks for the underlying deformation field that best maps one image onto another. This is a classic ill-posed inverse problem, which is usually solved by adding a regularization term. Here, we propose a multiplicative coupling between the registration term and the regularization term, which turns out to be equivalent to embed the deformation field in a weighted minimal surface problem. Then, the deformation field is driven by a minimization flow toward a harmonic map corresponding to the solution of the registration problem. This proposed approach for registration shares close similarities with the well-known geodesic active contours model in image segmentation, where the segmentation term (the edge detector function) is coupled with the regularization term (the length functional) via multiplication as well. As a matter of fact, our proposed geometric model is actually the exact mathematical generalization to vector fields of the weighted length problem for curves and surfaces introduced by Caselles-Kimmel-Sapiro. The energy of the deformation field is measured with the Polyakov energy weighted by a suitable image distance, borrowed from standard registration models. We investigate three different weighting functions, the squared error and the approximated absolute error for monomodal images, and the local joint entropy for multimodal images. As compared to specialized state-of-the-art methods tailored for specific applications, our geometric framework involves important contributions. Firstly, our general formulation for registration works on any parametrizable, smooth and differentiable surface, including nonflat and multiscale images. In the latter case, multiscale images are registered at all scales simultaneously, and the relations between space and scale are intrinsically being accounted for. Second, this method is, to
Towards Stabilizing Parametric Active Contours
DEFF Research Database (Denmark)
Liu, Jinchao; Fan, Zhun; Olsen, Søren Ingvor;
2014-01-01
Numerical instability often occurs in evolving of parametric active contours. This is mainly due to the undesired change of parametrization during evolution. In this paper, we propose a new tangential diffusion term to compensate this undesired change. As a result, the parametrization will converge...
A multiresolution framework for ultrasound image segmentation by combinative active contours.
Wang, Weiming; Qin, Jing; Chui, Yim-Pan; Heng, Pheng-Ann
2013-01-01
We propose a novel multiresolution framework for ultrasound image segmentation in this paper. The framework exploits both local intensity and local phase information to tackle the degradations of ultrasound images. First, multiresolution scheme is adopted to build a Gaussian pyramid for each speckled image. Speckle noise is gradually smoothed out at higher levels of the pyramid. Then local intensity-driven active contours are employed to locate the coarse contour of the target from the coarsest image, followed by local phase-based geodesic active contours to further refine the contour in finer images. Compared with traditional gradient-based methods, phase-based methods are more suitable for ultrasound images because they are invariant to variations in image contrast. Experimental results on left ventricle segmentation from echocardiographic images demonstrate the advantages of the proposed model.
From Inpainting to Active Contours
DEFF Research Database (Denmark)
Lauze, Francois Bernard; Nielsen, Mads
2008-01-01
image and a guess on the location of the object to be segmented via variational inpainting method. A numerical evaluation of this reconstruction provides a "disocclusion measure" and the correct foreground segmentation region is expected to maximize this measure. This formulation is in fact an optimal...... control problem, where controls are shapes/regions and states are the corresponding inpaintings. Optimization of the disocclusion measure leads formally to a coupled contour evolution equation, an inpainting equation (the state equation) as well as a linear PDE depending on the inpainting (the adjoint...... state equation). The contour evolution is implemented in the framework of level sets. Finally, the proposed method is validated on various examples. We focus among others in the segmentation of calcified plaques observed in radiographs from human lumbar aortic regions. Keywords Segmentation - Inpainting...
An Active Contour for Range Image Segmentation
Khaldi Amine; Merouani Hayet Farida
2012-01-01
In this paper a new classification of range image segmentation method is proposed according to the criterion of homogeneity which obeys the segmentation, then, a deformable model-type active contour “Snake” is applied to segment range images.
Decoupled active contour (DAC) for boundary detection.
Mishra, Akshaya Kumar; Fieguth, Paul W; Clausi, David A
2011-02-01
The accurate detection of object boundaries via active contours is an ongoing research topic in computer vision. Most active contours converge toward some desired contour by minimizing a sum of internal (prior) and external (image measurement) energy terms. Such an approach is elegant, but suffers from a slow convergence rate and frequently misconverges in the presence of noise or complex contours. To address these limitations, a decoupled active contour (DAC) is developed which applies the two energy terms separately. Essentially, the DAC consists of a measurement update step, employing a Hidden Markov Model (HMM) and Viterbi search, and then a separate prior step, which modifies the updated curve based on the relative strengths of the measurement uncertainty and the nonstationary prior. By separating the measurement and prior steps, the algorithm is less likely to misconverge; furthermore, the use of a Viterbi optimizer allows the method to converge far more rapidly than energy-based iterative solvers. The results clearly demonstrate that the proposed approach is robust to noise, can capture regions of very high curvature, and exhibits limited dependence on contour initialization or parameter settings. Compared to five other published methods and across many image sets, the DAC is found to be faster with better or comparable segmentation accuracy.
An Active Contour for Range Image Segmentation
Directory of Open Access Journals (Sweden)
Khaldi Amine
2012-06-01
Full Text Available In this paper a new classification of range image segmentation method is proposed according to the criterion of homogeneity which obeys the segmentation, then, a deformable model-type active contour “Snake” is applied to segment range images.
Automatic Detection of Adenocarcinoma using Active Contours
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NeelapalaAnilKumar
2013-09-01
Full Text Available CT scan is the one of the image representation for abdomen, where the tumour to be located and specified effectively with clarity, by the medical expert. This role can be hold by using one of the image processing techniques called segmentation. Image segmentation is the technique which isolates the image into different regions to simplify the image and identify the Tumour easily. Image segmentation has been extensively studied by various approaches. This work, focus on the one of the image segmentation technique with a new regularization term that yields an unsupervised segmentation model which identifies different Tumour locations in a given CT image. Active contours form a boundary around a particular part of the image based on an energy function. The energy function may include intensity values of pixels or gradient values. Chen-Vase method of active contour algorithm is adopted for image segmentation. The segmentation is done after properly masking of CT scan image. The cancer prone area is generalized prior to the masking of the image. Effected abdomen cancer can be identified for better analysis of medical experts using image processing MATLAB tools. This paper describes a new method to detect and extract the features in CT scan images, which shows good performance in detection of difficult features. And the developed technique makes use of major image processing methods and fundamentals to detect the cancer with minimum possible human interaction.
Pottmann, Helmut
2010-07-26
Geodesic curves in surfaces are not only minimizers of distance, but they are also the curves of zero geodesic (sideways) curvature. It turns out that this property makes patterns of geodesics the basic geometric entity when dealing with the cladding of a freeform surface with wooden panels which do not bend sideways. Likewise a geodesic is the favored shape of timber support elements in freeform architecture, for reasons of manufacturing and statics. Both problem areas are fundamental in freeform architecture, but so far only experimental solutions have been available. This paper provides a systematic treatment and shows how to design geodesic patterns in different ways: The evolution of geodesic curves is good for local studies and simple patterns; the level set formulation can deal with the global layout of multiple patterns of geodesics; finally geodesic vector fields allow us to interactively model geodesic patterns and perform surface segmentation into panelizable parts. © 2010 ACM.
Ali, Sahirzeeshan; Madabhushi, Anant
2011-03-01
Active contours and active shape models (ASM) have been widely employed in image segmentation. A major limitation of active contours, however, is in their (a) inability to resolve boundaries of intersecting objects and to (b) handle occlusion. Multiple overlapping objects are typically segmented out as a single object. On the other hand, ASMs are limited by point correspondence issues since object landmarks need to be identified across multiple objects for initial object alignment. ASMs are also are constrained in that they can usually only segment a single object in an image. In this paper, we present a novel synergistic boundary and region-based active contour model that incorporates shape priors in a level set formulation. We demonstrate an application of these synergistic active contour models using multiple level sets to segment nuclear and glandular structures on digitized histopathology images of breast and prostate biopsy specimens. Unlike previous related approaches, our model is able to resolve object overlap and separate occluded boundaries of multiple objects simultaneously. The energy functional of the active contour is comprised of three terms. The first term comprises the prior shape term, modeled on the object of interest, thereby constraining the deformation achievable by the active contour. The second term, a boundary based term detects object boundaries from image gradients. The third term drives the shape prior and the contour towards the object boundary based on region statistics. The results of qualitative and quantitative evaluation on 100 prostate and 14 breast cancer histology images for the task of detecting and segmenting nuclei, lymphocytes, and glands reveals that the model easily outperforms two state of the art segmentation schemes (Geodesic Active Contour (GAC) and Roussons shape based model) and resolves up to 92% of overlapping/occluded lymphocytes and nuclei on prostate and breast cancer histology images.
Incorporating Prior Shape into Geometric Active Contours for Face Contour Detection
Institute of Scientific and Technical Information of China (English)
HUANGFuzhen; SUJianbo; XIYugeng
2004-01-01
In this paper a new method that incorporates prior shape information into geometric active contours for face contour detection is proposed. As in general a human face can be treated as an ellipse with a little shape variation, the prior face shape is represented as an elliptical curve. By combining the prior face shape with the powerful geometric active model proposed by Chan and Vese, the improved geometric active model can retain all the advantage of the Chan-Vese model and can detect face contours in images with complex backgrounds accurately even if the image is noisy. Moreover, by implementing the new model in a variational level set framework, automatic topological changes of the model can be achieved naturally and the transformation parameters that map the face boundary to the prior shape can be roughly estimated simultaneously. The experimental results show our procedure to be eiTicient.
Institute of Scientific and Technical Information of China (English)
DONG Hai-yan; WANG Hui-nan
2006-01-01
Intravascular ultrasound can provide high-resolution real-time crosssectional images about lumen, plaque and tissue. Traditionally, the luminal border and medial-adventitial border are traced manually. This process is extremely timeconsuming and the subjective difference would be large. In this paper, a new automated contour detection method is introduced based on fast active contour model.Experimental results found that lumen and vessel area measurements after automated detection showed good agreement with manual tracings with high correlation coefficients (0.94 and 0.95, respectively) and small system difference ( -0.32 and 0.56, respectively). So it can be a reliable and accurate diagnostic tool.
An active contour method for bone cement reconstruction from C-arm x-ray images.
Lucas, Blake C; Otake, Yoshito; Armand, Mehran; Taylor, Russell H
2012-04-01
A novel algorithm is presented to segment and reconstruct injected bone cement from a sparse set of X-ray images acquired at arbitrary poses. The sparse X-ray multi-view active contour (SxMAC-pronounced "smack") can 1) reconstruct objects for which the background partially occludes the object in X-ray images, 2) use X-ray images acquired on a noncircular trajectory, and 3) incorporate prior computed tomography (CT) information. The algorithm's inputs are preprocessed X-ray images, their associated pose information, and prior CT, if available. The algorithm initiates automated reconstruction using visual hull computation from a sparse number of X-ray images. It then improves the accuracy of the reconstruction by optimizing a geodesic active contour. Experiments with mathematical phantoms demonstrate improvements over a conventional silhouette based approach, and a cadaver experiment demonstrates SxMAC's ability to reconstruct high contrast bone cement that has been injected into a femur and achieve sub-millimeter accuracy with four images.
Directory of Open Access Journals (Sweden)
YU Jintao
2016-09-01
Full Text Available After the characteristics of geodesic active contour model (GAC, Chan-Vese model(CV and local binary fitting model(LBF are analyzed, and the active contour model based on regions and edges is combined with image segmentation method based on quad-tree, a waterline extraction method based on quad-tree and multiple active contour model is proposed in this paper. Firstly, the method provides an initial contour according to quad-tree segmentation. Secondly, a new signed pressure force(SPF function based on global image statistics information of CV model and local image statistics information of LBF model has been defined, and then ,the edge stopping function(ESF is replaced by the proposed SPF function, which solves the problem such as evolution stopped in advance and excessive evolution. Finally, the selective binary and Gaussian filtering level set method is used to avoid reinitializing and regularization to improve the evolution efficiency. The experimental results show that this method can effectively extract the weak edges and serious concave edges, and owns some properties such as sub-pixel accuracy, high efficiency and reliability for waterline extraction.
Medical Image Segmentation through Bat-Active Contour Algorithm
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Rabiu O. Isah
2017-01-01
Full Text Available In this research work, an improved active contour method called Bat-Active Contour Method (BAACM using bat algorithm has been developed. The bat algorithm is incorporated in order to escape local minima entrapped into by the classical active contour method, stabilize contour (snake movement and accurately, reach boundary concavity. Then, the developed Bat-Active Contour Method was applied to a dataset of medical images of the human heart, bone of knee and vertebra which were obtained from Auckland MRI Research Group (Cardiac Atlas Website, University of Auckland. Set of similarity metrics, including Jaccard index and Dice similarity measures were adopted to evaluate the performance of the developed algorithm. Jaccard index values of 0.9310, 0.9234 and 0.8947 and Dice similarity values of 0.8341, 0.8616 and 0.9138 were obtained from the human heart, vertebra and bone of knee images respectively. The results obtained show high similarity measures between BA-ACM algorithm and expert segmented images. Moreso, traditional ACM produced Jaccard index values 0.5873, 0.5601, 0.6009 and Dice similarity values of 0.5974, 0.6079, 0.6102 in the human heart, vertebra and bone of knee images respectively. The results obtained for traditional ACM show low similarity measures between it and expertly segmented images. It is evident from the results obtained that the developed algorithm performed better compared to the traditional ACM
Active contour model based on force field analysis
Institute of Scientific and Technical Information of China (English)
HOU Zhi-qiang; HAN Chong-zhao
2006-01-01
The traditional snake initial contour should be close to the true boundary of an object of interest in an image;otherwise,an incorrect result will be obtained.Next,active contours have difficulties progressing into boundary concavities.Moreover,the traditional snake as well as almost all of its improved methods can be easily obtained from the local minimum because snake models are nonconvex.An active contour model based on force field analysis (FFA),namely,FFA snake model,is presented in this paper.Based on analyzing force distribution rules of the distance potential force field,a standard is introduced here to distinguish the false one from contour points.The result is not considered as the final solution when the snake energy is minimal.Furthermore,estimation and calculation should be made according to the established standard;only then can the result be considered final.Thus,the snake is prevented from running into the local minimum.The simulation results show that the FFA snake model has a large capture range and can move a snake into the boundary concavities,and that it is able to obtain the object of interest's contour precisely.Compared with the gradient vector flow snake,this new model has a low computational cost.
Automatic segmentation of leg bones by using active contours.
Kim, Sunhee; Kim, Youngjun; Park, Sehyung; Lee, Deukhee
2014-01-01
In this paper, we present a new active contours model to segment human leg bones in computed tomography images that is based on a variable-weighted combination of local and global intensity. This model can split an object surrounded by both weak and strong boundaries, and also distinguish very adjacent objects with those boundaries. The ability of this model is required for segmentation in medical images, e.g., human leg bones, which are usually composed of highly inhomogeneous objects and where the distances among organs are very close. We developed an evolution equation of a level set function whose zero level set represents a contour. An initial contour is automatically obtained by applying a histogram based multiphase segmentation method. We experimented with computed tomography images from three patients, and demonstrate the efficiency of the proposed method in experimental results.
Active contours for localizing polyps in colonoscopic NBI image data
Breier, Matthias; Gross, Sebastian; Behrens, Alexander; Stehle, Thomas; Aach, Til
2011-03-01
Colon cancer is the third most common type of cancer in the United States of America. Every year about 140,000 people are newly diagnosed with colon cancer. Early detection is crucial for a successful therapy. The standard screening procedure is called colonoscopy. Using this endoscopic examination physicians can find colon polyps and remove them if necessary. Adenomatous colon polyps are deemed a preliminary stage of colon cancer. The removal of a polyp, though, can lead to complications like severe bleedings or colon perforation. Thus, only polyps diagnosed as adenomatous should be removed. To decide whether a polyp is adenomatous the polyp's surface structure including vascular patterns has to be inspected. Narrow-Band imaging (NBI) is a new tool to improve visibility of vascular patterns of the polyps. The first step for an automatic polyp classification system is the localization of the polyp. We investigate active contours for the localization of colon polyps in NBI image data. The shape of polyps, though roughly approximated by an elliptic form, is highly variable. Active contours offer the flexibility to adapt to polyp variation well. To avoid clustering of contour polygon points we propose the application of active rays. The quality of the results was evaluated based on manually segmented polyps as ground truth data. The results were compared to a template matching approach and to the Generalized Hough Transform. Active contours are superior to the Hough transform and perform equally well as the template matching approach.
Automatic Image Segmentation Using Active Contours with Univariate Marginal Distribution
Directory of Open Access Journals (Sweden)
I. Cruz-Aceves
2013-01-01
Full Text Available This paper presents a novel automatic image segmentation method based on the theory of active contour models and estimation of distribution algorithms. The proposed method uses the univariate marginal distribution model to infer statistical dependencies between the control points on different active contours. These contours have been generated through an alignment process of reference shape priors, in order to increase the exploration and exploitation capabilities regarding different interactive segmentation techniques. This proposed method is applied in the segmentation of the hollow core in microscopic images of photonic crystal fibers and it is also used to segment the human heart and ventricular areas from datasets of computed tomography and magnetic resonance images, respectively. Moreover, to evaluate the performance of the medical image segmentations compared to regions outlined by experts, a set of similarity measures has been adopted. The experimental results suggest that the proposed image segmentation method outperforms the traditional active contour model and the interactive Tseng method in terms of segmentation accuracy and stability.
Segmentation of Coronal Holes Using Active Contours Without Edges
Boucheron, L E; McAteer, R T J
2016-01-01
An application of active contours without edges is presented as an efficient and effective means of extracting and characterizing coronal holes. Coronal holes are regions of low-density plasma on the Sun with open magnetic field lines. As the source of the fast solar wind, the detection and characterization of these regions is important for both testing theories of their formation and evolution and from a space weather perspective. Coronal holes are detected in full disk extreme ultraviolet (EUV) images of the corona obtained with the Solar Dynamics Observatory Atmospheric Imaging Assembly (SDO/AIA). The proposed method detects coronal boundaries without determining any fixed intensity value in the data. Instead, the active contour segmentation employs an energy-minimization in which coronal holes are assumed to have more homogeneous intensities than surrounding active regions and quiet Sun. The segmented coronal holes tend to correspond to unipolar magnetic regions, are consistent with concurrent solar wind ...
Fast Graph Partitioning Active Contours for Image Segmentation Using Histograms
Directory of Open Access Journals (Sweden)
Nath SumitK
2009-01-01
Full Text Available Abstract We present a method to improve the accuracy and speed, as well as significantly reduce the memory requirements, for the recently proposed Graph Partitioning Active Contours (GPACs algorithm for image segmentation in the work of Sumengen and Manjunath (2006. Instead of computing an approximate but still expensive dissimilarity matrix of quadratic size, , for a 2D image of size and regular image tiles of size , we use fixed length histograms and an intensity-based symmetric-centrosymmetric extensor matrix to jointly compute terms associated with the complete dissimilarity matrix. This computationally efficient reformulation of GPAC using a very small memory footprint offers two distinct advantages over the original implementation. It speeds up convergence of the evolving active contour and seamlessly extends performance of GPAC to multidimensional images.
Region-based active contour with noise and shape priors
Lecellier, François; Fadili, Jalal; Aubert, Gilles; Revenu, Marinette; Saloux, Eric
2008-01-01
In this paper, we propose to combine formally noise and shape priors in region-based active contours. On the one hand, we use the general framework of exponential family as a prior model for noise. On the other hand, translation and scale invariant Legendre moments are considered to incorporate the shape prior (e.g. fidelity to a reference shape). The combination of the two prior terms in the active contour functional yields the final evolution equation whose evolution speed is rigorously derived using shape derivative tools. Experimental results on both synthetic images and real life cardiac echography data clearly demonstrate the robustness to initialization and noise, flexibility and large potential applicability of our segmentation algorithm.
Hongchuan Yu; Zhang, Jian J.; Zheng Jiao
2014-01-01
We present a novel framework to compute geodesics on implicit surfaces and point clouds. Our framework consists of three parts, particle based approximate geodesics on implicit surfaces, Cartesian grid based approximate geodesics on point clouds, and geodesic correction. The first two parts can effectively generate approximate geodesics on implicit surfaces and point clouds, respectively. By introducing the geodesic curvature flow, the third part produces smooth and accurate geodesic solution...
On radial geodesic forcing of zonal modes
Kendl, Alexander
2011-01-01
The elementary local and global influence of geodesic field line curvature on radial dispersion of zonal modes in magnetised plasmas is analysed with a primitive drift wave turbulence model. A net radial geodesic forcing of zonal flows and geodesic acoustic modes can not be expected in any closed toroidal magnetic confinement configuration, since the flux surface average of geodesic curvature identically vanishes. Radial motion of poloidally elongated zonal jets may occur in the presence of geodesic acoustic mode activity. Phenomenologically a radial propagation of zonal modes shows some characteristics of a classical analogon to second sound in quantum condensates.
Segmentation of Coronal Holes Using Active Contours Without Edges
Boucheron, L. E.; Valluri, M.; McAteer, R. T. J.
2016-10-01
An application of active contours without edges is presented as an efficient and effective means of extracting and characterizing coronal holes. Coronal holes are regions of low-density plasma on the Sun with open magnetic field lines. The detection and characterization of these regions is important for testing theories of their formation and evolution, and also from a space weather perspective because they are the source of the fast solar wind. Coronal holes are detected in full-disk extreme ultraviolet (EUV) images of the corona obtained with the Solar Dynamics Observatory Atmospheric Imaging Assembly (SDO/AIA). The proposed method detects coronal boundaries without determining any fixed intensity value in the data. Instead, the active contour segmentation employs an energy-minimization in which coronal holes are assumed to have more homogeneous intensities than the surrounding active regions and quiet Sun. The segmented coronal holes tend to correspond to unipolar magnetic regions, are consistent with concurrent solar wind observations, and qualitatively match the coronal holes segmented by other methods. The means to identify a coronal hole without specifying a final intensity threshold may allow this algorithm to be more robust across multiple datasets, regardless of data type, resolution, and quality.
Segmentation of Coronal Holes Using Active Contours Without Edges
Boucheron, L. E.; Valluri, M.; McAteer, R. T. J.
2016-09-01
An application of active contours without edges is presented as an efficient and effective means of extracting and characterizing coronal holes. Coronal holes are regions of low-density plasma on the Sun with open magnetic field lines. The detection and characterization of these regions is important for testing theories of their formation and evolution, and also from a space weather perspective because they are the source of the fast solar wind. Coronal holes are detected in full-disk extreme ultraviolet (EUV) images of the corona obtained with the Solar Dynamics Observatory Atmospheric Imaging Assembly (SDO/AIA). The proposed method detects coronal boundaries without determining any fixed intensity value in the data. Instead, the active contour segmentation employs an energy-minimization in which coronal holes are assumed to have more homogeneous intensities than the surrounding active regions and quiet Sun. The segmented coronal holes tend to correspond to unipolar magnetic regions, are consistent with concurrent solar wind observations, and qualitatively match the coronal holes segmented by other methods. The means to identify a coronal hole without specifying a final intensity threshold may allow this algorithm to be more robust across multiple datasets, regardless of data type, resolution, and quality.
Pupil segmentation using active contour with shape prior
Ukpai, Charles O.; Dlay, Satnam S.; Woo, Wai L.
2015-03-01
Iris segmentation is the process of defining the valid part of the eye image used for further processing (feature extraction, matching and decision making). Segmentation of the iris mostly starts with pupil boundary segmentation. Most pupil segmentation techniques are based on the assumption that the pupil is circular shape. In this paper, we propose a new pupil segmentation technique which combines shape, location and spatial information for accurate and efficient segmentation of the pupil. Initially, the pupil's position and radius is estimated using a statistical approach and circular Hough transform. In order to segment the irregular boundary of the pupil, an active contour model is initialized close to the estimated boundary using information from the first step and segmentation is achieved using energy minimization based active contour. Pre-processing and post-processing were carried out to remove noise and occlusions respectively. Experimental results on CASIA V1.0 and 4.0 shows that the proposed method is highly effective at segmenting irregular boundaries of the pupil.
Fast Virtual Stenting with Active Contour Models in Intracranical Aneurysm.
Zhong, Jingru; Long, Yunling; Yan, Huagang; Meng, Qianqian; Zhao, Jing; Zhang, Ying; Yang, Xinjian; Li, Haiyun
2016-02-15
Intracranial stents are becoming increasingly a useful option in the treatment of intracranial aneurysms (IAs). Image simulation of the releasing stent configuration together with computational fluid dynamics (CFD) simulation prior to intervention will help surgeons optimize intervention scheme. This paper proposed a fast virtual stenting of IAs based on active contour model (ACM) which was able to virtually release stents within any patient-specific shaped vessel and aneurysm models built on real medical image data. In this method, an initial stent mesh was generated along the centerline of the parent artery without the need for registration between the stent contour and the vessel. Additionally, the diameter of the initial stent volumetric mesh was set to the maximum inscribed sphere diameter of the parent artery to improve the stenting accuracy and save computational cost. At last, a novel criterion for terminating virtual stent expanding that was based on the collision detection of the axis aligned bounding boxes was applied, making the stent expansion free of edge effect. The experiment results of the virtual stenting and the corresponding CFD simulations exhibited the efficacy and accuracy of the ACM based method, which are valuable to intervention scheme selection and therapy plan confirmation.
Statistical region-based active contours with exponential family observations
Lecellier, François; Fadili, Jalal; Aubert, Gilles; Revenu, Marinette
2008-01-01
In this paper, we focus on statistical region-based active contour models where image features (e.g. intensity) are random variables whose distribution belongs to some parametric family (e.g. exponential) rather than confining ourselves to the special Gaussian case. Using shape derivation tools, our effort focuses on constructing a general expression for the derivative of the energy (with respect to a domain) and derive the corresponding evolution speed. A general result is stated within the framework of multi-parameter exponential family. More particularly, when using Maximum Likelihood estimators, the evolution speed has a closed-form expression that depends simply on the probability density function, while complicating additive terms appear when using other estimators, e.g. moments method. Experimental results on both synthesized and real images demonstrate the applicability of our approach.
Hough Transform and Active Contour for Enhanced Iris Segmentation
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Alaa Hilal
2012-11-01
Full Text Available Iris segmentation is considered as the most difficult and fundamental step in an iris recognition system. While iris boundaries are largely approximated by two circles or ellipses, other methods define more accurately the iris resulting in better recognition results. In this paper we propose an iris segmentation method using Hough transform and active contour to detect a circular approximation of the outer iris boundary and to accurately segment the inner boundary in its real shape motivated by the fact that richer iris textures are closer to the pupil than to the sclera. Normalization, encoding and matching are implemented according to Daugmans method. The method, tested on CASIA-V3 iris images database is compared to Daugmans iris recognition system. Recognition performance is measured in terms of decidability, accuracy at the equal error rate and ROC curves. Improved recognition performance is obtained using our segmentation model proposing its use for better iris recognition system.
RBF neural network and active circles based algorithm for contours extraction
Institute of Scientific and Technical Information of China (English)
Zhou Zhiheng; Zeng Delu; Xie Shengli
2007-01-01
For the contours extraction from the images, active contour model and self-organizing map based approach are popular nowadays. But they are still confronted with the problems that the optimization of energy function will trap in local minimums and the contour evolutions greatly depend on the initial contour selection. Addressing to these problems, a contours extraction algorithm based on RBF neural network is proposed here. A series of circles with adaptive radius and center is firstly used to search image feature points that are scattered enough. After the feature points are clustered, a group of radial basis functions are constructed. Using the pixels' intensities and gradients as the input vector, the final object contour can be obtained by the predicting ability of the neural network. The RBF neural network based algorithm is tested on three kinds of images, such as changing topology, complicated background, and blurring or noisy boundary. Simulation results show that the proposed algorithm performs contours extraction greatly.
COMPARISON OF THREE DIFFERENT IMAGE FORCES FOR ACTIVE CONTOURS ON ABDOMINAL IMAGE BOUNDARY DETECTION
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Cherry Galatia Ballangan
2005-01-01
Full Text Available Active contour, or snake, is an energy minimizing spline that is useful in image boundary detection. Active contours are stimulated by internal forces, image forces and external forces which maintain the shape of the contours while attract the contours to some desired features, usually edges. Problems in implementing active contours such as convergence and initialization have motivated researchers to modify image forces of the active contours. This paper presents a comparative study among three different image forces: traditional snakes, balloon and gradient vector flow (GVF. The study is validated by experiments on abdominal image boundaries detection. These lead to the conclusion that GVF gives the most appropriate results among the other approaches.
Poudel, P.; Illanes, A.; Arens, C.; Hansen, C.; Friebe, M.
2017-03-01
Thyroid segmentation in tracked 2D ultrasound (US) using active contours has a low segmentation accuracy mainly due to the fact that smaller structures cannot be efficiently recognized and segmented. To address this issue, we propose a new similarity indicator with the main objective to provide information to the active contour algorithm concerning the regions that the active contour should continue to expand or should stop. First, a preprocessing step is carried out in order to attenuate the noise present in the US image and to increase its contrast, using histogram equalization and a median filter. In the second step, active contours are used to segment the thyroid in each 2D image of the dataset. After performing a first segmentation, two similarity indicators (ratio of mean square error, MSE and correlation between histograms) are computed at each contour point of the initial segmented thyroid between rectangles located inside and outside the obtained contour. A threshold is used on a final indicator computed from the other two indicators to find the probable regions for further segmentation using active contours. This process is repeated until no new segmentation region is identified. Finally, all the segmented thyroid images passed through a 3D reconstruction algorithm to obtain a 3D volume segmented thyroid. The results showed that including similarity indicators based on histogram equalization and MSE between inside and outside regions of the contour can help to segment difficult areas that active contours have problem to segment.
Multiplatform GPGPU implementation of the active contours without edges algorithm
Zavala-Romero, Olmo; Meyer-Baese, Anke; Meyer-Baese, Uwe
2012-05-01
An OpenCL implementation of the Active Contours Without Edges algorithm is presented. The proposed algorithm uses the General Purpose Computing on Graphics Processing Units (GPGPU) to accelerate the original model by parallelizing the two main steps of the segmentation process, the computation of the Signed Distance Function (SDF) and the evolution of the segmented curve. The proposed scheme for the computation of the SDF is based on the iterative construction of partial Voronoi diagrams of a reduced dimension and obtains the exact Euclidean distance in a time of order O(N/p), where N is the number of pixels and p the number of processors. With high resolution images the segmentation algorithm runs 10 times faster than its equivalent sequential implementation. This work is being done as an open source software that, being programmed in OpenCL, can be used in dierent platforms allowing a broad number of nal users and can be applied in dierent areas of computer vision, like medical imaging, tracking, robotics, etc. This work uses OpenGL to visualize the algorithm results in real time.
Multimode geodesic branching components
Schulz, D.; Voges, E.
1983-01-01
Geodesic branching components are investigated for multimode guided wave optics. Geodesic structures with particular properties, e.g. focussing star couplers, are derived by a synthesis technique based on a theorem of Toraldo di Francia. Experimentally, the geodesic surfaces are printed on acrylic glass and are spin-coated with organic film waveguides.
Nonrelativistic Geodesic Motion
Mangiarotti, L
1999-01-01
We show that any second order dynamic equation on a configuration space $X\\to R$ of nonrelativistic mechanics can be seen as a geodesic equation with respect to some (nonlinear) connection on the tangent bundle $TX\\to X$ of relativistic velocities. We compare relativistic and nonrelativistic geodesic equations, and study the Jacobi vector fields along nonrelativistic geodesics.
H. Bogunović; J.M. Pozo; M.C. Villa-Uriol; C.B.L.M. Majoie; R. van den Berg; H.A.F.G. van Andel; J.M. Macho; J. Blasco; L.S. Román; A.F. Frangi
2011-01-01
Purpose: To evaluate the suitability of an improved version of an automatic segmentation method based on geodesic active regions (GAR) for segmenting cerebral vasculature with aneurysms from 3D x-ray reconstruction angiography (3DRA) and time of flight magnetic resonance angiography (TOF-MRA) images
Active Contour Model Coupling with Higher Order Diffusion for Medical Image Segmentation
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Guodong Wang
2014-01-01
Full Text Available Active contour models are very popular in image segmentation. Different features such as mean gray and variance are selected for different purpose. But for image with intensity inhomogeneities, there are no features for segmentation using the active contour model. The images with intensity inhomogeneities often occurred in real world especially in medical images. To deal with the difficulties raised in image segmentation with intensity inhomogeneities, a new active contour model with higher-order diffusion method is proposed. With the addition of gradient and Laplace information, the active contour model can converge to the edge of the image even with the intensity inhomogeneities. Because of the introduction of Laplace information, the difference scheme becomes more difficult. To enhance the efficiency of the segmentation, the fast Split Bregman algorithm is designed for the segmentation implementation. The performance of our method is demonstrated through numerical experiments of some medical image segmentations with intensity inhomogeneities.
2016-01-01
We study geodesics on surfaces in the setting of classical differential geometry. We define the curvature of curves and surfaces in three-space and use the fundamental forms of a surface to measure lengths, angles, and areas. We follow Riemann and adopt a more abstract approach, and use tensor notation to discuss Gaussian curvature, Gauss's Theorema Egregium, geodesic curves, and the Gauss-Bonnet theorem. Properties of geodesics are proven by variational methods, showing the connection betwee...
Brain MR image segmentation using local and global intensity fitting active contours/surfaces.
Wang, Li; Li, Chunming; Sun, Quansen; Xia, Deshen; Kao, Chiu-Yen
2008-01-01
In this paper, we present an improved region-based active contour/surface model for 2D/3D brain MR image segmentation. Our model combines the advantages of both local and global intensity information, which enable the model to cope with intensity inhomogeneity. We define an energy functional with a local intensity fitting term and an auxiliary global intensity fitting term. In the associated curve evolution, the motion of the contour is driven by a local intensity fitting force and a global intensity fitting force, induced by the local and global terms in the proposed energy functional, respectively. The influence of these two forces on the curve evolution is complementary. When the contour is close to object boundaries, the local intensity fitting force became dominant, which attracts the contour toward object boundaries and finally stops the contour there. The global intensity fitting force is dominant when the contour is far away from object boundaries, and it allows more flexible initialization of contours by using global image information. The proposed model has been applied to both 2D and 3D brain MR image segmentation with promising results.
Geodesics of simultaneity in Schwarzschild
Paiva, F M
2010-01-01
Geodesic of simultaneity is a spacelike geodesic in which every pair of neighbour events are simultaneous ($g_{0\\mu}\\dd x^\\mu=0$). These geodesics are studied in the exterior region of \\Sch's metric.
A multi-scale approach to mass segmentation using active contour models
Yu, Hongwei; Li, Lihua; Xu, Weidong; Liu, Wei
2010-03-01
As an important step of mass classification, mass segmentation plays an important role in computer-aided diagnosis (CAD). In this paper, we propose a novel scheme for breast mass segmentation in mammograms, which is based on level set method and multi-scale analysis. Mammogram is firstly decomposed by Gaussian pyramid into a sequence of images from fine to coarse, the C-V model is then applied at the coarse scale, and the obtained rough contour is used as the initial contour for segmentation at the fine scale. A local active contour (LAC) model based on image local information is utilized to refine the rough contour locally at the fine scale. In addition, the feature of area and gray level extracted from coarse segmentation is used to set the parameters of LAC model automatically to improve the adaptivity of our method. The results show the higher accuracy and robustness of the proposed multi-scale segmentation method than the conventional ones.
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
Active contour modeling (ACM) has been shown to be a powerful method in object boundary extraction. In this paper,a new ACM based on vector bundle constraint for particle swarm optimization (VBCPSO-ACM) is proposed. Different from the traditional.particle swarm optimization (PSO), in the process of velocity update, a vector bundle is predefined for each particle and velocity update of the particle is restricted to its bundle. Applying this idea to ACM, control points on the contour are treated as particles in PSO and the evolution of the contour is driven by the particles. Meanwhile, global searching is shifted to local searching in ACM by decreasing the number of neighbors and inertia. In addition, the addition and deletion of particles on the active contour make this new model possible for representing the real boundaries more precisely. The proposed VBCPSO-ACM can avoid self-intersection during contour evolving and also extract inhomogeneous boundaries. The simulation results proved its great performance in performing contour extraction.
A Partition-Based Active Contour Model Incorporating Local Information for Image Segmentation
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Jiao Shi
2014-01-01
Full Text Available Active contour models are always designed on the assumption that images are approximated by regions with piecewise-constant intensities. This assumption, however, cannot be satisfied when describing intensity inhomogeneous images which frequently occur in real world images and induced considerable difficulties in image segmentation. A milder assumption that the image is statistically homogeneous within different local regions may better suit real world images. By taking local image information into consideration, an enhanced active contour model is proposed to overcome difficulties caused by intensity inhomogeneity. In addition, according to curve evolution theory, only the region near contour boundaries is supposed to be evolved in each iteration. We try to detect the regions near contour boundaries adaptively for satisfying the requirement of curve evolution theory. In the proposed method, pixels within a selected region near contour boundaries have the opportunity to be updated in each iteration, which enables the contour to be evolved gradually. Experimental results on synthetic and real world images demonstrate the advantages of the proposed model when dealing with intensity inhomogeneity images.
A partition-based active contour model incorporating local information for image segmentation.
Shi, Jiao; Wu, Jiaji; Paul, Anand; Jiao, Licheng; Gong, Maoguo
2014-01-01
Active contour models are always designed on the assumption that images are approximated by regions with piecewise-constant intensities. This assumption, however, cannot be satisfied when describing intensity inhomogeneous images which frequently occur in real world images and induced considerable difficulties in image segmentation. A milder assumption that the image is statistically homogeneous within different local regions may better suit real world images. By taking local image information into consideration, an enhanced active contour model is proposed to overcome difficulties caused by intensity inhomogeneity. In addition, according to curve evolution theory, only the region near contour boundaries is supposed to be evolved in each iteration. We try to detect the regions near contour boundaries adaptively for satisfying the requirement of curve evolution theory. In the proposed method, pixels within a selected region near contour boundaries have the opportunity to be updated in each iteration, which enables the contour to be evolved gradually. Experimental results on synthetic and real world images demonstrate the advantages of the proposed model when dealing with intensity inhomogeneity images.
A 3-Step Algorithm Using Region-Based Active Contours for Video Objects Detection
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Stéphanie Jehan-Besson
2002-06-01
Full Text Available We propose a 3-step algorithm for the automatic detection of moving objects in video sequences using region-based active contours. First, we introduce a very full general framework for region-based active contours with a new Eulerian method to compute the evolution equation of the active contour from a criterion including both region-based and boundary-based terms. This framework can be easily adapted to various applications, thanks to the introduction of functions named descriptors of the different regions. With this new Eulerian method based on shape optimization principles, we can easily take into account the case of descriptors depending upon features globally attached to the regions. Second, we propose a 3-step algorithm for detection of moving objects, with a static or a mobile camera, using region-based active contours. The basic idea is to hierarchically associate temporal and spatial information. The active contour evolves with successively three sets of descriptors: a temporal one, and then two spatial ones. The third spatial descriptor takes advantage of the segmentation of the image in intensity homogeneous regions. User interaction is reduced to the choice of a few parameters at the beginning of the process. Some experimental results are supplied.
Acho, Sussan Nkwenti; Rae, William Ian Duncombe
2016-10-01
A convex active contour model requires a predefined threshold value to determine the global solution for the best contour to use when doing mass segmentation. Fixed thresholds or manual tuning of threshold values for optimum mass boundary delineation are impracticable. A proposed method is presented to determine an optimized mass-specific threshold value for the convex active contour derived from the probability matrix of the mass with the particle swarm optimization method. We compared our results with the Chan-Vese segmentation and a published global segmentation model on masses detected on direct digital mammograms. The regional term of the convex active contour model maximizes the posterior partitioning probability for binary segmentation. Suppose the probability matrix is binary thresholded using the particle swarm optimization to obtain a value T1, we define the optimal threshold value for the global minimizer of the convex active contour as the mean intensity of all pixels whose probabilities are greater than T1. The mean Jaccard similarity indices were 0.89±0.07 for the proposed/Chan-Vese method and 0.88±0.06 for the proposed/published segmentation model. The mean Euclidean distance between Fourier descriptors of the segmented areas was 0.05±0.03 for the proposed/Chan-Vese method and 0.06±0.04 for the proposed/published segmentation model. This efficient method avoids problems of initial level set contour placement and contour re-initialization. Moreover, optimum segmentation results are realized for all masses improving on the fixed threshold value of 0.5 proposed elsewhere. Copyright © 2016 Associazione Italiana di Fisica Medica. Published by Elsevier Ltd. All rights reserved.
梯度向量场通量能量驱动的主动轮廓模型%Active Contours Driven by Image Gradient Flux Energy
Institute of Scientific and Technical Information of China (English)
杨勇; 徐春; 潘伟民
2009-01-01
A new image segmentation algorithm using level set method was presented, which is based on the gradient vector field flux fitting energy. Combing with the penalizing energy term of signed distance function and minimizing the energy functional, we obtain the variational formulation which has four main advantages over the traditional active contour models. First, the difficulty of segmentation with weak edge can be addressed. Second, the level set function allows for flexible initialization and needs no re-initialization during evolution. Third, the level set function can be easily implemented by simple finite difference scheme and is computationally more efficient. Fourth, the interior contour of object can be automatically detected with only one initial contour. The proposed algorithm has been applied to both synthetic and real images with promising results and the results of segmenting weak edge objects and images with intensity inhomogeneity are better than using either geodesic active contour (CAC) model or C-V active contour model, respectively.%提出了一种基于梯度向量场通量能量的水平集图像分割算法.通过加入约束符号距离函数的能量项,并极小化该能量函数得到的变分表达式主要具有4条优于传统主动轮廓模型的优点.一是可以克服分割弱边界目标的困难;二是水平集函数不但可以灵活初始化,而且可避免在演化过程中重新初始化为符号距离甬数;三是水平集函数数值化可采用简单的有限差分方法,计算效率得到了极大的提高;四是仅用一个初始轮廓就可以自动检测带孑L目标的内轮廓.对合成和真实图像的分割结果表明:对弱边界目标和灰度分布不均目标的分割效果分别优于测地线模型(GAC)和C-V主动轮廓模型.
Multiple Active Contours Guided by Differential Evolution for Medical Image Segmentation
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I. Cruz-Aceves
2013-01-01
Full Text Available This paper presents a new image segmentation method based on multiple active contours guided by differential evolution, called MACDE. The segmentation method uses differential evolution over a polar coordinate system to increase the exploration and exploitation capabilities regarding the classical active contour model. To evaluate the performance of the proposed method, a set of synthetic images with complex objects, Gaussian noise, and deep concavities is introduced. Subsequently, MACDE is applied on datasets of sequential computed tomography and magnetic resonance images which contain the human heart and the human left ventricle, respectively. Finally, to obtain a quantitative and qualitative evaluation of the medical image segmentations compared to regions outlined by experts, a set of distance and similarity metrics has been adopted. According to the experimental results, MACDE outperforms the classical active contour model and the interactive Tseng method in terms of efficiency and robustness for obtaining the optimal control points and attains a high accuracy segmentation.
Wang, Yin; Jiang, Han
2014-01-01
We present a nonparametric shape constrained algorithm for segmentation of coronary arteries in computed tomography images within the framework of active contours. An adaptive scale selection scheme, based on the global histogram information of the image data, is employed to determine the appropriate window size for each point on the active contour, which improves the performance of the active contour model in the low contrast local image regions. The possible leakage, which cannot be identified by using intensity features alone, is reduced through the application of the proposed shape constraint, where the shape of circular sampled intensity profile is used to evaluate the likelihood of current segmentation being considered vascular structures. Experiments on both synthetic and clinical datasets have demonstrated the efficiency and robustness of the proposed method. The results on clinical datasets have shown that the proposed approach is capable of extracting more detailed coronary vessels with subvoxel accuracy. PMID:24803950
Directory of Open Access Journals (Sweden)
Yin Wang
2014-01-01
Full Text Available We present a nonparametric shape constrained algorithm for segmentation of coronary arteries in computed tomography images within the framework of active contours. An adaptive scale selection scheme, based on the global histogram information of the image data, is employed to determine the appropriate window size for each point on the active contour, which improves the performance of the active contour model in the low contrast local image regions. The possible leakage, which cannot be identified by using intensity features alone, is reduced through the application of the proposed shape constraint, where the shape of circular sampled intensity profile is used to evaluate the likelihood of current segmentation being considered vascular structures. Experiments on both synthetic and clinical datasets have demonstrated the efficiency and robustness of the proposed method. The results on clinical datasets have shown that the proposed approach is capable of extracting more detailed coronary vessels with subvoxel accuracy.
Method for non-referential defect characterization using fractal encoding and active contours
Gleason, Shaun S.; Sari-Sarraf, Hamed
2007-05-15
A method for identification of anomalous structures, such as defects, includes the steps of providing a digital image and applying fractal encoding to identify a location of at least one anomalous portion of the image. The method does not require a reference image to identify the location of the anomalous portion. The method can further include the step of initializing an active contour based on the location information obtained from the fractal encoding step and deforming an active contour to enhance the boundary delineation of the anomalous portion.
Busemann, Herbert
2005-01-01
A comprehensive approach to qualitative problems in intrinsic differential geometry, this text examines Desarguesian spaces, perpendiculars and parallels, covering spaces, the influence of the sign of the curvature on geodesics, more. 1955 edition. Includes 66 figures.
NSCT BASED LOCAL ENHANCEMENT FOR ACTIVE CONTOUR BASED IMAGE SEGMENTATION APPLICATION
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Hiren Mewada
2010-08-01
Full Text Available Because of cross-disciplinary nature, Active Contour modeling techniques have been utilized extensively for the image segmentation. In traditional active contour based segmentation techniques based on level set methods, the energy functions are defined based on the intensity gradient. This makes them highly sensitive to the situation where the underlying image content is characterized by image nonhomogeneities due to illumination and contrast condition. This is the most difficult problem to make them as fully automatic image segmentation techniques. This paper introduces one of the approaches based on image enhancement to this problem. The enhanced image is obtained using NonSubsampled Contourlet Transform, which improves the edges strengths in the direction where the illumination is not proper and then active contour model based on level set technique is utilized to segment the object. Experiment results demonstrate that proposed method can be utilized along with existing active contour model based segmentation method under situation characterized by intensity non-homogeneity to make them fully automatic.
An implicit evolution scheme for active contours and surfaces based on IIR filtering.
Delibasis, Konstantinos K; Asvestas, Pantelis A; Kechriniotis, Aristides I; Matsopoulos, George K
2014-05-01
In this work, we present an approach for implementing an implicit scheme for the numerical solution of the partial differential equation of the evolution of an active contour/surface. The proposed scheme is applicable to any variant of the traditional active contour (AC), irrespectively of the calculation of the image-based force field and it is readily applicable to explicitly parameterized active surfaces (AS). The proposed approach is formulated as an infinite impulse response (IIR) filtering of the coordinates of the contour/surface points. The poles of the filter are determined by the parameters controlling the shape of the active contour/surface. We show that the proposed IIR-based implicit evolution scheme has very low complexity. Furthermore, the proposed scheme is numerically stable, thus it allows the convergence of the AC/AS with significantly fewer iterations than the explicit evolution scheme. It also possesses the separability property along the two parameters of the AS, thus it may be applied to deformable surfaces, without the need to store and invert large sparse matrices. We implemented the proposed IIR-based implicit evolution scheme in the Vector Field Convolution (VFC) AC/AS using synthetic and clinical volumetric data. We compared the segmentation results with those of the explicit AC/AS evolution, in terms of accuracy and efficiency. Results show that the VFC AC/AS with the proposed IIR-based implicit evolution scheme achieves the same segmentation results with the explicit scheme, with considerably less computation time.
Using an active contour method to detect bilge dumps from SAR imagery
CSIR Research Space (South Africa)
Mdakane, Lizwe W
2016-07-01
Full Text Available An automatic approach to detect bilge dumping in synthetic aperture radar (SAR) images over Southern African oceans is proposed. The approach uses a threshold-based algorithm and a region-based active contour model (ACM) algorithm to achieve...
Directory of Open Access Journals (Sweden)
Yali Huang
2015-01-01
Full Text Available The paper proposes an improved active contour model for segmenting and tracking accurate boundaries of the single lymphocyte in phase-contrast microscopic images. Active contour models have been widely used in object segmentation and tracking. However, current external-force-inspired methods are weak at handling low-contrast edges and suffer from initialization sensitivity. In order to segment low-contrast boundaries, we combine the region information of the object, extracted by morphology gray-scale reconstruction, and the edge information, extracted by the Laplacian of Gaussian filter, to obtain an improved feature map to compute the external force field for the evolution of active contours. To alleviate initial location sensitivity, we set the initial contour close to the real boundaries by performing morphological image processing. The proposed method was tested on live lymphocyte images acquired through the phase-contrast microscope from the blood samples of mice, and comparative experimental results showed the advantages of the proposed method in terms of the accuracy and the speed. Tracking experiments showed that the proposed method can accurately segment and track lymphocyte boundaries in microscopic images over time even in the presence of low-contrast edges, which will provide a good prerequisite for the quantitative analysis of lymphocyte morphology and motility.
Active Contours and Mumford-Shah Segmentation Based on Level Sets
Institute of Scientific and Technical Information of China (English)
NASSIR H.SALMAN; LIU Chong-qing(刘重庆)
2003-01-01
This paper is to detect regions (objects) boundaries, also to isolate and extract individual componentsfrom a medical image. This can be done using an active contours to detect regions in a given image, based on tech-niques of curve evolution, Mumford-Shah functional for segmentation and level sets. The paper classified the im-ages into different intensity regions based on Markov random field, then detected regions whose boundaries are notnecessarily defined by gradient by minimizing an energy of Mumford-Shah functional for segmentation which can beseen as a particular case of the minimal partition problem. In the level set formulation, the problem becomes amean-curvature flow like evolving the active contour, which will stop on the desired boundary. The stopping termdoes not depend on the gradient of the image, as in the classical active contour and the initial curve of level set canbe anywhere in the image, and interior contours are automatically detected. The final image segmentation is oneclosed boundary per actual region in the image.
Histace, A.; Meziou, B J; Matuszewski, Bogdan; Precioso, F.; Murphy, M F; Carreiras, F
2013-01-01
We propose an unsupervised statistical region based active contour approach integrating an original fractional entropy measure for image segmentation with a particular application to single channel actin tagged fluorescence confocal microscopy image segmentation. Following description of statistical based active contour segmentation and the mathematical definition of the proposed fractional entropy descriptor, we demonstrate comparative segmentation results between the proposed approach and s...
Liver segmentation with new supervised method to create initial curve for active contour.
Zareei, Abouzar; Karimi, Abbas
2016-08-01
The liver performs a critical task in the human body; therefore, detecting liver diseases and preparing a robust plan for treating them are both crucial. Liver diseases kill nearly 25,000 Americans every year. A variety of image segmentation methods are available to determine the liver's position and to detect possible liver tumors. Among these is the Active Contour Model (ACM), a framework which has proven very sensitive to initial contour delineation and control parameters. In the proposed method based on image energy, we attempted to obtain an initial segmentation close to the liver's boundary, and then implemented an ACM to improve the initial segmentation. The ACM used in this work incorporates gradient vector flow (GVF) and balloon energy in order to overcome ACM limitations, such as local minima entrapment and initial contour dependency. Additionally, in order to adjust active contour control parameters, we applied a genetic algorithm to produce a proper parameter set close to the optimal solution. The pre-processing method has a better ability to segment the liver tissue during a short time with respect to other mentioned methods in this paper. The proposed method was performed using Sliver CT image datasets. The results show high accuracy, precision, sensitivity, specificity and low overlap error, MSD and runtime with few ACM iterations.
Automatic Segmentation of Nature Object Using Salient Edge Points Based Active Contour
Directory of Open Access Journals (Sweden)
Shangbing Gao
2015-01-01
Full Text Available Natural image segmentation is often a crucial first step for high-level image understanding, significantly reducing the complexity of content analysis of images. LRAC may have some disadvantages. (1 Segmentation results heavily depend on the initial contour selection which is a very skillful task. (2 In some situations, manual interactions are infeasible. To overcome these shortcomings, we propose a novel model for unsupervised segmentation of viewer’s attention object from natural images based on localizing region-based active model (LRAC. With aid of the color boosting Harris detector and the core saliency map, we get the salient object edge points. Then, these points are employed as the seeds of initial convex hull. Finally, this convex hull is improved by the edge-preserving filter to generate the initial contour for our automatic object segmentation system. In contrast with localizing region-based active contours that require considerable user interaction, the proposed method does not require it; that is, the segmentation task is fulfilled in a fully automatic manner. Extensive experiments results on a large variety of natural images demonstrate that our algorithm consistently outperforms the popular existing salient object segmentation methods, yielding higher precision and better recall rates. Our framework can reliably and automatically extract the object contour from the complex background.
Active contour-based cell segmentation during freezing and its application in cryopreservation.
Wu, Pengxiang; Yi, Jingru; Zhao, Gang; Huang, Zhangjin; Qiu, Bensheng; Gao, Dayong
2015-01-01
Water permeability of the plasma membrane plays an important role in making optimal cryopreservation protocols for different types of cells. To quantify water permeability effectively, automated cell volume segmentation during freezing is necessary. Unfortunately, there exists so far no efficient and accurate segmentation method to handle this kind of image processing task gracefully. The existence of extracellular ice and variable background present significant challenges for most traditional segmentation algorithms. In this paper, we propose a novel approach to reliably extract cells from the extracellular ice, which attaches to or surrounds cells. Our method operates on temporal image sequences and is composed of two steps. First, for each image from the sequence, a greedy search strategy is employed to track approximate locations of cells in motion. Second, we utilize a localized competitive active contour model to obtain the contour of each cell. Based on the first step's result, the initial contour for level set evolution can be determined appropriately, thus considerably easing the pain of initialization for an active contour model. Experimental results demonstrate that the proposed method is efficient and effective in segmenting cells during freezing.
Spherical geodesic mesh generation
Energy Technology Data Exchange (ETDEWEB)
Fung, Jimmy [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Kenamond, Mark Andrew [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Burton, Donald E. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Shashkov, Mikhail Jurievich [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2015-02-27
In ALE simulations with moving meshes, mesh topology has a direct influence on feature representation and code robustness. In three-dimensional simulations, modeling spherical volumes and features is particularly challenging for a hydrodynamics code. Calculations on traditional spherical meshes (such as spin meshes) often lead to errors and symmetry breaking. Although the underlying differencing scheme may be modified to rectify this, the differencing scheme may not be accessible. This work documents the use of spherical geodesic meshes to mitigate solution-mesh coupling. These meshes are generated notionally by connecting geodesic surface meshes to produce triangular-prismatic volume meshes. This mesh topology is fundamentally different from traditional mesh topologies and displays superior qualities such as topological symmetry. This work describes the geodesic mesh topology as well as motivating demonstrations with the FLAG hydrocode.
Energy Technology Data Exchange (ETDEWEB)
Townsend, Paul K [Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA (United Kingdom); Wohlfarth, Mattias N R [Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA (United Kingdom)
2004-12-07
For gravity coupled to N scalar fields, with arbitrary potential V, it is shown that all flat (homogeneous and isotropic) cosmologies correspond to geodesics in an (N + 1)-dimensional 'augmented' target space of Lorentzian signature (1, N), timelike if V > 0, null if V = 0 and spacelike if V < 0. Accelerating cosmologies correspond to timelike geodesics that lie within an 'acceleration subcone' of the 'lightcone'. Non-flat (k = {+-}1) cosmologies are shown to evolve as projections of geodesic motion in a space of dimension N + 2, of signature (1, N + 1) for k = -1 and signature (2, N) for k = +1. This formalism is illustrated by cosmological solutions of models with an exponential potential, which are comprehensively analysed; the late-time behaviour for other potentials of current interest is deduced by comparison.
Townsend, P K; Townsend, Paul K.; Wohlfarth, Mattias N.R.
2004-01-01
For gravity coupled to N scalar fields with arbitrary potential V, it is shown that all flat (homogeneous and isotropic) cosmologies correspond to geodesics in an (N+1)-dimensional `extended target space' of Lorentzian signature (1,N), timelike if V>0 and spacelike if V<0. Accelerating cosmologies correspond to timelike geodesics that lie within an `acceleration subcone' of the `lightcone'. Non-flat (k=-1,+1) cosmologies are shown to evolve as projections of geodesic motion in a space of dimension N+2, of signature (1,N+1) for k=-1 and signature (2,N) for k=+1. We illustrate these results for various potentials of current interest, including exponential and inverse power potentials.
An efficient topology adaptation system for parametric active contour segmentation of 3D images
Abhau, Jochen; Scherzer, Otmar
2008-03-01
Active contour models have already been used succesfully for segmentation of organs from medical images in 3D. In implicit models, the contour is given as the isosurface of a scalar function, and therefore topology adaptations are handled naturally during a contour evolution. Nevertheless, explicit or parametric models are often preferred since user interaction and special geometric constraints are usually easier to incorporate. Although many researchers have studied topology adaptation algorithms in explicit mesh evolutions, no stable algorithm is known for interactive applications. In this paper, we present a topology adaptation system, which consists of two novel ingredients: A spatial hashing technique is used to detect self-colliding triangles of the mesh whose expected running time is linear with respect to the number of mesh vertices. For the topology change procedure, we have developed formulas by homology theory. During a contour evolution, we just have to choose between a few possible mesh retriangulations by local triangle-triangle intersection tests. Our algorithm has several advantages compared to existing ones: Since the new algorithm does not require any global mesh reparametrizations, it is very efficient. Since the topology adaptation system does not require constant sampling density of the mesh vertices nor especially smooth meshes, mesh evolution steps can be performed in a stable way with a rather coarse mesh. We apply our algorithm to 3D ultrasonic data, showing that accurate segmentation is obtained in some seconds.
Implicit Active Contour Model with Local and Global Intensity Fitting Energies
Directory of Open Access Journals (Sweden)
Xiaozeng Xu
2013-01-01
Full Text Available We propose a new active contour model which integrates a local intensity fitting (LIF energy with an auxiliary global intensity fitting (GIF energy. The LIF energy is responsible for attracting the contour toward object boundaries and is dominant near object boundaries, while the GIF energy incorporates global image information to improve the robustness to initialization of the contours. The proposed model not only can provide desirable segmentation results in the presence of intensity inhomogeneity but also allows for more flexible initialization of the contour compared to the RSF and LIF models, and we give a theoretical proof to compute a unique steady state regardless of the initialization; that is, the convergence of the zero-level line is irrespective of the initial function. This means that we can obtain the same zero-level line in the steady state, if we choose the initial function as a bounded function. In particular, our proposed model has the capability of detecting multiple objects or objects with interior holes or blurred edges.
Gao, Yi; Kikinis, Ron; Bouix, Sylvain; Shenton, Martha; Tannenbaum, Allen
2012-08-01
Extracting anatomical and functional significant structures renders one of the important tasks for both the theoretical study of the medical image analysis, and the clinical and practical community. In the past, much work has been dedicated only to the algorithmic development. Nevertheless, for clinical end users, a well designed algorithm with an interactive software is necessary for an algorithm to be utilized in their daily work. Furthermore, the software would better be open sourced in order to be used and validated by not only the authors but also the entire community. Therefore, the contribution of the present work is twofolds: first, we propose a new robust statistics based conformal metric and the conformal area driven multiple active contour framework, to simultaneously extract multiple targets from MR and CT medical imagery in 3D. Second, an open source graphically interactive 3D segmentation tool based on the aforementioned contour evolution is implemented and is publicly available for end users on multiple platforms. In using this software for the segmentation task, the process is initiated by the user drawn strokes (seeds) in the target region in the image. Then, the local robust statistics are used to describe the object features, and such features are learned adaptively from the seeds under a non-parametric estimation scheme. Subsequently, several active contours evolve simultaneously with their interactions being motivated by the principles of action and reaction-this not only guarantees mutual exclusiveness among the contours, but also no longer relies upon the assumption that the multiple objects fill the entire image domain, which was tacitly or explicitly assumed in many previous works. In doing so, the contours interact and converge to equilibrium at the desired positions of the desired multiple objects. Furthermore, with the aim of not only validating the algorithm and the software, but also demonstrating how the tool is to be used, we provide
Aichholzer, Oswin; Korman Cozzetti, Matías; Pilz, Alexander; Vogtenhuber, Birgit
2014-01-01
The geodesic between two points a and b in the interior of a simple polygon P is the shortest polygonal path inside P that connects a to b. It is thus the natural generalization of straight line segments on unconstrained point sets to polygonal environments. In this paper we use this extension to generalize the concept of the order type of a set of points in the Euclidean plane to geodesic order types. In particular, we show that, for any set S of points and an ordered subset of at least four...
Ciller Ruiz, Carlos
2012-01-01
[ANGLÈS] This work presents an analysis and optimization, both in terms of optimal parameters and speed, of the novel geodesic active fields framework for surface image registration on the sphere, presented by Zosso, Dominique in his PhD thesis at the École Polytechnique Fédérale de Lausanne. The relevance of surface registration to medical imaging is that there is a lot of anatomical information in the form of collected surface points, giving information about the cortical folding pattern. H...
Mikulka, J.; Gescheidtova, E.; Bartusek, K.
2012-01-01
The paper deals with modern methods of image processing, especially image segmentation, classification and evaluation of parameters. It focuses primarily on processing medical images of soft tissues obtained by magnetic resonance tomography (MR). It is easy to describe edges of the sought objects using segmented images. The edges found can be useful for further processing of monitored object such as calculating the perimeter, surface and volume evaluation or even three-dimensional shape reconstruction. The proposed solutions can be used for the classification of healthy/unhealthy tissues in MR or other imaging. Application examples of the proposed segmentation methods are shown. Research in the area of image segmentation focuses on methods based on solving partial differential equations. This is a modern method for image processing, often called the active contour method. It is of great advantage in the segmentation of real images degraded by noise with fuzzy edges and transitions between objects. In the paper, results of the segmentation of medical images by the active contour method are compared with results of the segmentation by other existing methods. Experimental applications which demonstrate the very good properties of the active contour method are given.
Active contour segmentation using level set function with enhanced image from prior intensity.
Kim, Sunhee; Kim, Youngjun; Lee, Deukhee; Park, Sehyung
2015-01-01
This paper presents a new active contour segmentation model using a level set function that can correctly capture both the strong and the weak boundaries of a target enclosed by bright and dark regions at the same time. We introduce an enhanced image obtained from prior information about the intensity of the target. The enhanced image emphasizes the regions where pixels have intensities close to the prior intensity. This enables a desirable segmentation of an image having a partially low contrast with the target surrounded by regions that are brighter or darker than the target. We define an edge indicator function on an original image, and local and regularization forces on an enhanced image. An edge indicator function and two forces are incorporated in order to identify the strong and weak boundaries, respectively. We established an evolution equation of contours in the level set formulation and experimented with several medical images to show the performance of the proposed method.
Automatic brain cropping enhancement using active contours initialized by a PCNN
Swathanthira Kumar, Murali Murugavel; Sullivan, John M., Jr.
2009-02-01
Active contours are a popular medical image segmentation strategy. However in practice, its accuracy is dependent on the initialization of the process. The PCNN (Pulse Coupled Neural Network) algorithm developed by Eckhorn to model the observed synchronization of neural assemblies in small mammals such as cats allows for segmenting regions of similar intensity but it lacks a convergence criterion. In this paper we report a novel PCNN based strategy to initialize the zero level contour for automatic brain cropping of T2 weighted MRI image volumes of Long-Evans rats. Individual 2D anatomy slices of the rat brain volume were processed by means of a PCNN and a surrogate image 'signature' was constructed for each slice. By employing a previously trained artificial neural network (ANN) an approximate PCNN iteration (binary mask) was selected. This mask was then used to initialize a region based active contour model to crop the brain region. We tested this hybrid algorithm on 30 rat brain (256*256*12) volumes and compared the results against manually cropped gold standard. The Dice and Jaccard similarity indices were used for numerical evaluation of the proposed hybrid model. The highly successful system yielded an average of 0.97 and 0.94 respectively.
Xing, Fuyong; Yang, Lin
2015-10-01
Efficient and effective cell segmentation of neuroendocrine tumor (NET) in whole slide scanned images is a difficult task due to a large number of cells. The weak or misleading cell boundaries also present significant challenges. In this paper, we propose a fast, high throughput cell segmentation algorithm by combining top-down shape models and bottom-up image appearance information. A scalable sparse manifold learning method is proposed to model multiple subpopulations of different cell shape priors. Followed by a shape clustering on the manifold, a novel affine transform-approximated active contour model is derived to deform contours without solving a large amount of computationally-expensive Euler-Lagrange equations, and thus dramatically reduces the computational time. To the best of our knowledge, this is the first report of a high throughput cell segmentation algorithm for whole slide scanned pathology specimens using manifold learning to accelerate active contour models. The proposed approach is tested using 12 NET images, and the comparative experiments with the state of the arts demonstrate its superior performance in terms of both efficiency and effectiveness.
Tracking fuzzy borders using geodesic curves with application to liver segmentation on planning CT.
Yuan, Yading; Chao, Ming; Sheu, Ren-Dih; Rosenzweig, Kenneth; Lo, Yeh-Chi
2015-07-01
This work aims to develop a robust and efficient method to track the fuzzy borders between liver and the abutted organs where automatic liver segmentation usually suffers, and to investigate its applications in automatic liver segmentation on noncontrast-enhanced planning computed tomography (CT) images. In order to track the fuzzy liver-chestwall and liver-heart borders where oversegmentation is often found, a starting point and an ending point were first identified on the coronal view images; the fuzzy border was then determined as a geodesic curve constructed by minimizing the gradient-weighted path length between these two points near the fuzzy border. The minimization of path length was numerically solved by fast-marching method. The resultant fuzzy borders were incorporated into the authors' automatic segmentation scheme, in which the liver was initially estimated by a patient-specific adaptive thresholding and then refined by a geodesic active contour model. By using planning CT images of 15 liver patients treated with stereotactic body radiation therapy, the liver contours extracted by the proposed computerized scheme were compared with those manually delineated by a radiation oncologist. The proposed automatic liver segmentation method yielded an average Dice similarity coefficient of 0.930 ± 0.015, whereas it was 0.912 ± 0.020 if the fuzzy border tracking was not used. The application of fuzzy border tracking was found to significantly improve the segmentation performance. The mean liver volume obtained by the proposed method was 1727 cm(3), whereas it was 1719 cm(3) for manual-outlined volumes. The computer-generated liver volumes achieved excellent agreement with manual-outlined volumes with correlation coefficient of 0.98. The proposed method was shown to provide accurate segmentation for liver in the planning CT images where contrast agent is not applied. The authors' results also clearly demonstrated that the application of tracking the fuzzy
On Properties of Geodesic -Preinvex Functions
Directory of Open Access Journals (Sweden)
I. Ahmad
2009-01-01
Full Text Available The present paper deals with the properties of geodesic -preinvex functions and their relationships with -invex functions and strictly geodesic -preinvex functions. The geodesic -pre-pseudo-invex and geodesic -pre-quasi-invex functions on the geodesic invex set are introduced and some of their properties are discussed.
A moving object segmentation algorithm for static camera via active contours and GMM
Institute of Scientific and Technical Information of China (English)
WAN ChengKai; YUAN BaoZong; MIAO ZhenJiang
2009-01-01
Moving object segmentation is one of the most challenging Issues In computer vision. In this paper, we propose a new algorithm for static camera foreground segmentation. It combines Gaussian mix-ture model (GMM) and active contours method, and produces much better results than conventional background subtraction methods. It formulates foreground segmentation as an energy minimization problem and minimizes the energy function using curve evolution method. Our algorithm integrates the GMM background model, shadow elimination term and curve evolution edge stopping term into energy function. It achieves more accurate segmentation than existing methods of the same type. Promising results on real images demonstrate the potential of the presented method.
Directory of Open Access Journals (Sweden)
J Farley Norman
Full Text Available It is well known that motion facilitates the visual perception of solid object shape, particularly when surface texture or other identifiable features (e.g., corners are present. Conventional models of structure-from-motion require the presence of texture or identifiable object features in order to recover 3-D structure. Is the facilitation in 3-D shape perception similar in magnitude when surface texture is absent? On any given trial in the current experiments, participants were presented with a single randomly-selected solid object (bell pepper or randomly-shaped "glaven" for 12 seconds and were required to indicate which of 12 (for bell peppers or 8 (for glavens simultaneously visible objects possessed the same shape. The initial single object's shape was defined either by boundary contours alone (i.e., presented as a silhouette, specular highlights alone, specular highlights combined with boundary contours, or texture. In addition, there was a haptic condition: in this condition, the participants haptically explored with both hands (but could not see the initial single object for 12 seconds; they then performed the same shape-matching task used in the visual conditions. For both the visual and haptic conditions, motion (rotation in depth or active object manipulation was present in half of the trials and was not present for the remaining trials. The effect of motion was quantitatively similar for all of the visual and haptic conditions-e.g., the participants' performance in Experiment 1 was 93.5 percent higher in the motion or active haptic manipulation conditions (when compared to the static conditions. The current results demonstrate that deforming specular highlights or boundary contours facilitate 3-D shape perception as much as the motion of objects that possess texture. The current results also indicate that the improvement with motion that occurs for haptics is similar in magnitude to that which occurs for vision.
Cheeseman, Jacob R.; Thomason, Kelsey E.; Ronning, Cecilia; Behari, Kriti; Kleinman, Kayla; Calloway, Autum B.; Lamirande, Davora
2016-01-01
It is well known that motion facilitates the visual perception of solid object shape, particularly when surface texture or other identifiable features (e.g., corners) are present. Conventional models of structure-from-motion require the presence of texture or identifiable object features in order to recover 3-D structure. Is the facilitation in 3-D shape perception similar in magnitude when surface texture is absent? On any given trial in the current experiments, participants were presented with a single randomly-selected solid object (bell pepper or randomly-shaped “glaven”) for 12 seconds and were required to indicate which of 12 (for bell peppers) or 8 (for glavens) simultaneously visible objects possessed the same shape. The initial single object’s shape was defined either by boundary contours alone (i.e., presented as a silhouette), specular highlights alone, specular highlights combined with boundary contours, or texture. In addition, there was a haptic condition: in this condition, the participants haptically explored with both hands (but could not see) the initial single object for 12 seconds; they then performed the same shape-matching task used in the visual conditions. For both the visual and haptic conditions, motion (rotation in depth or active object manipulation) was present in half of the trials and was not present for the remaining trials. The effect of motion was quantitatively similar for all of the visual and haptic conditions–e.g., the participants’ performance in Experiment 1 was 93.5 percent higher in the motion or active haptic manipulation conditions (when compared to the static conditions). The current results demonstrate that deforming specular highlights or boundary contours facilitate 3-D shape perception as much as the motion of objects that possess texture. The current results also indicate that the improvement with motion that occurs for haptics is similar in magnitude to that which occurs for vision. PMID:26863531
Wang, Li; Li, Chunming; Sun, Quansen; Xia, Deshen; Kao, Chiu-Yen
2009-10-01
In this paper, we propose an improved region-based active contour model in a variational level set formulation. We define an energy functional with a local intensity fitting term, which induces a local force to attract the contour and stops it at object boundaries, and an auxiliary global intensity fitting term, which drives the motion of the contour far away from object boundaries. Therefore, the combination of these two forces allows for flexible initialization of the contours. This energy is then incorporated into a level set formulation with a level set regularization term that is necessary for accurate computation in the corresponding level set method. The proposed model is first presented as a two-phase level set formulation and then extended to a multi-phase formulation. Experimental results show the advantages of our method in terms of accuracy and robustness. In particular, our method has been applied to brain MR image segmentation with desirable results.
Cohen, Assaf; Rivlin, Ehud; Shimshoni, Ilan; Sabo, Edmond
2015-07-01
In this paper, we introduce a novel method for detection and segmentation of crypts in colon biopsies. Most of the approaches proposed in the literature try to segment the crypts using only the biopsy image without understanding the meaning of each pixel. The proposed method differs in that we segment the crypts using an automatically generated pixel-level classification image of the original biopsy image and handle the artifacts due to the sectioning process and variance in color, shape and size of the crypts. The biopsy image pixels are classified to nuclei, immune system, lumen, cytoplasm, stroma and goblet cells. The crypts are then segmented using a novel active contour approach, where the external force is determined by the semantics of each pixel and the model of the crypt. The active contour is applied for every lumen candidate detected using the pixel-level classification. Finally, a false positive crypt elimination process is performed to remove segmentation errors. This is done by measuring their adherence to the crypt model using the pixel level classification results. The method was tested on 54 biopsy images containing 4944 healthy and 2236 cancerous crypts, resulting in 87% detection of the crypts with 9% of false positive segments (segments that do not represent a crypt). The segmentation accuracy of the true positive segments is 96%.
Barba-J, Leiner; Escalante-Ramírez, Boris
2016-04-01
Early detection of cardiac affections is fundamental to address a correct treatment that allows preserving the patient's life. Since heart disease is one of the main causes of death in most countries, analysis of cardiac images is of great value for cardiac assessment. Cardiac MR has become essential for heart evaluation. In this work we present a segmentation framework for shape analysis in cardiac magnetic resonance (MR) images. The method consists of an active contour model which is guided by the spectral coefficients obtained from the Hermite transform (HT) of the data. The HT is used as model to code image features of the analyzed images. Region and boundary based energies are coded using the zero and first order coefficients. An additional shape constraint based on an elliptical function is used for controlling the active contour deformations. The proposed framework is applied to the segmentation of the endocardial and epicardial boundaries of the left ventricle using MR images with short axis view. The segmentation is sequential for both regions: the endocardium is segmented followed by the epicardium. The algorithm is evaluated with several MR images at different phases of the cardiac cycle demonstrating the effectiveness of the proposed method. Several metrics are used for performance evaluation.
Kang, Sukryool; Lee, Chen-Yu; Gonçalves, Monira; Chisholm, Andrew D; Cosman, Pamela C
2015-04-01
Quantitative analysis of cell shape in live samples is an important goal in developmental biology. Automated or semi-automated segmentation and tracking of cell nuclei has been successfully implemented in several biological systems. Segmentation and tracking of cell surfaces has been more challenging. Here, we present a new approach to tracking cell junctions in the developing epidermis of C. elegans embryos. Epithelial junctions as visualized with DLG-1::GFP form lines at the subapical circumference of differentiated epidermal cells and delineate changes in epidermal cell shape and position. We develop and compare two approaches for junction segmentation. For the first method (projection approach), 3-D cell boundaries are projected into 2D for segmentation using active contours with a nonintersecting force, and subsequently tracked using scale-invariant feature transform (SIFT) flow. The resulting 2-D tracked boundaries are then back-projected into 3-D space. The second method (volumetric approach) uses a 3-D extended version of active contours guided by SIFT flow in 3-D space. In both methods, cell junctions are manually located at the first time point and tracked in a fully automated way for the remainder of the video. Using these methods, we have generated the first quantitative description of ventral epidermal cell movements and shape changes during epidermal enclosure.
Fast Texture Segmentation Based on Semi-Local Region Descriptor and Active Contour
Institute of Scientific and Technical Information of China (English)
Nawal Houhou; Jean-Philippe Thiran; Xavier Bresson
2009-01-01
In this paper, we present an efficient approach for unsupervised segmentation of natural and textural images based on the extraction of image features and a fast active contour segmentation model. We address the problem of textures where neither the gray-level information nor the boundary information is adequate for object extraction. This is often the case of natural images composed of both homogeneous and textured regions. Because these images cannot be in general directly processed by the gray-level information, we propose a new texture descriptor which intrinsically defines the geometry of textures using semi-local image information and tools from differential geometry. Then, we use the popular Kullback-Leibler distance to design an active contour model which distinguishes the background and textures of interest. The existence of a minimizing solution to the proposed segmentation model is proven. Finally, a texture segmentation algorithm based on the Split-Bregman method is introduced to extract meaningful objects in a fast way. Promising synthetic and real-world results for gray-scale and color images are presented.
Active contour external force using vector field convolution for image segmentation.
Li, Bing; Acton, Scott T
2007-08-01
Snakes, or active contours, have been widely used in image processing applications. Typical roadblocks to consistent performance include limited capture range, noise sensitivity, and poor convergence to concavities. This paper proposes a new external force for active contours, called vector field convolution (VFC), to address these problems. VFC is calculated by convolving the edge map generated from the image with the user-defined vector field kernel. We propose two structures for the magnitude function of the vector field kernel, and we provide an analytical method to estimate the parameter of the magnitude function. Mixed VFC is introduced to alleviate the possible leakage problem caused by choosing inappropriate parameters. We also demonstrate that the standard external force and the gradient vector flow (GVF) external force are special cases of VFC in certain scenarios. Examples and comparisons with GVF are presented in this paper to show the advantages of this innovation, including superior noise robustness, reduced computational cost, and the flexibility of tailoring the force field.
Automatic Detection of the Ice Edge in SAR Imagery Using Curvelet Transform and Active Contour
Directory of Open Access Journals (Sweden)
Jiange Liu
2016-06-01
Full Text Available A novel method based on the curvelet transform and active contour method to automatically detect the ice edge in Synthetic Aperture Radar (SAR imagery is proposed. The method utilizes the location of high curvelet coefficients to determine regions in the image likely to contain the ice edge. Using an ice edge from passive microwave sea ice concentration for initialization, these regions are then joined using the active contour method to obtain the final ice edge. The method is evaluated on four dual polarization SAR scenes of the Labrador sea. Through comparison of the ice edge with that from image analysis charts, it is demonstrated that the proposed method can detect the ice edge effectively in SAR images. This is particularly relevant when the marginal ice zone is diffuse or the ice is thin, and using the definition of ice edge from the passive microwave ice concentration would underestimate the ice edge location. It is expected that the method may be useful for operations in marginal ice zones, such as offshore drilling, where a high resolution estimate of the ice edge location is required. It could also be useful as a first guess for an ice analyst, or for the assimilation of SAR data.
Deployable geodesic truss structure
Mikulas, Martin M., Jr. (Inventor); Rhodes, Marvin D. (Inventor); Simonton, J. Wayne (Inventor)
1987-01-01
A deployable geodesic truss structure which can be deployed from a stowed state to an erected state is described. The truss structure includes a series of bays, each bay having sets of battens connected by longitudinal cross members which give the bay its axial and torsional stiffness. The cross members are hinged at their mid point by a joint so that the cross members are foldable for deployment or collapsing. The bays are deployed and stabilized by actuator means connected between the mid point joints of the cross members. Hinged longerons may be provided to also connect the sets of battens and to collapse for stowing with the rest of the truss structure.
Horndeski black hole geodesics
Tretyakova, D A
2016-01-01
We examine geodesics for the scalar-tensor black holes in the Horndeski-Galileon framework. Our analysis shows that first kind relativistic orbits may not be present within some model parameters range. This is a highly pathological behavior contradicting to the black hole accretion and Solar System observations. We also present a new (although very similar to those previously known) solution, which contains the orbits we expect from a compact object, admits regular scalar field at the horizon and and can fit into the known stability criteria.
Song, Tzu-Hsi; Sanchez, Victor; EIDaly, Hesham; Rajpoot, Nasir M.
2015-03-01
The assessment of megakaryocytes (MKs) in bone marrow trephine images is an important step in the classification of different subtypes of myeloproliferative neoplasms (MPNs). In general, bone marrow trephine images include several types of cells mixed together, which make it quite difficult to visually identify MKs. In order to aid hematopathologists in the identification and study of MKs, we develop an image processing framework with supervised machine learning approaches and a novel circumscribing active contour model to identify potential MKs and then to accurately delineate the corresponding nucleus and membrane. Specifically, a number of color and texture features are used in a nave Bayesian classifier and an Adaboost classifier to locate the regions with a high probability of depicting MKs. A region-based active contour is used on the candidate MKs to accurately delineate the boundaries of nucleus and membrane. The proposed circumscribing active contour model employs external forces not only based on pixel intensities, but also on the probabilities of depicting MKs as computed by the classifiers. Experimental results suggest that the machine learning approach can detect potential MKs with an accuracy of more than 75%. When our circumscribing active contour model is employed on the candidate MKs, the nucleus and membrane boundaries are segmented with an accuracy of more than 80% as measured by the Dice similarity coefficient. Compared to traditional region-based active contours, the use of additional external forces based on the probability of depicting MKs improves segmentation performance and computational time by an average 5%.
Real-time 3D medical structure segmentation using fast evolving active contours
Wang, Xiaotao; Wang, Qiang; Hao, Zhihui; Xu, Kuanhong; Guo, Ping; Ren, Haibing; Jang, Wooyoung; Kim, Jung-bae
2014-03-01
Segmentation of 3D medical structures in real-time is an important as well as intractable problem for clinical applications due to the high computation and memory cost. We propose a novel fast evolving active contour model in this paper to reduce the requirements of computation and memory. The basic idea is to evolve the brief represented dynamic contour interface as far as possible per iteration. Our method encodes zero level set via a single unordered list, and evolves the list recursively by adding activated adjacent neighbors to its end, resulting in active parts of the zero level set moves far enough per iteration along with list scanning. To guarantee the robustness of this process, a new approximation of curvature for integer valued level set is proposed as the internal force to penalize the list smoothness and restrain the list continual growth. Besides, list scanning times are also used as an upper hard constraint to control the list growing. Together with the internal force, efficient regional and constrained external forces, whose computations are only performed along the unordered list, are also provided to attract the list toward object boundaries. Specially, our model calculates regional force only in a narrowband outside the zero level set and can efficiently segment multiple regions simultaneously as well as handle the background with multiple components. Compared with state-of-the-art algorithms, our algorithm is one-order of magnitude faster with similar segmentation accuracy and can achieve real-time performance for the segmentation of 3D medical structures on a standard PC.
Fast hybrid fitting energy-based active contour model for target detection
Institute of Scientific and Technical Information of China (English)
Dengwei Wang; Tianxu Zhang; Luxin Yan
2011-01-01
A novel hybrid fitting energy-based active contour model in the level set framework is proposed.The method fuses the region and boundary information of the target to achieve accurate and robust detection performance.A special extra term that penalizes the deviation of the level set function from a signed distance function is also included in our method. This term allows the time-consuming redistancing operation to be removed completely.Moreover,a fast unconditionally stable numerical scheme is introduced to solve the problem.Experimental results on real infrared images show that our method can improve target detection performance efficiently in terms of the number of iterations and the wasted central processing unit(CPU) time.
Directory of Open Access Journals (Sweden)
Manjunatha Hiremath
2014-06-01
Full Text Available Medical imaging is the technique and process used to create images of the human body or medical science. Digital image processing is the use of computer algorithms to perform image processing on digital images. Microscope image processing dates back a half century when it was realized that some of the techniques of image capture and manipulation, first developed for television, could also be applied to images captured through the microscope. This paper presents semi-automated segmentation and identification of adenovirus particles using active contour with multi grid segmentation model. The geometric features are employed to identify the adenovirus particles in digital microscopic image. The min-max, 3 rules are used for recognition of adenovirus particles. The results are compared with manual method obtained by microbiologist.
Flame front detection by active contour method from OH-PLIF images under microgravity
Institute of Scientific and Technical Information of China (English)
Yandong Tang; Yue Wang; Christian Eigenbrod
2006-01-01
@@ It is difficult and high-cost to detect flame fronts by laser-sheet diagnostics under microgravity (μg),thus image processing is critical to obtain valuable information from the raw data. In the present study,premixed V-flames were detected under μg by OH planar laser-induced fluorescence (PLIF) and an effective method based on active contour model (ACM) is presented for automatic detecting and tracking flame fronts in the PLIF images. ACM can effectively detect the flame front in the images with low contrast and noises. Compared with other methods of flame front detection, the advantage of this method is that the image smoothing and image enhancement are not necessary for the correct detection of flame fronts in raw PLIF images.
Mandal, Subhamoy; Razansky, Daniel
2015-01-01
Segmentation of biomedical images is essential for studying and characterizing anatomical structures, detection and evaluation of pathological tissues. Segmentation has been further shown to enhance the reconstruction performance in many tomographic imaging modalities by accounting for heterogeneities of the excitation field and tissue properties in the imaged region. This is particularly relevant in optoacoustic tomography, where discontinuities in the optical and acoustic tissue properties, if not properly accounted for, may result in deterioration of the imaging performance. Efficient segmentation of optoacoustic images is often hampered by the relatively low intrinsic contrast of large anatomical structures, which is further impaired by the limited angular coverage of some commonly employed tomographic imaging configurations. Herein, we analyze the performance of active contour models for boundary segmentation in cross-sectional optoacoustic tomography. The segmented mask is employed to construct a two co...
Ghayoumi Zadeh, Hossein; Haddadnia, Javad; Montazeri, Alimohammad
2016-05-01
The segmentation of cancerous areas in breast images is important for the early detection of disease. Thermal imaging has advantages, such as being non-invasive, non-radiation, passive, quick, painless, inexpensive, and non-contact. Imaging technique is the focus of this research. The proposed model in this paper is a combination of surf and corners that are very resistant. Obtained features are resistant to changes in rotation and revolution then with the help of active contours, this feature has been used for segmenting cancerous areas. Comparing the obtained results from the proposed method and mammogram show that proposed method is Accurate and appropriate. Benign and malignance of segmented areas are detected by Lyapunov exponent. Values obtained include TP=91.31%, FN=8.69%, FP=7.26%. The proposed method can classify those abnormally segmented areas of the breast, to the Benign and malignant cancer.
B-Spline Active Contour with Handling of Topology Changes for Fast Video Segmentation
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Frederic Precioso
2002-06-01
Full Text Available This paper deals with video segmentation for MPEG-4 and MPEG-7 applications. Region-based active contour is a powerful technique for segmentation. However most of these methods are implemented using level sets. Although level-set methods provide accurate segmentation, they suffer from large computational cost. We propose to use a regular B-spline parametric method to provide a fast and accurate segmentation. Our B-spline interpolation is based on a fixed number of points 2j depending on the level of the desired details. Through this spatial multiresolution approach, the computational cost of the segmentation is reduced. We introduce a length penalty. This results in improving both smoothness and accuracy. Then we show some experiments on real-video sequences.
SOM-based nonlinear least squares twin SVM via active contours for noisy image segmentation
Xie, Xiaomin; Wang, Tingting
2017-02-01
In this paper, a nonlinear least square twin support vector machine (NLSTSVM) with the integration of active contour model (ACM) is proposed for noisy image segmentation. Efforts have been made to seek the kernel-generated surfaces instead of hyper-planes for the pixels belonging to the foreground and background, respectively, using the kernel trick to enhance the performance. The concurrent self organizing maps (SOMs) are applied to approximate the intensity distributions in a supervised way, so as to establish the original training sets for the NLSTSVM. Further, the two sets are updated by adding the global region average intensities at each iteration. Moreover, a local variable regional term rather than edge stop function is adopted in the energy function to ameliorate the noise robustness. Experiment results demonstrate that our model holds the higher segmentation accuracy and more noise robustness.
Adaptively Active Contours Based on Variable Exponent Lp(|∇I| Norm for Image Segmentation
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Wenying Wen
2012-01-01
Full Text Available We propose an Lp(|∇I|-based adaptively active contours model for image segmentation which is derived from the well-known Chan-Vese (C-V model. Unlike the C-V model, the proposed model uses the Lp(|∇I| (p(|∇I|>2 norm instead of the L2 norm to define the external energy and incorporates an extra internal energy into the overall energy. Due to the variable exponent p(|∇I| which could fit the image gradient information adaptively, the proposed Lp(|∇I|-based model has the hope of segmenting those images with low contrast and blurred boundaries. Experimental results show that the proposed model with p(|∇I|>2 really can effectively and quickly segment those images with low contrast and blurred boundaries.
Fast Image Segmentation Based on a Two-Stage Geometrical Active Contour
Institute of Scientific and Technical Information of China (English)
肖昌炎; 张素; 陈亚珠
2005-01-01
A fast two-stage geometric active contour algorithm for image segmentation is developed. First, the Eikonal equation problem is quickly solved using an improved fast sweeping method, and a criterion of local minimum of area gradient (LMAG) is presented to extract the optimal arrival time. Then, the final time function is passed as an initial state to an area and length minimizing flow model, which adjusts the interface more accurately and prevents it from leaking. For object with complete and salient edge, using the first stage only is able to obtain an ideal result, and this results in a time complexity of O(M), where M is the number of points in each coordinate direction. Both stages are needed for convoluted shapes, but the computation cost can be drastically reduced. Efficiency of the algorithm is verified in segmentation experiments of real images with different feature.
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Cary, Theodore W.; Sultan, Laith R.; Sehgal, Chandra M., E-mail: sehgalc@uphs.upenn.edu [Department of Radiology, Perelman School of Medicine, University of Pennsylvania, Philadelphia, Pennsylvania 19104 (United States); Reamer, Courtney B.; Mohler, Emile R. [Department of Medicine, Division of Cardiovascular Medicine, Section of Vascular Medicine, Perelman School of Medicine, University of Pennsylvania, Philadelphia, Pennsylvania 19104 (United States)
2014-02-15
Purpose: To use feed-forward active contours (snakes) to track and measure brachial artery vasomotion on ultrasound images recorded in both transverse and longitudinal views; and to compare the algorithm's performance in each view. Methods: Longitudinal and transverse view ultrasound image sequences of 45 brachial arteries were segmented by feed-forward active contour (FFAC). The segmented regions were used to measure vasomotion artery diameter, cross-sectional area, and distention both as peak-to-peak diameter and as area. ECG waveforms were also simultaneously extracted frame-by-frame by thresholding a running finite-difference image between consecutive images. The arterial and ECG waveforms were compared as they traced each phase of the cardiac cycle. Results: FFAC successfully segmented arteries in longitudinal and transverse views in all 45 cases. The automated analysis took significantly less time than manual tracing, but produced superior, well-behaved arterial waveforms. Automated arterial measurements also had lower interobserver variability as measured by correlation, difference in mean values, and coefficient of variation. Although FFAC successfully segmented both the longitudinal and transverse images, transverse measurements were less variable. The cross-sectional area computed from the longitudinal images was 27% lower than the area measured from transverse images, possibly due to the compression of the artery along the image depth by transducer pressure. Conclusions: FFAC is a robust and sensitive vasomotion segmentation algorithm in both transverse and longitudinal views. Transverse imaging may offer advantages over longitudinal imaging: transverse measurements are more consistent, possibly because the method is less sensitive to variations in transducer pressure during imaging.
Geodesically Complete Universe
Bars, Itzhak
2011-01-01
This talk is about solving cosmological equations analytically without approximations, and discovering new phenomena that could not be noticed with approximate solutions. We found all the solutions of the Friedmann equations for a specific model, including all the zero-size-bounce solutions that do not violate the null energy condition, as well as all the finite-size-bounce solutions, and then discovered model independent phenomena. Among them is the notion of geodesic completeness for the geometry of the universe. From this we learned a few new general lessons for cosmology. Among them is that anisotropy provides a model independent attractor mechanism to some specific initial values for cosmological fields, and that there is a period of antigravity in the history of the universe. The results are obtained only at the classical gravity level. Effects of quantum gravity or string theory are unknown, they are not even formulated, so there are new theoretical challenges.
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Mehmet KILIÇ
2016-09-01
Full Text Available The notion of geodesic, which may be regarded as an extension of the line segment in Euclidean geometry to the space we study in, has an important place in many branches of geometry, such as Riemannian geometry, Metric geometry, to name but a few. In this article, the concept of geodesic in a metric space will be introduced, then geodesics in the space (Rn, d1 will be characterized. Furthermore, some examples will be presented to demonstrate the effectiveness of the main result.
Automatic corpus callosum segmentation using a deformable active Fourier contour model
Vachet, Clement; Yvernault, Benjamin; Bhatt, Kshamta; Smith, Rachel G.; Gerig, Guido; Cody Hazlett, Heather; Styner, Martin
2012-03-01
The corpus callosum (CC) is a structure of interest in many neuroimaging studies of neuro-developmental pathology such as autism. It plays an integral role in relaying sensory, motor and cognitive information from homologous regions in both hemispheres. We have developed a framework that allows automatic segmentation of the corpus callosum and its lobar subdivisions. Our approach employs constrained elastic deformation of flexible Fourier contour model, and is an extension of Szekely's 2D Fourier descriptor based Active Shape Model. The shape and appearance model, derived from a large mixed population of 150+ subjects, is described with complex Fourier descriptors in a principal component shape space. Using MNI space aligned T1w MRI data, the CC segmentation is initialized on the mid-sagittal plane using the tissue segmentation. A multi-step optimization strategy, with two constrained steps and a final unconstrained step, is then applied. If needed, interactive segmentation can be performed via contour repulsion points. Lobar connectivity based parcellation of the corpus callosum can finally be computed via the use of a probabilistic CC subdivision model. Our analysis framework has been integrated in an open-source, end-to-end application called CCSeg both with a command line and Qt-based graphical user interface (available on NITRC). A study has been performed to quantify the reliability of the semi-automatic segmentation on a small pediatric dataset. Using 5 subjects randomly segmented 3 times by two experts, the intra-class correlation coefficient showed a superb reliability (0.99). CCSeg is currently applied to a large longitudinal pediatric study of brain development in autism.
Region-based geometric active contour for classification using hyperspectral remote sensing images
Yan, Lin
2011-12-01
The high spectral resolution of hyperspectral imaging (HSI) systems greatly enhances the capabilities of discrimination, identification and quantification of objects of different materials from remote sensing images, but they also bring challenges to the processing and analysis of HSI data. One issue is the high computation cost and the curse of dimensionality associated with the high dimensions of HSI data. A second issue is how to effectively utilize the information including spectral and spatial information embedded in HSI data. Geometric Active Contour (GAC) is a widely used image segmentation method that utilizes the geometric information of objects within images. One category of GAC models, the region-based GAC models (RGAC), have good potential for remote sensing image processing because they use both spectral and geometry information in images are robust to initial contour placement. These models have been introduced to target extractions and classifications on remote sensing images. However, there are some restrictions on the applications of the RGAC models on remote sensing. First, the heavy involvement of iterative contour evolutions makes GAC applications time-consuming and inconvenient to use. Second, the current RGAC models must be based on a certain distance metric and the performance of RGAC classifiers are restricted by the performance of the employed distance metrics. According to the key features of the RGAC models analyzed in this dissertation, a classification framework is developed for remote sensing image classifications using the RGAC models. This framework allows the RGAC models to be combined with conventional pixel-based classifiers to promote them to spectral-spatial classifiers and also greatly reduces the iterations of contour evolutions. An extended Chan-Vese (ECV) model is proposed that is able to incorporate the widely used distance metrics in remote sensing image processing. A new type of RGAC model, the edge-oriented RGAC model
Ali, Sahirzeeshan; Veltri, Robert; Epstein, Jonathan I; Christudass, Christhunesa; Madabhushi, Anant
2011-01-01
Shape based active contours have emerged as a natural solution to overlap resolution. However, most of these shape-based methods are computationally expensive. There are instances in an image where no overlapping objects are present and applying these schemes results in significant computational overhead without any accompanying, additional benefit. In this paper we present a novel adaptive active contour scheme (AdACM) that combines boundary and region based energy terms with a shape prior in a multi level set formulation. To reduce the computational overhead, the shape prior term in the variational formulation is only invoked for those instances in the image where overlaps between objects are identified; these overlaps being identified via a contour concavity detection scheme. By not having to invoke all 3 terms (shape, boundary, region) for segmenting every object in the scene, the computational expense of the integrated active contour model is dramatically reduced, a particularly relevant consideration when multiple objects have to be segmented on very large histopathological images. The AdACM was employed for the task of segmenting nuclei on 80 prostate cancer tissue microarray images. Morphological features extracted from these segmentations were found to able to discriminate different Gleason grade patterns with a classification accuracy of 84% via a Support Vector Machine classifier. On average the AdACM model provided 100% savings in computational times compared to a non-optimized hybrid AC model involving a shape prior.
Adams, Gareth; Vick, G. W., III; Bordelon, Cassius; Insull, William; Morrisett, Joel
2002-05-01
A new algorithm for measuring carotid artery volumes and estimating atherosclerotic plaque volumes from MRI images has been developed and validated using pressure-perfusion-fixed cadaveric carotid arteries. Our method uses an active contour algorithm with the generalized gradient vector field force as the external force to localize the boundaries of the artery on each MRI cross-section. Plaque volume is estimated by an automated algorithm based on estimating the normal wall thickness for each branch of the carotid. Triplicate volume measurements were performed by a single observer on thirty-eight pairs of cadaveric carotid arteries. The coefficient of variance (COV) was used to quantify measurement reproducibility. Aggregate volumes were computed for nine contiguous slices bounding the carotid bifurcation. The median (mean +/- SD) COV for the 76 aggregate arterial volumes was 0.93% (1.47% +/- 1.52%) for the lumen volume, 0.95% (1.06% +/- 0.67%) for the total artery volume, and 4.69% (5.39% +/- 3.97%) for the plaque volume. These results indicate that our algorithm provides repeatable measures of arterial volumes and a repeatable estimate of plaque volume of cadaveric carotid specimens through analysis of MRI images. The algorithm also significantly decreases the amount of time necessary to generate these measurements.
Target Region Location Based on Texture Analysis and Active Contour Model
Institute of Scientific and Technical Information of China (English)
YANG Zhaoxuan; BAI Zhuofu; WU Jiapeng; CHEN Yang
2009-01-01
Traditional texture region location methods with Gabor features are often limited in the selection of Gabor filters and fail to deal with the target which contains both texture and non-texture parts.Thus,to solve this problem,a two-step new model was proposed.In the first step,the original features extracted by Gabor filters are applied to training a self-organizing map (SOM) neural network and a novel merging scheme is presented to achieve the clustering.A back propagation (BP) network is used as a classifier to locate the target region approximately.In the second step,Chan-Vese active contour model is applied to detecting the boundary of the target region accurately and morphological processing is used to create a connected domain whose convex hull can cover the target region.In the experiments,the proposed method is demonstrated accurate and robust in localizing target on texture database and practical barcode location system as well.
Segmentation of Brain Tumors in MRI Images Using Three-Dimensional Active Contour without Edge
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Ali M. Hasan
2016-11-01
Full Text Available Brain tumor segmentation in magnetic resonance imaging (MRI is considered a complex procedure because of the variability of tumor shapes and the complexity of determining the tumor location, size, and texture. Manual tumor segmentation is a time-consuming task highly prone to human error. Hence, this study proposes an automated method that can identify tumor slices and segment the tumor across all image slices in volumetric MRI brain scans. First, a set of algorithms in the pre-processing stage is used to clean and standardize the collected data. A modified gray-level co-occurrence matrix and Analysis of Variance (ANOVA are employed for feature extraction and feature selection, respectively. A multi-layer perceptron neural network is adopted as a classifier, and a bounding 3D-box-based genetic algorithm is used to identify the location of pathological tissues in the MRI slices. Finally, the 3D active contour without edge is applied to segment the brain tumors in volumetric MRI scans. The experimental dataset consists of 165 patient images collected from the MRI Unit of Al-Kadhimiya Teaching Hospital in Iraq. Results of the tumor segmentation achieved an accuracy of 89% ± 4.7% compared with manual processes.
Dermoscopic diagnosis of melanoma in a 4D space constructed by active contour extracted features.
Mete, Mutlu; Sirakov, Nikolay Metodiev
2012-10-01
Dermoscopy, also known as epiluminescence microscopy, is a major imaging technique used in the assessment of melanoma and other diseases of skin. In this study we propose a computer aided method and tools for fast and automated diagnosis of malignant skin lesions using non-linear classifiers. The method consists of three main stages: (1) skin lesion features extraction from images; (2) features measurement and digitization; and (3) skin lesion binary diagnosis (classification), using the extracted features. A shrinking active contour (S-ACES) extracts color regions boundaries, the number of colors, and lesion's boundary, which is used to calculate the abrupt boundary. Quantification methods for measurements of asymmetry and abrupt endings in skin lesions are elaborated to approach the second stage of the method. The total dermoscopy score (TDS) formula of the ABCD rule is modeled as linear support vector machines (SVM). Further a polynomial SVM classifier is developed. To validate the proposed framework a dataset of 64 lesion images were selected from a collection with a ground truth. The lesions were classified as benign or malignant by the TDS based model and the SVM polynomial classifier. Comparing the results, we showed that the latter model has a better f-measure then the TDS-based model (linear classifier) in the classification of skin lesions into two groups, malignant and benign. Copyright © 2012 Elsevier Ltd. All rights reserved.
Tasel, Serdar F; Mumcuoglu, Erkan U; Hassanpour, Reza Z; Perkins, Guy
2016-06-01
Recent studies reveal that mitochondria take substantial responsibility in cellular functions that are closely related to aging diseases caused by degeneration of neurons. These studies emphasize that the membrane and crista morphology of a mitochondrion should receive attention in order to investigate the link between mitochondrial function and its physical structure. Electron microscope tomography (EMT) allows analysis of the inner structures of mitochondria by providing highly detailed visual data from large volumes. Computerized segmentation of mitochondria with minimum manual effort is essential to accelerate the study of mitochondrial structure/function relationships. In this work, we improved and extended our previous attempts to detect and segment mitochondria from transmission electron microcopy (TEM) images. A parabolic arc model was utilized to extract membrane structures. Then, curve energy based active contours were employed to obtain roughly outlined candidate mitochondrial regions. Finally, a validation process was applied to obtain the final segmentation data. 3D extension of the algorithm is also presented in this paper. Our method achieved an average F-score performance of 0.84. Average Dice Similarity Coefficient and boundary error were measured as 0.87 and 14nm respectively.
Tasel, Serdar F.; Mumcuoglu, Erkan U.; Hassanpour, Reza Z.; Perkins, Guy
2017-01-01
Recent studies reveal that mitochondria take substantial responsibility in cellular functions that are closely related to aging diseases caused by degeneration of neurons. These studies emphasize that the membrane and crista morphology of a mitochondrion should receive attention in order to investigate the link between mitochondrial function and its physical structure. Electron microscope tomography (EMT) allows analysis of the inner structures of mitochondria by providing highly detailed visual data from large volumes. Computerized segmentation of mitochondria with minimum manual effort is essential to accelerate the study of mitochondrial structure/function relationships. In this work, we improved and extended our previous attempts to detect and segment mitochondria from transmission electron microcopy (TEM) images. A parabolic arc model was utilized to extract membrane structures. Then, curve energy based active contours were employed to obtain roughly outlined candidate mitochondrial regions. Finally, a validation process was applied to obtain the final segmentation data. 3D extension of the algorithm is also presented in this paper. Our method achieved an average F-score performance of 0.84. Average Dice Similarity Coefficient and boundary error were measured as 0.87 and 14 nm respectively. PMID:26956730
Geodesics and Geodesic Deviation for Impulsive Gravitational Waves
Steinbauer, R
1998-01-01
The geometry of impulsive pp-waves is explored via the analysis of the geodesic and geodesic deviation equation using the distributional form of the metric. The geodesic equation involves formally ill-defined products of distributions due to the nonlinearity of the equations and the presence of the Dirac delta distribution. Thus, strictly speaking, it cannot be treated within Schwartz's linear theory of distributions. To cope with this problem we proceed by first regularizing the delta singularity, then solving the regularized equation within classical smooth functions and, finally, obtaining a distributional, regularization-idependent limit as solution to the original problem. We also treat the Jacobi equation which, despite being linear in the deviation vector field, involves even more delicate singular expressions, like the ``square'' of the delta distribution. Again the same regularization procedure provides us with a perfectly well behaved smooth regularization and a regularization-independent distributi...
Zakeri, Fahimeh Sadat; Setarehdan, Seyed Kamaledin; Norouzi, Somayye
2017-03-25
Segmentation of the arterial wall boundaries from intravascular ultrasound images is an important image processing task in order to quantify arterial wall characteristics such as shape, area, thickness and eccentricity. Since manual segmentation of these boundaries is a laborious and time consuming procedure, many researchers attempted to develop (semi-) automatic segmentation techniques as a powerful tool for educational and clinical purposes in the past but as yet there is no any clinically approved method in the market. This paper presents a deterministic-statistical strategy for automatic media-adventitia border detection by a fourfold algorithm. First, a smoothed initial contour is extracted based on the classification in the sparse representation framework which is combined with the dynamic directional convolution vector field. Next, an active contour model is utilized for the propagation of the initial contour toward the interested borders. Finally, the extracted contour is refined in the leakage, side branch openings and calcification regions based on the image texture patterns. The performance of the proposed algorithm is evaluated by comparing the results to those manually traced borders by an expert on 312 different IVUS images obtained from four different patients. The statistical analysis of the results demonstrates the efficiency of the proposed method in the media-adventitia border detection with enough consistency in the leakage and calcification regions. Copyright © 2017 Elsevier Ltd. All rights reserved.
Discrete geodesics and cellular automata
Arrighi, Pablo
2015-01-01
This paper proposes a dynamical notion of discrete geodesics, understood as straightest trajectories in discretized curved spacetime. The notion is generic, as it is formulated in terms of a general deviation function, but readily specializes to metric spaces such as discretized pseudo-riemannian manifolds. It is effective: an algorithm for computing these geodesics naturally follows, which allows numerical validation---as shown by computing the perihelion shift of a Mercury-like planet. It is consistent, in the continuum limit, with the standard notion of timelike geodesics in a pseudo-riemannian manifold. Whether the algorithm fits within the framework of cellular automata is discussed at length. KEYWORDS: Discrete connection, parallel transport, general relativity, Regge calculus.
On radial geodesic forcing of zonal modes
Kendl, Alexander
2011-01-01
The elementary local and global influence of geodesic field line curvature on radial dispersion of zonal modes in magnetised plasmas is analysed with a primitive drift wave turbulence model. A net radial geodesic forcing of zonal flows and geodesic acoustic modes can not be expected in any closed toroidal magnetic confinement configuration, since the flux surface average of geodesic curvature identically vanishes. Radial motion of poloidally elongated zonal jets may occur in the presence of g...
Geodesic components for guided wave optics
Chang, W. L.; Voges, E.
1980-10-01
Geodesic elements for beam displacement, beam deflection, beam splitting, and imaging are derived for passive optical devices. The elements are suitable in particular for multimode devices, and a complex performance is achievable by the combined action of different geodesic structures on a common substrate. A general theorem of Toraldo di Francia (1957) on the geodesics of rotational surfaces is used to develop geodesic components for beam deflection and multiple beam splitting in a prescribed manner.
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Mohamed Ben Gharsallah
2015-01-01
Full Text Available Radiography is one of the most used techniques in weld defect inspection. Weld defect detection becomes a complex task when uneven illumination and low contrast characterize radiographic images. In this paper we propose a new active contour based level set method for weld defect detection in radiography images. An off-center saliency map exploited as a feature to represent image pixels is embedded into a region energy minimization function to guide the level set active contour to defects boundaries. The aim behind using salient feature is that a small defect can frequently attract attention of human eyes which permits enhancing defects in low contrasted image. Experiment results on different weld radiographic images with various kinds of defects show robustness and good performance of the proposed approach comparing with other segmentation methods.
Yip, Moira
1989-01-01
Argues that contour tones in East Asian languages behave as melodic units consisting of a root node [upper] dominating a branching specification. It is also argued that, with upper as the tonal root node, no more than two rising or falling tones will contrast underlying. (49 references) (JL)
Nonlinear quasimodes near elliptic periodic geodesics
Albin, Pierre; Marzuola, Jeremy L; Thomann, Laurent
2011-01-01
We consider the nonlinear Schr\\"odinger equation on a compact manifold near an elliptic periodic geodesic. Using a geometric optics construction, we construct quasimodes to a nonlinear stationary problem which are highly localized near the periodic geodesic. We show the nonlinear Schr\\"odinger evolution of such a quasimode remains localized near the geodesic, at least for short times.
Xu, Jun; Monaco, James P; Madabhushi, Anant
2010-01-01
In this paper we present a Markov random field (MRF) driven region-based active contour model (MaRACel) for medical image segmentation. State-of-the-art region-based active contour (RAC) models assume that every spatial location in the image is statistically independent of the others, thereby ignoring valuable contextual information. To address this shortcoming we incorporate a MRF prior into the AC model, further generalizing Chan & Vese's (CV) and Rousson and Deriche's (RD) AC models. This incorporation requires a Markov prior that is consistent with the continuous variational framework characteristic of active contours; consequently, we introduce a continuous analogue to the discrete Potts model. To demonstrate the effectiveness of MaRACel, we compare its performance to those of the CV and RD AC models in the following scenarios: (1) the qualitative segmentation of a cancerous lesion in a breast DCE-MR image and (2) the qualitative and quantitative segmentations of prostatic acini (glands) in 200 histopathology images. Across the 200 prostate needle core biopsy histology images, MaRACel yielded an average sensitivity, specificity, and positive predictive value of 71%, 95%, 74% with respect to the segmented gland boundaries; the CV and RD models have corresponding values of 19%, 81%, 20% and 53%, 88%, 56%, respectively.
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
On the path space over a compact Riemannian manifold, the global existence and the global uniqueness of the quasi-invariant geodesic flows with respect to a negative Markov connection are obtained in this paper. The results answer affirmatively a left problem of Li.
Jing, Yu; Wang, Yaxuan; Liu, Jianxin; Liu, Zhaoxia
2015-08-01
Edge detection is a crucial method for the location and quantity estimation of oil slick when oil spills on the sea. In this paper, we present a robust active contour edge detection algorithm for oil spill remote sensing images. In the proposed algorithm, we define a local Gaussian data fitting energy term with spatially varying means and variances, and this data fitting energy term is introduced into a global minimization active contour (GMAC) framework. The energy function minimization is achieved fast by a dual formulation of the weighted total variation norm. The proposed algorithm avoids the existence of local minima, does not require the definition of initial contour, and is robust to weak boundaries, high noise and severe intensity inhomogeneity exiting in oil slick remote sensing images. Furthermore, the edge detection of oil slick and the correction of intensity inhomogeneity are simultaneously achieved via the proposed algorithm. The experiment results have shown that a superior performance of proposed algorithm over state-of-the-art edge detection algorithms. In addition, the proposed algorithm can also deal with the special images with the object and background of the same intensity means but different variances.
On General Plane Fronted Waves. Geodesics
Candela, A M; Sánchez, M; Sanchez, Miguel
2003-01-01
A general class of Lorentzian metrics, $M_0 x R^2$, $ds^2 = + 2 du dv + H(x,u) du^2$, with $(M_0, $ any Riemannian manifold, is introduced in order to generalize classical exact plane fronted waves. Here, we start a systematic study of their main geodesic properties: geodesic completeness, geodesic connectedness and multiplicity, causal character of connecting geodesics. These results are independent of the possibility of a full integration of geodesic equations. Variational and geometrical techniques are applied systematically. In particular, we prove that the asymptotic behavior of $H(x,u)$ with $x$ at infinity determines many properties of geodesics. Essentially, a subquadratic growth of $H$ ensures geodesic completeness and connectedness, while the critical situation appears when $H(x,u)$ behaves in some direction as $|x|^2$, as in the classical model of exact gravitational waves
Feed-forward active contour analysis for improved brachial artery reactivity testing.
Pugliese, Daniel N; Sehgal, Chandra M; Sultan, Laith R; Reamer, Courtney B; Mohler, Emile R
2016-08-01
The object of this study was to utilize a novel feed-forward active contour (FFAC) algorithm to find a reproducible technique for analysis of brachial artery reactivity. Flow-mediated dilation (FMD) is an important marker of vascular endothelial function but has not been adopted for widespread clinical use given its technical limitations, including inter-observer variability and differences in technique across clinical sites. We developed a novel FFAC algorithm with the goal of validating a more reliable standard. Forty-six healthy volunteers underwent FMD measurement according to the standard technique. Ultrasound videos lasting 5-10 seconds each were obtained pre-cuff inflation and at minutes 1 through 5 post-cuff deflation in longitudinal and transverse views. Automated segmentation using the FFAC algorithm with initial boundary definition from three different observers was used to analyze the images to measure diameter/cross-sectional area over the cardiac cycle. The %FMD was calculated for average, minimum, and maximum diameters/areas. Using the FFAC algorithm, the population-specific coefficient of variation (CV) at end-diastole was 3.24% for transverse compared to 9.96% for longitudinal measurements; the subject-specific CV was 15.03% compared to 57.41%, respectively. For longitudinal measurements made via the conventional method, the population-specific CV was 4.77% and subject-specific CV was 117.79%. The intraclass correlation coefficient (ICC) for transverse measurements was 0.97 (95% CI: 0.95-0.98) compared to 0.90 (95% CI: 0.84-0.94) for longitudinal measurements with FFAC and 0.72 (95% CI: 0.51-0.84) for conventional measurements. In conclusion, transverse views using the novel FFAC method provide less inter-observer variability than traditional longitudinal views. Improved reproducibility may allow adoption of FMD testing in a clinical setting. The FFAC algorithm is a robust technique that should be evaluated further for its ability to replace the
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Bogunovic, Hrvoje; Pozo, Jose Maria; Villa-Uriol, Maria Cruz [Center for Computational Imaging and Simulation Technologies in Biomedicine (CISTIB), Universitat Pompeu Fabra (UPF) and Networking Biomedical Research Center on Bioengineering, Biomaterials and Nanomedicine - CIBER-BBN, Barcelona 08018 (Spain); and others
2011-01-15
Purpose: To evaluate the suitability of an improved version of an automatic segmentation method based on geodesic active regions (GAR) for segmenting cerebral vasculature with aneurysms from 3D x-ray reconstruction angiography (3DRA) and time of flight magnetic resonance angiography (TOF-MRA) images available in the clinical routine. Methods: Three aspects of the GAR method have been improved: execution time, robustness to variability in imaging protocols, and robustness to variability in image spatial resolutions. The improved GAR was retrospectively evaluated on images from patients containing intracranial aneurysms in the area of the Circle of Willis and imaged with two modalities: 3DRA and TOF-MRA. Images were obtained from two clinical centers, each using different imaging equipment. Evaluation included qualitative and quantitative analyses of the segmentation results on 20 images from 10 patients. The gold standard was built from 660 cross-sections (33 per image) of vessels and aneurysms, manually measured by interventional neuroradiologists. GAR has also been compared to an interactive segmentation method: isointensity surface extraction (ISE). In addition, since patients had been imaged with the two modalities, we performed an intermodality agreement analysis with respect to both the manual measurements and each of the two segmentation methods. Results: Both GAR and ISE differed from the gold standard within acceptable limits compared to the imaging resolution. GAR (ISE) had an average accuracy of 0.20 (0.24) mm for 3DRA and 0.27 (0.30) mm for TOF-MRA, and had a repeatability of 0.05 (0.20) mm. Compared to ISE, GAR had a lower qualitative error in the vessel region and a lower quantitative error in the aneurysm region. The repeatability of GAR was superior to manual measurements and ISE. The intermodality agreement was similar between GAR and the manual measurements. Conclusions: The improved GAR method outperformed ISE qualitatively as well as
Stability of Geodesically Complete Cosmologies
Creminelli, Paolo; Santoni, Luca; Trincherini, Enrico
2016-01-01
We study the stability of spatially flat FRW solutions which are geodesically complete, i.e. for which one can follow null (graviton) geodesics both in the past and in the future without ever encountering singularities. This is the case of NEC-violating cosmologies such as smooth bounces or solutions which approach Minkowski in the past. We study the EFT of linear perturbations around a solution of this kind, including the possibility of multiple fields and fluids. One generally faces a gradient instability which can be avoided only if the operator $~^{(3)}{R} \\delta N~$ is present and its coefficient changes sign along the evolution. This operator (typical of beyond-Horndeski theories) does not lead to extra degrees of freedom, but cannot arise starting from any theory with second-order equations of motion. The change of sign of this operator prevents to set it to zero with a generalised disformal transformation.
Indian Academy of Sciences (India)
D B Lortan; S D Maharaj; N K Dadhich
2001-06-01
We investigate the propagation equations for the expansion, vorticity and shear for perfect ﬂuid space-times which are geodesic. It is assumed that space-time admits a conformal Killing vector which is inheriting so that ﬂuid ﬂow lines are mapped conformally. Simple constraints on the electric and magnetic parts of the Weyl tensor are found for conformal symmetry. For homothetic vectors the vorticity and shear are free; they vanish for nonhomothetic vectors. We prove a conjecture for conformal symmetries in the special case of inheriting geodesic ﬂows: there exist no proper conformal Killing vectors ( ≠ 0) for perfect ﬂuids except for Robertson–Walker space-times. For a nonhomothetic vector ﬁeld the propagation of the quantity ln () along the integral curves of the symmetry vector is homogeneous.
MHD modeling on geodesic grids
Florinski, V; Balsara, D S; Meyer, C
2013-01-01
This report describes a new magnetohydrodynamic numerical model based on a hexagonal spherical geodesic grid. The model is designed to simulate astrophysical flows of partially ionized plasmas around a central compact object, such as a star or a planet with a magnetic field. The geodesic grid, produced by a recursive subdivision of a base platonic solid (an icosahedron), is free from control volume singularities inherent in spherical polar grids. Multiple populations of plasma and neutral particles, coupled via charge-exchange interactions, can be simulated simultaneously with this model. Our numerical scheme uses piecewise linear reconstruction on a surface of a sphere in a local two-dimensional "Cartesian" frame. The code employs HLL-type approximate Riemann solvers and includes facilities to control the divergence of magnetic field and maintain pressure positivity. Several test solutions are discussed, including a problem of an interaction between the solar wind and the local interstellar medium, and a sim...
Stability of geodesically complete cosmologies
Energy Technology Data Exchange (ETDEWEB)
Creminelli, Paolo [Abdus Salam International Centre for Theoretical Physics (ICTP),Strada Costiera 11, Trieste, 34151 (Italy); Pirtskhalava, David [Institute of Physics, École Polytechnique Fédérale de Lausanne,Lausanne, CH-1015 (Switzerland); Santoni, Luca; Trincherini, Enrico [Scuola Normale Superiore,Piazza dei Cavalieri 7, Pisa, 56126 (Italy); INFN - Sezione di Pisa,Largo B. Pontecorvo 3, Pisa, 56100 (Italy)
2016-11-22
We study the stability of spatially flat FRW solutions which are geodesically complete, i.e. for which one can follow null (graviton) geodesics both in the past and in the future without ever encountering singularities. This is the case of NEC-violating cosmologies such as smooth bounces or solutions which approach Minkowski in the past. We study the EFT of linear perturbations around a solution of this kind, including the possibility of multiple fields and fluids. One generally faces a gradient instability which can be avoided only if the operator {sup (3)} RδN is present and its coefficient changes sign along the evolution. This operator (typical of beyond-Horndeski theories) does not lead to extra degrees of freedom, but cannot arise starting from any theory with second-order equations of motion. The change of sign of this operator prevents to set it to zero with a generalised disformal transformation.
Active Contours for Multispectral Images With Non-Homogeneous Sub-Regions
2005-09-16
often referred to Heaviside function. 16 descent directions by an artificial time t is given by ∂φ(x, y) ∂t = δ(φ(x, y))κ(φ(x, y)). (3.13) The contour...Robotics: Control, Sensing, Vision, and Inteligence . New York: McGraw-Hill, 1987. [22] W. Snyder and H. Qi, Machine Vision. Cambridge University Press...International Conference on Artificial Neural Net- works, (U.K.), September 1992. [33] M. Symonds, W. Snyder, and P. Santago, “Segmentation of phase-coded
Geodesic congruences in warped spacetimes
Ghosh, Suman; Kar, Sayan
2010-01-01
In this article, we explore the kinematics of timelike geodesic congruences in warped five dimensional bulk spacetimes, with and without thick or thin branes. We begin our investigations with the simplest case, namely geodesic flows in the Randall--Sundrum AdS (Anti de Sitter) geometry without and with branes. Analytical expressions for the expansion scalar are obtained and the effect of including one or more thin branes (i.e. a background which is a slice of AdS spacetime) on its evolution, is pointed out. Subsequently, we move on to studying such congruences in more general warped bulk geometries with a cosmological thick brane and a time-dependent extra dimensional scale. Using the analytical expressions for the velocity field components, we interpret the expansion, shear and rotation (ESR) along the flows. The evolution of a cross-sectional area orthogonal to the congruence, as seen from a local observer's point of view, is also shown graphically. Finally, the Raychaudhuri and geodesic equations in the ba...
Constrained Geodesic Centers of a Simple Polygon
Oh, Eunjin; Son, Wanbin; Ahn, Hee-Kap
2016-01-01
For any two points in a simple polygon P, the geodesic distance between them is the length of the shortest path contained in P that connects them. A geodesic center of a set S of sites (points) with respect to P is a point in P that minimizes the geodesic distance to its farthest site. In many realistic facility location problems, however, the facilities are constrained to lie in feasible regions. In this paper, we show how to compute the geodesic centers constrained to a set of line segment...
Directory of Open Access Journals (Sweden)
Ajay Khunteta
2016-01-01
Full Text Available Active contour models, colloquially known as snakes, are quite popular for several applications such as object boundary detection, image segmentation, object tracking, and classification via energy minimization. While energy minimization may be accomplished using traditional optimization methods, approaches based on nature-inspired evolutionary algorithms have been developed in recent years. One such evolutionary algorithm that has been used extensively in active contours is the particle swarm optimization (PSO. However, conventional PSO converges slowly and gets trapped in local minimum easily which results in inaccurate detection of concavities in the object boundary. This is taken care of by using proposed multiswarm PSO in which a swarm is set for every control point in the snake and then all the swarms search for their best points simultaneously through information sharing among them. The performance of the multiswarm PSO-based search process is further enhanced by using dynamic adaptation of the inertia factor. In this paper, we propose using a set of fuzzy rules to adjust the inertia weight on the basis of the current normalized snake energy and the current value of inertia. Experimental results demonstrate the effectiveness of the proposed method compared to conventional approaches.
Sun, Min; Chen, Xinjian; Zhang, Zhiqiang; Ma, Chiyuan
2017-02-01
Accurate volume measurements of pituitary adenoma are important to the diagnosis and treatment for this kind of sellar tumor. The pituitary adenomas have different pathological representations and various shapes. Particularly, in the case of infiltrating to surrounding soft tissues, they present similar intensities and indistinct boundary in T1-weighted (T1W) magnetic resonance (MR) images. Then the extraction of pituitary adenoma from MR images is still a challenging task. In this paper, we propose an interactive method to segment the pituitary adenoma from brain MR data, by combining graph cuts based active contour model (GCACM) and random walk algorithm. By using the GCACM method, the segmentation task is formulated as an energy minimization problem by a hybrid active contour model (ACM), and then the problem is solved by the graph cuts method. The region-based term in the hybrid ACM considers the local image intensities as described by Gaussian distributions with different means and variances, expressed as maximum a posteriori probability (MAP). Random walk is utilized as an initialization tool to provide initialized surface for GCACM. The proposed method is evaluated on the three-dimensional (3-D) T1W MR data of 23 patients and compared with the standard graph cuts method, the random walk method, the hybrid ACM method, a GCACM method which considers global mean intensity in region forces, and a competitive region-growing based GrowCut method planted in 3D Slicer. Based on the experimental results, the proposed method is superior to those methods.
Li, Bin; Chen, Kan; Tian, Lianfang; Yeboah, Yao; Ou, Shanxing
2013-01-01
The segmentation and detection of various types of nodules in a Computer-aided detection (CAD) system present various challenges, especially when (1) the nodule is connected to a vessel and they have very similar intensities; (2) the nodule with ground-glass opacity (GGO) characteristic possesses typical weak edges and intensity inhomogeneity, and hence it is difficult to define the boundaries. Traditional segmentation methods may cause problems of boundary leakage and "weak" local minima. This paper deals with the above mentioned problems. An improved detection method which combines a fuzzy integrated active contour model (FIACM)-based segmentation method, a segmentation refinement method based on Parametric Mixture Model (PMM) of juxta-vascular nodules, and a knowledge-based C-SVM (Cost-sensitive Support Vector Machines) classifier, is proposed for detecting various types of pulmonary nodules in computerized tomography (CT) images. Our approach has several novel aspects: (1) In the proposed FIACM model, edge and local region information is incorporated. The fuzzy energy is used as the motivation power for the evolution of the active contour. (2) A hybrid PMM Model of juxta-vascular nodules combining appearance and geometric information is constructed for segmentation refinement of juxta-vascular nodules. Experimental results of detection for pulmonary nodules show desirable performances of the proposed method.
Liu, Bo; Cheng, H D; Huang, Jianhua; Tian, Jiawei; Liu, Jiafeng; Tang, Xianglong
2009-08-01
Because of its complicated structure, low signal/noise ratio, low contrast and blurry boundaries, fully automated segmentation of a breast ultrasound (BUS) image is a difficult task. In this paper, a novel segmentation method for BUS images without human intervention is proposed. Unlike most published approaches, the proposed method handles the segmentation problem by using a two-step strategy: ROI generation and ROI segmentation. First, a well-trained texture classifier categorizes the tissues into different classes, and the background knowledge rules are used for selecting the regions of interest (ROIs) from them. Second, a novel probability distance-based active contour model is applied for segmenting the ROIs and finding the accurate positions of the breast tumors. The active contour model combines both global statistical information and local edge information, using a level set approach. The proposed segmentation method was performed on 103 BUS images (48 benign and 55 malignant). To validate the performance, the results were compared with the corresponding tumor regions marked by an experienced radiologist. Three error metrics, true-positive ratio (TP), false-negative ratio (FN) and false-positive ratio (FP) were used for measuring the performance of the proposed method. The final results (TP = 91.31%, FN = 8.69% and FP = 7.26%) demonstrate that the proposed method can segment BUS images efficiently, quickly and automatically.
Contour polygonal approximation using shortest path in networks
Backes, André Ricardo; Bruno, Odemir Martinez
2013-01-01
Contour polygonal approximation is a simplified representation of a contour by line segments, so that the main characteristics of the contour remain in a small number of line segments. This paper presents a novel method for polygonal approximation based on the Complex Networks theory. We convert each point of the contour into a vertex, so that we model a regular network. Then we transform this network into a Small-World Complex Network by applying some transformations over its edges. By analyzing of network properties, especially the geodesic path, we compute the polygonal approximation. The paper presents the main characteristics of the method, as well as its functionality. We evaluate the proposed method using benchmark contours, and compare its results with other polygonal approximation methods.
Quantum frictionless trajectories versus geodesics
Barbado, Luis C; Garay, Luis J
2015-01-01
Moving particles outside a star will generally experience quantum friction caused by Unruh radiation reaction. There exist however radial trajectories that lack this effect (in the outgoing radiation sector, and ignoring back-scattering). They turn out to have the property that the variations of the Doppler and the gravitational shifts compensate each other. They are not geodesics, and their proper acceleration obeys an inverse square law, which means that could in principle be generated by outgoing stellar radiation. In the case of a black hole emitting Hawking radiation, this may lead to a buoyancy scenario. The ingoing radiation sector has little effect and seems to slow down the fall even further.
基于区域统计的遥感地物半自动提取%Target Extraction Based on Polygon Statistical Region-based Active Contour
Institute of Scientific and Technical Information of China (English)
张煜; 陈文龙; 魏思奇; 叶松; 曹波
2016-01-01
Active contour is an important method to segment images. Its segmentation strategy is usually edge-based or region-based and based on the contour energy minimization. But the classical active contour is difficult to deal with the region which has weak edges or is in the complicated background. In this paper, we implement an im-proved statistical region-based active contour and propose a strategy to extract region of interest by polygon. Within the family of exponential probability density function, statistical region-based active contour can run by fast algo-rithm. We give details of the realization of the algorithm and simplify the contour by the minimum description length. Experiment results illustrate the efficiency of our proposed method in contour extraction.%由于遥感影像的复杂性,面状地物的提取存在着一定的难度.区域统计活动轮廓法有着较强的稳定性和适应性,且在一定的概率密度分布下存在着快速的算法.针对交互式操作的特点,提出了一种基于多边形区域统计活动轮廓的面状地物半自动提取方法,并使用最小描述长度法简化面状地物的轮廓.实验结果显示了该方法在面状地物提取问题上的有效性和实用性.
A Note on Geodesically Bounded -Trees
Directory of Open Access Journals (Sweden)
Kirk WA
2010-01-01
Full Text Available It is proved that a complete geodesically bounded -tree is the closed convex hull of the set of its extreme points. It is also noted that if is a closed convex geodesically bounded subset of a complete -tree and if a nonexpansive mapping satisfies then has a fixed point. The latter result fails if is only continuous.
On Non-commutative Geodesic Motion
Ulhoa, S C; Santos, A F
2013-01-01
In this work we study the geodesic motion on a noncommutative space-time. As a result we find a non-commutative geodesic equation and then we derive corrections of the deviation angle per revolution in terms of the non-commutative parameter when we specify the problem of Mercury's perihelion. In this way, we estimate the noncommutative parameter based in experimental data.
On non-commutative geodesic motion
Ulhoa, S. C.; Amorim, R. G. G.; Santos, A. F.
2014-07-01
In this work we study the geodesic motion on a noncommutative space-time. As a result we find a non-commutative geodesic equation and then we derive corrections of the deviation angle per revolution in terms of the non-commutative parameter when we specify the problem of Mercury's perihelion. In this way, we estimate the noncommutative parameter based in experimental data.
Duay, Valérie; Bresson, Xavier; Castro, Javier Sanchez; Pollo, Claudio; Cuadra, Meritxell Bach; Thiran, Jean-Philippe
2008-01-01
This paper presents a new non parametric atlas registration framework, derived from the optical flow model and the active contour theory, applied to automatic subthalamic nucleus (STN) targeting in deep brain stimulation (DBS) surgery. In a previous work, we demonstrated that the STN position can be predicted based on the position of surrounding visible structures, namely the lateral and third ventricles. A STN targeting process can thus be obtained by registering these structures of interest between a brain atlas and the patient image. Here we aim to improve the results of the state of the art targeting methods and at the same time to reduce the computational time. Our simultaneous segmentation and registration model shows mean STN localization errors statistically similar to the most performing registration algorithms tested so far and to the targeting expert's variability. Moreover, the computational time of our registration method is much lower, which is a worthwhile improvement from a clinical point of view.
Zheng, Qiang; Li, Honglun; Fan, Baode; Wu, Shuanhu; Xu, Jindong
2017-09-01
Active contour model (ACM) has been one of the most widely utilized methods in magnetic resonance (MR) brain image segmentation because of its ability of capturing topology changes. However, most of the existing ACMs only consider single-slice information in MR brain image data, i.e., the information used in ACMs based segmentation method is extracted only from one slice of MR brain image, which cannot take full advantage of the adjacent slice images' information, and cannot satisfy the local segmentation of MR brain images. In this paper, a novel ACM is proposed to solve the problem discussed above, which is based on multi-variate local Gaussian distribution and combines the adjacent slice images' information in MR brain image data to satisfy segmentation. The segmentation is finally achieved through maximizing the likelihood estimation. Experiments demonstrate the advantages of the proposed ACM over the single-slice ACM in local segmentation of MR brain image series.
Energy Technology Data Exchange (ETDEWEB)
Liu, Hui; Liu, Yiping; Qiu, Tianshuang [Department of Biomedical Engineering, Dalian University of Technology, Dalian 116024 (China); Zhao, Zuowei, E-mail: liuhui@dlut.edu.cn [Second Affiliated Hospital, Dalian Medical University, Dalian 116027 (China); Zhang, Lina [Department of Radiology, First Affiliated Hospital, Dalian Medical University, Dalian 116027 (China)
2014-08-15
Purpose: To develop and evaluate a computerized semiautomatic segmentation method for accurate extraction of three-dimensional lesions from dynamic contrast-enhanced magnetic resonance images (DCE-MRIs) of the breast. Methods: The authors propose a new background distribution-based active contour model using level set (BDACMLS) to segment lesions in breast DCE-MRIs. The method starts with manual selection of a region of interest (ROI) that contains the entire lesion in a single slice where the lesion is enhanced. Then the lesion volume from the volume data of interest, which is captured automatically, is separated. The core idea of BDACMLS is a new signed pressure function which is based solely on the intensity distribution combined with pathophysiological basis. To compare the algorithm results, two experienced radiologists delineated all lesions jointly to obtain the ground truth. In addition, results generated by other different methods based on level set (LS) are also compared with the authors’ method. Finally, the performance of the proposed method is evaluated by several region-based metrics such as the overlap ratio. Results: Forty-two studies with 46 lesions that contain 29 benign and 17 malignant lesions are evaluated. The dataset includes various typical pathologies of the breast such as invasive ductal carcinoma, ductal carcinomain situ, scar carcinoma, phyllodes tumor, breast cysts, fibroadenoma, etc. The overlap ratio for BDACMLS with respect to manual segmentation is 79.55% ± 12.60% (mean ± s.d.). Conclusions: A new active contour model method has been developed and shown to successfully segment breast DCE-MRI three-dimensional lesions. The results from this model correspond more closely to manual segmentation, solve the weak-edge-passed problem, and improve the robustness in segmenting different lesions.
Anatomy of geodesic Witten diagrams
Chen, Heng-Yu; Kuo, En-Jui; Kyono, Hideki
2017-05-01
We revisit the so-called "Geodesic Witten Diagrams" (GWDs) [1], proposed to be the holographic dual configuration of scalar conformal partial waves, from the perspectives of CFT operator product expansions. To this end, we explicitly consider three point GWDs which are natural building blocks of all possible four point GWDs, discuss their gluing procedure through integration over spectral parameter, and this leads us to a direct identification with the integral representation of CFT conformal partial waves. As a main application of this general construction, we consider the holographic dual of the conformal partial waves for external primary operators with spins. Moreover, we consider the closely related "split representation" for the bulk to bulk spinning propagator, to demonstrate how ordinary scalar Witten diagram with arbitrary spin exchange, can be systematically decomposed into scalar GWDs. We also discuss how to generalize to spinning cases.
Quantum frictionless trajectories versus geodesics
Barbado, Luis C.; Barceló, Carlos; Garay, Luis J.
2015-10-01
Moving particles outside a star will generally experience quantum friction caused by the Unruh radiation reaction. There exist however radial trajectories that lack this effect (in the outgoing radiation sector, and ignoring backscattering). Along these trajectories, observers perceive just stellar emission, without further contribution from the Unruh effect. They turn out to have the property that the variations of the Doppler and the gravitational shifts compensate each other. They are not geodesics, and their proper acceleration obeys an inverse square law, which means that it could in principle be generated by outgoing stellar radiation. In the case of a black hole emitting Hawking radiation, this may lead to a buoyancy scenario. The ingoing radiation sector has little effect and seems to slow down the fall even further.
Simplifying Massive Contour Maps
DEFF Research Database (Denmark)
Arge, Lars; Deleuran, Lasse Kosetski; Mølhave, Thomas;
2012-01-01
We present a simple, efficient and practical algorithm for constructing and subsequently simplifying contour maps from massive high-resolution DEMs, under some practically realistic assumptions on the DEM and contours.......We present a simple, efficient and practical algorithm for constructing and subsequently simplifying contour maps from massive high-resolution DEMs, under some practically realistic assumptions on the DEM and contours....
Null Geodesics in Brane World Scenarios
Institute of Scientific and Technical Information of China (English)
ZHANG Li-Feng; ZHANG Yuan-Zhong
2004-01-01
We study the null bulk geodesic motion in the brane world in which the bulk metric has an un-stabilized extra spatial dimension. We find that the null bulk geodesic motion as observed on the 3-brane with Z2 symmetry would be a timelike geodesic motion even though there exists an extra non-gravitational force in contrast with the case of the stabilized extra spatial dimension. In other words the presence of the extra non-gravitational force would not violate thc Z2 symmetry.
Line graphs and $2$-geodesic transitivity
Devillers, Alice; Jin, Wei; Li, Cai Heng; Praeger, Cheryl E.
2012-01-01
For a graph $\\Gamma$, a positive integer $s$ and a subgroup $G\\leq \\Aut(\\Gamma)$, we prove that $G$ is transitive on the set of $s$-arcs of $\\Gamma$ if and only if $\\Gamma$ has girth at least $2(s-1)$ and $G$ is transitive on the set of $(s-1)$-geodesics of its line graph. As applications, we first prove that the only non-complete locally cyclic $2$-geodesic transitive graphs are the complete multipartite graph $K_{3[2]}$ and the icosahedron. Secondly we classify 2-geodesic transitive graphs ...
Multichannel image regularization using anisotropic geodesic filtering
Energy Technology Data Exchange (ETDEWEB)
Grazzini, Jacopo A [Los Alamos National Laboratory
2010-01-01
This paper extends a recent image-dependent regularization approach introduced in aiming at edge-preserving smoothing. For that purpose, geodesic distances equipped with a Riemannian metric need to be estimated in local neighbourhoods. By deriving an appropriate metric from the gradient structure tensor, the associated geodesic paths are constrained to follow salient features in images. Following, we design a generalized anisotropic geodesic filter; incorporating not only a measure of the edge strength, like in the original method, but also further directional information about the image structures. The proposed filter is particularly efficient at smoothing heterogeneous areas while preserving relevant structures in multichannel images.
Separable geodesic action slicing in stationary spacetimes
Bini, Donato; Jantzen, Robert T
2014-01-01
A simple observation about the action for geodesics in a stationary spacetime with separable geodesic equations leads to a natural class of slicings of that spacetime whose orthogonal geodesic trajectories represent freely falling observers. The time coordinate function can then be taken to be the observer proper time, leading to a unit lapse function. This explains some of the properties of the original Painlev\\'e-Gullstrand coordinates on the Schwarzschild spacetime and their generalization to the Kerr-Newman family of spacetimes, reproducible also locally for the G\\"odel spacetime. For the static spherically symmetric case the slicing can be chosen to be intrinsically flat with spherically symmetric geodesic observers, leaving all the gravitational field information in the shift vector field.
Ramified optimal transportation in geodesic metric spaces
Xia, Qinglan
2009-01-01
An optimal transport path may be viewed as a geodesic in the space of probability measures under a suitable family of metrics. This geodesic may exhibit a tree-shaped branching structure in many applications such as trees, blood vessels, draining and irrigation systems. Here, we extend the study of ramified optimal transportation between probability measures from Euclidean spaces to a geodesic metric space. We investigate the existence as well as the behavior of optimal transport paths under various properties of the metric such as completeness, doubling, or curvature upper boundedness. We also introduce the transport dimension of a probability measure on a complete geodesic metric space, and show that the transport dimension of a probability measure is bounded above by the Minkowski dimension and below by the Hausdorff dimension of the measure. Moreover, we introduce a metric, called "the dimensional distance", on the space of probability measures. This metric gives a geometric meaning to the transport dimen...
Dissertation: Geodesics of Random Riemannian Metrics
LaGatta, Tom
2011-01-01
We introduce Riemannian First-Passage Percolation (Riemannian FPP) as a new model of random differential geometry, by considering a random, smooth Riemannian metric on $\\mathbb R^d$. We are motivated in our study by the random geometry of first-passage percolation (FPP), a lattice model which was developed to model fluid flow through porous media. By adapting techniques from standard FPP, we prove a shape theorem for our model, which says that large balls under this metric converge to a deterministic shape under rescaling. As a consequence, we show that smooth random Riemannian metrics are geodesically complete with probability one. In differential geometry, geodesics are curves which locally minimize length. They need not do so globally: consider great circles on a sphere. For lattice models of FPP, there are many open questions related to minimizing geodesics; similarly, it is interesting from a geometric perspective when geodesics are globally minimizing. In the present study, we show that for any fixed st...
On superintegrable systems closed to geodesic motion
Tsiganov, A V
1997-01-01
In this work we consider superintegrable systems in the classical $r$-matrix method. By using other authomorphisms of the loop algebras we construct new superintegrable systems with rational potentials from geodesic motion on $R^{2n}$.
On geodesic deviation in Schwarzschild spacetime
Philipp, Dennis; Laemmerzahl, Claus; Deshpande, Kaustubh
2015-01-01
For metrology, geodesy and gravimetry in space, satellite based instruments and measurement techniques are used and the orbits of the satellites as well as possible deviations between nearby ones are of central interest. The measurement of this deviation itself gives insight into the underlying structure of the spacetime geometry, which is curved and therefore described by the theory of general relativity (GR). In the context of GR, the deviation of nearby geodesics can be described by the Jacobi equation that is a result of linearizing the geodesic equation around a known reference geodesic with respect to the deviation vector and the relative velocity. We review the derivation of this Jacobi equation and restrict ourselves to the simple case of the spacetime outside a spherically symmetric mass distribution and circular reference geodesics to find solutions by projecting the Jacobi equation on a parallel propagated tetrad as done by Fuchs. Using his results, we construct solutions of the Jacobi equation for...
Geodesics in the static Mallett spacetime
Olum, Ken D
2010-01-01
Mallett has exhibited a cylindrically symmetric spacetime containing closed timelike curves produced by a light beam circulating around a line singularity. I analyze the static version of this spacetime obtained by setting the intensity of the light to zero. Some null geodesics can escape to infinity, but all timelike geodesics in this spacetime originate and terminate at the singularity. Freely falling matter originally at rest quickly attains relativistic velocity inward and is destroyed at the singularity.
Characterization of Null Geodesics on Kerr Spacetimes
Paganini, Claudio F; Oancea, Marius A
2016-01-01
We consider null geodesics in the domain of outer communication of a sub-extremal Kerr spacetime. We show, that most fundamental properties of null geodesics can be represented in one plot. In particular one can see immediately that the ergoregion and trapping are separated in phase space. Furthermore we show that from the point of view of any timelike observer outside of a black hole, trapping can be understood as a smooth set of spacelike directions on the observers' celestial sphere.
Photon Geodesics in FRW Cosmologies
Bikwa, Ojeh; Shevchuk, Andrew
2011-01-01
The Hubble radius is a particular manifestation of the Universe's gravitational horizon, R_h(t_0)=c/H_0, the distance beyond which physical processes remain unobservable to us at the present epoch. Based on recent observations of the cosmic microwave background (CMB) with WMAP, and ground-based and HST searches for Type Ia supernovae, we now know that R_h(t_0)~13.5 Glyr. This coincides with the maximum distance (ct_0~13.7 Glyr) light could have traveled since the big bang. However, the physical meaning of R_h is still not universally understood or accepted, though the minimalist view holds that it is merely the proper distance at which the rate of cosmic recession reaches the speed of light c. Even so, it is sometimes argued that we can see light from sources beyond R_h, the claim being that R_h lies at a redshift of only ~2, whereas the CMB was produced at a much greater redshift (~1100). In this paper, we build on recent developments with the gravitational radius by actually calculating null geodesics for a...
Institute of Scientific and Technical Information of China (English)
XIANG; Kainan
2001-01-01
［1］ Cruzeiro, A. B., Malliavin, P., Renormalized differential geometry on path spaces: Structural equation, curvature, J. Funct. Anal., 1996, 139: 119-181.［2］ Stroock, D. W., Some thoughts about Riemannian structures on path spaces, preprint, 1996.［3］ Driver, B., A Cameron-Martin type quasi-invariance theorem for Brownian motion on a compact manifold, J. Funct. Anal., 1992, 109: 272-376.［4］ Enchev, O., Stroock, D. W., Towards a Riemannian geometry on the path space over a Riemannian manifold, J. Funct. Anal., 1995, 134: 392-416.［5］ Hsu, E., Quasi-invariance of the Wiener measure on the path space over a compact Riemannian manifold, J. Funct. Anal., 1995, 134: 417-450.［6］ Lyons, T. J., Qian, Z. M., A class of vector fields on path space, J.Funct. Anal., 1997, 145: 205-223.［7］ Li, X. D., Existence and uniqueness of geodesics on path spaces, J. Funct. Anal., to be published.［8］ Driver, B., Towards calculus and geometry on path spaces, in Proc. Symp. Pure and Appl. Math. 57 (ed. Cranston, M., Pinsky, M.), Cornell: AMS, 1993, 1995.
Seow, P.; Win, M. T.; Wong, J. H. D.; Abdullah, N. A.; Ramli, N.
2016-03-01
Gliomas are tumours arising from the interstitial tissue of the brain which are heterogeneous, infiltrative and possess ill-defined borders. Tumour subregions (e.g. solid enhancing part, edema and necrosis) are often used for tumour characterisation. Tumour demarcation into substructures facilitates glioma staging and provides essential information. Manual segmentation had several drawbacks that include laborious, time consuming, subjected to intra and inter-rater variability and hindered by diversity in the appearance of tumour tissues. In this work, active contour model (ACM) was used to segment the solid enhancing subregion of the tumour. 2D brain image acquisition data using 3T MRI fast spoiled gradient echo sequence in post gadolinium of four histologically proven high-grade glioma patients were obtained. Preprocessing of the images which includes subtraction and skull stripping were performed and then followed by ACM segmentation. The results of the automatic segmentation method were compared against the manual delineation of the tumour by a trainee radiologist. Both results were further validated by an experienced neuroradiologist and a brief quantitative evaluations (pixel area and difference ratio) were performed. Preliminary results of the clinical data showed the potential of ACM model in the application of fast and large scale tumour segmentation in medical imaging.
Directory of Open Access Journals (Sweden)
Chao Ma
2017-01-01
Full Text Available Segmentation of the left atrium (LA from cardiac magnetic resonance imaging (MRI datasets is of great importance for image guided atrial fibrillation ablation, LA fibrosis quantification, and cardiac biophysical modelling. However, automated LA segmentation from cardiac MRI is challenging due to limited image resolution, considerable variability in anatomical structures across subjects, and dynamic motion of the heart. In this work, we propose a combined random forests (RFs and active contour model (ACM approach for fully automatic segmentation of the LA from cardiac volumetric MRI. Specifically, we employ the RFs within an autocontext scheme to effectively integrate contextual and appearance information from multisource images together for LA shape inferring. The inferred shape is then incorporated into a volume-scalable ACM for further improving the segmentation accuracy. We validated the proposed method on the cardiac volumetric MRI datasets from the STACOM 2013 and HVSMR 2016 databases and showed that it outperforms other latest automated LA segmentation methods. Validation metrics, average Dice coefficient (DC and average surface-to-surface distance (S2S, were computed as 0.9227±0.0598 and 1.14±1.205 mm, versus those of 0.6222–0.878 and 1.34–8.72 mm, obtained by other methods, respectively.
Luo, Gongning
2017-01-01
Segmentation of the left atrium (LA) from cardiac magnetic resonance imaging (MRI) datasets is of great importance for image guided atrial fibrillation ablation, LA fibrosis quantification, and cardiac biophysical modelling. However, automated LA segmentation from cardiac MRI is challenging due to limited image resolution, considerable variability in anatomical structures across subjects, and dynamic motion of the heart. In this work, we propose a combined random forests (RFs) and active contour model (ACM) approach for fully automatic segmentation of the LA from cardiac volumetric MRI. Specifically, we employ the RFs within an autocontext scheme to effectively integrate contextual and appearance information from multisource images together for LA shape inferring. The inferred shape is then incorporated into a volume-scalable ACM for further improving the segmentation accuracy. We validated the proposed method on the cardiac volumetric MRI datasets from the STACOM 2013 and HVSMR 2016 databases and showed that it outperforms other latest automated LA segmentation methods. Validation metrics, average Dice coefficient (DC) and average surface-to-surface distance (S2S), were computed as 0.9227 ± 0.0598 and 1.14 ± 1.205 mm, versus those of 0.6222–0.878 and 1.34–8.72 mm, obtained by other methods, respectively. PMID:28316992
Embedded Real-Time Architecture for Level-Set-Based Active Contours
Directory of Open Access Journals (Sweden)
Dejnožková Eva
2005-01-01
Full Text Available Methods described by partial differential equations have gained a considerable interest because of undoubtful advantages such as an easy mathematical description of the underlying physics phenomena, subpixel precision, isotropy, or direct extension to higher dimensions. Though their implementation within the level set framework offers other interesting advantages, their vast industrial deployment on embedded systems is slowed down by their considerable computational effort. This paper exploits the high parallelization potential of the operators from the level set framework and proposes a scalable, asynchronous, multiprocessor platform suitable for system-on-chip solutions. We concentrate on obtaining real-time execution capabilities. The performance is evaluated on a continuous watershed and an object-tracking application based on a simple gradient-based attraction force driving the active countour. The proposed architecture can be realized on commercially available FPGAs. It is built around general-purpose processor cores, and can run code developed with usual tools.
Ocean Sediment Thickness Contours
National Oceanic and Atmospheric Administration, Department of Commerce — Ocean sediment thickness contours in 200 meter intervals for water depths ranging from 0 - 18,000 meters. These contours were derived from a global sediment...
Kansas Data Access and Support Center — The Kansas Tagged Vector Contour (TVC) dataset consists of digitized contours from the 7.5 minute topographic quadrangle maps. Coverage for the state is incomplete....
Federal Emergency Management Agency, Department of Homeland Security — This layer contains contours that were derived from the digital terrain model made up of irregularly spaced mass points and breaklines. The contours are 5 foot...
High Resolution Elevation Contours
Minnesota Department of Natural Resources — This dataset contains contours generated from high resolution data sources such as LiDAR. Generally speaking this data is 2 foot or less contour interval.
基于区域显著性的活动轮廓分割模型%An Active Contour Model Based on Region Saliency for Image Segmentation
Institute of Scientific and Technical Information of China (English)
白雪飞; 王文剑; 梁吉业
2012-01-01
Image segmentation refers to the process of partitioning an image into some no-overlapped meaningful regions, and it is vital for the higher-level image processing such as image analysis and understanding. During the past few decades, there has been substantial progress in the field of image segmentation and its application. Recently, segmentation algorithms based on active contours have been given wide attention by many internal and foreign researchers due to their variable forms, flexible structure and excellent performance. However, most available active contour models suffer from lacking adaptive initial contour and priori information of target region. In this paper, an active contour model for image segmentation based on visual saliency detection mechanism is proposed. Firstly, priori shape information of target objects in input images which is used to describe the initial curve adaptively is extracted with the visual saliency detection method in order to reduce the influence of initial contour position. Furthermore, the proposed active model can segment images adaptively and automatically, and the segmented results accord with the property of human visual perception. Experimental results demonstrate that the proposed model can achieve better segmentation results than some traditional active contour models. Meanwhile it requires less iteration and is much more computationally efficient.%提出一种新的活动轮廓分割模型,结合视觉显著性检测机制自动获取待分割图像中目标物体的先验形状信息,并自适应地构造初始轮廓,从而降低了初始轮廓位置对分割算法的影响.同时实现了活动轮廓模型对图像的自适应分割和自动分割,使得分割结果更符合人类视觉感知特性.实验结果表明,该模型有较好的分割效果,迭代次数少,且运行时间短.
Craniofacial Reconstruction Evaluation by Geodesic Network
Directory of Open Access Journals (Sweden)
Junli Zhao
2014-01-01
Full Text Available Craniofacial reconstruction is to estimate an individual’s face model from its skull. It has a widespread application in forensic medicine, archeology, medical cosmetic surgery, and so forth. However, little attention is paid to the evaluation of craniofacial reconstruction. This paper proposes an objective method to evaluate globally and locally the reconstructed craniofacial faces based on the geodesic network. Firstly, the geodesic networks of the reconstructed craniofacial face and the original face are built, respectively, by geodesics and isogeodesics, whose intersections are network vertices. Then, the absolute value of the correlation coefficient of the features of all corresponding geodesic network vertices between two models is taken as the holistic similarity, where the weighted average of the shape index values in a neighborhood is defined as the feature of each network vertex. Moreover, the geodesic network vertices of each model are divided into six subareas, that is, forehead, eyes, nose, mouth, cheeks, and chin, and the local similarity is measured for each subarea. Experiments using 100 pairs of reconstructed craniofacial faces and their corresponding original faces show that the evaluation by our method is roughly consistent with the subjective evaluation derived from thirty-five persons in five groups.
Iterated index formulae for closed geodesics with applications
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
In this paper, various precise iteration equalities and inequalities of Morse indices for the closed geodesics are established. As applications of these formulae, multiplicity results of closed geodesics on some Riemannian manifolds are proved.
Orbifold Riemann surfaces and geodesic algebras
Energy Technology Data Exchange (ETDEWEB)
Chekhov, L O [Steklov Mathematical Institute, Moscow (Russian Federation)], E-mail: chekhov@mi.ras.ru
2009-07-31
We study the Teichmueller theory of Riemann surfaces with orbifold points of order 2 using the fat graph technique. The previously developed technique of quantization, classical and quantum mapping-class group transformations, and Poisson and quantum algebras of geodesic functions is applicable to the surfaces with orbifold points. We describe classical and quantum braid group relations for particular sets of geodesic functions corresponding to A{sub n} and D{sub n} algebras and describe their central elements for the Poisson and quantum algebras.
'Proper acceleration' of a null geodesic in curved spacetime
Tian Gui Hua; Liang Can Bin
2002-01-01
Given a null geodesic in Minkowski spacetime, there exists a one-parameter family of observers in 'hyperbolic' motion which approaches the null geodesic as the parameter x sub 0 approaches zero. It is well known that the proper acceleration of the observers in the family approaches infinity as their world line approaches the null geodesic. The main purpose of this paper is to generalize this result to future-complete null geodesics in curved spacetimes.
A Conformal Extension Theorem based on Null Conformal Geodesics
Lübbe, Christian
2008-01-01
In this article we describe the formulation of null geodesics as null conformal geodesics and their description in the tractor formalism. A conformal extension theorem through an isotropic singularity is proven by requiring the boundedness of the tractor curvature and its derivatives to sufficient order along a congruence of null conformal geodesic. This article extends earlier work by Tod and Luebbe.
Energy Technology Data Exchange (ETDEWEB)
Morozov, Dmitriy; Weber, Gunther H.
2014-03-31
Topological techniques provide robust tools for data analysis. They are used, for example, for feature extraction, for data de-noising, and for comparison of data sets. This chapter concerns contour trees, a topological descriptor that records the connectivity of the isosurfaces of scalar functions. These trees are fundamental to analysis and visualization of physical phenomena modeled by real-valued measurements. We study the parallel analysis of contour trees. After describing a particular representation of a contour tree, called local{global representation, we illustrate how di erent problems that rely on contour trees can be solved in parallel with minimal communication.
Zhang, Shuangxi
2014-01-01
The past studies treated the perturbed distribution of circulating electrons as adiabatic one when studying the dispersion relation of electrostatic geodesic acoustic mode(GAM). In this paper, the flow of electron geodesic current (FEGC) is added to modify this adiabatic distribution. Based on the drift kinetic theory, it is found that FEGC obviously increases the magnitude of the standard GAM's frequency and reduces its damping rate. The increase of frequency results from the contribution of...
Geodesic curvature driven surface microdomain formation.
Adkins, Melissa R; Zhou, Y C
2017-09-15
Lipid bilayer membranes are not uniform and clusters of lipids in a more ordered state exist within the generally disorder lipid milieu of the membrane. These clusters of ordered lipids microdomains are now referred to as lipid rafts. Recent reports attribute the formation of these microdomains to the geometrical and molecular mechanical mismatch of lipids of different species on the boundary. Here we introduce the geodesic curvature to characterize the geometry of the domain boundary, and develop a geodesic curvature energy model to describe the formation of these microdomains as a result of energy minimization. Our model accepts the intrinsic geodesic curvature of any binary lipid mixture as an input, and will produce microdomains of the given geodesic curvature as demonstrated by three sets of numerical simulations. Our results are in contrast to the surface phase separation predicted by the classical surface Cahn-Hilliard equation, which tends to generate large domains as a result of the minimizing line tension. Our model provides a direct and quantified description of the structure inhomogeneity of lipid bilayer membrane, and can be coupled to the investigations of biological processes on membranes for which such inhomogeneity plays essential roles.
Geodesic curvature driven surface microdomain formation
Adkins, Melissa R.; Zhou, Y. C.
2017-09-01
Lipid bilayer membranes are not uniform and clusters of lipids in a more ordered state exist within the generally disorder lipid milieu of the membrane. These clusters of ordered lipids microdomains are now referred to as lipid rafts. Recent reports attribute the formation of these microdomains to the geometrical and molecular mechanical mismatch of lipids of different species on the boundary. Here we introduce the geodesic curvature to characterize the geometry of the domain boundary, and develop a geodesic curvature energy model to describe the formation of these microdomains as a result of energy minimization. Our model accepts the intrinsic geodesic curvature of any binary lipid mixture as an input, and will produce microdomains of the given geodesic curvature as demonstrated by three sets of numerical simulations. Our results are in contrast to the surface phase separation predicted by the classical surface Cahn-Hilliard equation, which tends to generate large domains as a result of the minimizing line tension. Our model provides a direct and quantified description of the structure inhomogeneity of lipid bilayer membrane, and can be coupled to the investigations of biological processes on membranes for which such inhomogeneity plays essential roles.
Patra Yosandha, Fiet; Adi, Kusworo; Edi Widodo, Catur
2017-06-01
In this research, calculation process of the lung cancer volume of target based on computed tomography (CT) thorax images was done. Volume of the target calculation was done in purpose to treatment planning system in radiotherapy. The calculation of the target volume consists of gross tumor volume (GTV), clinical target volume (CTV), planning target volume (PTV) and organs at risk (OAR). The calculation of the target volume was done by adding the target area on each slices and then multiply the result with the slice thickness. Calculations of area using of digital image processing techniques with active contour segmentation method. This segmentation for contouring to obtain the target volume. The calculation of volume produced on each of the targets is 577.2 cm3 for GTV, 769.9 cm3 for CTV, 877.8 cm3 for PTV, 618.7 cm3 for OAR 1, 1,162 cm3 for OAR 2 right, and 1,597 cm3 for OAR 2 left. These values indicate that the image processing techniques developed can be implemented to calculate the lung cancer target volume based on CT thorax images. This research expected to help doctors and medical physicists in determining and contouring the target volume quickly and precisely.
Analytical solution methods for geodesic motion
Hackmann, Eva
2015-01-01
The observation of the motion of particles and light near a gravitating object is until now the only way to explore and to measure the gravitational field. In the case of exact black hole solutions of the Einstein equations the gravitational field is characterized by a small number of parameters which can be read off from the observables related to the orbits of test particles and light rays. Here we review the state of the art of analytical solutions of geodesic equations in various space--times. In particular we consider the four dimensional black hole space--times of Pleba\\'nski--Demia\\'nski type as far as the geodesic equation separates, as well as solutions in higher dimensions, and also solutions with cosmic strings. The mathematical tools used are elliptic and hyperelliptic functions. We present a list of analytic solutions which can be found in the literature.
Geodesic Acoustic Propagation and Ballooning Mode Formalism
Li, M. B.; Diamond, P. H.; Young, G. G.; Arakawa, M.
2005-10-01
Relevance of ballooning formalism (BMF) in nonlinear interaction of toroidal electromagnetic drift waves in the presence of zonal flows and Geodesic Acoustic Oscillation (GAO) is critically examined from a physical argument of radial propagation of wave packets. To achieve the quasi-translational invariance of poloidal harmonics which is necessary for the BMF, the geodesic curvature induced transfer [1] of fluctuation energy in radial direction should occur faster than the time scale of physical interest. Of course, this does not happen necessarily in drift-Alfven (DALF) turbulence simulations [2]. This observation casts considerable doubts on the applicability of various codes based on the BMF concept to nonlinear electromagnetic problems. [1] B. Scott, Phys. Letters A 320 (2003) 53. [2] B. Scott, New J. Phys 7 (2005) 92.
Free of centrifugal acceleration spacetime - Geodesics
Culetu, Hristu
2013-01-01
A static spacetime with no centrifugal repulsion, previously studied by Dadhich, is investigate in this paper. The source of curvature is considered to be an anisotropic fluid with $\\rho = -p_{r}$ and constant angular pressures. The positive parameter from the line-element is interpreted as the invariant acceleration of a static observer. We found that the Tolman-Komar gravitational energy is finite everywhere. The timelike and null geodesics of the spacetime are examined.
On the Geodesic Nature of Wegner's Flow
Itto, Yuichi; Abe, Sumiyoshi
2008-01-01
Wegner's method of flow equations offers a useful tool for diagonalizing a given Hamiltonian and is widely used in various branches of quantum physics. Here, generalizing this method, a condition is derived, under which the corresponding flow of a quantum state becomes geodesic in a submanifold of the projective Hilbert space, independently of specific initial conditions. This implies the geometric optimality of the present method as an algorithm of generating stationary states. The result is...
Relativistic and non-relativistic geodesic equations
Energy Technology Data Exchange (ETDEWEB)
Giambo' , R.; Mangiarotti, L.; Sardanashvily, G. [Camerino Univ., Camerino, MC (Italy). Dipt. di Matematica e Fisica
1999-07-01
It is shown that any dynamic equation on a configuration space of non-relativistic time-dependent mechanics is associated with connections on its tangent bundle. As a consequence, every non-relativistic dynamic equation can be seen as a geodesic equation with respect to a (non-linear) connection on this tangent bundle. Using this fact, the relationships between relativistic and non-relativistic equations of motion is studied.
Studying null and time-like geodesics in the classroom
Müller, Thomas; 10.1088/0143-0807/32/3/011
2011-01-01
In a first course of general relativity it is usually quite difficult for students to grasp the concept of a geodesic. It is supposed to be straight (auto-parallel) and yet it 'looks' curved. In these situations it is very useful to have some explicit examples available which show the different behaviour of geodesics. In this paper we present the GeodesicViewer, an interactive tool for studying the behaviour of geodesics in many different space-times. The geodesics can be represented in several ways, depending on the space-time in question. The use of a local reference frame and 'Cartesian-like' coordinates helps the students to develop some intuition in various situations. We present the various features of the GeodesicViewer in the form of readily formulated exercises for the students.
Sivalingam, Udhayaraj; Wels, Michael; Rempfler, Markus; Grosskopf, Stefan; Suehling, Michael; Menze, Bjoern H.
2016-03-01
In this paper, we present a fully automated approach to coronary vessel segmentation, which involves calcification or soft plaque delineation in addition to accurate lumen delineation, from 3D Cardiac Computed Tomography Angiography data. Adequately virtualizing the coronary lumen plays a crucial role for simulating blood ow by means of fluid dynamics while additionally identifying the outer vessel wall in the case of arteriosclerosis is a prerequisite for further plaque compartment analysis. Our method is a hybrid approach complementing Active Contour Model-based segmentation with an external image force that relies on a Random Forest Regression model generated off-line. The regression model provides a strong estimate of the distance to the true vessel surface for every surface candidate point taking into account 3D wavelet-encoded contextual image features, which are aligned with the current surface hypothesis. The associated external image force is integrated in the objective function of the active contour model, such that the overall segmentation approach benefits from the advantages associated with snakes and from the ones associated with machine learning-based regression alike. This yields an integrated approach achieving competitive results on a publicly available benchmark data collection (Rotterdam segmentation challenge).
Symmetries of geodesic motion in Gödel-type spacetimes
Energy Technology Data Exchange (ETDEWEB)
Camci, U., E-mail: ucamci@akdeniz.edu.tr [Department of Physics, Akdeniz University, 07058 Antalya (Turkey)
2014-07-01
In this paper, we study Noether gauge symmetries of geodesic motion for geodesic Lagrangian of four classes of metrics of Gödel-type spacetimes for which we calculated the Noether gauge symmetries for all classes I-IV, and find the first integrals of corresponding classes to derive a complete characterization of the geodesic motion. Using the obtained expressions for t-dot , r-dot ,φ-dot and ż of each classes I-IV which depends essentially on two independent parameters m and w, we explicitly integrated the geodesic equations of motion for the corresponding Gödel-type spacetimes.
Geodesics and Newton's Law in Brane Backgrounds
Mück, W; Volovich, I V
2000-01-01
In brane world models our universe is considered as a brane imbedded into ahigher dimensional space. We discuss the behaviour of geodesics in theRandall-Sundrum background and point out that free massive particles cannotmove along the brane only. The brane is repulsive, and matter will be expelledfrom the brane into the extra dimension. This is rather undesirable, and hencewe study an alternative model with a non-compact extra dimension, but with anattractive brane embedded into the higher dimensional space. We study thelinearized gravity equations and show that Newton's gravitational law is validon the brane also in the alternative background.
On a nonlinear gravitational wave. Geodesics
Culetu, Hristu
2016-01-01
An exact, plane wave solution of the gravitational field equations is investigated. The source stress tensor is represented by an anisotropic null fluid with energy flux to which the energy density $\\rho$ and the pressure $p_{z}$ are negative but finite throughout the spacetime. They depend on a constant length (taken of the order of the Planck length) and acquire Planck values close to the null surface $t - z = 0$, $Oz$ axis being the direction of propagation. The timelike geodesics of a test particle are contained in a plane whose normal has constant direction and the null trajectories are comoving with a plane of fixed direction.
Focal properties of geodesic waveguide lenses
Verber, C. M.; Vahey, D. W.; Wood, V. E.
1976-01-01
The focal properties of uncorrected geodesic lenses in ion-exchanged glass waveguides are reported. A 13.8-mm-focal-length lens resolved beams with an angular separation of 27.6 mrad, while a 28-mm-focal-length lens resolved beams with an angular separation of only 3.3 mrad. Intensity profiles of the focal region of the former lens revealed a 40-micron spot size when the input aperture was 5 mm, and a spot size of 7.7 microns when the aperture was reduced to 1 mm. This value is close to the diffraction-limited spot size of 5.7 microns.
Light geodesics near an evaporating black hole
Energy Technology Data Exchange (ETDEWEB)
Guerreiro, Thiago, E-mail: thiago.barbosa@unige.ch; Monteiro, Fernando, E-mail: fernando.monteiro@unige.ch
2015-10-16
Quantum effects imply that an infalling observer cannot cross the event horizon of an evaporating black hole, even in her proper time. The Penrose diagram of an evaporating black hole is different from the one usually reported in the literature. We show that before the observer can cross the horizon the black hole disappears. Possible observational consequences are discussed. - Highlights: • We calculate the in-falling light geodesics in an evaporating black hole. • For our calculation we use a non-static metric called Vaydia metric. • We show that in-falling light cannot cross the event horizon. • In this case there is no information paradox.
Geodesic least squares regression on information manifolds
Energy Technology Data Exchange (ETDEWEB)
Verdoolaege, Geert, E-mail: geert.verdoolaege@ugent.be [Department of Applied Physics, Ghent University, Ghent, Belgium and Laboratory for Plasma Physics, Royal Military Academy, Brussels (Belgium)
2014-12-05
We present a novel regression method targeted at situations with significant uncertainty on both the dependent and independent variables or with non-Gaussian distribution models. Unlike the classic regression model, the conditional distribution of the response variable suggested by the data need not be the same as the modeled distribution. Instead they are matched by minimizing the Rao geodesic distance between them. This yields a more flexible regression method that is less constrained by the assumptions imposed through the regression model. As an example, we demonstrate the improved resistance of our method against some flawed model assumptions and we apply this to scaling laws in magnetic confinement fusion.
Black Hole Decay as Geodesic Motion
Sen-Gupta, K; Gupta, Kumar S.; Sen, Siddhartha
2003-01-01
We show that a formalism for analyzing the near-horizon conformal symmetry of Schwarzschild black holes using a scalar field probe is capable of describing black hole decay. The decay rate is shown to be correctly described by geodesic motion in the space of black hole masses. This provides a novel geometric interpretation for the decay of black holes. We also show that the near-horizon conformal symmetry predicts a precise correction term to the usual expression for the decay rate of black holes. The results obtained here are a consequence of the holographic nature of the system.
Geodesics in the (anti-)de Sitter spacetime
Tho, Nguyen Phuc Ky
2016-01-01
A class of exact solutions of the geodesic equations in (anti-)de Sitter spacetimes is presented. The geodesics for test particles in $AdS_4$ and $dS_4$ spacetimes are respectively sinusoidal and hyperbolic sine world lines. The world line for light rays is straight lines as known. The world lines of test particles are not dependent on their energy as noted. Spontaneous symmetry breaking of $AdS_4$ spacetime provides a physical explanation for arising of the virtual particle and antiparticle pairs in the vacuum. Interestingly, the energy of a pair and the time its particles moving along their geodesics can be related by a relation similar to Heisenberg uncertainty one pertaining quantum vacuum fluctuations. The sinusoidal geodesics of $AdS_4$ spacetime can describe the world lines of the virtual particles and antiparticles. The hyperbolic sine geodesics of $dS_4$ spacetime can explain why galaxies move apart with positive accelerations.
A Dynamical Systems Approach to Geodesics in Bianchi Cosmologies
Nilsson, Ulf S.; Uggla, Claes; Wainwright, John
2000-10-01
To understand the observational properties of cosmological models, in particular, the temperature of the cosmic microwave background radiation, it is necessary to study their null geodesics. Dynamical systems theory, in conjunction with the orthonormal frame approach, has proved to be an invaluable tool for analyzing spatially homogeneous cosmologies. It is thus natural to use such techniques to study the geodesics of these models. We therefore augment the Einstein field equations with the geodesic equations, all written in dimensionless form, obtaining an extended system of first-order ordinary differential equations that simultaneously describes the evolution of the gravitational field and the behavior of the associated geodesics. It is shown that the extended system is a powerful tool for investigating the effect of space-time anisotropies on the temperature of the cosmic microwave background radiation, and that it can also be used for studying geodesic chaos.
A Perspicuous Description of the Schwarzschild Black Hole Geodesics
Arik, Metin
2016-01-01
Schwarzschild black hole is the simplest black hole that is studied most in detail. Its behavior is best understood by looking at the geodesics of the particles under the influence of its gravitational field. In this paper, the focus of attention is giving a perspicuous description of the Schwarzschild geodesics by using analogue potential approach. Specifically we discuss geodesics of light and of a massive particle in the case that their angular momentum is non zero in the Schwarzschild spacetime. This discussion is done by defining analogue potentials out of geodesic equations and defining relevant dimensionless conserved quantities. Then, we designate how geodesics change in response to the change of these quantities. Our results indicate the relation between the particles' motion near black hole horizon and their angular momentum. Furthermore, we make a comparison between Newtonian Physics (NP) and General Relativity (GR) in the language of the analogue potential approach.
Spin-geodesic deviations in the Schwarzschild spacetime
Bini, Donato; Geralico, Andrea; Jantzen, Robert T.
2011-04-01
The deviation of the path of a spinning particle from a circular geodesic in the Schwarzschild spacetime is studied by an extension of the idea of geodesic deviation. Within the Mathisson-Papapetrou-Dixon model and assuming the spin parameter to be sufficiently small so that it makes sense to linearize the equations of motion in the spin variables as well as in the geodesic deviation, the spin-curvature force adds an additional driving term to the second order system of linear ordinary differential equations satisfied by nearby geodesics. Choosing initial conditions for geodesic motion leads to solutions for which the deviations are entirely due to the spin-curvature force, and one finds that the spinning particle position for a given fixed total spin oscillates roughly within an ellipse in the plane perpendicular to the motion, while the azimuthal motion undergoes similar oscillations plus an additional secular drift which varies with spin orientation.
Spin-geodesic deviations in the Schwarzschild spacetime
Bini, Donato; Jantzen, Robert T
2014-01-01
The deviation of the path of a spinning particle from a circular geodesic in the Schwarzschild spacetime is studied by an extension of the idea of geodesic deviation. Within the Mathisson-Papapetrou-Dixon model and assuming the spin parameter to be sufficiently small so that it makes sense to linearize the equations of motion in the spin variables as well as in the geodesic deviation, the spin-curvature force adds an additional driving term to the second order system of linear ordinary differential equations satisfied by nearby geodesics. Choosing initial conditions for geodesic motion leads to solutions for which the deviations are entirely due to the spin-curvature force, and one finds that the spinning particle position for a given fixed total spin oscillates roughly within an ellipse in the plane perpendicular to the motion, while the azimuthal motion undergoes similar oscillations plus an additional secular drift which varies with spin orientation.
Focusing of geodesic congruences in an accelerated expanding Universe
Albareti, F D; de la Cruz-Dombriz, A
2012-01-01
We study the accelerated expansion of the Universe through its consequences on a congruence of geodesics. We make use of the Raychaudhuri equation which describes the evolution of the expansion rate for a congruence of timelike or null geodesics. In particular, we focus on the space-time geometry contribution to this equation. By straightforward calculation from the metric of a Robertson-Walker cosmological model, it follows that in an accelerated expanding Universe the space-time contribution to the Raychaudhuri equation is positive for the fundamental congruence, favoring a non-focusing of the congruence of geodesics. However, the accelerated expansion of the present Universe does not imply a tendency of the fundamental congruence to diverge. It is shown that this is in fact the case for certain congruences of timelike geodesics without vorticity. Therefore, the focusing of geodesics remains feasible in an accelerated expanding Universe. Furthermore, a negative contribution to the Raychaudhuri equation from...
Integrable vs Nonintegrable Geodesic Soliton Behavior
Fringer, O B
1999-01-01
We study confined solutions of certain evolutionary partial differential equations (pde) in 1+1 space-time. The pde we study are Lie-Poisson Hamiltonian systems for quadratic Hamiltonians defined on the dual of the Lie algebra of vector fields on the real line. These systems are also Euler-Poincare equations for geodesic motion on the diffeomorphism group in the sense of the Arnold program for ideal fluids, but where the kinetic energy metric is different from the L2 norm of the velocity. These pde possess a finite-dimensional invariant manifold of particle-like (measure-valued) solutions we call ``pulsons.'' We solve the particle dynamics of the two-pulson interaction analytically as a canonical Hamiltonian system for geodesic motion with two degrees of freedom and a conserved momentum. The result of this two-pulson interaction for rear-end collisions is elastic scattering with a phase shift, as occurs with solitons. In contrast, head-on antisymmetric collisons of pulsons tend to form singularities.
Zhang, Shuangxi
2014-01-01
The past studies treated the perturbed distribution of circulating electrons as adiabatic one when studying the dispersion relation of electrostatic geodesic acoustic mode(GAM). In this paper, the flow of electron geodesic current (FEGC) is added to modify this adiabatic distribution. Based on the drift kinetic theory, it is found that FEGC obviously increases the magnitude of the standard GAM's frequency and reduces its damping rate. The increase of frequency results from the contribution of FEGC to the radial flow. The reason for the reduction of damping rate is that when the effect of FEGC counts, the new resonant velocity becomes much larger than ions thermal velocity with equilibrium distribution obeying Maxwellian distribution, compared with unmodified Landau resonant velocity. Especially, FEGC changes the characters of the frequency and damping rate of low-frequency GAM as functions of safety factor $q$ .
Visualization of Uncertain Contour Trees
DEFF Research Database (Denmark)
Kraus, Martin
2010-01-01
Contour trees can represent the topology of large volume data sets in a relatively compact, discrete data structure. However, the resulting trees often contain many thousands of nodes; thus, many graph drawing techniques fail to produce satisfactory results. Therefore, several visualization methods...... were proposed recently for the visualization of contour trees. Unfortunately, none of these techniques is able to handle uncertain contour trees although any uncertainty of the volume data inevitably results in partially uncertain contour trees. In this work, we visualize uncertain contour trees...... by combining the contour trees of two morphologically filtered versions of a volume data set, which represent the range of uncertainty. These two contour trees are combined and visualized within a single image such that a range of potential contour trees is represented by the resulting visualization. Thus...
An Algorithm for Constructing Principal Geodesics in Phylogenetic Treespace.
Nye, Tom M W
2014-01-01
Most phylogenetic analyses result in a sample of trees, but summarizing and visualizing these samples can be challenging. Consensus trees often provide limited information about a sample, and so methods such as consensus networks, clustering and multidimensional scaling have been developed and applied to tree samples. This paper describes a stochastic algorithm for constructing a principal geodesic or line through treespace which is analogous to the first principal component in standard principal components analysis. A principal geodesic summarizes the most variable features of a sample of trees, in terms of both tree topology and branch lengths, and it can be visualized as an animation of smoothly changing trees. The algorithm performs a stochastic search through parameter space for a geodesic which minimizes the sum of squared projected distances of the data points. This procedure aims to identify the globally optimal principal geodesic, though convergence to locally optimal geodesics is possible. The methodology is illustrated by constructing principal geodesics for experimental and simulated data sets, demonstrating the insight into samples of trees that can be gained and how the method improves on a previously published approach. A java package called GeoPhytter for constructing and visualizing principal geodesics is freely available from www.ncl.ac.uk/ ntmwn/geophytter.
Geodesic models generated by Lie symmetries
Abebe, G Z; Govinder, K S
2014-01-01
We study the junction condition relating the pressure to the heat flux at the boundary of a shearing and expanding spherically symmetric radiating star when the fluid particles are travelling in geodesic motion. The Lie symmetry generators that leave the junction condition invariant are identified and the optimal system is generated. We use each element of the optimal system to transform the partial differential equation to an ordinary differential equation. New exact solutions, which are group invariant under the action of Lie point infinitesimal symmetries, are found. We obtain families of traveling wave solutions and self-similar solutions, amongst others. The gravitational potentials are given in terms of elementary functions, and the line elements can be given explicitly in all cases. We show that the Friedmann dust model is regained as a special case, and we can connect our results to earlier investigations.
A geodesic model in conformal superspace
Gomes, Henrique de A
2016-01-01
In this paper, I look for the most general geometrodynamical symmetries compatible with spatial relational principles. I argue that they lead either to a completely static Universe, or one embodying spatial conformal diffeomorphisms. Demanding locality for an action compatible with these principles severely limits its form, both for the gravitational part as well as all matter couplings. The simplest and most natural choice for pure gravity has two propagating physical degrees of freedom (and no refoliation-invariance). The system has a geometric interpretation as a geodesic model in infinite dimensional conformal superspace. Conformal superspace is a stratified manifold, with different strata corresponding to different isometry groups. Choosing space to be (homeomorphic to) $S^3$, conformal superspace has a preferred stratum with maximal stabilizer group. This stratum consists of a single point -- corresponding to the conformal geometry of the round 3-sphere. This is the most homogeneous non-degenerate geome...
Drift effects on electromagnetic geodesic acoustic modes
Energy Technology Data Exchange (ETDEWEB)
Sgalla, R. J. F., E-mail: reneesgalla@gmail.com [Institute of Physics, University of São Paulo, São Paulo 05508-900 (Brazil)
2015-02-15
A two fluid model with parallel viscosity is employed to derive the dispersion relation for electromagnetic geodesic acoustic modes (GAMs) in the presence of drift (diamagnetic) effects. Concerning the influence of the electron dynamics on the high frequency GAM, it is shown that the frequency of the electromagnetic GAM is independent of the equilibrium parallel current but, in contrast with purely electrostatic GAMs, significantly depends on the electron temperature gradient. The electromagnetic GAM may explain the discrepancy between the f ∼ 40 kHz oscillation observed in tokamak TCABR [Yu. K. Kuznetsov et al., Nucl. Fusion 52, 063044 (2012)] and the former prediction for the electrostatic GAM frequency. The radial wave length associated with this oscillation, estimated presently from this analytical model, is λ{sub r} ∼ 25 cm, i.e., an order of magnitude higher than the usual value for zonal flows (ZFs)
Geodesic motion in a stationary dihole spacetime
Dubeibe, F L
2016-01-01
The knowledge of the properties of the different exact solutions modeling binary systems, is a necessary step towards the classification of physically suitable solutions and its corresponding limits of applicability. In the present paper, we perform an analysis of the geodesics around two counter--rotating Kerr--Newman black holes endowed with opposite electric charges, which achieve equilibrium by means of a strut between their constituents. We find that bounded and unbounded orbits are possible. However, test particles may cross between the black holes only if their angular momentum equals zero, otherwise, there exist a repulsive potential, which prohibits such orbits. Two important aspects are pointed out for these trajectories: ({\\it i}) the motion of photons is affected once crossing the strut; and ({\\it ii}) massive particles exhibit oscillatory motion, as a first analog of the Sitnikov problem in general relativity. The radius of the innermost stable circular orbit as a function of the physical paramet...
On the Morris - Thorne wormhole geodesics
Culetu, Hristu
2014-01-01
The properties of a particular Misner - Thorne wormhole are investigated. The "exotic stress-energy" needed to maintain the wormhole open corresponds to a massless scalar field whose Lagrangean density contains a negative kinetic term. While the Komar energy of the spacetime is vanishing due to the negative energy density and radial pressure, the ADM energy is (minus) the Planck energy. The timelike geodesics are hyperbolae and any static observer is inertial. The null radial trajectories are also hyperbolae and Lorentz invariant as Coleman- de Luccia expanding bubble or Ipser-Sikivie domain wall. Using a different equation of state for the fluid on the dynamic wormhole throat of Redmount and Suen, we reached an equation of motion for the throat (a hyperbola) that leads to a negative surface energy density and the throat expands with the same acceleration $2\\pi |\\sigma|$ as the Ipser-Sikivie domain wall.
Geodesic exponential kernels: When Curvature and Linearity Conflict
DEFF Research Database (Denmark)
Feragen, Aase; Lauze, François; Hauberg, Søren
2015-01-01
We consider kernel methods on general geodesic metric spaces and provide both negative and positive results. First we show that the common Gaussian kernel can only be generalized to a positive definite kernel on a geodesic metric space if the space is flat. As a result, for data on a Riemannian...... Laplacian kernel can be generalized while retaining positive definiteness. This implies that geodesic Laplacian kernels can be generalized to some curved spaces, including spheres and hyperbolic spaces. Our theoretical results are verified empirically....
A Visualization of Null Geodesics for the Bonnor Massive Dipole
Oliva-Mercado, Guillermo Andree; Cordero-García, Iván; Frutos-Alfaro, Francisco
2015-01-01
In this work we simulate null geodesics for the Bonnor massive dipole metric by implementing a symbolic-numerical algorithm in Sage and Python. This program is also capable of visualizing in 3D, in principle, the geodesics for any given metric. Geodesics are launched from a common point, collectively forming a cone of light beams, simulating a solid-angle section of a point source in front of a massive object with a magnetic field. Parallel light beams also were considered, and their bending due to the curvature of the space-time was simulated.
A visualization of null geodesics for the bonnor massive dipole
Directory of Open Access Journals (Sweden)
G. Andree Oliva Mercado
2015-08-01
Full Text Available In this work we simulate null geodesics for the Bonnor massive dipole metric by implementing a symbolic-numerical algorithm in Sage and Python. This program is also capable of visualizing in 3D, in principle, the geodesics for any given metric. Geodesics are launched from a common point, collectively forming a cone of light beams, simulating a solid-angle section of a point source in front of a massive object with a magnetic field. Parallel light beams also were considered, and their bending due to the curvature of the space-time was simulated.
Geodesic Witten diagrams with an external spinning field
Nishida, Mitsuhiro; Tamaoka, Kotaro
2017-05-01
We explore AdS/CFT correspondence between geodesic Witten diagrams and conformal blocks (conformal partial waves) with an external symmetric traceless tensor field. We derive an expression for the conformal partial wave with an external spin-1 field and show that this expression is equivalent to the amplitude of the geodesic Witten diagram. We also show the equivalence by using a conformal Casimir equation in embedding formalism. Furthermore, we extend the construction of the amplitude of the geodesic Witten diagram to an external arbitrary symmetric traceless tensor field. We show that our construction agrees with the known result of the conformal partial waves.
Geodesic Witten diagrams with an external spinning field
Nishida, Mitsuhiro
2016-01-01
We explore AdS/CFT correspondence between geodesic Witten diagrams and conformal blocks (conformal partial waves) with an external symmetric traceless tensor field. We derive an expression for the conformal partial wave with an external spin-1 field and show that this expression is equivalent to the amplitude of the geodesic Witten diagram. We also show the equivalence by using conformal Casimir equation in embedding formalism. Furthermore, we extend the construction of the amplitude of the geodesic Witten diagram to an external arbitrary symmetric traceless tensor field. We show our construction agrees with the known result of the conformal partial waves.
Geodesic Motion in a Charged 2D Stringy Blackhole Spacetime
Uniyal, Rashmi; Purohit, K D
2014-01-01
We study the timelike geodesics and geodesic deviation for a two-dimensional stringy blackhole spacetime in Schwarzschild gauge. We have analyzed the properties of effective potential along with the structure of the possible orbits for test particles with different settings of blackhole parameters. The exactly solvable geodesic deviation equation is used to obtain corresponding deviation vector. The nature of deviation and tidal force is also examined in view of the behavior of corresponding deviation vector.The results are also compared with an another two-dimensional stringy blackhole spacetime.
de Sitter geodesics: reappraising the notion of motion
Pereira, J G
2011-01-01
de Sitter spacetime is transitive under a combination of translations and proper conformal transformations. Its usual family of geodesics, however, does not take into account this property. As a consequence, there are points in de Sitter spacetime which cannot be joined by any one of these geodesics. By taking into account the appropriate transitivity properties, a new family of geodesics is obtained whose trajectories are able to connect any two points of the de Sitter spacetime. They are, furthermore, consistent with the de Sitter momentum conservation. These geodesics introduce a new notion of motion, given by a combination of translations and proper conformal transformations, which may be important at very-high energies, where conformal symmetry plays a significant role.
Spin-geodesic deviations in the Kerr spacetime
Bini, D.; Geralico, A.
2011-11-01
The dynamics of extended spinning bodies in the Kerr spacetime is investigated in the pole-dipole particle approximation and under the assumption that the spin-curvature force only slightly deviates the particle from a geodesic path. The spin parameter is thus assumed to be very small and the back reaction on the spacetime geometry neglected. This approach naturally leads to solve the Mathisson-Papapetrou-Dixon equations linearized in the spin variables as well as in the deviation vector, with the same initial conditions as for geodesic motion. General deviations from generic geodesic motion are studied, generalizing previous results limited to the very special case of an equatorial circular geodesic as the reference path.
Spin-geodesic deviations in the Kerr spacetime
Bini, Donato
2014-01-01
The dynamics of extended spinning bodies in the Kerr spacetime is investigated in the pole-dipole particle approximation and under the assumption that the spin-curvature force only slightly deviates the particle from a geodesic path. The spin parameter is thus assumed to be very small and the back reaction on the spacetime geometry neglected. This approach naturally leads to solve the Mathisson-Papapetrou-Dixon equations linearized in the spin variables as well as in the deviation vector, with the same initial conditions as for geodesic motion. General deviations from generic geodesic motion are studied, generalizing previous results limited to the very special case of an equatorial circular geodesic as the reference path.
Closed timelike geodesics in a gas of cosmic strings
Grøn, Ø; Gron, Oyvind; Johannesen, Steinar
2007-01-01
We find a class of solutions of Einstein's field equations representing spacetime outside a spinning cosmic string surrounded by a gas of non-spinning cosmic strings, and show that there exist closed timelike geodesics in this spacetime.
Geodesic motion on closed spaces: Two numerical examples
Energy Technology Data Exchange (ETDEWEB)
Müller, Daniel, E-mail: muller@fis.unb.br [Universidade de Brasília, Instituto de Física, Cxp 04455, Asa Norte, 70919-900, Brasília, DF (Brazil)
2012-01-09
The geodesic structure is very closely related to the trace of the Laplace operator, involved in the calculation of the expectation value of the energy–momentum tensor in Universes with non-trivial topology. The purpose of this work is to provide concrete numerical examples of geodesic flows. Two manifolds with genus g=0 are given. In one the chaotic regions, form sets of negligible or zero measure. In the second example the geodesic flow shows the presence of measurable chaotic regions. The approach is “experimental”, numerical, and there is no attempt to an analytical calculation. -- Highlights: ► Elementary differential geometry of surfaces and the Gauss–Bonnet theorem. ► The geodesic equation is numerically solved for two metrics on the sphere. ► With the Poincare surface, chaotic and regular regions are identified. ► Chaotic regions increase as the curvature fluctuation of the manifold increases.
Lie symmetries of the geodesic equations and projective collineations
Energy Technology Data Exchange (ETDEWEB)
Tsamparlis, Michael; Paliathanasis, Andronikos, E-mail: mtsampa@phys.uoa.g, E-mail: paliathanasis@gmail.co [Department of Physics, Section Astrophysics Astronomy Mechanics, University of Athens, University of Athens, Zografos 15783, Athens (Greece)
2009-10-01
We study the Lie symmetries of the geodesic equations in a Riemannian space and show that they coincide with the projective symmetries of the Riemannian metric. We apply the result to the spaces of constant curvature.
A Note on Geodesically Bounded ℝ-Trees
Directory of Open Access Journals (Sweden)
W. A. Kirk
2010-01-01
Full Text Available It is proved that a complete geodesically bounded R-tree is the closed convex hull of the set of its extreme points. It is also noted that if X is a closed convex geodesically bounded subset of a complete R-tree Y, and if a nonexpansive mapping T:X→Y satisfies inf{d(x,T(x:x∈X}=0, then T has a fixed point. The latter result fails if T is only continuous.
The Lorentzian oscillator group as a geodesic orbit space
Energy Technology Data Exchange (ETDEWEB)
Batat, W. [Ecole Normale Superieure d' Enseignement Technologique d' Oran, Departement de Mathematiques et Informatique, B.P. 1523, El M' Naouar, Oran (Algeria); Gadea, P. M. [Instituto de Fisica Fundamental, CSIC, Serrano 113-bis, 28006 Madrid (Spain); Oubina, J. A. [Departamento de Xeometria e Topoloxia, Facultade de Matematicas, Universidade de Santiago de Compostela, 15782 Santiago de Compostela (Spain)
2012-10-15
We prove that the four-dimensional oscillator group Os, endowed with any of its usual left-invariant Lorentzian metrics, is a Lorentzian geodesic (so, in particular, null-geodesic) orbit space with some of its homogeneous descriptions corresponding to certain homogeneous Lorentzian structures. Each time that Os is endowed with a suitable metric and an appropriate homogeneous Lorentzian structure, it is a candidate for constructing solutions in d-dimensional supergravity with at least 24 of the 32 possible supersymmetries.
Dey, Susmita; Sarkar, Ripon; Chatterjee, Kabita; Datta, Pallab; Barui, Ananya; Maity, Santi P
2017-02-09
Habitual smokers are known to be at higher risk for developing oral cancer, which is increasing at an alarming rate globally. Conventionally, oral cancer is associated with high mortality rates, although recent reports show the improved survival outcomes by early diagnosis of disease. An effective prediction system which will enable to identify the probability of cancer development amongst the habitual smokers, is thus expected to benefit sizable number of populations. Present work describes a non-invasive, integrated method for early detection of cellular abnormalities based on analysis of different cyto-morphological features of exfoliative oral epithelial cells. Differential interference contrast (DIC) microscopy provides a potential optical tool as this mode provides a pseudo three dimensional (3-D) image with detailed morphological and textural features obtained from noninvasive, label free epithelial cells. For segmentation of DIC images, gradient vector flow snake model active contour process has been adopted. To evaluate cellular abnormalities amongst habitual smokers, the selected morphological and textural features of epithelial cells are compared with the non-smoker (-ve control group) group and clinically diagnosed pre-cancer patients (+ve control group) using support vector machine (SVM) classifier. Accuracy of the developed SVM based classification has been found to be 86% with 80% sensitivity and 89% specificity in classifying the features from the volunteers having smoking habit.
Directory of Open Access Journals (Sweden)
L. Meziou
2014-01-01
Full Text Available Visualization of the entire length of the gastrointestinal tract through natural orifices is a challenge for endoscopists. Videoendoscopy is currently the “gold standard” technique for diagnosis of different pathologies of the intestinal tract. Wireless capsule endoscopy (WCE has been developed in the 1990s as an alternative to videoendoscopy to allow direct examination of the gastrointestinal tract without any need for sedation. Nevertheless, the systematic postexamination by the specialist of the 50,000 (for the small bowel to 150,000 images (for the colon of a complete acquisition using WCE remains time-consuming and challenging due to the poor quality of WCE images. In this paper, a semiautomatic segmentation for analysis of WCE images is proposed. Based on active contour segmentation, the proposed method introduces alpha-divergences, a flexible statistical similarity measure that gives a real flexibility to different types of gastrointestinal pathologies. Results of segmentation using the proposed approach are shown on different types of real-case examinations, from (multipolyp(s segmentation, to radiation enteritis delineation.
Patel, Nirmal; Sultana, Sharmin; Rashid, Tanweer; Krusienski, Dean; Audette, Michel A.
2015-03-01
This paper presents a methodology for the digital formatting of a printed atlas of the brainstem and the delineation of cranial nerves from this digital atlas. It also describes on-going work on the 3D resampling and refinement of the 2D functional regions and nerve contours. In MRI-based anatomical modeling for neurosurgery planning and simulation, the complexity of the functional anatomy entails a digital atlas approach, rather than less descriptive voxel or surface-based approaches. However, there is an insufficiency of descriptive digital atlases, in particular of the brainstem. Our approach proceeds from a series of numbered, contour-based sketches coinciding with slices of the brainstem featuring both closed and open contours. The closed contours coincide with functionally relevant regions, whereby our objective is to fill in each corresponding label, which is analogous to painting numbered regions in a paint-by-numbers kit. Any open contour typically coincides with a cranial nerve. This 2D phase is needed in order to produce densely labeled regions that can be stacked to produce 3D regions, as well as identifying the embedded paths and outer attachment points of cranial nerves. Cranial nerves are modeled using an explicit contour based technique called 1-Simplex. The relevance of cranial nerves modeling of this project is two-fold: i) this atlas will fill a void left by the brain segmentation communities, as no suitable digital atlas of the brainstem exists, and ii) this atlas is necessary to make explicit the attachment points of major nerves (except I and II) having a cranial origin. Keywords: digital atlas, contour models, surface models
GEODESIC RECONSTRUCTION, SADDLE ZONES & HIERARCHICAL SEGMENTATION
Directory of Open Access Journals (Sweden)
Serge Beucher
2011-05-01
Full Text Available The morphological reconstruction based on geodesic operators, is a powerful tool in mathematical morphology. The general definition of this reconstruction supposes the use of a marker function f which is not necessarily related to the function g to be built. However, this paper deals with operations where the marker function is defined from given characteristic regions of the initial function f, as it is the case, for instance, for the extrema (maxima or minima but also for the saddle zones. Firstly, we show that the intuitive definition of a saddle zone is not easy to handle, especially when digitised images are involved. However, some of these saddle zones (regional ones also called overflow zones can be defined, this definition providing a simple algorithm to extract them. The second part of the paper is devoted to the use of these overflow zones as markers in image reconstruction. This reconstruction provides a new function which exhibits a new hierarchy of extrema. This hierarchy is equivalent to the hierarchy produced by the so-called waterfall algorithm. We explain why the waterfall algorithm can be achieved by performing a watershed transform of the function reconstructed by its initial watershed lines. Finally, some examples of use of this hierarchical segmentation are described.
Geodesics and Acceleration in Influence Theory
Walsh, James; Knuth, Kevin
Influence theory is concerned with a foundational approach where it is assumed that particles influence one another in a discrete one-to-one fashion. This results in a partially ordered set of influence events, called the influence network, where particles are represented by totally ordered chains of events. Information physics considers physical laws to result from consistent quantification of physical phenomena. Knuth and Bahreyni (2014) demonstrated that the mathematics of spacetime emerges from consistent quantification of influence events by embedded coordinated observers. Knuth (2014) showed that in 1 +1 dimensions observer-based predictions about a free (uninfluenced) particle result in the Dirac equation. Here, we show that when a particle in 1 +1 dimensions is influenced, it is uniquely and consistently described in terms of relativistic acceleration for constant rate of influence and in general obeys equations of the form of the geodesic equations of general relativity. This suggests that Influence Theory can also account for forces (like gravity), which give rise to well-known relativistic effects such as time dilation.
Contour detection by surround suppression of texture
Petkov, Nicolai; Tavares, JMRS; Jorge, RMN
2007-01-01
Based on a keynote lecture at Complmage 2006, Coimbra, Oct. 20-21, 2006, an overview is given of our activities in modelling and using surround inhibition for contour detection. The effect of suppression of a line or edge stimulus by similar surrounding stimuli is known from visual perception studie
Image Demosaicking with Contour Stencils
Directory of Open Access Journals (Sweden)
Pascal Getreuer
2012-03-01
Full Text Available Demosaicking (or demosaicing is the problem of interpolating full color information on an image where only one color component is known at each pixel. Most demosaicking methods involve some kind of estimation of the underlying image structure, for example, choosing adaptively between interpolating in the horizontal or vertical direction. This article discusses the implementation details of the method introduced in Getreuer, “Color Demosaicing with Contour Stencils,” 2011. Mosaicked contour stencils first estimate the image contour orientations directly from the mosaicked data. The mosaicked contour stencils are then used to guide a simple demosaicking method based on graph regularization.
基于混合能量活动轮廓模型的人脸分割方法∗%Face Segmentation Based on a Hybrid Energy Based Active Contour Model
Institute of Scientific and Technical Information of China (English)
龚勋; 王国胤; 李天瑞; 李昕昕; 夏冉; 冯林
2013-01-01
Influenced by factors like facial features, accessories, facial outer contours are extracted by the traditional geometric active contour models and conatin depressions and result in fragmentation, etc. To address these problems, according to the characteristics of human face image, the study proposes a hybrid energy based geometric active contour model via combining the energies of contour outer tension force and skin color with the global energy. First an outwards tension force, computed by neighborhoods of contour points, is added to the contour. This force makes the curve insusceptible to the facial features and accessories, but move towards to the facial outer contour. As skin color is the major feature of a human face. Skin color energy is integrated to ensure a more robust algorithm. Finally, an improved skin tone detection model is proposed based on the single Gaussian function. It could generate initial position that are close to the real facial contour, laying a good foundation for contour evolution. The proposed method gives essentially accurate face segmentations on two public face databases. Take the manually segmentations as the ground truth, the proposed method compares favorably to both traditional global and local energy algorithms. Next a more challenging set containing 100 faces of life photos with variances in pose is introduced with illumination and backgrounds. Segmentation results have validated that the proposed method could extract outer facial contour steadily and accurately under such variances.% 由于受到面部五官、饰物等因素的影响，传统几何活动轮廓模型获取人脸外轮廓会产生凹陷、分片等现象。针对人脸图像的特点，将边缘外张力能量及肤色能量与全局能量结合，提出一种基于混合能量泛函的几何活动轮廓模型，有效地避免了这些问题。首先，根据演化曲线的邻域信息赋予边缘点向外的张力，使曲线能够克服面部特征及
A Finsler geodesic spray paradigm for wildfire spread modelling
DEFF Research Database (Denmark)
Markvorsen, Steen
2015-01-01
represents the local fire templates. The ‘paradigm’ part of the present proposal is thus concerned with the corresponding shift of attention from the actual fire-lines to consider instead the geodesic spray - the ‘fire-particles’ - which together, side by side, mold the fire-lines at each instant of time...... sensitive - geodesic solutions to the wildfire spread problem. The methods presented here stem directly from first principles of 2-dimensional Finsler geometry, and they can be readily extracted from the seminal monographs [10] and [11], but we will take special care to introduce and exemplify the necessary...... framework for the implementation of the geometric machinery into this new application - not least in order to facilitate and support the dialog between geometers and the wildfire modelling community. The ‘integration’ part alluded to above is obtained via the geodesics of the ensuing Finsler metric which...
Geodesics on Surfaces with Helical Symmetry: Cavatappi Geometry
Jantzen, Robert T
2013-01-01
A 3-parameter family of helical tubular surfaces obtained by screw revolving a circle provides a useful pedagogical example of how to study geodesics on a surface that admits a 1-parameter symmetry group, but is not as simple as a surface of revolution like the torus which it contains as a special case. It serves as a simple example of helically symmetric surfaces which are the generalizations of surfaces of revolution in which an initial plane curve is screw-revolved around an axis in its plane. The physics description of geodesic motion on these surfaces requires a slightly more involved effective potential approach than the torus case due to the nonorthogonal coordinate grid necessary to describe this problem. Amazingly this discussion allows one to very nicely describe the geodesics of the surface of the more complicated ridged cavatappi pasta.
Null geodesics in a magnetically charged stringy black hole spacetime
Kuniyal, Ravi Shankar; Uniyal, Rashmi; Nandan, Hemwati; Purohit, K. D.
2016-04-01
We study the null geodesics of a four-dimensional magnetic charged black hole spacetime arising in string theory. The behaviour of effective potential in view of the different values of black hole parameters are analysed in the equatorial plane. The possible orbits for null geodesics are also discussed in view of the different values of the impact parameter. We have also calculated the frequency shift of photons in this spacetime. The results are compared to those obtained for the electrically charged stringy black hole spacetime and the Schwarzschild black hole spacetime in general relativity.
Coherent states and geodesics cut locus and conjugate locus
Berceanu, S
1997-01-01
The intimate relationship between coherent states and geodesics is pointed out. For homogenous manifolds on which the exponential from the Lie algebra to the Lie group equals the geodesic exponential, and in particular for symmetric spaces, it is proved that the cut locus of the point $0$ is equal to the set of coherent vectors orthogonal to $\\vert 0>$. A simple method to calculate the conjugate locus in Hermitian symmetric spaces with significance in the coherent state approach is presented. The results are illustrated on the complex Grassmann manifold.
An Efficient Geodesic Path Solution for Prolate Spheroids
1979-07-01
unit tangent vector is determinr 4, the other relevant parameter in the ray analysis , namely, the unit binprmal vector 6 can readily be obtained via...geodesic shown in Fig. S . Recall that the unit tangent vectors for the geodesic are given by Equations (1l)-(15). Assuming at a particular point (e )on the...Aeronautics and Space Adi&inistration, ’,,ashington, D.C. 20546. [3] M.M. Lipschutz, Theory and Problems of Di-fferentia-l_(eni ret-rv, Schaums Outline
Global structure and geodesics for Koenigs superintegrable systems
Valent, Galliano
2016-09-01
We present a new derivation of the local structure of Koenigs metrics using a framework laid down by Matveev and Shevchishin. All of these dynamical systems allow for a potential preserving their superintegrability (SI) and most of them are shown to be globally defined on either ℝ2 or ℍ2. Their geodesic flows are easily determined thanks to their quadratic integrals. Using Carter (or minimal) quantization, we show that the formal SI is preserved at the quantum level and for two metrics, for which all of the geodesics are closed, it is even possible to compute the classical action variables and the point spectrum of the quantum Hamiltonian.
Entropy-expansiveness of Geodesic Flows on Closed Manifolds without Conjugate Points
Institute of Scientific and Technical Information of China (English)
Fei LIU; Fang WANG
2016-01-01
In this article, we consider the entropy-expansiveness of geodesic flows on closed Rieman-nian manifolds without conjugate points. We prove that, if the manifold has no focal points, or if the manifold is bounded asymptote, then the geodesic flow is entropy-expansive. Moreover, for the compact oriented surfaces without conjugate points, we prove that the geodesic flows are entropy-expansive. We also give an estimation of distance between two positively asymptotic geodesics of an uniform visibility manifold.
Recognizing the authenticity of emotional expressions: F0 contour matters when you need to know.
Drolet, Matthis; Schubotz, Ricarda I; Fischer, Julia
2014-01-01
Authenticity of vocal emotion expression affects emotion recognition and brain activity in the so-called Theory of Mind (ToM) network, which is implied in the ability to explain and predict behavior by attributing mental states to other individuals. Exploiting the variability of the fundamental frequency (F0 contour), which varies more (higher contour) in play-acted expressions than authentic ones, we examined whether contour biases explicit categorization toward a particular authenticity or emotion category. Moreover, we tested whether contour modulates blood-oxygen-level dependent (BOLD) response in the ToM network and explored the role of task as a top-down modulator. The effects of contour on BOLD signal were analyzed by contrasting high and low contour stimuli within two previous fMRI studies that implemented emotion and authenticity rating tasks. Participants preferentially categorized higher contour stimuli as play-acted and lower contour stimuli as sad. Higher contour was found to up-regulate activation task-independently in the primary auditory cortex. Stimulus contour and task were found to interact in a network including medial prefrontal cortex, with an increase in BOLD signal for low-contour stimuli during explicit perception of authenticity and an increase for high-contour stimuli during explicit perception of emotion. Contour-induced BOLD effects appear to be purely stimulus-driven in early auditory and intonation perception, while being strongly task-dependent in regions involved in higher cognition.
Contours - MO 2012 Greene County 5ft Contours (SHP)
NSGIC State | GIS Inventory — 5ft cartographic contour file for Greene County, Missouri. This file was created using the elevation data from the 2011 LiDAR flight. It includes indexes for 10, 25,...
Contours - MO 2012 Greene County 5ft Contours (SHP)
NSGIC GIS Inventory (aka Ramona) — 5ft cartographic contour file for Greene County, Missouri. This file was created using the elevation data from the 2011 LiDAR flight. It includes indexes for 10, 25,...
Contours - MO 2012 Greene County NW 1ft Contours (SHP)
NSGIC GIS Inventory (aka Ramona) — 1ft contour file for the northwest portion of Greene County, Missouri. This file was created using the USGS corrected elevation data from the 2011 LiDAR flight. It...
Contours - MO 2012 Greene County SE 1ft Contours (SHP)
NSGIC GIS Inventory (aka Ramona) — 1ft contour file for the southeast portion of Greene County, Missouri. This file was created using the USGS corrected elevation data from the 2011 LiDAR flight. It...
Contours - MO 2012 Greene County SW 1ft Contours (SHP)
NSGIC GIS Inventory (aka Ramona) — 1ft contour file for the southwest portion of Greene County, Missouri. This file was created using the USGS corrected elevation data from the 2011 LiDAR flight. It...
Contours - MO 2012 Greene County NE 1ft Contours (SHP)
NSGIC GIS Inventory (aka Ramona) — 1ft contour file for the northeast portion of Greene County, Missouri. This file was created using the USGS corrected elevation data from the 2011 LiDAR flight. It...
基于聚类信息的活动轮廓图像分割模型%Active Contour Model for Image Segmentation Based on Clustering Information
Institute of Scientific and Technical Information of China (English)
李敏; 梁久祯; 廖翠萃
2015-01-01
Based on traditional Chan-Vese ( CV) model, combining image clustering information, an effective active contour model for image segmentation is proposed in this paper. Firstly, the energy functional of CV model is improved, the gradient information of image is considered, and the accuracy of image segmentation is improved. Then, the coefficient K based on image clustering information is added in energy functional. And the image clustering information is used to initialize the level set curves automatically. In color image segmentation processing, weighting process on the RGB channel is proposed to improve the efficiency of segmentation. Finally, regularization term is added in energy functional to avoid re-initialization of the level set. The gray images and color images are segmented quickly and accurately. Experimental results shows the effectiveness of the proposed method.%基于传统Chan-Vese( CV)模型,结合图像聚类信息,提出一种有效的活动轮廓模型图像分割方法。该方法首先改进CV模型的能量泛函,考虑图像的梯度信息,提高图像分割的精确度。其次在能量泛函中添加图像的聚类信息系数K,并使用图像的聚类信息实现对水平集轮廓曲线的自动初始化。在分割处理彩色图像时,为提高分割效率,对彩色RGB图像的三通道进行加权处理。最后为能量泛函添加正则项,避免水平集的重新初始化,完成对灰度图像及彩色图像的快速精确分割。实验表明该方法的有效性。
Wavelet Representation of Contour Sets
Energy Technology Data Exchange (ETDEWEB)
Bertram, M; Laney, D E; Duchaineau, M A; Hansen, C D; Hamann, B; Joy, K I
2001-07-19
We present a new wavelet compression and multiresolution modeling approach for sets of contours (level sets). In contrast to previous wavelet schemes, our algorithm creates a parametrization of a scalar field induced by its contoum and compactly stores this parametrization rather than function values sampled on a regular grid. Our representation is based on hierarchical polygon meshes with subdivision connectivity whose vertices are transformed into wavelet coefficients. From this sparse set of coefficients, every set of contours can be efficiently reconstructed at multiple levels of resolution. When applying lossy compression, introducing high quantization errors, our method preserves contour topology, in contrast to compression methods applied to the corresponding field function. We provide numerical results for scalar fields defined on planar domains. Our approach generalizes to volumetric domains, time-varying contours, and level sets of vector fields.
Visualizing Contour Trees within Histograms
DEFF Research Database (Denmark)
Kraus, Martin
2010-01-01
Many of the topological features of the isosurfaces of a scalar volume field can be compactly represented by its contour tree. Unfortunately, the contour trees of most real-world volume data sets are too complex to be visualized by dot-and-line diagrams. Therefore, we propose a new visualization...... that is suitable for large contour trees and efficiently conveys the topological structure of the most important isosurface components. This visualization is integrated into a histogram of the volume data; thus, it offers strictly more information than a traditional histogram. We present algorithms...... to automatically compute the graph layout and to calculate appropriate approximations of the contour tree and the surface area of the relevant isosurface components. The benefits of this new visualization are demonstrated with the help of several publicly available volume data sets....
Contours--Offshore Monterey, California
U.S. Geological Survey, Department of the Interior — This part of DS 781 presents bathymetric contours for several seafloor maps of the Monterey Canyon and Vicinity map area, California. The raster data file is...
Contours--Offshore Aptos, California
U.S. Geological Survey, Department of the Interior — This part of DS 781 presents data for the bathymetric contours for several seafloor maps of the Offshore of Aptos map area, California. The vector data file is...
Contours--Offshore Aptos, California
U.S. Geological Survey, Department of the Interior — This part of DS 781 presents data for the bathymetric contours for several seafloor maps of the Offshore of Aptos map area, California. The vector data file is...
Contours--Offshore Monterey, California
U.S. Geological Survey, Department of the Interior — This part of DS 781 presents bathymetric contours for several seafloor maps of the Monterey Canyon and Vicinity map area, California. The raster data file is...
Optimality of human contour integration.
Directory of Open Access Journals (Sweden)
Udo A Ernst
Full Text Available For processing and segmenting visual scenes, the brain is required to combine a multitude of features and sensory channels. It is neither known if these complex tasks involve optimal integration of information, nor according to which objectives computations might be performed. Here, we investigate if optimal inference can explain contour integration in human subjects. We performed experiments where observers detected contours of curvilinearly aligned edge configurations embedded into randomly oriented distractors. The key feature of our framework is to use a generative process for creating the contours, for which it is possible to derive a class of ideal detection models. This allowed us to compare human detection for contours with different statistical properties to the corresponding ideal detection models for the same stimuli. We then subjected the detection models to realistic constraints and required them to reproduce human decisions for every stimulus as well as possible. By independently varying the four model parameters, we identify a single detection model which quantitatively captures all correlations of human decision behaviour for more than 2000 stimuli from 42 contour ensembles with greatly varying statistical properties. This model reveals specific interactions between edges closely matching independent findings from physiology and psychophysics. These interactions imply a statistics of contours for which edge stimuli are indeed optimally integrated by the visual system, with the objective of inferring the presence of contours in cluttered scenes. The recurrent algorithm of our model makes testable predictions about the temporal dynamics of neuronal populations engaged in contour integration, and it suggests a strong directionality of the underlying functional anatomy.
A Few Endpoint Geodesic Restriction Estimates for Eigenfunctions
Chen, Xuehua; Sogge, Christopher D.
2014-07-01
We prove a couple of new endpoint geodesic restriction estimates for eigenfunctions. In the case of general 3-dimensional compact manifolds, after a TT* argument, simply by using the L 2-boundedness of the Hilbert transform on , we are able to improve the corresponding L 2-restriction bounds of Burq, Gérard and Tzvetkov (Duke Math J 138:445-486, 2007) and Hu (Forum Math 6:1021-1052, 2009). Also, in the case of 2-dimensional compact manifolds with nonpositive curvature, we obtain improved L 4-estimates for restrictions to geodesics, which, by Hölder's inequality and interpolation, implies improved L p -bounds for all exponents p ≥ 2. We do this by using oscillatory integral theorems of Hörmander (Ark Mat 11:1-11, 1973), Greenleaf and Seeger (J Reine Angew Math 455:35-56, 1994) and Phong and Stein (Int Math Res Notices 4:49-60, 1991), along with a simple geometric lemma (Lemma 3.2) about properties of the mixed-Hessian of the Riemannian distance function restricted to pairs of geodesics in Riemannian surfaces. We are also able to get further improvements beyond our new results in three dimensions under the assumption of constant nonpositive curvature by exploiting the fact that, in this case, there are many totally geodesic submanifolds.
Integrability of Invariant Geodesic Flows on n-Symmetric Spaces
Jovanovic, Bozidar
2010-01-01
In this paper, by modifying the argument shift method,we prove Liouville integrability of geodesic flows of normal metrics (invariant Einstein metrics) on the Ledger-Obata $n$-symmetric spaces $K^n/\\diag(K)$, where $K$ is a semisimple (respectively, simple) compact Lie group.
Monodromic vs geodesic computation of Virasoro classical conformal blocks
Directory of Open Access Journals (Sweden)
Konstantin Alkalaev
2016-03-01
Full Text Available We compute 5-point classical conformal blocks with two heavy, two light, and one superlight operator using the monodromy approach up to third order in the superlight expansion. By virtue of the AdS/CFT correspondence we show the equivalence of the resulting expressions to those obtained in the bulk computation for the corresponding geodesic configuration.
Thermodynamic Geodesics of a Reissner Nordstr\\"om Black Hole
Farrugia, Christine
2016-01-01
Starting from a Geometrothermodynamics metric for the space of thermodynamic equilibrium states in the mass representation, we use numerical techniques to analyse the thermodynamic geodesics of a supermassive Reissner Nordstr\\"om black hole in isolation. Appropriate constraints are obtained by taking into account the processes of Hawking radiation and Schwinger pair-production. We model the black hole in line with the work of Hiscock and Weems. It can be deduced that the relation which the geodesics establish between the entropy $S$ and electric charge $Q$ of the black hole extremises changes in the black hole's mass. Indeed, at any given point along a geodesic, the value of $\\text{d}S/\\text{d}Q$ is of the same order of magnitude as the rate at which entropy changes with charge during a constant-mass perturbation. Our claim is further justified by the fact that the expression for the entropy of an extremal black hole is an exact solution to the geodesic equation.
On the regularity of geodesic rays associated to test configurations
Phong, D. H.; Sturm, Jacob
2007-01-01
Geodesic rays of class C^{1,1} are constructed for any test configuration of a positive line bundle L on X using resolution of singularities. The construction reduces to finding a subsolution of the corresponding Monge-Ampere equation. Geometrically, this is accomplished by the use a positive line bundle on the resolution which is trivial outside of the exceptional divisor.
Geodesics in the space of K\\"ahler cone metrics
Calama, Simone
2012-01-01
In this paper, we prove the existence and uniqueness of the weak cone geodesics in the space of K\\"ahler cone metrics by solving the singular, homogeneous complex Monge-Amp\\`{e}re equation. As an application, we prove the metric space structure of the appropriate subspace of the space of K\\"ahler cone metrics.
A hierarchical scheme for geodesic anatomical labeling of airway trees
DEFF Research Database (Denmark)
Feragen, Aasa; Petersen, Jens; Owen, Megan;
2012-01-01
We present a fast and robust supervised algorithm for label- ing anatomical airway trees, based on geodesic distances in a geometric tree-space. Possible branch label configurations for a given unlabeled air- way tree are evaluated based on the distances to a training set of labeled airway trees....
Geodesic atlas-based labeling of anatomical trees
DEFF Research Database (Denmark)
Feragen, Aasa; Petersen, Jens; Owen, Megan
2015-01-01
We present a fast and robust atlas-based algorithm for labeling airway trees, using geodesic distances in a geometric tree-space. Possible branch label configurations for an unlabeled airway tree are evaluated using distances to a training set of labeled airway trees. In tree-space, airway tree t...
Analytical solutions for geodesics in black hole spacetimes
Hackmann, Eva
2015-01-01
We review the analytical solution methods for the geodesic equations in Kerr-Newman-Taub-NUT-de Sitter spacetimes and its subclasses in terms of elliptic and hyperelliptic functions. A short guide to corresponding literature for general timelike and lightlike motion is also presented.
A hierarchical scheme for geodesic anatomical labeling of airway trees
DEFF Research Database (Denmark)
Feragen, Aasa; Petersen, Jens; Owen, Megan
2012-01-01
We present a fast and robust supervised algorithm for label- ing anatomical airway trees, based on geodesic distances in a geometric tree-space. Possible branch label configurations for a given unlabeled air- way tree are evaluated based on the distances to a training set of labeled airway trees...
Geodesic flow, connecting orbits and almost full foliation
Institute of Scientific and Technical Information of China (English)
CHENG; Jian; MENG; Long
2006-01-01
We study in this article a special dynamical behavior of geodesic flow on T2.Our example shows that there is an area-preserving monotone twist map for which all minimal periodic orbits can be connected,and at the same time for a certain rational rotation number the minimal set is almost an invariant curve.
Non-Minimally Coupled Cosmology as Geodesic Motion
Elias, L A; Elias, Luciana A.; Saa, Alberto
2007-01-01
Recent works showing that homogeneous and isotropic cosmologies involving scalar fields correspond to geodesics of certain augmented spaces are generalized to the non-minimal coupling case. As the Maupertuis-Jacobi principle in classical mechanics, this result allows us, in principle, to infer some of the dynamical properties of the cosmologies from the geometry of the associated augmented spaces.
Iterated index formulae for closed geodesics with applications
Institute of Scientific and Technical Information of China (English)
LIU; Chungen
2002-01-01
［1］Klingenberg, W., Riemannian Geometry, Berlin: Walter de Gruyter, 1982.［2］Morse, M., The Calculus of Variations in the Large, Vol. 18,New York: Colloquium Publ., 1934.［3］Long, Y., Bott formula of the Maslov_type index theory, Pacific J. Math., 1999, 187: 113-149.［4］Hingston, N., On the lengths of closed geodesics on a two_sphere, Proc. Amer. Math. Soc., 1997, 125(10): 3099-3106.［5］Hingston, N., On the growth of the number of closed geodesics on the two_sphere, Inter. Math. Res. Notices, 1993, 9: 253-262.［6］Ballmann, W., Thorberrgsson, G., Ziller, W., Closed geodesics on positively curved manifolds, Annals of Math., 1982, 116: 213-247.［7］Bott, R., On the iteration of closed geodesics and the Sturm intersection theory, Commun. Pure Appl. Math., 1956, 9: 171-206.［8］Yakubovich, V., Starzhinskii, V., Linear Differential Equations with Periodic Ceofficients, New York: John Wiley & Sons, 1975.［9］Long, Y., Zhu, C., Closed characteristics on compact convex hypersurfaces in R2n, Nankai Inst. of Math., Preprint Series, No. 1999_M_002, Revised Dec. 2000.［10］Rademacher, H. _B., On the average indices of closed geodesics, J. Diff. Geom., 1989, 29: 65-83.［11］Liu, C., Long, Y., Iteration inequalities of the Maslov_type index theory with applications, J. Diff. Equa., 2000, 165: 355-376.［12］Liu, C., Long, Y., An optimal increasing estimate of the iterated Maslov_type indices, Chinese Science Bulletin, 1997, 42: 2275-2277.［13］Long, Y., Precise iteration formula of the Maslov_type index theory and ellipticity of closed characteristics,Advances in Math., 2000, 154: 76-131.［14］Bangert, V., On the existence of closed geodesics on two_spheres, Inter. J. of Math., 1993, 4: 1-10.［15］Bao, D., Chern, S. S., Shen, Z., An Introduction to Riemann_Finsler Geometry, New York: Springer_Verlag, 2000.［16］Bott, R., Lectures on More theory, old and new, Bull. Amer. Math. Soc., 1982, 7(2): 331-358.［17］Franks, J., Geodesics on S2 and
Haustral loop extraction for CT colonography using geodesics.
Liu, Yongkai; Duan, Chaijie; Liang, Jerome; Hu, Jing; Lu, Hongbing; Luo, Mingyue
2017-03-01
The human colon has complex geometric structures because of its haustral folds, which are thin flat protrusions on the colon wall. The haustral loop is the curve (approximately triangular in shape) that encircles the highly convex region of the haustral fold, and is regarded as the natural landmark of the colon, intersecting the longitude of the colon in the middle. Haustral loop extraction can assist in reducing the structural complexity of the colon, and the loops can also serve as anatomic markers for computed tomographic colonography (CTC). Moreover, haustral loop sectioning of the colon can help with the performance of precise prone-supine registration. We propose an accurate approach of extracting haustral loops for CT virtual colonoscopy based on geodesics. First, the longitudinal geodesic (LG) connecting the start and end points is tracked by the geodesic method and the colon is cut along the LG. Second, key points are extracted from the LG, after which paired points that are used for seeking the potential haustral loops are calculated according to the key points. Next, for each paired point, the shortest distance (geodesic line) between the paired points twice is calculated, namely one on the original surface and the other on the cut surface. Then, the two geodesics are combined to form a potential haustral loop. Finally, erroneous and nonstandard potential loops are removed. To evaluate the haustral loop extraction algorithm, we first utilized the algorithm to extract the haustral loops. Then, we let the clinicians determine whether the haustral loops were correct and then identify the missing haustral loops. The extraction algorithm successfully detected 91.87% of all of the haustral loops with a very low false positive rate. We believe that haustral loop extraction may benefit many post-procedures in CTC, such as supine-prone registration, computer-aided diagnosis, and taenia coli extraction.
Robust analysis of trends in noisy tokamak confinement data using geodesic least squares regression
Verdoolaege, G.; Shabbir, A.; Hornung, G.
2016-11-01
Regression analysis is a very common activity in fusion science for unveiling trends and parametric dependencies, but it can be a difficult matter. We have recently developed the method of geodesic least squares (GLS) regression that is able to handle errors in all variables, is robust against data outliers and uncertainty in the regression model, and can be used with arbitrary distribution models and regression functions. We here report on first results of application of GLS to estimation of the multi-machine scaling law for the energy confinement time in tokamaks, demonstrating improved consistency of the GLS results compared to standard least squares.
Brzhozovsky, B. M.; Zimnyakov, D. A.; Zinina, E. P.; Martynov, V. V.; Pleshakova, E. S.; Yuvchenko, S. A.
2016-04-01
Basic features of combined-discharge low-temperature plasma formation around the surfaces of complex-contoured metal units are considered. It is shown that it makes the possibilities for synthesis of hardened high-durable coatings of hard tools appropriate for material processing in extreme load-temperature conditions. Experimental study of the coating formation was carried out in combination with the analysis of emission spectra of a low-temperature plasma cloud. Some practical examples of the coating applications are presented.
Institute of Scientific and Technical Information of China (English)
张丽梅; 张红; 罗钟铉; 董云影
2013-01-01
The images of some marine microalgae were segmented by a C-V active contour model of Chan and Vese whose improved model was described in this paper. When the curvature of the main boundaries of microalga images was changed greatly, namely the main boundaries were of " steep" , it is very difficult to obtain the boundary of the microalgae images by C-V active contour model directly. In the improved C-V active contour model, the rough initial boundaries were drawn through the man-machine interactive pattern at the zero level set, the symbolic function was introduced in the initial zero level set to define internal and external energy, and appropriate parameters were adjusted to execute the process of the evolution of the image boundary. The comparison between the two models for the typical marine microalga image boundaries revealed that for the microalga images with "steep" boundary it is difficult to obtain their boundaries or their boundaries slowly by C-V active contour model. The boundaries of the microalga images were quickly obtained as well as a lot of information of the boundaries when the improved C-V active contour model was used for the microalga image with "steep" boundary. The results showed die effectiveness of die improved C-V active contour model, indicating diat this provides a new skill for the segmentation of microalga images.%采用Chan和Vese的C-V主动轮廓模型以及本文中改进的C-V主动轮廓模型对几类典型的海洋微藻图像进行了分割.当微藻图像的主要边界曲率变化较大,即主边界“陡峭”时,直接使用C-V主动轮廓模型难以获得微藻图像的边界.在改进的C-V主动轮廓模型中,通过人机交互绘制粗略的初始边界,并将其设定为初始零水平集,将符号函数引入到初始水平集中定义内外能量,再通过适当的参数调整进行图像边界的演化.将采用两种模型算法获取典型的海洋微藻图像边界的过程进行对比可知,对于带“陡
Human Lips-Contour Recognition and Tracing
Directory of Open Access Journals (Sweden)
Md. Hasan Tareque
2014-01-01
Full Text Available Human-lip detection is an important criterion for many automated modern system in present day. Like computerized speech reading, face recognition etc. system can work more precisely if human-lip can detect accurately. There are many processes for detecting human-lip. In this paper an approach is developed so that the region of a human-lip can be detected, we called it lip contour. For this a region-based Active Contour Model (ACM is introduced with watershed segmentation. In this model we used global energy terms instead of local energy terms because, global energy gives better convergence rate for malicious environment. At the time of ACM initialization by using H8 based on Lyapunov stability theory, the system gives more accurate and stable result.
Body Image and Body Contouring Procedures.
Sarwer, David B; Polonsky, Heather M
2016-10-01
Dissatisfaction with physical appearance and body image is a common psychological phenomena in Western society. Body image dissatisfaction is frequently reported by those who have excess body weight, but also is seen in those of normal body weight. For both groups of individuals, this dissatisfaction impacts self-esteem and quality of life. Furthermore, it is believed to be the motivational catalyst to a range of appearance-enhancing behaviors, including weight loss efforts and physical activity. Body image dissatisfaction is also believed to play a role in the decision to seek the wide range of body contouring procedures offered by aesthetic physicians. Individuals who seek these procedures typically report increased body image dissatisfaction, focus on the feature they wish to alter with treatment, and often experience improvement in body image following treatment. At the same time, extreme body image dissatisfaction is a symptom of a number of recognized psychiatric disorders. These include anorexia nervosa, bulimia nervosa, and body dysmorphic disorder (BDD), all of which can contraindicate aesthetic treatment. This special topic review paper provides an overview of the relationship between body image dissatisfaction and aesthetic procedures designed to improve body contouring. The review specifically focuses on the relationship of body image and body weight, as well as the presentation of body image psychopathology that would contraindicate aesthetic surgery. The overall goal of the paper is to highlight the clinical implications of the existing research and provide suggestions for future research on the psychological aspects of body contouring procedures.
Null Geodesics in a Magnetically Charged Stringy Black Hole Spacetime
Kuniyal, Ravi Shankar; Nandan, Hemwati; Purohit, K D
2015-01-01
We study the geodesic motion of massless test particles in the background of a magnetic charged black hole spacetime in four dimensions in dilaton-Maxwell gravity. The behaviour of effective potential in view of the different values of black hole parameters is analysed in the equatorial plane. The possible orbits for null geodesics are also discussed in detail in view of the different values of the impact parameter. We have also calculated the frequency shift of photons in this spacetime. The results obtained are then compared with those for the electrically charged stringy black hole spacetime and the Schwarzschild black hole spacetime. It is observed that there exists no stable circular orbit outside the event horizon for massless test particles.
Phase mixing and nonlinearity in geodesic acoustic modes
Energy Technology Data Exchange (ETDEWEB)
Hung, C. P.; Hassam, A. B. [University of Maryland at College Park, College Park, Maryland 20742 (United States)
2013-09-15
Phase mixing and nonlinear resonance detuning of geodesic acoustic modes in a tokamak plasma are examined. Geodesic acoustic modes (GAMs) are tokamak normal modes with oscillations in poloidal flow constrained to lie within flux surfaces. The mode frequency is sonic, dependent on the local flux surface temperature. Consequently, mode oscillations between flux surfaces get rapidly out of phase, resulting in enhanced damping from the phase mixing. Damping rates are shown to scale as the negative 1/3 power of the large viscous Reynolds number. The effect of convective nonlinearities on the normal modes is also studied. The system of nonlinear GAM equations is shown to resemble the Duffing oscillator, which predicts resonance detuning of the oscillator. Resonant amplification is shown to be suppressed nonlinearly. All analyses are verified by numerical simulation. The findings are applied to a recently proposed GAM excitation experiment on the DIII-D tokamak.
Geodesic acoustic modes with poloidal mode couplings ad infinitum
Singh, Rameswar; Garbet, X; Hennequin, P; Vermare, L; Morel, P; Singh, R
2015-01-01
Geodesic acoustic modes (GAMs) are studied, for the first time, including all poloidal mode $(m)$ couplings using drift reduced fluid equations. The nearest neighbor coupling pattern, due to geodesic curvature, leads to a semi-infinite chain model of the GAM with the mode-mode coupling matrix elements proportional to the radial wave number $k_{r}$. The infinite chain can be reduced to a renormalized bi-nodal chain with a matrix continued fractions. Convergence study of linear GAM dispersion with respect to $k_{r}$ and the $m$-spectra confirms that high m couplings become increasingly important with $k_{r}$. The radially sorted roots overlap with experimentally measured GAM frequency profile in low collisionality shots in Tore Supra thus explaining the reduced frequency of GAM in Tore Supra.
Geodesics in the field of a rotating deformed gravitational source
Boshkayev, Kuantay; Abutalip, Marzhan; Kalymova, Zhanerke; Suleymanova, Sharara
2015-01-01
We investigate equatorial geodesics in the gravitational field of a rotating and deformed source described by the approximate Hartle-Thorne metric. In the case of massive particles, we derive within the same approximation analytic expressions for the orbital angular velocity, the specific angular momentum and energy, and the radii of marginally stable and marginally bound circular orbits. Moreover, we calculate the orbital angular velocity and the radius of lightlike circular geodesics. We study numerically the frame dragging effect and the influence of the quadrupolar deformation of the source on the motion of test particles. We show that the effects originating from the rotation can be balanced by the effects due to the oblateness of the source.
Detecting Einstein geodesics: Einstein metrics in projective and conformal geometry
Gover, A Rod
2013-01-01
Here we treat the problem: given a torsion-free connection do its geodesics, as unparametrised curves, coincide with the geodesics of an Einstein metric? We find projective invariants such that the vanishing of these is necessary for the existence of such a metric, and in generic settings the vanishing of these is also sufficient. We also obtain results for the problem of metrisability (without the Einstein condition): We show that the odd Chern type invariants of an affine connection are projective invariants that obstruct the existence of a projectively related Levi-Civita connection. In addition we discuss a concrete link between projective and conformal geometry and the application of this to the projective-Einstein problem.
Geodesics in the field of a rotating deformed gravitational source
Boshkayev, K. A.; Quevedo, H.; Abutalip, M. S.; Kalymova, Zh. A.; Suleymanova, Sh. S.
2016-01-01
We investigate equatorial geodesics in the gravitational field of a rotating and deformed source described by the approximate Hartle-Thorne metric. In the case of massive particles, we derive within the same approximation analytic expressions for the orbital angular velocity, the specific angular momentum and energy, and the radii of marginally stable and marginally bound circular orbits. Moreover, we calculate the orbital angular velocity and the radius of lightlike circular geodesics. We study numerically the frame dragging effect and the influence of the quadrupolar deformation of the source on the motion of test particles. We show that the effects originating from the rotation can be balanced by the effects due to the oblateness of the source.
Embedding spacetime via a geodesically equivalent metric of Euclidean signature
Jonsson, Rickard
2001-01-01
Starting from the equations of motion in a 1 + 1 static, diagonal, Lorentzian spacetime, such as the Schwarzschild radial line element, I find another metric, but with Euclidean signature, which produces the same geodesics x(t). This geodesically equivalent, or dual, metric can be embedded in ordinary Euclidean space. On the embedded surface freely falling particles move on the shortest path. Thus one can visualize how acceleration in a gravitational field is explained by particles moving freely in a curved spacetime. Freedom in the dual metric allows us to display, with substantial curvature, even the weak gravity of our Earth. This may provide a nice pedagogical tool for elementary lectures on general relativity. I also study extensions of the dual metric scheme to higher dimensions. In an addendum I extend the analysis concerning the shape of an embedding of the dual spacetime of a line through a planet of constant proper density.
Geodesic flows and their deformations in Bertrand spacetimes
Kumar, Prashant; Sarkar, Tapobrata
2012-01-01
In this article we will discuss some features of a particular spacetime called Bertrand space-time of Type II (BST-II). This spacetime is associated with multiple real parameters. The various energy conditions and geodesic equations of BST-II are used to find the limits of these parameters which can result in a meaningful and physical space-time. It will be shown that in certain circumstances where the weak and strong energy conditions hold BST-II can be thought of as a physically interesting spacetime. Further, the talk discusses about the ESR parameters in this spacetime. The properties of these parameters are nemerically analyzed keeping an eye on the focussing property of radial timelike and radial null geodesics.
van Vleck determinants geodesic focussing and defocussing in Lorentzian spacetimes
Visser, M
1993-01-01
The van Vleck determinant is an ubiquitous object, arising in many physically interesting situations such as: (1) WKB approximations to quantum time evolution operators and Green functions. (2) Adiabatic approximations to heat kernels. (3) One loop approximations to functional integrals. (4) The theory of caustics in geometrical optics and ultrasonics. (5) The focussing and defocussing of geodesic flows in Riemannian manifolds. While all of these topics are interrelated, the present paper is particularly concerned with the last case and presents extensive theoretical developments that aid in the computation of the van Vleck determinant associated with geodesic flows in Lorentzian spacetimes. {\\sl A fortiori} these developments have important implications for the entire array of topics indicated. PACS: 04.20.-q, 04.20.Cv, 04.60.+n. To appear in Physical Review D47 (1993) 15 March.
Quantization of black hole entropy from unstable circular null geodesics
Wei, Shao-Wen; Liu, Yu-Xiao; Fu, Chun-E.
2016-04-01
The quasinormal mode frequencies can be understood from the massless particles trapped at the unstable circular null geodesics and slowly leaking out to infinity. Based on this viewpoint, in this paper, we semiclassically construct the entropy spectrum of the static and stationary black holes from the null geodesics. The result shows that the spacing of the entropy spectrum only depends on the property of the black hole in the eikonal limit. Moreover, for a black hole far from the extremal case, the spacing is found to be smaller than 2πħ for any dimension, which is very different from the result of the previous work by using the usual quasinormal mode frequencies.
Polyaffine parametrization of image registration based on geodesic flows
DEFF Research Database (Denmark)
Hansen, Michael Sass; Thorup, Signe Strann; Warfield, Simon K.
2012-01-01
Image registration based on geodesic flows has gained much popularity in recent years. We describe a novel parametrization of the velocity field in a stationary flow equation. We show that the method offers both precision, flexibility, and simplicity of evaluation. With our representation, which...... of geodesic shooting for computational anatomy. We avoid to do warp field convolution by interpolation in a dense field, we can easily calculate warp derivatives in a reference frame of choice, and we can consequently avoid interpolation in the image space altogether....... is very similar to existing methods, we show that we can find an analytical solution. This solution converges exponentially to the true solution, and the gradients may be determined similarly. We compare to existing prominent methods; the log-euclidean polyaffine framework, and the DARTEL implementation...
Institute of Scientific and Technical Information of China (English)
郝明; 邓喀中; 张华
2012-01-01
针对传统的主动轮廓模型在提取建筑轮廓时不能区分与其具有相似反射率的地物和需要建筑物附近的初始轮廓等问题,从两方面对其进行了改进：1）将原始的单一数据改为利用高分辨率遥感影像与激光雷达（LiDAR）数据融合后的数据进行建筑物的提取;2）在原始模型的能量公式中加入比例系数,控制各波段在能量泛函中的比重.采用Matlab编程实现了所提出的算法,并对徐州市两个地区的快鸟（Quickbird）影像进行了分析.结果表明：改进后的模型可以很好的完成建筑物轮廓的自动提取,并且具有对噪声不敏感、不需要建筑物附近的初始轮廓和隐式改变拓扑结构的优点,达到了较好的效果,证明了改进主动轮廓模型的可行性.所提出的算法为建筑物的轮廓提取提供了有效手段.%Considering the problems that the buildings can't be distinguished from the objects with the same reflectivity and the initial contours nearby buildings are needed in the traditional- ly active contour model, two different methods are provided to improve the traditionally active contour model in the paper: 1) the high resolution remotely sensed images and LiDAR data are fused to replace the traditionally single data in the improved model; 2) scale coefficients are added into the initial model to control the proportion of each band in the energy functional. The improved model was implemented by Matlab coding and two experiments were performed to e- valuate the performance of the improved model using Quickbird images of two different areas in Xuzhou. Experimental results indicate that the improved model can automatically detect the buildings' contours with the advantages of low sensitivity to noise, no initial contours nearby buildings and changing topologies implicitly, and achieve good results, hence providing effec- tive methods for extracting buildings' contours.
Do electromagnetic waves always propagate along null geodesics?
Asenjo, Felipe A
2016-01-01
We find exact solutions to Maxwell equations written in terms of four-vector potentials in non--rotating, as well as in G\\"odel and Kerr spacetimes. Exact electromagnetic waves solutions are written on given gravitational field backgrounds where they evolve. We find that in non--rotating spherical symmetric spacetimes, electromagnetic plane waves travel along null geodesics. However, electromagnetic plane waves on G\\"odel and Kerr spacetimes do not exhibit that behavior.
Geodesic motion of test particles in Korkina-Grigoryev metric
2016-01-01
We study the geodesic structure of the Korkina-Grigoryev spacetime. The corresponding metric is a generalization of the Schwarzschild geometry to the case involving a massless scalar field. We investigate the relation between the angular momentum of the test particle and the charge of the field, which determines the shape of the effective-potential curves. The ratio for angular momentum of the particle, the charge of the scalar field and the dimensionless spatial parameter is found, under whi...
Landau damping of geodesic acoustic mode in toroidally rotating tokamaks
Energy Technology Data Exchange (ETDEWEB)
Ren, Haijun, E-mail: hjren@ustc.edu.cn [CAS Key Laboratory of Geospace Environment, The Collaborative Innovation Center for Advanced Fusion Energy and Plasma Science, and Department of Modern Physics, University of Science and Technology of China, Hefei 230026 (China); Cao, Jintao [Bejing National Laboratory for Condensed Matter Physics and CAS Key Laboratory of Soft Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190 (China)
2015-06-15
Geodesic acoustic mode (GAM) is analyzed by using modified gyro-kinetic (MGK) equation applicable to low-frequency microinstabilities in a rotating axisymmetric plasma. Dispersion relation of GAM in the presence of arbitrary toroidal Mach number is analytically derived. The effects of toroidal rotation on the GAM frequency and damping rate do not depend on the orientation of equilibrium flow. It is shown that the toroidal Mach number M increases the GAM frequency and dramatically decreases the Landau damping rate.
Lens rigidity with trapped geodesics in two dimensions
Croke, Christopher B
2011-01-01
We consider the scattering and lens rigidity of compact surfaces with boundary that have a trapped geodesic. In particular we show that the flat cylinder and the flat M\\"obius strip are determined by their lens data. We also see by example that the flat M\\"obius strip is not determined by it's scattering data. We then consider the case of negatively curved cylinders with convex boundary and show that they are lens rigid.
A Continuum Mechanical Approach to Geodesics in Shape Space
2010-01-01
A CONTINUUM MECHANICAL APPROACH TO GEODESICS IN SHAPE SPACE By Benedikt Wirth Leah Bar Martin Rumpf and Guillermo Sapiro IMA Preprint Series # 2295...Benedikt Wirth† Leah Bar‡ Martin Rumpf† Guillermo Sapiro‡ †Institute for Numerical Simulation, University of Bonn, Germany ‡Department of Electrical and...mean curvature flow equation. Calc. Var., 3:253–271, 1995. [30] Siddharth Manay, Daniel Cremers , Byung-Woo Hong, Anthony J. Yezzi, and Stefano Soatto
Stability of perturbed geodesics in nD axisymmetric spacetimes
Coimbra-Araújo, C. H.; Anjos, R. C.
2016-09-01
The effect of self-gravity of a disk matter is evaluated by the simplest modes of oscillation frequencies for perturbed circular geodesics. We plotted the radial profiles of free oscillations of an equatorial circular geodesic perturbed within the orbital plane or in the vertical direction. The calculation is carried out to geodesics of an axisymmetric n-dimensional spacetime. The profiles are computed by examples of disks embeded in five-dimensional or six-dimensional spacetime, where we studied the motion of free test particles for three axisymmetric cases: (i) the Newtonian limit of a general proposed 5D and 6D axisymmetric spacetime; (ii) a simple Randall-Sundrum (RS) 5D spacetime; (iii) general 5D and 6D RS spacetime. The equation of motion of such particles is derived and the stability study is computed for both horizontal and vertical directions, to see how extra dimensions could affect the system. In particular, we investigate a disk constructed from Miyamoto-Nagai and Chazy-Curzon with a cut parameter to generate a disk potential. Those solutions have a simple extension for extra dimensions in case (i), and by solving vacuum Einstein field equations for a kind of RS-Weyl metric in cases (ii) and (iii). We find that it is possible to compute a range of possible solutions where such perturbed geodesics are stable. Basically, the stable solutions appear, for the radial direction, in special cases when the system has 5D and in all cases when the system has 6D and, for the axial direction, in all cases when the system has both 5D or 6D.
Firmly nonexpansive mappings in classes of geodesic spaces
Ariza-Ruiz, David; Lopez-Acedo, Genaro
2012-01-01
Firmly nonexpansive mappings play an important role in metric fixed point theory and optimization due to their correspondence with maximal monotone operators. In this paper we do a thorough study of fixed point theory and the asymptotic behaviour of Picard iterates of these mappings in different classes of geodesic spaces, as (uniformly convex) $W$-hyperbolic spaces, Busemann spaces and CAT(0) spaces. Furthermore, we apply methods of proof mining to obtain effective rates of asymptotic egularity for the Picard iterations.
Geodesic completeness in a wormhole spacetime with horizons
Olmo, Gonzalo J; Sanchez-Puente, A
2015-01-01
The geometry of a spacetime containing a wormhole generated by a spherically symmetric electric field is investigated in detail. These solutions arise in high-energy extensions of General Relativity formulated within the Palatini approach and coupled to Maxwell electrodynamics. Even though curvature divergences generically arise at the wormhole throat, we find that these spacetimes are geodesically complete. This provides an explicit example where curvature divergences do not imply spacetime singularities.
Topological Cacti: Visualizing Contour-based Statistics
Energy Technology Data Exchange (ETDEWEB)
Weber, Gunther H.; Bremer, Peer-Timo; Pascucci, Valerio
2011-05-26
Contours, the connected components of level sets, play an important role in understanding the global structure of a scalar field. In particular their nestingbehavior and topology-often represented in form of a contour tree-have been used extensively for visualization and analysis. However, traditional contour trees onlyencode structural properties like number of contours or the nesting of contours, but little quantitative information such as volume or other statistics. Here we use thesegmentation implied by a contour tree to compute a large number of per-contour (interval) based statistics of both the function defining the contour tree as well asother co-located functions. We introduce a new visual metaphor for contour trees, called topological cacti, that extends the traditional toporrery display of acontour tree to display additional quantitative information as width of the cactus trunk and length of its spikes. We apply the new technique to scalar fields ofvarying dimension and different measures to demonstrate the effectiveness of the approach.
A Dynamical Systems Approach to Schwarzschild Null Geodesics
Belbruno, Edward
2011-01-01
The null geodesics of a Schwarzschild black hole are studied from a dynamical systems perspective. Written in terms of Kerr-Schild coordinates, the null geodesic equation takes on the simple form of a particle moving under the influence of a Newtonian central force with an inverse-cubic potential. We apply a McGehee transformation to these equations, which clearly elucidates the full phase space of solutions. All the null geodesics belong to one of four families of invariant manifolds and their limiting cases, further characterized by the angular momentum L of the orbit: for |L|>|L_c|, (1) the set that flow outward from the white hole, turn around, then fall into the black hole, (2) the set that fall inward from past null infinity, turn around outside the black hole to continue to future null infinity, and for |L|<|L_c|, (3) the set that flow outward from the white hole and continue to future null infinity, (4) the set that flow inward from past null infinity and into the black hole. The critical angular m...
Stability of perturbed geodesics in $nD$ axisymmetric spacetimes
Coimbra-Araujo, C H
2016-01-01
The effect of self-gravity of a disk matter is evaluated by the simplest modes of oscillation frequencies for perturbed circular geodesics. It is plotted the radial profiles of free oscillations of an equatorial circular geodesic perturbed within the orbital plane or in the vertical direction. The calculation is carried out to geodesics of an axisymmetric $n$-dimensional spacetime. The profiles are computed by examples of disks embeded in five-dimensional or six-dimensional spacetime, where it is studied the motion of free test particles for three axisymmetric cases: (i) the Newtonian limit of a general proposed $5D$ and $6D$ axisymmetric spacetime; (ii) a simple Randall-Sundrum $5D$ spacetime; (iii) general $5D$ and $6D$ Randall-Sundrum spacetime. The equation of motion of such particles is derived and the stability study is computed for both horizontal and vertical directions, to see how extra dimensions could affect the system. In particular, we investigate a disk constructed from Schwarzschild and Chazy-C...
Adaptive geodesic transform for segmentation of vertebrae on CT images
Gaonkar, Bilwaj; Shu, Liao; Hermosillo, Gerardo; Zhan, Yiqiang
2014-03-01
Vertebral segmentation is a critical first step in any quantitative evaluation of vertebral pathology using CT images. This is especially challenging because bone marrow tissue has the same intensity profile as the muscle surrounding the bone. Thus simple methods such as thresholding or adaptive k-means fail to accurately segment vertebrae. While several other algorithms such as level sets may be used for segmentation any algorithm that is clinically deployable has to work in under a few seconds. To address these dual challenges we present here, a new algorithm based on the geodesic distance transform that is capable of segmenting the spinal vertebrae in under one second. To achieve this we extend the theory of the geodesic distance transforms proposed in1 to incorporate high level anatomical knowledge through adaptive weighting of image gradients. Such knowledge may be provided by the user directly or may be automatically generated by another algorithm. We incorporate information 'learnt' using a previously published machine learning algorithm2 to segment the L1 to L5 vertebrae. While we present a particular application here, the adaptive geodesic transform is a generic concept which can be applied to segmentation of other organs as well.
Orbifold Riemann surfaces: Teichmueller spaces and algebras of geodesic functions
Energy Technology Data Exchange (ETDEWEB)
Mazzocco, Marta [Loughborough University, Loughborough (United Kingdom); Chekhov, Leonid O [Institute for Theoretical and Experimental Physics (Russian Federation State Scientific Center), Moscow (Russian Federation)
2009-12-31
A fat graph description is given for Teichmueller spaces of Riemann surfaces with holes and with Z{sub 2}- and Z{sub 3}-orbifold points (conical singularities) in the Poincare uniformization. The corresponding mapping class group transformations are presented, geodesic functions are constructed, and the Poisson structure is introduced. The resulting Poisson algebras are then quantized. In the particular cases of surfaces with n Z{sub 2}-orbifold points and with one and two holes, the respective algebras A{sub n} and D{sub n} of geodesic functions (classical and quantum) are obtained. The infinite-dimensional Poisson algebra D{sub n}, which is the semiclassical limit of the twisted q-Yangian algebra Y'{sub q}(o{sub n}) for the orthogonal Lie algebra o{sub n}, is associated with the algebra of geodesic functions on an annulus with n Z{sub 2}-orbifold points, and the braid group action on this algebra is found. From this result the braid group actions are constructed on the finite-dimensional reductions of this algebra: the p-level reduction and the algebra D{sub n}. The central elements for these reductions are found. Also, the algebra D{sub n} is interpreted as the Poisson algebra of monodromy data of a Frobenius manifold in the vicinity of a non-semisimple point. Bibliography: 36 titles.
Joseph, Shiju; Adnan, Asif; Adlam, David
2016-10-01
Lumen segmentation from clinical intravascular optical coherence tomography (IV-OCT) images has clinical relevance as it provides a full three-dimensional perspective of diseased coronary artery sections. Inaccurate segmentation may occur when there are artifacts in the image, resulting from issues such as inadequate blood clearance. This study proposes a transmittance-based lumen intensity enhancement method that ensures only lumen regions are highlighted. A level-set-based active contour method that utilizes the local speckle distribution properties of the image is then employed to drive an image-specific active contour toward the true lumen boundaries. By utilizing local speckle properties, the intensity variation issues within the image are resolved. This combined approach has been successfully applied to challenging clinical IV-OCT datasets that contains multiple lumens, residual blood flow, and its shadowing artifact. A method to identify the guide-wire and interpolate the lost lumen segments has been implemented. This approach is fast and can be performed even when guide-wire boundaries are not easily identified. Lumen enhancement also makes it easy to identify vessel side branches. This automated approach is not only able to extract the arterial lumen, but also the smaller microvascular lumens that are associated with the vasa vasorum and with atherosclerotic plaque.
Illusory contour formation survives crowding.
Lau, Jonathan Siu Fung; Cheung, Sing-Hang
2012-06-12
Flanked objects are difficult to identify using peripheral vision due to visual crowding, which limits conscious access to target identity. Nonetheless, certain types of visual information have been shown to survive crowding. Such resilience to crowding provides valuable information about the underlying neural mechanism of crowding. Here we ask whether illusory contour formation survives crowding of the inducers. We manipulated the presence of illusory contours through the (mis)alignment of the four inducers of a Kanizsa square. In the inducer-aligned condition, the observers judged the perceived shape (thin vs. fat) of the illusory Kanizsa square, manipulated by small rotations of the inducers. In the inducer-misaligned condition, three of the four inducers (all except the upper-left) were rotated 90°. The observers judged the orientation of the upper-left inducer. Crowding of the inducers worsened observers' performance significantly only in the inducer-misaligned condition. Our findings suggest that information for illusory contour formation survives crowding of the inducers. Crowding happens at a stage where the low-level featural information is integrated for inducer orientation discrimination, but not at a stage where the same information is used for illusory contour formation.
Contour Detection by CORF Operator
Azzopardi, George; Petkov, Nicolai
2012-01-01
We propose a contour operator, called CORF, inspired by the properties of simple cells in visual cortex. It combines, by a weighted geometric mean, the blurred responses of difference-of-Gaussian operators that model cells in the lateral geniculate nucleus (LGN). An operator that has gained
Geodesic B-Preinvex Functions and Multiobjective Optimization Problems on Riemannian Manifolds
Directory of Open Access Journals (Sweden)
Sheng-lan Chen
2014-01-01
Full Text Available We introduce a class of functions called geodesic B-preinvex and geodesic B-invex functions on Riemannian manifolds and generalize the notions to the so-called geodesic quasi/pseudo B-preinvex and geodesic quasi/pseudo B-invex functions. We discuss the links among these functions under appropriate conditions and obtain results concerning extremum points of a nonsmooth geodesic B-preinvex function by using the proximal subdifferential. Moreover, we study a differentiable multiobjective optimization problem involving new classes of generalized geodesic B-invex functions and derive Kuhn-Tucker-type sufficient conditions for a feasible point to be an efficient or properly efficient solution. Finally, a Mond-Weir type duality is formulated and some duality results are given for the pair of primal and dual programming.
Every timelike geodesic in anti--de Sitter spacetime is a circle of the same radius
Sokołowski, Leszek M
2016-01-01
We refine and analytically prove an old proposition due to Calabi and Markus on the shape of timelike geodesics of anti--de Sitter space in the ambient flat space. We prove that each timelike geodesic forms in the ambient space a circle of the radius determined by $\\Lambda$, lying on a Euclidean two--plane. Then we outline an alternative proof for $AdS_4$. We also make a comment on the shape of timelike geodesics in de Sitter space.
Symmetries of geodesic motion in G\\"{o}del-type spacetimes
Camci, U
2014-01-01
In this paper, we study Noether gauge symmetries of geodesic motion for geodesic Lagrangian of four classes of metrics of G\\"{o}del-type spacetimes for which we calculated the Noether gauge symmetries for all classes I-IV, and find the first integrals of corresponding classes to derive a complete characterization of the geodesic motion. Using the obtained expressions for $\\dot{t}, \\dot{r}, \\dot{\\phi}$ and $\\dot{z}$ of each classes I-IV which depends essentially on two independent parameters $m$ and $w$, we explicitly integrated the geodesic equations of motion for the corresponding G\\"{o}del-type spacetimes.
Simple computation of null-geodesics, with applications to vortex boundary detection
Serra, Mattia; Haller, George
2016-11-01
Recent results show that boundaries of coherent vortices (elliptic coherent structures) can be computed as closed null-geodesics of appropriate Lorentzian metrics defined on the physical domain of the underlying fluid. Here we derive a new method for computing null-geodesics of general Lorentzian metrics, founded on the geometry of geodesic flows. We also derive the correct set of initial conditions for the computation of closed null-geodesics, based on simple topological properties of planar closed curves. This makes the computation of coherent vortex boundaries fully automated, simpler and more accurate compared to the existing procedure. As an illustration, we compute objective coherent vortex boundaries in Oceanic and Atmospheric Flows.
Gulf of Mexico Deepwater Bathymetry Contours
Bureau of Ocean Energy Management, Department of the Interior — Gulf of Mexico Depth Contours derived from NOAA's NGDC bathymetric grids and from BOEM's seismic grid compilation. Both NOAA and BOEM contours are shown in meters or...
The Poggendorff illusion driven by real and illusory contour: Behavioral and neural mechanisms.
Shen, Lu; Zhang, Ming; Chen, Qi
2016-05-01
The Poggendorff illusion refers to the phenomenon that the human brain misperceives a diagonal line as being apparently misaligned once the diagonal line is interrupted by two parallel edges, and the size of illusion is negatively correlated with the angle of interception of the oblique, i.e. the sharper the oblique angle, the larger the illusion. This optical illusion can be produced by both real and illusory contour. In this fMRI study, by parametrically varying the oblique angle, we investigated the shared and specific neural mechanisms underlying the Poggendorff illusion induced by real and illusory contour. At the behavioral level, not only the real but also the illusory contours were capable of inducing significant Poggendorff illusion. The size of illusion induced by the real contour, however, was larger than that induced by the illusory contour. At the neural level, real and illusory contours commonly activated more dorsal visual areas, and the real contours specifically activated more ventral visual areas. More importantly, examinations on the parametric modulation effects of the size of illusion revealed the specific neural mechanisms underlying the Poggendorff illusion induced by the real and the illusory contours, respectively. Left precentral gyrus and right middle occipital cortex were specifically involved in the Poggendorff illusion induced by the real contour. On the other hand, bilateral intraparietal sulcus (IPS) and right lateral occipital complex (LOC) were specifically involved in the Poggendorff illusion induced by the illusory contour. Functional implications of the above findings were further discussed.
Visually-salient contour detection using a V1 neural model with horizontal connections
Loxley, P N
2011-01-01
A convolution model which accounts for neural activity dynamics in the primary visual cortex is derived and used to detect visually salient contours in images. Image inputs to the model are modulated by long-range horizontal connections, allowing contextual effects in the image to determine visual saliency, i.e. line segments arranged in a closed contour elicit a larger neural response than line segments forming background clutter. The model is tested on 3 types of contour, including a line, a circular closed contour, and a non-circular closed contour. Using a modified association field to describe horizontal connections the model is found to perform well for different parameter values. For each type of contour a different facilitation mechanism is found. Operating as a feed-forward network, the model assigns saliency by increasing the neural activity of line segments facilitated by the horizontal connections. Alternatively, operating as a feedback network, the model can achieve further improvement over sever...
Divided Spheres Geodesics and the Orderly Subdivision of the Sphere
Popko, Edward S
2012-01-01
This well-illustrated book-in color throughout-presents a thorough introduction to the mathematics of Buckminster Fuller's invention of the geodesic dome, which paved the way for a flood of practical applications as diverse as weather forecasting and fish farms. The author explains the principles of spherical design and the three main categories of subdivision based on geometric solids (polyhedra). He illustrates how basic and advanced CAD techniques apply to spherical subdivision and covers modern applications in product design, engineering, science, games, and sports balls.
Tifinagh Character Recognition Using Geodesic Distances, Decision Trees & Neural Networks
Directory of Open Access Journals (Sweden)
O.BENCHAREF
2011-09-01
Full Text Available The recognition of Tifinagh characters cannot be perfectly carried out using the conventional methods which are based on the invariance, this is due to the similarity that exists between some characters which differ from each other only by size or rotation, hence the need to come up with new methods to remedy this shortage. In this paper we propose a direct method based on the calculation of what is called Geodesic Descriptors which have shown significant reliability vis-à-vis the change of scale, noise presence and geometric distortions. For classification, we have opted for a method based on the hybridization of decision trees and neural networks.
A Mean Value Theorem for Closed Geodesics on Congruence Surfaces
Lukianov, Vladimir
2005-01-01
We define a weighted multiplicity function for closed geodesics of given length on a finite area Riemann surface. These weighted multiplicities appear naturally in the Selberg trace formula, and in particular their mean square plays an important role in the study of statistics of the eigenvalues of the Laplacian on the surface. In the case of the modular domain, E. Bogomolny, F. Leyvraz and C. Schmit gave a formula for the mean square, which was rigorously proved by M. Peter. In this paper we...
3+1 geodesic equation and images in numerical spacetimes
Vincent, Frederic H; Novak, Jérôme
2012-01-01
The equations governing null and timelike geodesics are derived within the 3+1 formalism of general relativity. In addition to the particle's position, they encompass an evolution equation for the particle's energy leading to a 3+1 expression of the redshift factor for photons. An important application is the computation of images and spectra in spacetimes arising from numerical relativity, via the ray-tracing technique. This is illustrated here by images of numerically computed stationary neutron stars and dynamical neutron stars collapsing to a black hole.
Rapid Mixing of Geodesic Walks on Manifolds with Positive Curvature
Mangoubi, Oren; Smith, Aaron
2016-01-01
We introduce a Markov chain for sampling from the uniform distribution on a Riemannian manifold $\\mathcal{M}$, which we call the $\\textit{geodesic walk}$. We prove that the mixing time of this walk on any manifold with positive sectional curvature $C_{x}(u,v)$ bounded both above and below by $0 < \\mathfrak{m}_{2} \\leq C_{x}(u,v) \\leq \\mathfrak{M}_2 < \\infty$ is $\\mathcal{O}^*\\left(\\frac{\\mathfrak{M}_2}{\\mathfrak{m}_2}\\right)$. In particular, this bound on the mixing time does not depend expli...
基于两步几何主动轮廓的快速图像分割%Fast Image Segmentation Based on a Two-Stage Geometrical Active Contour
Institute of Scientific and Technical Information of China (English)
XIAO Chang-yan; ZHANG Su; CHEN Ya-zhu
2005-01-01
A fast two-stage geometric active contour algorithm for image segmentation is developed. First, the Eikonal equation problem is quickly solved using an improved fast sweeping method, and a criterion of local minimum of area gradient (LMAG) is presented to extract the optimal arrival time. Then, the final time function is passed as an initial state to an area and length minimizing flow model,which adjusts the interface more accurately and prevents it from leaking. For object with complete and salient edge, using the first stage only is able to obtain an ideal result, and this results in a time complexity of O ( M), where M is the number of points in each coordinate direction. Both stages are needed for convoluted shapes, but the computation cost can be drastically reduced. Efficiency of the algorithm is verified in segmentation experiments of real images with different feature.
Grouping by proximity in haptic contour detection.
Directory of Open Access Journals (Sweden)
Krista E Overvliet
Full Text Available We investigated the applicability of the Gestalt principle of perceptual grouping by proximity in the haptic modality. To do so, we investigated the influence of element proximity on haptic contour detection. In the course of four sessions ten participants performed a haptic contour detection task in which they freely explored a haptic random dot display that contained a contour in 50% of the trials. A contour was defined by a higher density of elements (raised dots, relative to the background surface. Proximity of the contour elements as well as the average proximity of background elements was systematically varied. We hypothesized that if proximity of contour elements influences haptic contour detection, detection will be more likely when contour elements are in closer proximity. This should be irrespective of the ratio with the proximity of the background elements. Results showed indeed that the closer the contour elements were, the higher the detection rates. Moreover, this was the case independent of the contour/background ratio. We conclude that the Gestalt law of proximity applies to haptic contour detection.
Smooth and Energy Saving Gait Planning for Humanoid Robot Using Geodesics
Directory of Open Access Journals (Sweden)
Liandong Zhang
2012-01-01
Full Text Available A novel gait planning method using geodesics for humanoid robot is given in this paper. Both the linear inverted pendulum model and the exact Single Support Phase (SSP are studied in our energy optimal gait planning based on geodesics. The kinetic energy of a 2-dimension linear inverted pendulum is obtained at first. We regard the kinetic energy as the Riemannian metric and the geodesic on this metric is studied and this is the shortest line between two points on the Riemannian surface. This geodesic is the optimal kinetic energy gait for the COG because the kinetic energy along geodesic is invariant according to the geometric property of geodesics and the walking is smooth and energy saving. Then the walking in Single Support Phase is studied and the energy optimal gait for the swing leg is obtained using our geodesics method. Finally, experiments using state-of-the-art method and using our geodesics optimization method are carried out respectively and the corresponding currents of the joint motors are recorded. With the currents comparing results, the feasibility of this new gait planning method is verified.
Dome, Sweet Dome--Geodesic Structures Teach Math, Science, and Technology Principles
Shackelford, Ray; Fitzgerald, Michael
2007-01-01
Today, geodesic domes are found on playgrounds, homes, over radar installations, storage facilities, at Disney's Epcot Center, and at World's Fairs. The inventor of the design, Buckminster Fuller, thought that geodesic domes could be used to cover large areas and even designed one to cover all of New York's Manhattan Island. This article details…
Optimal three-dimensional biped walking pattern generation based on geodesics
Directory of Open Access Journals (Sweden)
Liandong Zhang
2017-03-01
Full Text Available The innovative three-dimensional humanoid biped gait planning method using geodesics is introduced in this article. In order to control three-dimensional walking, the three-dimensional linear inverted pendulum model is studied in our energy-optimal gait planning based on geodesics. The kinetic energy of the three-dimensional linear inverted pendulum model is calculated at first. Based on this kinetic energy model, the Riemannian metric is defined and the Riemannian surface is further determined by this Riemannian metric. The geodesic is the shortest line between two points on the Riemannian surface. This geodesic is the optimal kinetic energy gait for the center of gravity because the kinetic energy along the geodesic is invariant according to the geometric property of geodesics and the walking is energy-saving. Finally, a simulation experiment using a 12-degree-of-freedom biped robot model is implemented. The gait sequences of the simulated RoboErectus humanoid robot are obtained in the ROS (Robot Operating System Gazebo environment. The proposed geodesics approach is compared with the traditional sinusoidal interpolation method by analyzing the torque feedback of each joint of both legs, and our geodesics optimization gait planning method for three-dimensional linear inverted pendulum model walking control is verified by the assessment results.
Equidistribution of geodesics on homology classes and analogues for free groups
DEFF Research Database (Denmark)
Petridis, Y.N.; Risager, Morten
2005-01-01
We investigate how often geodesics have homology in a fixed set of the homology lattice of a compact Riemann surface. We prove that closed geodesics are equidistributed on a random set of homology classes and certain arithmetic sets. We explain the analogues for free groups, conjugacy classes...
Equidistribution of geodesics on homology classes and analogues for free groups
DEFF Research Database (Denmark)
Petridis, Yiannis N.; Risager, Morten S.
2008-01-01
We investigate how often geodesics have homology in a fixed set of the homology lattice of a compact Riemann surface. We prove that closed geodesics are equidistributed on any set with asymptotic density with respect to a specific norm. We explain the analogues for free groups, conjugacy classes...
Spectral segmentation via midlevel cues integrating geodesic and intensity.
Lu, Huchuan; Zhang, Ruixuan; Li, Shifeng; Li, Xuelong
2013-12-01
Image segmentation still remains as a challenge in image processing and pattern recognition when involving complex natural scenes. In this paper, we present a new affinity model for spectral segmentation based on midlevel cues. In contrast to most existing methods that operate directly on low-level cues, we first oversegment the image into superpixel images and then integrate the geodesic line edge and intensity cue to form the similarity matrix W so that it more accurately describes the similarity between data. The geodesic line edge could avoid strong boundary and represent the true boundary between two superpixels while the mean red green blue vector could describe the intensity of superpixels better. As far as we know, this is a totally new kind of affinity model to represent superpixels. Based on this model, we use the spectral clustering in the superpixel level and then achieve the image segmentation in the pixel level. The experimental results show that the proposed method performs steadily and well on various natural images. The evaluation comparisons also prove that our method achieves comparable accuracy and significantly performs better than most state-of-the-art algorithms.
Ricci magnetic geodesic motion of vortices and lumps
Alqahtani, L S
2014-01-01
Ricci magnetic geodesic (RMG) motion in a k\\"ahler manifold is the analogue of geodesic motion in the presence of a magnetic field proportional to the ricci form. It has been conjectured to model low-energy dynamics of vortex solitons in the presence of a Chern-Simons term, the k\\"ahler manifold in question being the $n$-vortex moduli space. This paper presents a detailed study of RMG motion in soliton moduli spaces, focusing on the cases of hyperbolic vortices and spherical $\\mathbb{C}P^1$ lumps. It is shown that RMG flow localizes on fixed point sets of groups of holomorphic isometries, but that the flow on such submanifolds does not, in general, coincide with their intrinsic RMG flow. For planar vortices, it is shown that RMG flow differs from an earlier reduced dynamics proposed by Kim and Lee, and that the latter flow is ill-defined on the vortex coincidence set. An explicit formula for the metric on the whole moduli space of hyperbolic two-vortices is computed (extending an old result of Strachan's), an...
Maxwell Fields and Shear-Free Null Geodesic Congruences
Newman, E
2004-01-01
We study and report on the class of vacuum Maxwell fields in Minkowski space that possess a non-degenerate, diverging, principle null vector field (null eigenvector field of the Maxwell tensor) that is tangent to a shear-free null geodesics congruence. These congruences can be either surface forming (the tangent vectors proportional to gradients) or not, i.e., the twisting congruences. In the non-twisting case, the associated Maxwell fields are precisely the Lienard-Wiechert fields, i.e., those Maxwell fields arising from an electric monopole moving on an arbitrary worldline. The null geodesic congruence is given by the generators of the light-cones with apex on the world-line. The twisting case is much richer, more interesting and far more complicated. In a twisting subcase, where our main interests lie, it can be given the following strange interpretation. If we allow the real Minkowski space to be complexified so that the real Minkowski coordinates x^a take complex values, i.e., x^a => z^a=x^a+iy^a with co...
Cold Scalar-Tensor Black Holes Causal Structure, Geodesics, Stability
Bronnikov, K A; Constantinidis, C P; Fabris, J C
1998-01-01
We study the structure and stability of spherically symmetric Brans-Dicke black-hole type solutions with an infinite horizon area and zero Hawking temperature, existing for negative values of the coupling constant $\\omega$. These solutions split into two classes, depending on finite (B1) or infinite (B2) proper time needed for an infalling particle to reach the horizon. Class B1 metrics can be extended through the horizon only for discrete values of mass and scalar charge, depending on two integers m and n. For even m-n, the space-time is globally regular; for odd m, the metric changes its signature on the horizon but remains Lorentzian. Geodesics are smoothly continued across the horizon, but for odd m timelike geodesics become spacelike and vice versa. Causality problems, arising in some cases, are discussed. Tidal forces are shown to grow infinitely near type B1 horizons. All vacuum static, spherically symmetric solutions of the Brans-Dicke theory with $\\omega<-3/2$ are found to be linearly stable again...
Black-Box Optimization Using Geodesics in Statistical Manifolds
Directory of Open Access Journals (Sweden)
Jérémy Bensadon
2015-01-01
Full Text Available Information geometric optimization (IGO is a general framework for stochastic optimization problems aiming at limiting the influence of arbitrary parametrization choices: the initial problem is transformed into the optimization of a smooth function on a Riemannian manifold, defining a parametrization-invariant first order differential equation and, thus, yielding an approximately parametrization-invariant algorithm (up to second order in the step size. We define the geodesic IGO update, a fully parametrization-invariant algorithm using the Riemannian structure, and we compute it for the manifold of Gaussians, thanks to Noether’s theorem. However, in similar algorithms, such as CMA-ES (Covariance Matrix Adaptation - Evolution Strategy and xNES (exponential Natural Evolution Strategy, the time steps for the mean and the covariance are decoupled. We suggest two ways of doing so: twisted geodesic IGO (GIGO and blockwise GIGO. Finally, we show that while the xNES algorithm is not GIGO, it is an instance of blockwise GIGO applied to the mean and covariance matrix separately. Therefore, xNES has an almost parametrization-invariant description.
Dynamic realization of the Unruh effect for a geodesic observer
Lochan, Kinjalk; Padmanabhan, T
2016-01-01
We study a dynamic version of the Unruh effect in a two dimensional collapse model forming a black hole. In this two-dimensional collapse model a scalar field coupled to the dilaton gravity, moving leftwards, collapses to form a black hole. There are two sets of asymptotic ($t\\to\\infty$) observers, around $x\\to\\infty$ and $x\\to-\\infty$. The observers at the right null infinity witness a thermal flux of radiation associated with time dependent geometry leading to a black hole formation and its subsequent Hawking evaporation, in an expected manner. We show that even the observers at left null infinity witness a thermal radiation, without experiencing any change of spacetime geometry all along their trajectories. They remain geodesic observers in a flat region of spacetime. Thus these observers measure a late time thermal radiation, with exactly the same temperature as measured by the observers at right null infinity, despite moving geodesically in flat spacetime throughout their trajectories. However such radia...
A thermodynamic study of zatrikean geodesics resulting from a discrete-geometry model
Geroyannis, V. S.; Dallas, T. G.
We attempt a connection between thermodynamics and zatrikean pregeometry, i.e., a chess-like pregeometry (Geroyannis 1993, hereafter G93). In zatrikean pregeometry space is represented by the abacus, a discrete chessboard-like structure consisting of a sufficiently large number of plaquettes called geobits. The particles move on the abacus from one geobit to the next following certain rules that resemble the game of chess. The sets of rules imposed on the motions of particles on the abacus are called premetrics. There is a variety of paths (called subabaces) leading from one geobit to another, and there is a class consisting of subabaces with the minimum number of geobits. These are called alyssoids (respectively, class of alyssoids) for the particular premetric, while those alyssoids with minimum length are called geodesics (respectively, class of geodesics) for the particular premetric. The so-called zatrikean geodesic was originally defined in G93 (Section 2) as the geodesic most closely following the line segment joining the two geobits. It is also called algorithmic geodesic since it is drawn with the assistance of four simple algorithms. This is a rectifiable curve; and a connection between rectifiable curves and thermodynamics is already available (DuPain, Kamae and Mendes-France 1986). Consequently, the so-called thermodynamic geodesic is defined as the particular member of the class of geodesics with maximum entropy. Since it does not necessarily correspond to the algorithmic geodesic, a new algorithm is devised that draws the geodesic with maximum entropy. Furthermore, the probability of each member of the class of geodesics can be determined as the difference of its entropy from the entropy of the thermodynamicgeodesic.
After massive weight loss: patients' expectations of body contouring surgery.
Kitzinger, Hugo B; Abayev, Sara; Pittermann, Anna; Karle, Birgit; Bohdjalian, Arthur; Langer, Felix B; Prager, Gerhard; Frey, Manfred
2012-04-01
Massive weight loss following bariatric surgery leads to excess skin with functional and aesthetic impairments. Surplus skin can then contribute to problems with additional weight loss or gain. The aims of the current study were to evaluate the frequency of massive soft tissue development in gastric bypass patients, to determine whether males and females experience similar post-bypass body changes, and to learn about the expectations and impairments related to body contouring surgery. A questionnaire addressing information on the satisfaction of body image, quality of life, and expectation of body contouring surgery following massive weight loss was mailed to 425 patients who had undergone gastric bypass surgery between 2003 and 2009. Of these 425 individuals, 252 (59%) patients completed the survey. Ninety percent of women and 88% of men surveyed rated their appearance following massive weight loss as satisfactory, good, or very good. However, 96% of all patients developed surplus skin, which caused intertriginous dermatitis and itching. In addition, patients reported problems with physical activity (playing sports) and finding clothing that fit appropriately. Moreover, 75% of female and 68% of male patients reported desiring body contouring surgery. The most important expectation of body contouring surgery was improved appearance, followed by improved self-confidence and quality of life. Surplus skin resulting from gastric bypass surgery is a common issue that causes functional and aesthetic impairments in patients. Consequently, this increases the desire for body contouring surgery with high expectations for the aesthetic outcome as well as improved life satisfaction.
Brightness Alteration with Interweaving Contours
Directory of Open Access Journals (Sweden)
Sergio Roncato
2012-12-01
Full Text Available Chromatic induction is observed whenever the perceived colour of a target surface shifts towards the hue of a neighbouring surface. Some vivid manifestations may be seen in a white background where thin coloured lines have been drawn (assimilation or when lines of different colours are collinear (neon effect or adjacent (watercolour to each other. This study examines a particular colour induction that manifests in concomitance with an opposite effect of colour saturation (or anti-spread. The two phenomena can be observed when a repetitive pattern is drawn in which outline thin contours intercept wider contours or surfaces, colour spreading appear to fill the surface occupied by surfaces or thick lines whereas the background traversed by thin lines is seen as brighter or filled of a saturated white. These phenomena were first observed by Bozzi (1975 and Kanizsa (1979 in figural conditions that did not allow them to document their conjunction. Here we illustrate various manifestations of this twofold phenomenon and compare its effects with the known effects of brightness and colour induction. Some conjectures on the nature of these effects are discussed.
Contour Extraction in Prostate Ultrasound Images Using the Wavelet Transform and Snakes
2007-11-02
signal noise levels. In this paper we present a semi-automatic prostate contour extraction scheme, which is based on the wavelet transform and active...contour models, or snakes. The ultrasound image is first decomposed into edge naps at different resolutions via the wavelet transform . Seed points are
Contours, 2 Ft. Contours, Published in 2006, North Georgia College and State University.
NSGIC GIS Inventory (aka Ramona) — This Contours dataset, was produced all or in part from LIDAR information as of 2006. It is described as '2 Ft. Contours'. Data by this publisher are often provided...
NY_GOME_CONTOURS: New York Bight and Gulf of Maine bathymetric contours
U.S. Geological Survey, Department of the Interior — This bathymetric shapefile contains 10 m contours for the continental shelf and 100 m beyond the 200 m shelf edge. The contours have been derived from the National...
NY_GOME_CONTOURS: New York Bight and Gulf of Maine bathymetric contours
U.S. Geological Survey, Department of the Interior — This bathymetric shapefile contains 10 m contours for the continental shelf and 100 m beyond the 200 m shelf edge. The contours have been derived from the National...
Contours, Two Foot Contours, Published in 2007, Not Applicable scale, Dunn County, WI.
NSGIC GIS Inventory (aka Ramona) — This Contours dataset, published at Not Applicable scale, was produced all or in part from LIDAR information as of 2007. It is described as 'Two Foot Contours'....
From laboratory experiments to LISA Pathfinder: achieving LISA geodesic motion
Antonucci, F.; Armano, M.; Audley, H.; Auger, G.; Benedetti, M.; Binetruy, P.; Boatella, C.; Bogenstahl, J.; Bortoluzzi, D.; Bosetti, P.; Brandt, N.; Caleno, M.; Cavalleri, A.; Cesa, M.; Chmeissani, M.; Ciani, G.; Conchillo, A.; Congedo, G.; Cristofolini, I.; Cruise, M.; Danzmann, K.; De Marchi, F.; Diaz-Aguilo, M.; Diepholz, I.; Dixon, G.; Dolesi, R.; Dunbar, N.; Fauste, J.; Ferraioli, L.; Fertin, D.; Fichter, W.; Fitzsimons, E.; Freschi, M.; García Marin, A.; García Marirrodriga, C.; Gerndt, R.; Gesa, L.; Giardini, D.; Gibert, F.; Grimani, C.; Grynagier, A.; Guillaume, B.; Guzmán, F.; Harrison, I.; Heinzel, G.; Hewitson, M.; Hollington, D.; Hough, J.; Hoyland, D.; Hueller, M.; Huesler, J.; Jeannin, O.; Jennrich, O.; Jetzer, P.; Johlander, B.; Killow, C.; Llamas, X.; Lloro, I.; Lobo, A.; Maarschalkerweerd, R.; Madden, S.; Mance, D.; Mateos, I.; McNamara, P. W.; Mendes, J.; Mitchell, E.; Monsky, A.; Nicolini, D.; Nicolodi, D.; Nofrarias, M.; Pedersen, F.; Perreur-Lloyd, M.; Perreca, A.; Plagnol, E.; Prat, P.; Racca, G. D.; Rais, B.; Ramos-Castro, J.; Reiche, J.; Romera Perez, J. A.; Robertson, D.; Rozemeijer, H.; Sanjuan, J.; Schleicher, A.; Schulte, M.; Shaul, D.; Stagnaro, L.; Strandmoe, S.; Steier, F.; Sumner, T. J.; Taylor, A.; Texier, D.; Trenkel, C.; Tombolato, D.; Vitale, S.; Wanner, G.; Ward, H.; Waschke, S.; Wass, P.; Weber, W. J.; Zweifel, P.
2011-05-01
This paper presents a quantitative assessment of the performance of the upcoming LISA Pathfinder geodesic explorer mission. The findings are based on the results of extensive ground testing and simulation campaigns using flight hardware, flight control and operations algorithms. The results show that, for the central experiment of measuring the stray differential acceleration between the LISA test masses, LISA Pathfinder will be able to verify the overall acceleration noise to within a factor 2 of the LISA requirement at 1 mHz and within a factor 6 at 0.1 mHz. We also discuss the key elements of the physical model of disturbances, coming from LISA Pathfinder and ground measurement that will guarantee the LISA performance.
From laboratory experiments to LISA Pathfinder: achieving LISA geodesic motion
Energy Technology Data Exchange (ETDEWEB)
Antonucci, F; Cavalleri, A; Congedo, G [Dipartimento di Fisica, Universita di Trento and INFN, Gruppo Collegato di Trento, 38050 Povo, Trento (Italy); Armano, M [European Space Astronomy Centre, European Space Agency, Villanueva de la Canada, 28692 Madrid (Spain); Audley, H; Bogenstahl, J [Albert-Einstein-Institut, Max-Planck-Institut fuer Gravitationsphysik und Universitaet Hannover, 30167 Hannover (Germany); Auger, G; Binetruy, P [APC UMR7164, Universite Paris Diderot, Paris (France); Benedetti, M [Dipartimento di Ingegneria dei Materiali e Tecnologie Industriali, Universita di Trento and INFN, Gruppo Collegato di Trento, Mesiano, Trento (Italy); Boatella, C [CNES, DCT/AQ/EC, 18 Avenue Edouard Belin, 31401 Toulouse, Cedex 9 (France); Bortoluzzi, D; Bosetti, P; Cristofolini, I [Dipartimento di Ingegneria Meccanica e Strutturale, Universita di Trento and INFN, Gruppo Collegato di Trento, Mesiano, Trento (Italy); Brandt, N [Astrium GmbH Claude-Dornier-Strasse, 88090 Immenstaad (Germany); Caleno, M; Cesa, M [European Space Technology Centre, European Space Agency, Keplerlaan 1, 2200 AG Noordwijk (Netherlands); Chmeissani, M [IFAE, Universitat Autonoma de Barcelona, E-08193 Bellaterra, Barcelona (Spain); Ciani, G [Department of Physics, University of Florida, Gainesville, FL 32611-8440 (United States); Conchillo, A [ICE-CSIC/IEEC, Facultat de Ciencies, E-08193 Bellaterra, Barcelona (Spain); Cruise, M, E-mail: Stefano.Vitale@unitn.it [Department of Physics and Astronomy, University of Birmingham, Birmingham (United Kingdom)
2011-05-07
This paper presents a quantitative assessment of the performance of the upcoming LISA Pathfinder geodesic explorer mission. The findings are based on the results of extensive ground testing and simulation campaigns using flight hardware, flight control and operations algorithms. The results show that, for the central experiment of measuring the stray differential acceleration between the LISA test masses, LISA Pathfinder will be able to verify the overall acceleration noise to within a factor 2 of the LISA requirement at 1 mHz and within a factor 6 at 0.1 mHz. We also discuss the key elements of the physical model of disturbances, coming from LISA Pathfinder and ground measurement that will guarantee the LISA performance.
Timelike geodesics around a charged spherically symmetric dilaton black hole
Directory of Open Access Journals (Sweden)
Blaga C.
2015-01-01
Full Text Available In this paper we study the timelike geodesics around a spherically symmetric charged dilaton black hole. The trajectories around the black hole are classified using the effective potential of a free test particle. This qualitative approach enables us to determine the type of orbit described by test particle without solving the equations of motion, if the parameters of the black hole and the particle are known. The connections between these parameters and the type of orbit described by the particle are obtained. To visualize the orbits we solve numerically the equation of motion for different values of parameters envolved in our analysis. The effective potential of a free test particle looks different for a non-extremal and an extremal black hole, therefore we have examined separately these two types of black holes.
Geodesic motion of test particles in Korkina-Grigoryev metric
Bormotova, Irina
2016-01-01
We study the geodesic structure of the Korkina-Grigoryev spacetime. The corresponding metric is a generalization of the Schwarzschild geometry to the case involving a massless scalar field. We investigate the relation between the angular momentum of the test particle and the charge of the field, which determines the shape of the effective-potential curves. The ratio for angular momentum of the particle, the charge of the scalar field and the dimensionless spatial parameter is found, under which the finite motion of particles occurs. From the behavior of the potential curves the radii of both stable and unstable circular orbits around a black hole are found, as well as the corresponding energies of the test particles. The effective-potential curves for the Korkina-Grigoryev, the Schwarzschild and the Reissner-Nordstrom fields are compared. It is shown, that in the case of the Korkina-Grigoryev metric the stable orbits eventually vanish with increasing charge.
About some diophantine equation and the resulting chaos in geodesics
Perrine, Serge
2001-06-01
We announce results about a complete Markoff theory for the diophantine equation: x2+y2+z2=3xyz+2x All its solutions can be computed. For positive integers, they are organized in two trees. With them, we build a new tree thanks to related continued fractions, and associated binary quadratic forms. In an infinite number of cases, the corresponding approximation and Markoff constants have the form: ((m-2)/√9m2-4 ) For other cases, we conjecture the expression of the constants. All of them converge towards (1/3) by lower values, similarly but differently from the classical Markoff theory. We conclude considering very briefly the link between such equations and geodesics on some Riemann surfaces.
Geodesic acoustic mode in anisotropic plasma with heat flux
Energy Technology Data Exchange (ETDEWEB)
Ren, Haijun, E-mail: hjren@ustc.edu.cn [CAS Key Laboratory of Geospace Environment and Department of Modern Physics, University of Science and Technology of China, Hefei 230026 (China)
2015-10-15
Geodesic acoustic mode (GAM) in an anisotropic tokamak plasma is investigated in fluid approximation. The collisionless anisotropic plasma is described within the 16-momentum magnetohydrodynamic (MHD) fluid closure model, which takes into account not only the pressure anisotropy but also the anisotropic heat flux. It is shown that the GAM frequency agrees better with the kinetic result than the standard Chew-Goldberger-Low (CGL) MHD model. When zeroing the anisotropy, the 16-momentum result is identical with the kinetic one to the order of 1/q{sup 2}, while the CGL result agrees with the kinetic result only on the leading order. The discrepancies between the results of the CGL fluid model and the kinetic theory are well removed by considering the heat flux effect in the fluid approximation.
CUDA-Accelerated Geodesic Ray-Tracing for Fiber Tracking.
van Aart, Evert; Sepasian, Neda; Jalba, Andrei; Vilanova, Anna
2011-01-01
Diffusion Tensor Imaging (DTI) allows to noninvasively measure the diffusion of water in fibrous tissue. By reconstructing the fibers from DTI data using a fiber-tracking algorithm, we can deduce the structure of the tissue. In this paper, we outline an approach to accelerating such a fiber-tracking algorithm using a Graphics Processing Unit (GPU). This algorithm, which is based on the calculation of geodesics, has shown promising results for both synthetic and real data, but is limited in its applicability by its high computational requirements. We present a solution which uses the parallelism offered by modern GPUs, in combination with the CUDA platform by NVIDIA, to significantly reduce the execution time of the fiber-tracking algorithm. Compared to a multithreaded CPU implementation of the same algorithm, our GPU mapping achieves a speedup factor of up to 40 times.
Interpreting spacetimes of any dimension using geodesic deviation
Podolsky, Jiri
2012-01-01
We present a general method which can be used for geometrical and physical interpretation of an arbitrary spacetime in four or any higher number of dimensions. It is based on the systematic analysis of relative motion of free test particles. We demonstrate that local effect of the gravitational field on particles, as described by equation of geodesic deviation with respect to a natural orthonormal frame, can always be decomposed into a canonical set of transverse, longitudinal and Newton-Coulomb-type components, isotropic influence of a cosmological constant, and contributions arising from specific matter content of the universe. In particular, exact gravitational waves in Einstein's theory always exhibit themselves via purely transverse effects with D(D-3)/2 independent polarization states. To illustrate the utility of this approach we study the family of pp-wave spacetimes in higher dimensions and discuss specific measurable effects on a detector located in four spacetime dimensions. For example, the corres...
Geodesic deviation in Kundt spacetimes of any dimension
Svarc, Robert
2012-01-01
Using the invariant form of the equation of geodesic deviation, which describes relative motion of free test particles, we investigate a general family of D-dimensional Kundt spacetimes. We demonstrate that local influence of the gravitational field can be naturally decomposed into Newton-type tidal effects typical for type II spacetimes, longitudinal deformations mainly present in spacetimes of algebraic type III, and type N purely transverse effects corresponding to gravitational waves with D(D-3)/2 independent polarization states. We explicitly study the most important examples, namely exact pp-waves, gyratons, and VSI spacetimes. This analysis helps us to clarify the geometrical and physical interpretation of the Kundt class of nonexpanding, nontwisting and shearfree geometries.
Rational first integrals of geodesic equations and generalised hidden symmetries
Aoki, Arata; Tomoda, Kentaro
2016-01-01
We discuss novel generalisations of Killing tensors, which are introduced by considering rational first integrals of geodesic equations. We introduce the notion of inconstructible generalised Killing tensors, which cannot be constructed from ordinary Killing tensors. Moreover, we introduce inconstructible rational first integrals, which are constructed from inconstructible generalised Killing tensors, and provide a method for checking the inconstructibility of a rational first integral. Using the method, we show that the rational first integral of the Collinson-O'Donnell solution is not inconstructible. We also provide several examples of metrics admitting an inconstructible rational first integral in two and four dimensions, by using the Maciejewski-Przybylska system. Furthermore, we attempt to generalise other hidden symmetries such as Killing-Yano tensors.
CUDA-Accelerated Geodesic Ray-Tracing for Fiber Tracking
Directory of Open Access Journals (Sweden)
Evert van Aart
2011-01-01
Full Text Available Diffusion Tensor Imaging (DTI allows to noninvasively measure the diffusion of water in fibrous tissue. By reconstructing the fibers from DTI data using a fiber-tracking algorithm, we can deduce the structure of the tissue. In this paper, we outline an approach to accelerating such a fiber-tracking algorithm using a Graphics Processing Unit (GPU. This algorithm, which is based on the calculation of geodesics, has shown promising results for both synthetic and real data, but is limited in its applicability by its high computational requirements. We present a solution which uses the parallelism offered by modern GPUs, in combination with the CUDA platform by NVIDIA, to significantly reduce the execution time of the fiber-tracking algorithm. Compared to a multithreaded CPU implementation of the same algorithm, our GPU mapping achieves a speedup factor of up to 40 times.
Geodesic-light-cone coordinates and the Bianchi I spacetime
Fleury, Pierre; Fanizza, Giuseppe
2016-01-01
The geodesic-light-cone (GLC) coordinates are a useful tool to analyse light propagation and observations in cosmological models. In this article, we propose a detailed, pedagogical, and rigorous introduction to this coordinate system, explore its gauge degrees of freedom, and emphasize its interest when geometric optics is at stake. We then apply the GLC formalism to the homogeneous and anisotropic Bianchi I cosmology. More than a simple illustration, this application (i) allows us to show that the Weinberg conjecture according to which gravitational lensing does not affect the proper area of constant-redshift surfaces is significantly violated in a globally anisotropic universe; and (ii) offers a glimpse into new ways to constrain cosmic isotropy from the Hubble diagram.
Geodesic-light-cone coordinates and the Bianchi I spacetime
Fleury, Pierre; Nugier, Fabien; Fanizza, Giuseppe
2016-06-01
The geodesic-light-cone (GLC) coordinates are a useful tool to analyse light propagation and observations in cosmological models. In this article, we propose a detailed, pedagogical, and rigorous introduction to this coordinate system, explore its gauge degrees of freedom, and emphasize its interest when geometric optics is at stake. We then apply the GLC formalism to the homogeneous and anisotropic Bianchi I cosmology. More than a simple illustration, this application (i) allows us to show that the Weinberg conjecture according to which gravitational lensing does not affect the proper area of constant-redshift surfaces is significantly violated in a globally anisotropic universe; and (ii) offers a glimpse into new ways to constrain cosmic isotropy from the Hubble diagram.
From laboratory experiments to LISA Pathfinder: achieving LISA geodesic motion
Antonucci, F; Audley, H; Auger, G; Benedetti, M; Binetruy, P; Boatella, C; Bogenstahl, J; Bortoluzzi, D; Bosetti, P; Brandt, N; Caleno, M; Cavalleri, A; Cesa, M; Chmeissani, M; Ciani, G; Conchillo, A; Congedo, G; Cristofolini, I; Cruise, M; Danzmann, K; De Marchi, F; Diaz-Aguilo, M; Diepholz, I; Dixon, G; Dolesi, R; Dunbar, N; Fauste, J; Ferraioli, L; Fertin, D; Fichter, W; Fitzsimons, E; Freschi, M; Marin, A García; Marirrodriga, C García; Gerndt, R; Gesa, L; Giardini, D; Gibert, F; Grimani, C; Grynagier, A; Guillaume, B; Guzmán, F; Harrison, I; Heinzel, G; Hewitson, M; Hollington, D; Hough, J; Hoyland, D; Hueller, M; Huesler, J; Jeannin, O; Jennrich, O; Jetzer, P; Johlander, B; Killow, C; Llamas, X; Lloro, I; Lobo, A; Maarschalkerweerd, R; Madden, S; Mance, D; Mateos, I; McNamara, P W; Mendestì, J; Mitchell, E; Monsky, A; Nicolini, D; Nicolodi, D; Nofrarias, M; Pedersen, F; Perreur-Lloyd, M; Perreca, A; Plagnol, E; Prat, P; Racca, G D; Rais, B; Ramos-Castro, J; Reiche, J; Perez, J A Romera; Robertson, D; Rozemeijer, H; Sanjuan, J; Schleicher, A; Schulte, M; Shaul, D; Stagnaro, L; Strandmoe, S; Steier, F; Sumner, T J; Taylor, A; Texier, D; Trenkel, C; Tombolato, D; Vitale, S; Wanner, G; Ward, H; Waschke, S; Wass, P; Weber, W J; Zweifel, P
2010-01-01
This paper presents a quantitative assessment of the performance of the upcoming LISA Pathfinder geodesic explorer mission. The findings are based on the results of extensive ground testing and simulation campaigns using flight hardware and flight control and operations algorithms. The results show that, for the central experiment of measuring the stray differential acceleration between the LISA test masses, LISA Pathfinder will be able to verify the overall acceleration noise to within a factor two of the LISA requirement at 1 mHz and within a factor 10 at 0.1 mHz. We also discuss the key elements of the physical model of disturbances, coming from LISA Pathfinder and ground measurement, that will guarantee the LISA performance.
On the applicability of the geodesic deviation equation in General Relativity
Philipp, Dennis; Laemmerzahl, Claus
2016-01-01
Within the theory of General Relativity we study the solution and range of applicability of the standard geodesic deviation equation in highly symmetric spacetimes. The deviation equation is used to model satellite orbit constellations around the earth. In particular, we reconsider the deviation equation in Newtonian gravity and then determine relativistic effects within the theory of General Relativity. The deviation of nearby orbits, as constructed from exact solutions of the underlying geodesic equation, is compared to the solution of the geodesic deviation equation to assess the accuracy of the latter. Furthermore, we comment on the so-called Shirokov effect in Schwarzschild spacetime.
Powers of the space forms curvature operator and geodesics of the tangent bundle
Saharova, Yelena; Yampolsky, Alexander
2005-01-01
It is well-known that if a curve is a geodesic line of the tangent (sphere) bundle with Sasaki metric of a locally symmetric Riemannian manifold then the projected curve has all its geodesic curvatures constant. In this paper we consider the case of tangent (sphere) bundle over the real, complex and quaternionic space form and give a unified proof of the following property: all geodesic curvatures of projected curve are zero starting from k_3,k_6 and k_{10} for the real, complex and quaternio...
On the number and location of short geodesics in moduli space
Leininger, Christopher J
2011-01-01
A closed Teichmuller geodesic in the moduli space M_g of Riemann surfaces of genus g is called L-short if it has length at most L/g. We show that, for any L > 0, there exist e_2 > e_1 > 0, independent of g, so that the L-short geodesics in M_g all lie in the intersection of the e_1-thick part and the e_2-thin part. We also estimate the number of L-short geodesics in M_g, bounding this from above and below by polynomials in g whose degrees depend on L and tend to infinity as L does.
Contour extracting networks in early extrastriate cortex
Dumoulin, Serge O.; Hess, Robert F.; May, Keith A.; Harvey, Ben M.; Rokers, Bas; Barendregt, Martijn
2014-01-01
Neurons in the visual cortex process a local region of visual space, but in order to adequately analyze natural images, neurons need to interact. The notion of an ''association field'' proposes that neurons interact to extract extended contours. Here, we identify the site and properties of contour
RFP for the Comet Nuclei Tour (CONTOUR)
DEFF Research Database (Denmark)
Jørgensen, John Leif; Madsen, Peter Buch; Betto, Maurizio
1999-01-01
This document describes the ASC Star Tracker (performance, functionality, requirements etc.) to The Johns Hopkins University - Applied Physics Laboratory for their Comet Nuclei TOUR (CONTOUR) Program.......This document describes the ASC Star Tracker (performance, functionality, requirements etc.) to The Johns Hopkins University - Applied Physics Laboratory for their Comet Nuclei TOUR (CONTOUR) Program....
Contour extracting networks in early extrastriate cortex
Dumoulin, Serge O.; Hess, Robert F.; May, Keith A.; Harvey, Ben M.; Rokers, Bas; Barendregt, Martijn
2014-01-01
Neurons in the visual cortex process a local region of visual space, but in order to adequately analyze natural images, neurons need to interact. The notion of an ''association field'' proposes that neurons interact to extract extended contours. Here, we identify the site and properties of contour i
Contour Propagation Using Feature-Based Deformable Registration for Lung Cancer
Directory of Open Access Journals (Sweden)
Yuhan Yang
2013-01-01
Full Text Available Accurate target delineation of CT image is a critical step in radiotherapy treatment planning. This paper describes a novel strategy for automatic contour propagation, based on deformable registration, for CT images of lung cancer. The proposed strategy starts with a manual-delineated contour in one slice of a 3D CT image. By means of feature-based deformable registration, the initial contour in other slices of the image can be propagated automatically, and then refined by active contour approach. Three algorithms are employed in the strategy: the Speeded-Up Robust Features (SURF, Thin-Plate Spline (TPS, and an adapted active contour (Snake, used to refine and modify the initial contours. Five pulmonary cancer cases with about 400 slices and 1000 contours have been used to verify the proposed strategy. Experiments demonstrate that the proposed strategy can improve the segmentation performance in the pulmonary CT images. Jaccard similarity (JS mean is about 0.88 and the maximum of Hausdorff distance (HD is about 90%. In addition, delineation time has been considerably reduced. The proposed feature-based deformable registration method in the automatic contour propagation improves the delineation efficiency significantly.
Institute of Scientific and Technical Information of China (English)
杨华; 陈善静; 曾凯; 张红
2012-01-01
针对跟踪目标尺度变化问题,提出了基于灰度对数似然图像分割的快速主动轮廓跟踪算法.改进的主动轮廓跟踪算法将根据以目标与背景的颜色差异而建立的对数似然图对图像进行阈值分割和数学形态学处理,再将Kalman滤波器结合到主动轮廓跟踪算法进行目标跟踪.改进的主动轮廓跟踪算法对目标分割准确,轮廓特征显著,跟踪效果稳定,算法能很好地适应跟踪目标尺度变化.通过Kalman滤波器对目标位置点的预测减少了主动轮廓跟踪算法收敛的迭代次数,使算法的运算效率提高了33％左右.%A fast active contour tracking(ACT) algorithm based on log-likelihood image segmentation has been proposed to solve the scale change problem in the process of target tracking. The algorithm adopts the log-likelihood image segmentation method, which segments images according to their log-likelihood images built based on the color difference between target and background, and the mathematical morphology method, and tracks the target with conventional ACT algorithm combined with Kalman filter. It tracks the target precisely with distinct contour features and stable tracking performance, and can well adapt to the target scale change. The Kalman filter adopted reduces the number of iterations for algorithm convergence through its forecast of the target position, and thus the fast ACT algorithm is about 33% more efficient than the conventional one.
Constructing PDE-based surfaces bounded by geodesics or lines of curvature
National Research Council Canada - National Science Library
Huang, Wei-Xian; Wu, Hua-Jing-Ling; Wang, Guo-Jin
2013-01-01
In order to explore a new approach to construct surfaces bounded by geodesics or lines of curvature, a method of surface modeling based on fourth-order partial differential equations (PDEs) is presented...
Wide Field-of-view and Broadband Terahertz Beam Steering Based on Gap Plasmon Geodesic Antennas.
Liu, Kaipeng; Guo, Yinghui; Pu, Mingbo; Ma, Xiaoliang; Li, Xiong; Luo, Xiangang
2017-01-30
Despite a plethora of applications ranging from wireless communications to sensing and spectroscopy, the current terahertz beam steering technologies suffer from tremendous insert loss, stringent control of electric bias, limited scanning angle, relatively complicated configuration and narrow operation bandwidth, preventing further practical application. We propose and demonstrate a conceptually new approach for terahertz beam steering by virtue of gap plasmon geodesic antennas. By adjusting the geometric dimension of the gap plasmon geodesic antennas, all gap plasmon modes add coherently along a peculiar direction that depends on the geodesic mean surface. Consequently, high directive beams are generated through the antenna, whose direction could be changed within a wide-angle range spanning ±45° by lateral motion of the feed. Furthermore, an assembled antenna structure consisting of four-element geodesic antennas array is proposed for full 360° beam steering, which can operate in a broadband range from 0.8 THz to 1.2 THz.
Thermodynamic geodesics of a Reissner Nordström black hole
Farrugia, Christine; Sultana, Joseph
2017-01-01
Starting from a Geometrothermodynamics metric for the space of thermodynamic equilibrium states in the mass representation, we use numerical techniques to analyse the thermodynamic geodesics of a supermassive Reissner Nordström black hole in isolation. Appropriate constraints are obtained by taking into account the processes of Hawking radiation and Schwinger pair-production. We model the black hole in line with the work of Hiscock and Weems (Phys Rev D 41:1142-1151, 1990). It can be deduced that the relation which the geodesics establish between the entropy S and electric charge Q of the black hole extremises changes in the black hole's mass. Indeed, the expression for the entropy of an extremal black hole is an exact solution to the geodesic equation. We also find that in certain cases, the geodesics describe the evolution brought about by the constant emission of Hawking radiation and charged-particle pairs.
Energy Technology Data Exchange (ETDEWEB)
Rowland, D R [Student Support Services, University of Queensland, Brisbane QLD 4072 (Australia)
2006-01-01
Introductory courses covering modern physics sometimes introduce some elementary ideas from general relativity, though the idea of a geodesic is generally limited to shortest Euclidean length on a curved surface of two spatial dimensions rather than extremal aging in spacetime. It is shown that Epstein charts provide a simple geometric picture of geodesics in one space and one time dimension and that for a hypothetical uniform gravitational field, geodesics are straight lines on a planar diagram. This means that the properties of geodesics in a uniform field can be calculated with only a knowledge of elementary geometry and trigonometry, thus making the calculation of some basic results of general relativity accessible to students even in an algebra-based survey course on physics.
Wide Field-of-view and Broadband Terahertz Beam Steering Based on Gap Plasmon Geodesic Antennas
Liu, Kaipeng; Guo, Yinghui; Pu, Mingbo; Ma, Xiaoliang; Li, Xiong; Luo, Xiangang
2017-01-01
Despite a plethora of applications ranging from wireless communications to sensing and spectroscopy, the current terahertz beam steering technologies suffer from tremendous insert loss, stringent control of electric bias, limited scanning angle, relatively complicated configuration and narrow operation bandwidth, preventing further practical application. We propose and demonstrate a conceptually new approach for terahertz beam steering by virtue of gap plasmon geodesic antennas. By adjusting the geometric dimension of the gap plasmon geodesic antennas, all gap plasmon modes add coherently along a peculiar direction that depends on the geodesic mean surface. Consequently, high directive beams are generated through the antenna, whose direction could be changed within a wide-angle range spanning ±45° by lateral motion of the feed. Furthermore, an assembled antenna structure consisting of four-element geodesic antennas array is proposed for full 360° beam steering, which can operate in a broadband range from 0.8 THz to 1.2 THz.
Are eikonal quasinormal modes linked to the unstable circular null geodesics?
Konoplya, R. A.; Stuchlík, Z.
2017-08-01
In Cardoso et al. [6] it was claimed that quasinormal modes which any stationary, spherically symmetric and asymptotically flat black hole emits in the eikonal regime are determined by the parameters of the circular null geodesic: the real and imaginary parts of the quasinormal mode are multiples of the frequency and instability timescale of the circular null geodesics respectively. We shall consider asymptotically flat black hole in the Einstein-Lovelock theory, find analytical expressions for gravitational quasinormal modes in the eikonal regime and analyze the null geodesics. Comparison of the both phenomena shows that the expected link between the null geodesics and quasinormal modes is violated in the Einstein-Lovelock theory. Nevertheless, the correspondence exists for a number of other cases and here we formulate its actual limits.
Proper Accelerations of Time-Like Curves near a Null Geodesic
Institute of Scientific and Technical Information of China (English)
田贵花; 赵峥
2003-01-01
It is well known that when given a null geodesic γ0(λ) with a point r in (p, q) conjugate to p along γ0(λ), there will be a variation of γ0(λ) which can give a time-like curve from p to q. Here we prove that the time-like curves coming from the above-mentioned variation (with the second derivative β2 ≠ 0) have a proper acceleration A = √AaAa which approaches infinity as the time-like curve approaches the null geodesic. Because the curve obtained from variation of the null geodesic must be everywhere time-like, we also discuss the constraint of the vector field Za on the null geodesic γ0(λ) cannot be zero.
Institute of Scientific and Technical Information of China (English)
赖均; 解梅
2011-01-01
In order to segment out the candidate pulmonary nodule in the CT images, considering the statistical feature of the lung field, this paper proposed an algorithm for segmentation of the juxta-pleural nodules and inner nodules of a lung.And the algorithm was consisting of the pulse coupled neuron network with four neighbor linking weights and the active contour with the prior shape energy.Experiments demonstrate that the algorithm can segment the candidate pulmonary nodules correctly and it is one kind of effective segmentation method of exchuding the false position pulmonary nodules.%为了对肺CT图像中的候选肺结节实施正确的分割,针对二维图像肺区统计特征,提出一种四邻域连接权的脉冲耦合神经网络(PCNN)结合先验形状能量函数的主动轮廓模型来分割候选肺内与近胸膜两类肺结节的算法.实验结果表明,算法能够正确地完成对候选肺结节的分割,并且它是一种能有效剔除大量假阳性结节的肺结节分割方法.
Energy Technology Data Exchange (ETDEWEB)
Reboucas Filho, Pedro Pedrosa; Cortez, Paulo Cesar [Universidade Federal do Ceara (UFC), Fortaleza, CE (Brazil). Dept. de Engenharia de Teleinformatica; Holanda, Marcelo Alcantara [Universidade Federal do Ceara (UFC), Fortaleza, CE (Brazil). Hospital Universitario Walter Cantidio. Dept. de Pneumologia
2011-12-15
This paper proposes a new active contour model (ACM), called ACM Crisp, and evaluates the segmentation of lungs in computed tomography (CT) images. An ACM draws a curve around or within the object of interest. This curve changes its shape, when some energy acts on it and moves towards the edges of the object. This process is performed by successive iterations of minimization of a given energy, associated with the curve. The ACMs described in the literature have limitations when used for segmentations of CT lung images. The ACM Crisp model overcomes these limitations, since it proposes automatic initiation and new external energy based on rules and radiological pulmonary densities. The paper compares other ACMs with the proposed method, which is shown to be superior. In order to validate the algorithm a medical expert in the field of Pulmonology of the Walter Cantidio University Hospital from the Federal University of Ceara carried out a qualitative analysis. In these analyses 100 CT lung images were used. The segmentation efficiency was evaluated into 5 categories with the following results for the ACM Crisp: 73% excellent, without errors, 20% acceptable, with small errors, and 7% reasonable, with large errors, 0% poor, covering only a small part of the lung, and 0% very bad, making a totally incorrect segmentation. In conclusion the ACM Crisp is considered a useful algorithm to segment CT lung images, and with potential to integrate medical diagnosis systems. (author)
Menon, Govind
2008-01-01
The structural properties of geodesic currents in an ambient Kerr background is studied from an analytical point of view. The geodesics in the congruence correspond to charged particles that carry energy and angular momentum from the black hole through the Blandford-Znajek mechanism. It is shown that the resulting magnetosphere naturally satisfies the Znajek regularity condition. Particular attention is paid here to the energy extracted by matter currents rather than by electromagnetic Poynting fluxes.
Physical meaning of the conserved quantities on anti-de Sitter geodesics
Cotǎescu, Ion I.
2017-05-01
The geodesic motion on anti-de Sitter spacetimes is studied, pointing out how the trajectories are determined by the ten independent conserved quantities associated with the specific S O (2 ,3 ) isometries of these manifolds. The new result is that there are two conserved S O (3 ) vectors which play the same role as the Runge-Lenz vector of the Kepler problem, determining the major and minor semiaxes of the ellipsoidal anti-de Sitter geodesics.
On the Mass Neutrino Phase calculations along the geodesic line and the null line
Zhang, C. M.; Beesham, A.
2000-01-01
On the mass neutrino phase calculations along both the particle geodesic line and the photon null line, there exists a double counting error--factor of 2 when comparing the geodesic phase with the null phase. For the mass neutrino propagation in the flat spacetime, we study the neutrino interference phase calculation in the Minkowski diagram and find that the double counting effect originates from despising the velocity difference between two mass neutrinos. Moreover, we compare the phase cal...
A study of geodesic motion in a (2+1)-dimensional charged BTZ black hole
Soroushfar, Saheb; Jafari, Afsaneh
2015-01-01
This study is purposed to derive the equation of motion for geodesics in vicinity of spacetime of a (2 + 1)-dimensional charged BTZ black hole. In this paper, we solve geodesics for both massive and massless particles in terms of Weierstrass elliptic and Kleinian sigma hyper-elliptic functions. Then we determine different trajectories of motion for particles in terms of conserved energy and angular momentum and also using effective potential.
Analytic solutions of the geodesic equation for U(1)^2 dyonic rotating black holes
Flathmann, Kai
2016-01-01
In this article we derive the geodesic equations in the $\\text{U(1)}^2$ dyonic rotating black hole spacetime. We present their solutions in terms of the Kleinian $\\sigma$-function and in special cases in terms of the Weierstra{\\ss} $\\wp$-, $\\sigma$- and $\\zeta$-functions. To give a list of all possible orbits, we analyse the geodesic motion of test particles and light using parametric diagrams and effective potentials.
Geometry of Cyclic Quotients; 1, Knotted Totally Geodesic Submanifolds in Positively Curved Spheres
Reznikov, A G
1994-01-01
We prove that there exists a metric of positive curvature in a three-sphere which admits a given torus knot as a closed geodesic.We also sketch a construction of a metric in a four sphere, very likely of positive curvature, which admits a totally geodesic projective plane with Euler number four. Surpisingly, the technique borrows a lot from the Mostow-Siu-Gromov-Thurston constuction of exotic negatively curved manifolds.
Flathmann, Kai
2015-01-01
In this article we study the geodesic motion of test particles and light in the Einstein-Maxwell-Dilaton-Axion black hole spacetime. We derive the equations of motion and present their solutions in terms of the Weierstra{\\ss} $\\wp$-, $\\sigma$- and $\\zeta$-functions. With the help of parametric diagrams and effective potentials we analyze the geodesic motion and give a list of all possible orbit types.
Finsler geodesics in the presence of a convex function and their applications
Energy Technology Data Exchange (ETDEWEB)
Caponio, Erasmo; Masiello, Antonio [Dipartimento di Matematica, Politecnico di Bari, Via Orabona 4, 70125 Bari (Italy); Javaloyes, Miguel Angel [Departamento de GeometrIa y TopologIa, Facultad de Ciencias, Universidad de Granada, Campus Fuentenueva s/n, 18071 Granada (Spain)], E-mail: caponio@poliba.it, E-mail: ma.javaloyes@gmail.com, E-mail: majava@ugr.es, E-mail: masiello@poliba.it
2010-04-24
In this paper, we obtain a result about the existence of only a finite number of geodesics between two fixed non-conjugate points in a Finsler manifold endowed with a convex function. We apply it to Randers and Zermelo metrics. As a by-product, we also get a result about the finiteness of the number of lightlike and timelike geodesics connecting an event to a line in a standard stationary spacetime.
Curvature and geodesic instabilities in a geometrical approach to the planar three-body problem
Krishnaswami, Govind S.; Senapati, Himalaya
2016-10-01
The Maupertuis principle allows us to regard classical trajectories as reparametrized geodesics of the Jacobi-Maupertuis (JM) metric on configuration space. We study this geodesic reformulation of the planar three-body problem with both Newtonian and attractive inverse-square potentials. The associated JM metrics possess translation and rotation isometries in addition to scaling isometries for the inverse-square potential with zero energy E. The geodesic flow on the full configuration space ℂ3 (with collision points excluded) leads to corresponding flows on its Riemannian quotients: the center of mass configuration space ℂ2 and shape space ℝ3 (as well as 𝕊3 and the shape sphere 𝕊2 for the inverse-square potential when E = 0). The corresponding Riemannian submersions are described explicitly in "Hopf" coordinates which are particularly adapted to the isometries. For equal masses subject to inverse-square potentials, Montgomery shows that the zero-energy "pair of pants" JM metric on the shape sphere is geodesically complete and has negative gaussian curvature except at Lagrange points. We extend this to a proof of boundedness and strict negativity of scalar curvatures everywhere on ℂ2, ℝ3, and 𝕊3 with collision points removed. Sectional curvatures are also found to be largely negative, indicating widespread geodesic instabilities. We obtain asymptotic metrics near collisions, show that scalar curvatures have finite limits, and observe that the geodesic reformulation "regularizes" pairwise and triple collisions on ℂ2 and its quotients for arbitrary masses and allowed energies. For the Newtonian potential with equal masses and zero energy, we find that the scalar curvature on ℂ2 is strictly negative though it could have either sign on ℝ3. However, unlike for the inverse-square potential, geodesics can encounter curvature singularities at collisions in finite geodesic time.
Solar performance of an electrochromic geodesic dome roof
Energy Technology Data Exchange (ETDEWEB)
Porta-Gandara, M.A. [Centro de Investigaciones Biologicas del Noroeste, BCS (Mexico); Gomez-Munoz, V. [Centro Interdisciplinario de Ciencas Marinas, BCS (Mexico)
2005-10-01
A Fuller type geodesic dome was modeled in terms of the variation of the solar energy that passes to the interior when the dome is covered with electrochromic glazing (ECG), compared with common glass, by means of two different solar control strategies: one discrete and the other continuous. With the discrete strategy, when a solar beam strikes any ECG pane at any angle, it is darkened to its maximum level. In the continuous strategy, each ECG pane is darkened by using a direct function of solar beam radiation. The results demonstrate the advantages of solar control achieved with the former strategy. For the discrete strategy, the daily reduction in solar energy intake, with respect to the ordinary glass, was around 86% for all considered latitudes along the year. The optimum values for the continuous strategy occurred during the equinoxes with a maximum reduction of 69% for all latitudes. During the summer solstice, the reduction percentages increase with the latitude from 52 to 57%. During the winter solstice, the energy reduction with the continuous strategy decreases with the latitude from 52% in the Equator to 46% at 40{sup o} north latitude. (author)
On geodesic dynamics in deformed black-hole fields
Semerák, Oldřich
2015-01-01
"Almost all" seems to be known about isolated stationary black holes in asymptotically flat space-times and about the behaviour of {\\em test} matter and fields in their backgrounds. The black holes likely present in galactic nuclei and in some X-ray binaries are commonly being represented by the Kerr metric, but actually they are not isolated (they are detected only thanks to a strong interaction with the surroundings), they are not stationary (black-hole sources are rather strongly variable) and they also probably do not live in an asymptotically flat universe. Such "perturbations" may query the classical black-hole theorems (how robust are the latter against them?) and certainly affect particles and fields around, which can have observational consequences. In the present contribution we examine how the geodesic structure of the static and axially symmetric black-hole space-time responds to the presence of an additional matter in the form of a thin disc or ring. We use several different methods to show that ...
Perfect imaging analysis of the spherical geodesic waveguide
González, Juan C.; Benítez, Pablo; Miñano, Juan C.; Grabovičkić, Dejan
2012-12-01
Negative Refractive Lens (NRL) has shown that an optical system can produce images with details below the classic Abbe diffraction limit. This optical system transmits the electromagnetic fields, emitted by an object plane, towards an image plane producing the same field distribution in both planes. In particular, a Dirac delta electric field in the object plane is focused without diffraction limit to the Dirac delta electric field in the image plane. Two devices with positive refraction, the Maxwell Fish Eye lens (MFE) and the Spherical Geodesic Waveguide (SGW) have been claimed to break the diffraction limit using positive refraction with a different meaning. In these cases, it has been considered the power transmission from a point source to a point receptor, which falls drastically when the receptor is displaced from the focus by a distance much smaller than the wavelength. Although these systems can detect displacements up to λ/3000, they cannot be compared to the NRL, since the concept of image is different. The SGW deals only with point source and drain, while in the case of the NRL, there is an object and an image surface. Here, it is presented an analysis of the SGW with defined object and image surfaces (both are conical surfaces), similarly as in the case of the NRL. The results show that a Dirac delta electric field on the object surface produces an image below the diffraction limit on the image surface.
Extreme super-resolution using the spherical geodesic waveguide
Miñano, Juan Carlos; González, Juan Carlos; Benítez, Pablo; Grabovičkić, Dejan
2012-06-01
Leonhardt demonstrated (2009) that the 2D Maxwell Fish Eye lens (MFE) can focus perfectly 2D Helmholtz waves of arbitrary frequency, i.e., it can transport perfectly an outward (monopole) 2D Helmholtz wave field, generated by a point source, towards a "perfect point drain" located at the corresponding image point. Moreover, a prototype with λ/5 super-resolution (SR) property for one microwave frequency has been manufactured and tested (Ma et al, 2010). Although this prototype has been loaded with an impedance different from the "perfect point drain", it has shown super-resolution property. However, neither software simulations nor experimental measurements for a broad band of frequencies have yet been reported. Here we present steady state simulations for two cases, using perfect drain as suggested by Leonhardt and without perfect drain as in the prototype. All the simulations have been done using a device equivalent to the MFE, called the Spherical Geodesic Waveguide (SGW). The results show the super-resolution up to λ/3000, for the system loaded with the perfect drain, and up to λ /500 for a not perfect load. In both cases super-resolution only happens for discrete number of frequencies. Out of these frequencies, the SGW does not show super-resolution in the analysis carried out.
Circuital model for the spherical geodesic waveguide perfect drain
González, Juan C.; Grabovičkić, Dejan; Benítez, Pablo; Miñano, Juan C.
2012-08-01
The perfect drain for the Maxwell fish eye (MFE) is a non-magnetic dissipative region placed in the focal point to absorb all the incident radiation without reflection or scattering. The perfect drain was recently designed as a material with complex permittivity that depends on frequency. However, this material is only a theoretical material, so it cannot be used in practical devices. The perfect drain has been claimed as necessary for achieving super-resolution (Leonhardt 2009 New J. Phys. 11 093040), which has increased the interest in practical perfect drains suitable for manufacturing. Here, we present a practical perfect drain that is designed using a simple circuit (made of a resistance and a capacitor) connected to the coaxial line. Moreover, we analyze the super-resolution properties of a device equivalent to the MFE, known as a spherical geodesic waveguide, loaded with this perfect drain. The super-resolution analysis for this device is carried out using COMSOL Multiphysics. The results of simulations predict a super-resolution of up to λ/3000.
Geodesic family of spherical instantons and cosmic quantum creation
Lapiedra, Ramon
2015-01-01
The Einstein field equations for any spherically symmetric metric and a geodesic perfect fluid source are cast in a canonical simple form, both for Lorentzian metrics and for instantons. Both kinds of metrics are explicitly written for the Lema{\\^{\\i}}tre-Tolman-Bondi family and for a general $\\Lambda$-Friedmann-Lema{\\^{\\i}}tre-Robertson-Walker universe. In the latter case (including of course the instanton version) we study whether the probability of quantum creation of our Universe vanishes or not. It is found, in accordance with previous results, that only the closed model can have a nonzero probability for quantum creation. To obtain this result, we resort to general assumptions, which are satisfied in the particular creation case considered by Vilenkin. On the other hand, Fomin and Tryon suggested that the energy of a quantically creatable universe should vanish. This is in accordance with the above result in which only the closed $\\Lambda$FLRW model is quantically creatable while the open and flat model...
Self-gravitating stellar collapse: explicit geodesics and path integration
Directory of Open Access Journals (Sweden)
Jayashree Balakrishna
2016-11-01
Full Text Available We extend the work of Oppenheimer-Synder to model the gravitational collapse of a star to a black hole by including quantum mechanical effects. We first derive closed-form solutions for classical paths followed by a particle on the surface of the collapsing star in Schwarzschild and Kruskal coordinates for space-like, time-like and light-like geodesics. We next present an application of these paths to model the collapse of ultra-light dark matter particles, which necessitates incorporating quantum effects. To do so we treat a particle on the surface of the star as a wavepacket and integrate over all possible paths taken by the particle. The waveform is computed in Schwarzschild coordinates and found to exhibit an ingoing and an outgoing component, where the former contains the probability of collapse, while the latter contains the probability that the star will disperse. These calculations pave the way for investigating the possibility of quantum collapse that does not lead to black hole formation as well as for exploring the nature of the wavefunction inside r = 2M.
Contours--Offshore of Santa Barbara, California
U.S. Geological Survey, Department of the Interior — This part of SIM 3281 presents data for the bathymetric contours for several seafloor maps (see sheets 1, 2, 3, 7, 10, SIM 3281) of the Offshore of Santa Barbara...
Contours--Offshore Coal Oil Point, California
U.S. Geological Survey, Department of the Interior — This part of SIM 3302 presents bathymetric contours for several seafloor maps of Offshore Coal Oil Point, California (vector data file is included in...
Transgressive Contours--Bolinas to Pescadero, California
U.S. Geological Survey, Department of the Interior — This part of DS 781 presents data for the transgressive contours for the Bolinas to Pescadero, California, region. The vector file is included in...
Contours-Offshore of Bodega Head, California
U.S. Geological Survey, Department of the Interior — This part of DS 781 presents data for the bathymetric contours for several seafloor maps of the Offshore of Bodega Head map area, California. The vector data file is...
Contours--Offshore of Pacifica, California
U.S. Geological Survey, Department of the Interior — This part of DS 781 presents data for the bathymetric contours for several seafloor maps of the Offshore of Pacifica map area, California. The vector data file is...
Contours--Drakes Bay and Vicinity, California
U.S. Geological Survey, Department of the Interior — This part of DS 781 presents data for the bathymetric contours for several seafloor maps of the Drakes Bay and Vicinity map area, California. The vector data file is...
Contours--Monterey Canyon and Vicinity, California
U.S. Geological Survey, Department of the Interior — This part of DS 781 presents bathymetric contours for several seafloor maps of the Monterey Canyon and Vicinity map area, California. The raster data file is...
Contours--Offshore Refugio Beach, California
U.S. Geological Survey, Department of the Interior — This part of SIM 3319 presents bathymetric contours for several seafloor maps of Offshore Refugio Beach, California (vector data file is included in...
Contours-Offshore of Bodega Head, California
U.S. Geological Survey, Department of the Interior — This part of DS 781 presents data for the bathymetric contours for several seafloor maps of the Offshore of Bodega Head map area, California. The vector data file is...
Water-table contours of Nevada
U.S. Geological Survey, Department of the Interior — This data set consists of water-table contours for Nevada. These data were created as part of an effort to provide statewide information on water table and depth to...
Contours--Offshore of Pacifica, California
U.S. Geological Survey, Department of the Interior — This part of DS 781 presents data for the bathymetric contours for several seafloor maps of the Offshore of Pacifica map area, California. The vector data file is...
Contours--Offshore of Fort Ross, California
U.S. Geological Survey, Department of the Interior — This part of DS 781 presents data for the bathymetric contours for several seafloor maps of the Offshore of Fort Ross map area, California. The vector data file is...
Contours Offshore of Tomales Point, California
U.S. Geological Survey, Department of the Interior — This part of DS 781 presents data for the bathymetric contours for several seafloor maps of the Offshore of Tomales Point map area, California. The vector data file...
Contours--Offshore Santa Cruz, California
U.S. Geological Survey, Department of the Interior — This part of DS 781 presents data for the bathymetric contours for several seafloor maps of the Offshore Santa Cruz map area, California. The vector data file is...
Contours--Offshore Pigeon Point, California
U.S. Geological Survey, Department of the Interior — This part of DS 781 presents data for the bathymetric contours for several seafloor maps of the Offshore Pigeon Point map area, California. The vector data file is...
Contours--Offshore of Fort Ross, California
U.S. Geological Survey, Department of the Interior — This part of DS 781 presents data for the bathymetric contours for several seafloor maps of the Offshore of Fort Ross map area, California. The vector data file is...
Contours--Offshore Scott Creek, California
U.S. Geological Survey, Department of the Interior — This part of DS 781 presents data for the bathymetric contours for several seafloor maps of the Offshore Scott Creek map area, California. The vector data file is...
Contours--Offshore of San Francisco, California
U.S. Geological Survey, Department of the Interior — This part of DS 781 presents data for the bathymetric contours for several seafloor maps of the Offshore of San Francisco map area, California. The vector data file...
Transgressive Contours--Bolinas to Pescadero, California
U.S. Geological Survey, Department of the Interior — This part of DS 781 presents data for the transgressive contours for the Bolinas to Pescadero, California, region. The vector file is included in...
Contours--Offshore Scott Creek, California
U.S. Geological Survey, Department of the Interior — This part of DS 781 presents data for the bathymetric contours for several seafloor maps of the Offshore Scott Creek map area, California. The vector data file is...
Contours--Offshore Santa Cruz, California
U.S. Geological Survey, Department of the Interior — This part of DS 781 presents data for the bathymetric contours for several seafloor maps of the Offshore Santa Cruz map area, California. The vector data file is...
Contours--Monterey Canyon and Vicinity, California
U.S. Geological Survey, Department of the Interior — This part of DS 781 presents bathymetric contours for several seafloor maps of the Monterey Canyon and Vicinity map area, California. The raster data file is...
Computation of the shortest path between two curves on a parametric surface by geodesic-like method
Chen, Wen-Haw
2010-01-01
In this paper, we present the geodesic-like algorithm for the computation of the shortest path between two objects on NURBS surfaces and periodic surfaces. This method can improve the distance problem not only on surfaces but in $\\mathbb{R}^3$. Moreover, the geodesic-like algorithm also provides an efficient approach to simulate the minimal geodesic between two holes on a NURBS surfaces.
Isolating contour information from arbitrary images
Jobson, Daniel J.
1989-01-01
Aspects of natural vision (physiological and perceptual) serve as a basis for attempting the development of a general processing scheme for contour extraction. Contour information is assumed to be central to visual recognition skills. While the scheme must be regarded as highly preliminary, initial results do compare favorably with the visual perception of structure. The scheme pays special attention to the construction of a smallest scale circular difference-of-Gaussian (DOG) convolution, calibration of multiscale edge detection thresholds with the visual perception of grayscale boundaries, and contour/texture discrimination methods derived from fundamental assumptions of connectivity and the characteristics of printed text. Contour information is required to fall between a minimum connectivity limit and maximum regional spatial density limit at each scale. Results support the idea that contour information, in images possessing good image quality, is (centered at about 10 cyc/deg and 30 cyc/deg). Further, lower spatial frequency channels appear to play a major role only in contour extraction from images with serious global image defects.
Perception of illusory contours enhanced in motion
Institute of Scientific and Technical Information of China (English)
倪睿; 王志宏; 吴新年; 汪云九; 李东光
2003-01-01
Investigation on illusory contours is important for understanding the mechanisms un-derlying the object recognition of human visual system. Numerous researches have shown that illusory contours formed in motion and stereopsis are generated by the unmatched features. Here we conduct three psychophysical experiments to test if Kanizsa illusory contours are also caused by unmatched information. Different types of motion (including horizontal translation, radial ex-panding and shrinking) are utilized in the experiments. The results show that no matter under what kind of motion, when figures or background move separately illusory contours are perceived stronger, and there is no significant difference between the perceived strength in these two types of motion. However, no such enhancement of perceived strength is found when figures and background move together. It is found that the strengthened unmatched features generate the enhancement effect of illusory contour perception in motion. Thus the results suggest that the process of unmatched information in visual system is a critical step in the formation of illusory contours.
The Relation of the Morse Index of Closed Geodesics with the Maslov-type Index of Symplectic Paths
Institute of Scientific and Technical Information of China (English)
Chun Gen LIU
2005-01-01
In this paper, we consider the relation of the Morse index of a closed geodesic with the Maslov-type index of a path in a symplectic group. More precisely, for a closed geodesic c on a Riemannian manifold M with its linear Poincare map P (a symplectic matrix), we construct a symplectic path γ(t) starting from identity I and ending at P, such that the Morse index of the closed geodesic c equals the Maslov-type index of γ. As an application of this result, we study the parity of the Morse index of any closed geodesic.
Refined contour analysis of giant unilamellar vesicles
Pécréaux, J.; Döbereiner, H.-G.; Prost, J.; Joanny, J.-F.; Bassereau, P.
2004-03-01
The fluctuation spectrum of giant unilamellar vesicles is measured using a high-resolution contour detection technique. An analysis at higher q vectors than previously achievable is now possible due to technical improvements of the experimental setup and of the detection algorithm. The global fluctuation spectrum is directly fitted to deduce the membrane tension and the bending modulus of lipid membranes. Moreover, we show that the planar analysis of fluctuations is valid for spherical objects, even at low wave vectors. Corrections due to the integration time of the video camera and to the section of a 3D object by the observation plane are introduced. A precise calculation of the error bars has been done in order to provide reliable error estimate. Eventually, using this technique, we have measured bending moduli for EPC, SOPC and \\chem{SOPC:CHOL} membranes confirming previously published values. An interesting application of this technique can be the measurement of the fluctuation spectra for non-equilibrium membranes, such as “active membranes”.
Geodesic distance on a Grassmannian for monitoring the progression of Alzheimer's disease.
Gui, Liangyan; Tang, Xiaoying; Moura, José M F
2017-02-01
We propose a geodesic distance on a Grassmannian manifold that can be used to quantify the shape progression patterns of the bilateral hippocampi, amygdalas, and lateral ventricles in healthy control (HC), mild cognitive impairment (MCI), and Alzheimer's disease (AD). Longitudinal magnetic resonance imaging (MRI) scans of 754 subjects (3092 scans in total) were used in this study. Longitudinally, the geodesic distance was found to be proportional to the elapsed time separating the two scans in question. Cross-sectionally, utilizing a linear mixed-effects statistical model, we found that each structure's annualized rate of change in the geodesic distance followed the order of AD>MCI>HC, with statistical significance being reached in every case. In addition, for each of the six structures of interest, within the same time interval (e.g., from baseline to the 6th month), we observed significant correlations between the geodesic distance and the cognitive deterioration as quantified by the ADAS-cog increase and the MMSE decrease. Furthermore, as the disease progresses over time, this linkage between the inter-shape geodesic distance and the cognitive decline becomes considerably stronger and more significant.
3D Facial Similarity Measure Based on Geodesic Network and Curvatures
Directory of Open Access Journals (Sweden)
Junli Zhao
2014-01-01
Full Text Available Automated 3D facial similarity measure is a challenging and valuable research topic in anthropology and computer graphics. It is widely used in various fields, such as criminal investigation, kinship confirmation, and face recognition. This paper proposes a 3D facial similarity measure method based on a combination of geodesic and curvature features. Firstly, a geodesic network is generated for each face with geodesics and iso-geodesics determined and these network points are adopted as the correspondence across face models. Then, four metrics associated with curvatures, that is, the mean curvature, Gaussian curvature, shape index, and curvedness, are computed for each network point by using a weighted average of its neighborhood points. Finally, correlation coefficients according to these metrics are computed, respectively, as the similarity measures between two 3D face models. Experiments of different persons’ 3D facial models and different 3D facial models of the same person are implemented and compared with a subjective face similarity study. The results show that the geodesic network plays an important role in 3D facial similarity measure. The similarity measure defined by shape index is consistent with human’s subjective evaluation basically, and it can measure the 3D face similarity more objectively than the other indices.
Variation in contour and cancer of stomach
Energy Technology Data Exchange (ETDEWEB)
Lee, Won Hong; Hwang, Seon Moon [Asan Medical Center, Asan (Korea, Republic of); Yoon, Kwon Ha [College of Medicine, Wonkwang Univ., Iksan (Korea, Republic of)
1999-04-01
There were four types of stomach contour included eutonic, hypotonic, steerhorn, and cascade. The aim of this study is to clarify relationship between incidence of stomach cancer and contour variation of the stomach. Double- contrast upper gastrointestinal study was performed in 1,546 patients, who had dyspepsia or other gastrointestinal tract symptoms. The radiographs were classified into the four types including eutonic, hypotonic, steerhorn, and cascade according to stomach contour in relation to body build. We also reviewed pathologic reports on endoscopic biopsy or surgical specimen. We studied the presence of relationship between incidence of stomach cancer and variation of stomach contour. We also examined the incidence of gastritis and gastric ulcer to the stomach contour variation. Of total 1,546 patients, eutonic stomach were 438(28.3%), hypotonic 911(58.9%), steerhorn 102(6.5%) and cascade 95(6.2%). Stomach cancer was found in 139(31.7%) of 438 eutonic stomachs, in 135(14.8%) of 911 hypotonic, in 42(41.2%) of 102 steerhorn, and in 24(36.9%) of 95 cascade (P=0.001). In hypotonic stomach, the incidence of stomach cancer was lower compared to the other three types significantly (p<0.05). Gastritis or gastric ulcer was found in 146(33.3%) of eutonic stomach, in 293(32.1%) of hypotonic, in 36(35.2%) of steerhorn, and in 26(27.3%) of cascade (p=0.640). In conclusion, gastric contour variation seems to be a factor affecting development of stomach cancer. The patients with hypotonic stomach may have lower incidence of stomach cancer than that of the other types. There was no relationship between the contour and gastric ulcer.
Exact solutions to the geodesic equations of linear dilaton black holes
Hamo, A H H
2015-01-01
In this paper, we analyze the geodesics of the 4-dimensional ($4D$) linear dilaton black hole (LDBH) spacetime, which is an exact solution to the Einstein-Maxwell-Dilaton (EMD) theory. LDBHs have non-asymptotically flat (NAF) geometry, and their Hawking radiation is an isothermal process. The geodesics motions of the test particles are studied via the standard Lagrangian method. After obtaining the Euler-Lagrange (EL) equations, we show that exact analytical solutions to the radial and angular geodesic equations can be obtained. In particular, it is shown that one of the possible solutions for the radial trajectories can be given in terms of the WeierstrassP-function ($\\wp$-function), which is an elliptic-type special function.
NVU dynamics. I. Geodesic motion on the constant-potential-energy hypersurface
DEFF Research Database (Denmark)
Ingebrigtsen, Trond; Toxværd, Søren; Heilmann, Ole
2011-01-01
An algorithm is derived for computer simulation of geodesics on the constant-potential-energy hypersurface of a system of N classical particles. First, a basic time-reversible geodesic algorithm is derived by discretizing the geodesic stationarity condition and implementing the constant......-potential-energy constraint via standard Lagrangian multipliers. The basic NVU algorithm is tested by single-precision computer simulations of the Lennard-Jones liquid. Excellent numerical stability is obtained if the force cutoff is smoothed and the two initial configurations have identical potential energy within machine...... that ensures potential-energy and step-length conservation; center-of-mass drift is also eliminated. Analytical arguments confirmed by simulations demonstrate that the modified NVU algorithm is absolutely stable. Finally, we present simulations showing that the NVU algorithm and the standard leap-frog NVE...
The Poincar\\'e reduction problem for geodesics on deformed spheres
Sinitsyn, D O
2011-01-01
We study geodesics on hypersurfaces close to the standard (n-1)-dimensional sphere in n-dimensional Euclidean space. Following Poincar\\'e, we treat the problem within the framework of the analytical mechanics, and employ the perturbation theory with the view of obtaining a topological classification of the set of geodesics on a manifold. To that end we use the X-ray transform familiar in the integral geometry, and obtain the system of averaged equations of motion, which turns out to be a Hamiltonian one. The system serves an asymptotic reduction of the initial exact system of 2n-2 equations to that of 2n-4 equations on the Grassmann manifold G(2,n). The Poisson brackets of the reduction system are determined by the Lie algebra of the group SO(n). In the important cases of two-dimensional and a range of three-dimensional hypersurfaces it allows a topological classification of the set of geodesics.
A FUZZY FILTERING MODEL FOR CONTOUR DETECTION
Directory of Open Access Journals (Sweden)
T.C. Rajakumar
2011-04-01
Full Text Available Contour detection is the basic property of image processing. Fuzzy Filtering technique is proposed to generate thick edges in two dimensional gray images. Fuzzy logic is applied to extract value for an image and is used for object contour detection. Fuzzy based pixel selection can reduce the drawbacks of conventional methods(Prewitt, Robert. In the traditional methods, filter mask is used for all kinds of images. It may succeed in one kind of image but fail in another one. In this frame work the threshold parameter values are obtained from the fuzzy histogram of the input image. The Fuzzy inference method selects the complete information about the border of the object and the resultant image has less impulse noise and the contrast of the edge is increased. The extracted object contour is thicker than the existing methods. The performance of the algorithm is tested with Peak Signal Noise Ratio(PSNR and Complex Wavelet Structural Similarity Metrics(CWSSIM.
Maintaining Contour Trees of Dynamic Terrains
DEFF Research Database (Denmark)
Agarwal, Pankaj K.; Arge, Lars; Mølhave, Thomas
We consider maintaining the contour tree T of a piecewise-linear triangulation M that is the graph of a time varying height function h:R2→R. We carefully describe the combinatorial change in T that happen as h varies over time and how these changes relate to topological changes in M. We present...... a kinetic data structure that maintains the contour tree of h over time. Our data structure maintains certificates that fail only when h(v)=h(u) for two adjacent vertices v and u in M, or when two saddle vertices lie on the same contour of M. A certificate failure is handled in O(log(n)) time. We also show...
Coding Long Contour Shapes of Binary Objects
Sánchez-Cruz, Hermilo; Rodríguez-Díaz, Mario A.
This is an extension of the paper appeared in [15]. This time, we compare four methods: Arithmetic coding applied to 3OT chain code (Arith-3OT), Arithmetic coding applied to DFCCE (Arith-DFCCE), Huffman coding applied to DFCCE chain code (Huff-DFCCE), and, to measure the efficiency of the chain codes, we propose to compare the methods with JBIG, which constitutes an international standard. In the aim to look for a suitable and better representation of contour shapes, our probes suggest that a sound method to represent contour shapes is 3OT, because Arithmetic coding applied to it gives the best results regarding JBIG, independently of the perimeter of the contour shapes.
Educational Facilities Labs., Inc., New York, NY.
A description is presented of the design features of a high school's geodesic dome field house. Following consideration of various design features and criteria for the physical education facility, a comprehensive analysis is given of comparative costs of a geodesic dome field house and conventional gymnasium. On the basis of the study it would…
A numerical study of the correspondence between paths in a causal set and geodesics in the continuum
Ilie, R; Thompson, G B; Ilie, Raluca; Reid, David D.; Thompson, Gregory B.
2006-01-01
This paper presents the results of a computational study related to the path-geodesic correspondence in causal sets. For intervals in flat spacetimes, and in selected curved spacetimes, we present evidence that the longest maximal chains (the longest paths) in the corresponding causal set intervals statistically approach the geodesic for that interval in the appropriate continuum limit.
Directory of Open Access Journals (Sweden)
Kun-Lin Wu
2016-01-01
Full Text Available In this paper, mobile robot navigation on a 3D terrain with a single obstacle is addressed. The terrain is modelled as a smooth, complete manifold with well-defined tangent planes and the hazardous region is modelled as an enclosing circle with a hazard grade tuned radius representing the obstacle projected onto the terrain to allow efficient path-obstacle intersection checking. To resolve the intersections along the initial geodesic, by resorting to the geodesic ideas from differential geometry on surfaces and manifolds, we present a geodesic-based planning and replanning algorithm as a new method for obstacle avoidance on a 3D terrain without using boundary following on the obstacle surface. The replanning algorithm generates two new paths, each a composition of two geodesics, connected via critical points whose locations are found to be heavily relying on the exploration of the terrain via directional scanning on the tangent plane at the first intersection point of the initial geodesic with the circle. An advantage of this geodesic path replanning procedure is that traversability of terrain on which the detour path traverses could be explored based on the local Gauss-Bonnet Theorem of the geodesic triangle at the planning stage. A simulation demonstrates the practicality of the analytical geodesic replanning procedure for navigating a constant speed point robot on a 3D hill-like terrain.
Institute of Scientific and Technical Information of China (English)
尚岩峰; 汪辉; 汪宁; 陈杰; 姚丽萍; 孙琨
2013-01-01
In this paper, we propose a nevo model for three dimensional vessel extraction. The model makes full use of tubular properties, which includes prior intensity of vessels, second tensor of tubular structures, and geometric curvatures. All this information makes the energy terms of the active contour model and thus leads to three forces of the iterative equation; the region competition force using prior intensity, the tubular vector field force and the dual curvature force. The first force help extracting big vessels accurately and robustly, the second force makes it possible to extract thin and weak vessels, and the last one is able to remove noise without changing the tubular geometry. As shown in the experiments extracting liver vessels, coronary, and lung vessels, the proposed model is able to extract the whole vessel trees automatically, accurately, and robustly.%针对血管树结构的复杂性,提出了基于管状特性和主动轮廓的3维血管的自动提取模型.该模型充分利用管状特性,包括血管的先验灰度分布、多尺度血管矢量场和血管几何曲率特征,把这些信息表示为主动轮廓模型的能量项并最小化,得到包括3个主要速度项的迭代方程:基于区域竞争和先验灰度的主动轮廓、血管矢量场和多曲率策略.基于区域竞争和先验灰度的主动轮廓可以准确健壮地提取大的血管；由Hessian矩阵主元分析得到的血管矢量场,可以驱使主动轮廓演化到细小血管内部；最小主曲率和平均曲率的多曲率策略,可以降噪平滑血管的同时,充分保持血管的几何形状.通过对肝脏、冠状动脉和肺部血管的分割,表明该模型可以自动地对整个血管树进行提取,不需要太多的预处理和后处理,是一种有效的血管自动提取模型.
A Fortran Code for Null Geodesic Solutions in the Lemaitre-Tolman-Bondi Spacetime
Ribeiro, Marcelo B.
2002-01-01
This paper describes the Fortran 77 code SIMU, version 1.1, designed for numerical simulations of observational relations along the past null geodesic in the Lemaitre-Tolman-Bondi (LTB) spacetime. SIMU aims at finding scale invariant solutions of the average density, but due to its full modularity it can be easily adapted to any application which requires LTB's null geodesic solutions. In version 1.1 the numerical output can be read by the GNUPLOT plotting package to produce a fully graphical...
A Fortran Code for Null Geodesic Solutions in the Lemaitre-Tolman-Bondi Spacetime
Ribeiro, M B
2002-01-01
This paper describes the Fortran 77 code SIMU, version 1.1, designed for numerical simulations of observational relations along the past null geodesic in the Lemaitre-Tolman-Bondi (LTB) spacetime. SIMU aims at finding scale invariant solutions of the average density, but due to its full modularity it can be easily adapted to any application which requires LTB's null geodesic solutions. In version 1.1 the numerical output can be read by the GNUPLOT plotting package to produce a fully graphical output, although other plotting routines can be easily adapted. Details of the code's subroutines are discussed, and an example of its output is shown.
A Fortran code for null geodesic solutions in the Lemaître-Tolman-Bondi spacetime
Ribeiro, Marcelo B.
2002-10-01
This paper describes the Fortran 77 code SIMU, version 1.1, designed for numerical simulations of observational relations along the past null geodesic in the Lemaître-Tolman-Bondi (LTB) spacetime. SIMU aims at finding scale invariant solutions of the average density, but due to its full modularity it can be easily adapted to any application which requires LTB's null geodesic solutions. In version 1.1 the numerical output can be read by the GNUPLOT plotting package to produce a fully graphical output, although other plotting routines can be easily adapted. Details of the code's subroutines are discussed, and an example of its output is shown.
Kazempour, Sobhan; Soroushfar, Saheb
2016-01-01
In this paper we add a compact dimension to Schwarzschild-(anti-) de sitter and Kerr-(anti-) de sitter spacetimes, which describes (rotating) black string-(anti-) de sitter spacetime. We study the geodesic motion of test particles and light rays in this spacetime. We present the analytical solutions of the geodesic equations in terms of Weierstrass elliptic and Kleinian sigma hyperelliptical functions. We also discuss the possible orbits and classify them according to particle's energy and angular momentum. Moreover, the obtained results, are compared to Schwarzschild-(anti-) de sitter and Kerr-(anti-) de sitter spacetimes.
Impact of Energetic-Particle-Driven Geodesic Acoustic Modes on Turbulence
Zarzoso, D.; Sarazin, Y.; Garbet, X.; Dumont, R.; Strugarek, A.; Abiteboul, J.; Cartier-Michaud, T.; Dif-Pradalier, G.; Ghendrih, Ph.; Grandgirard, V.; Latu, G.; Passeron, C.; Thomine, O.
2013-03-01
The impact on turbulent transport of geodesic acoustic modes excited by energetic particles is evidenced for the first time in flux-driven 5D gyrokinetic simulations using the Gysela code. Energetic geodesic acoustic modes (EGAMs) are excited in a regime with a transport barrier in the outer radial region. The interaction between EGAMs and turbulence is such that turbulent transport can be enhanced in the presence of EGAMs, with the subsequent destruction of the transport barrier. This scenario could be particularly critical in those plasmas, such as burning plasmas, exhibiting a rich population of suprathermal particles capable of exciting energetic modes.
On geodesics with negative energies in the ergoregions of dirty black holes
Zaslavskii, O B
2014-01-01
We consider behavior of equatorial geodesics with the negative energy in the ergoregion of a generic rotating "dirty" (surrounded by matter) black hole. It is shown that under very simple and generic conditions on the metric coefficients, there are no such circular orbits. This entails that such geodesic must originate and terminate under the event horizon. These results generalize the observation made for the Kerr metric in A. A. Grib, Yu. V. Pavlov, and V. D. Vertogradov, Mod. Phys. Lett. 29, 1450110 (2014) [arXiv:1304.7360].
Study of the geodesic equations of a spherical symmetric spacetime in conformal Weyl gravity
Hoseini, Bahareh; Saffari, Reza; Soroushfar, Saheb
2017-03-01
A set of analytic solutions of the geodesic equation in a spherical conformal spacetime is presented. Solutions of this geodesics can be expressed in terms of the Weierstrass \\wp function and the Kleinian σ function. Using conserved energy and angular momentum we can characterize the different orbits. Also, considering parametric diagrams and effective potentials, we plot some possible orbits. Moreover, with the help of analytical solutions, we investigate the light deflection for such an escape orbit. Finally, by using periastron advance we get to an upper bound for magnitude of γ.
Geodesic Structures of Lifshitz Black Holes in 2+1 Dimensions
Cruz, Norman; Villanueva, J R
2013-01-01
We present an study of the geodesic equations of a black hole spacetime which is a solution of the three-dimensional NMG theory and is asymptotically Lifshitz with $z=3$ and $d=1$ found in [Ayon-Beato E., Garbarz A., Giribet G. and Hassaine M., Phys. Rev.{\\bf D} 80, 104029 (2009)]. By means of the corresponding effective potentials for massive particles and photons we find the allowed motions by the energy levels. Exact solutions for radial and non radial geodesics are given in terms of the Weierstrass elliptic $\\wp$, $\\sigma$, and $\\zeta$ functions.
Soroushfar, Saheb; Saffari, Reza; Sahami, Ehsan
2016-07-01
In this paper, we consider the timelike and null geodesics around the static (GMGHS, magnetically charged GMGHS, electrically charged GMGHS) and the rotating (Kerr-Sen dilaton-axion) dilaton black holes. The geodesic equations are solved in terms of Weierstrass elliptic functions. To classify the trajectories around the black holes, we use the analytical solution and effective potential techniques and then characterize the different types of the resulting orbits in terms of the conserved energy and angular momentum. Also, using the obtained results we study astrophysical applications.
Paiva, F M
2011-01-01
In the homogeneous metric of Som-Raychaudhuri, in general relativity, we study the three types of geodesics: timelike, null, and spacelike; in particular, the little known geodesics of simultaneities. We also study the non-geodetic circular motion with constant velocity, particularly closed timelike curves, and time travel of a voyager. ------------------- ^Ce la ^Generala Relativeco, en homogena metriko de Som-Raychaudhuri, ni studas geodeziojn de la tri tipoj: tempa, nula, kaj spaca, speciale la malmulte konatajn samtempajn geodeziojn. Ni anka^u studas ne-geodezian cirklan movadon kun konstanta rapido, speciale fermitajn kurbojn de tempa tipo, kaj movadon de voja^ganto al estinto.
Conversion of contours to cartesian grids
Energy Technology Data Exchange (ETDEWEB)
Mann, J.; Broe, B. Riget
2006-07-15
A robust and efficient method of calculating a cartesian grid of heights or roughnesses from contour line maps is developed. The purpose of the grids is to serve as input for atmospheric flow solvers such as WAsP Engineering or EllipSys3D. The method builds on Delaunay triangulation constrained to include all contour segments in the triangulation. It is furthermore refined to avoid spurious flat areas produced by the Delaunay triangulation. Robust ways to extrapolate beyond the convex hull of the map points are provided. (au)
Conversion of contours to cartesian grids
DEFF Research Database (Denmark)
Mann, Jakob; Broe, Brian Riget
A robust and efficient method of calculating a cartesian grid of heights or roughnesses from contour line maps is developed. The purpose of the grids is to serve as input for atmospheric flow solvers such as WAsP Engineering or EllipSys3D. The method builds on Delaunay triangulation constrained t...... to include all contour segments in the triangulation. It is furthermore refined to avoid spurious flat areas produced by the Delaunay triangulation. Robust ways to extrapolate beyond the convex hull of the map points are provided....
Contours--Offshore of Carpinteria, California
U.S. Geological Survey, Department of the Interior — This part of SIM 3261 presents data for the bathymetric contours for several seafloor maps (see sheets 1, 2, 3, 5 [in figs. 1, 2, 3], 7, 10, SIM 3261) of the...
Contours--Offshore of Santa Barbara, California
U.S. Geological Survey, Department of the Interior — This part of SIM 3281 presents data for the bathymetric contours for several seafloor maps (see sheets 1, 2, 3, 7, 10, SIM 3281) of the Offshore of Santa Barbara map...
Maintaining Contour Trees of Dynamic Terrains
DEFF Research Database (Denmark)
Agarwal, Pankaj K.; Arge, Lars; Mølhave, Thomas
We consider maintaining the contour tree T of a piecewise-linear triangulation M that is the graph of a time varying height function h:R2→R. We carefully describe the combinatorial change in T that happen as h varies over time and how these changes relate to topological changes in M. We present...
Regression Model With Elliptically Contoured Errors
Arashi, M; Tabatabaey, S M M
2012-01-01
For the regression model where the errors follow the elliptically contoured distribution (ECD), we consider the least squares (LS), restricted LS (RLS), preliminary test (PT), Stein-type shrinkage (S) and positive-rule shrinkage (PRS) estimators for the regression parameters. We compare the quadratic risks of the estimators to determine the relative dominance properties of the five estimators.
Contours--Offshore of Carpinteria, California
U.S. Geological Survey, Department of the Interior — This part of SIM 3261 presents data for the bathymetric contours for several seafloor maps (see sheets 1, 2, 3, 5 [in figs. 1, 2, 3], 7, 10, SIM 3261) of the...
Automatic contour welder incorporates speed control system
Wall, W. A., Jr.
1968-01-01
Speed control system maintains the welding torch of an automatic welder at a substantially constant speed. The system is particularly useful when welding contoured or unusually shaped surfaces, which cause the distance from the work surface to the weld carriage to vary in a random manner.
Maintaining Contour Trees of Dynamic Terrains
DEFF Research Database (Denmark)
Agarwal, Pankaj K.; Mølhave, Thomas; Revsbæk, Morten;
2015-01-01
We study the problem of maintaining the contour tree T of a terrain Sigma, represented as a triangulated xy-monotone surface, as the heights of its vertices vary continuously with time. We characterize the combinatorial changes in T and how they relate to topological changes in Sigma. We present ...
Contours--Offshore of San Gregorio, California
U.S. Geological Survey, Department of the Interior — This part of SIM 3306 presents data for the bathymetric contours for several seafloor maps (see sheets 1, 2, 3, 7, 10, SIM 3306) of the Offshore of San Gregorio map...
Analysis of CVC roll contour and determination of roll crown
Institute of Scientific and Technical Information of China (English)
Guang Xu; Xianjun Liu; Jiarong Zhao; Junwei Xiong
2007-01-01
Mathematical analysis of continuous variable crown (CVC) roll contour used in CSP production line was conducted and the roll contour function of CVC roll was obtained. The validation with actual CVC roll contour shows that the calculation values of the roll contour function and the actual roll contour parameters given by equipment provider are the same, which proves that the roll contour function of CVC rolls given in this article is correct. The nonlinear relationship between the roll crown of CVC rolls and roll shift amounts was deduced. The concept of crown extremum was given.
Totally geodesic Seifert surfaces in hyperbolic knot and link complements II
DEFF Research Database (Denmark)
Adams, Colin; Bennett, Hanna; Davis, Christopher James;
2008-01-01
We generalize the results of Adams–Schoenfeld, finding large classes of totally geodesic Seifert surfaces in hyperbolic knot and link complements, each covering a rigid 2-orbifold embedded in some hyperbolic 3-orbifold. In addition, we provide a uniqueness theorem and demonstrate that many knots ...
Santoprete, Manuele
2002-01-01
Resorting to classical techniques of Riemannian geometry we develop a geometrical method suitable to investigate the nonintegrability of geodesic flows and of natural Hamiltonian systems. Then we apply such method to the Anisotropic Kepler Problem (AKP) and we prove that it is not analytically integrable.
Action-angle variables for geodesic motions in Sasaki-Einstein spaces Y
Visinescu, Mihai
2017-01-01
We use action-angle variables to describe the geodesic motions in the 5-dimensional Sasaki-Einstein spaces Y. This formulation allows us to study thoroughly the complete integrability of the system. We find that the Hamiltonian involves a reduced number of action variables. Therefore one of the fundamental frequencies is zero, indicating chaotic behavior when the system is perturbed.
Wide Field-of-view and Broadband Terahertz Beam Steering Based on Gap Plasmon Geodesic Antennas
Liu, Kaipeng; Guo, Yinghui; Pu, Mingbo; Ma, Xiaoliang; Li, Xiong; Luo, Xiangang
2017-01-01
Despite a plethora of applications ranging from wireless communications to sensing and spectroscopy, the current terahertz beam steering technologies suffer from tremendous insert loss, stringent control of electric bias, limited scanning angle, relatively complicated configuration and narrow operation bandwidth, preventing further practical application. We propose and demonstrate a conceptually new approach for terahertz beam steering by virtue of gap plasmon geodesic antennas. By adjusting the geometric dimension of the gap plasmon geodesic antennas, all gap plasmon modes add coherently along a peculiar direction that depends on the geodesic mean surface. Consequently, high directive beams are generated through the antenna, whose direction could be changed within a wide-angle range spanning ±45° by lateral motion of the feed. Furthermore, an assembled antenna structure consisting of four-element geodesic antennas array is proposed for full 360° beam steering, which can operate in a broadband range from 0.8 THz to 1.2 THz. PMID:28134324
Totally geodesic Seifert surfaces in hyperbolic knot and link complements II
DEFF Research Database (Denmark)
Adams, Colin; Bennett, Hanna; Davis, Christopher James
2008-01-01
We generalize the results of Adams–Schoenfeld, finding large classes of totally geodesic Seifert surfaces in hyperbolic knot and link complements, each covering a rigid 2-orbifold embedded in some hyperbolic 3-orbifold. In addition, we provide a uniqueness theorem and demonstrate that many knots...
Geodesic Acoustic Mode in Toroidally Axisymmetric Plasmas with Non-Circular Cross Sections
Institute of Scientific and Technical Information of China (English)
SHI Bing-Ren; LI Ji-Quan; DONG Jia-Qi
2005-01-01
@@ The geodesic acoustic mode in general toroidally axisymmetric plasmas such as Tokamak and spherical torus is studied in detail. The mode structure is found and the dispersion equation is derived and solved for arbitrary toroidally axi-symmetric plasmas. Besides the finite aspect ratio, effects of elongation and triangularity on this mode are clarified.
On Geodesic Flows and Their Deformations in Bertrand Space-times
Kumar, Prashant; Sarkar, Tapobrata
2012-01-01
We study the energy conditions and geodesic equations of Bertrand space-times. We show that these can be thought of as interesting physical space-times in certain regions of the parameter space where the weak and strong energy conditions hold. We further compute the ESR parameters for a class of such space-times and analyze them numerically.
Null geodesics in the Reissner-Nordstr\\"om Anti-de Sitter black holes
Cruz, Norman; Saavedra, Joel; Villanueva, J R
2011-01-01
In this work we address the study of null geodesics in the background of Reissner-Nordstr\\"om Anti de Sitter black holes. We compute the exact trajectories in terms of elliptic functions of Weierstrass, obtaining a detailed description of the orbits in terms of charge, mass and the cosmological constant. The trajectories of the photon are classified using the impact parameter.
Subsidence Contours for South Louisiana; UTM 15N NAD83; LRA (2005); [subsidence_contours
Louisiana Geographic Information Center — The GIS data shapefile represents average subsidence contour intervals (0.02 cm/year over 10,000 years) for Coastal LA derived from the following: Kulp, M.A., 2000,...
USGS Elevation Contours Overlay Map Service from The National Map
U.S. Geological Survey, Department of the Interior — The USGS Elevation Contours service from The National Map (TNM) consists of contours generated for the conterminous United States from 1- and 1/3 arc-second...
Automatic liver contouring for radiotherapy treatment planning
Li, Dengwang; Liu, Li; Kapp, Daniel S.; Xing, Lei
2015-09-01
To develop automatic and efficient liver contouring software for planning 3D-CT and four-dimensional computed tomography (4D-CT) for application in clinical radiation therapy treatment planning systems. The algorithm comprises three steps for overcoming the challenge of similar intensities between the liver region and its surrounding tissues. First, the total variation model with the L1 norm (TV-L1), which has the characteristic of multi-scale decomposition and an edge-preserving property, is used for removing the surrounding muscles and tissues. Second, an improved level set model that contains both global and local energy functions is utilized to extract liver contour information sequentially. In the global energy function, the local correlation coefficient (LCC) is constructed based on the gray level co-occurrence matrix both of the initial liver region and the background region. The LCC can calculate the correlation of a pixel with the foreground and background regions, respectively. The LCC is combined with intensity distribution models to classify pixels during the evolutionary process of the level set based method. The obtained liver contour is used as the candidate liver region for the following step. In the third step, voxel-based texture characterization is employed for refining the liver region and obtaining the final liver contours. The proposed method was validated based on the planning CT images of a group of 25 patients undergoing radiation therapy treatment planning. These included ten lung cancer patients with normal appearing livers and ten patients with hepatocellular carcinoma or liver metastases. The method was also tested on abdominal 4D-CT images of a group of five patients with hepatocellular carcinoma or liver metastases. The false positive volume percentage, the false negative volume percentage, and the dice similarity coefficient between liver contours obtained by a developed algorithm and a current standard delineated by the expert group
[External contour acquisition system for radiotherapy: an original solution].
Létourneau, D; Brochet, F; Bohémier, R; Gagnon, J
2000-01-01
A contour acquisition system has been designed in radiotherapy at the Sagamie Hospital complex (Chicoutimi, Québec) to measure the external contours of the patients who do not need a CT exam. This measuring system can produce transversal, sagittal or coronal patient contours in the treatment position. The absolute accuracy of the system is +/- 1 mm. The contours produced by this equipment can be transferred electronically or on paper to the planning system.
Integrability of geodesics and action-angle variables in Sasaki-Einstein space T{sup 1,1}
Energy Technology Data Exchange (ETDEWEB)
Visinescu, Mihai [National Institute of Physics and Nuclear Engineering, Department Theoretical Physics, Magurele, Bucharest (Romania)
2016-09-15
We briefly describe the construction of Staekel-Killing and Killing-Yano tensors on toric Sasaki-Einstein manifolds without working out intricate generalized Killing equations. The integrals of geodesic motions are expressed in terms of Killing vectors and Killing-Yano tensors of the homogeneous Sasaki-Einstein space T{sup 1,1}. We discuss the integrability of geodesics and construct explicitly the action-angle variables. Two pairs of frequencies of the geodesic motions are resonant giving way to chaotic behavior when the system is perturbed. (orig.)
Edge and line oriented contour detection : State of the art
Papari, Giuseppe; Petkov, Nicolai
We present an overview of various edge and line oriented approaches to contour detection that have been proposed in the last two decades. By edge and line oriented we mean methods that do not rely on segmentation. Distinction is made between edges and contours. Contour detectors are divided in local
Edge and line oriented contour detection : State of the art
Papari, Giuseppe; Petkov, Nicolai
2011-01-01
We present an overview of various edge and line oriented approaches to contour detection that have been proposed in the last two decades. By edge and line oriented we mean methods that do not rely on segmentation. Distinction is made between edges and contours. Contour detectors are divided in local
Maintaining Contour Trees of Dynamic Terrains
DEFF Research Database (Denmark)
Agarwal, Pankaj K.; Mølhave, Thomas; Revsbæk, Morten
2015-01-01
We study the problem of maintaining the contour tree T of a terrain Sigma, represented as a triangulated xy-monotone surface, as the heights of its vertices vary continuously with time. We characterize the combinatorial changes in T and how they relate to topological changes in Sigma. We present...... a kinetic data structure (KDS) for maintaining T efficiently. It maintains certificates that fail, i.e., an event occurs, only when the heights of two adjacent vertices become equal or two saddle vertices appear on the same contour. Assuming that the heights of two vertices of Sigma become equal only O(1......) times and these instances can be computed in O(1) time, the KDS processes O(kappa + n) events, where n is the number of vertices in Sigma and kappa is the number of events at which the combinatorial structure of T changes, and processes each event in O(log n) time. The KDS can be extended to maintain...
Contours, contours 500 ft, Published in 2008, 1:24000 (1in=2000ft) scale, Box Elder County.
NSGIC GIS Inventory (aka Ramona) — This Contours dataset, published at 1:24000 (1in=2000ft) scale, was produced all or in part from Other information as of 2008. It is described as 'contours 500 ft'....
Contours, ft 10 NED contours 2, Published in 2008, 1:24000 (1in=2000ft) scale, Box Elder County.
NSGIC GIS Inventory (aka Ramona) — This Contours dataset, published at 1:24000 (1in=2000ft) scale, was produced all or in part from Other information as of 2008. It is described as 'ft 10 NED contours...
Contours, contours 100 ft, Published in 2008, 1:24000 (1in=2000ft) scale, Box Elder County.
NSGIC GIS Inventory (aka Ramona) — This Contours dataset, published at 1:24000 (1in=2000ft) scale, was produced all or in part from Other information as of 2008. It is described as 'contours 100 ft'....
Contours, contours_2ft, Published in 2007, 1:1200 (1in=100ft) scale, Dodge County, Wisconsin.
NSGIC GIS Inventory (aka Ramona) — This Contours dataset, published at 1:1200 (1in=100ft) scale, was produced all or in part from LIDAR information as of 2007. It is described as 'contours_2ft'. Data...
Contours, ft 10 NED contours 1, Published in 2008, 1:24000 (1in=2000ft) scale, Box Elder County.
NSGIC GIS Inventory (aka Ramona) — This Contours dataset, published at 1:24000 (1in=2000ft) scale, was produced all or in part from Other information as of 2008. It is described as 'ft 10 NED contours...
NSGIC GIS Inventory (aka Ramona) — This Contours dataset, published at 1:24000 (1in=2000ft) scale as of 2003. It is described as 'Tagged Vector Contours obtained from DASC'. Data by this publisher...
Contours, contour 500 ft, Published in 2009, 1:24000 (1in=2000ft) scale, Washington County.
NSGIC GIS Inventory (aka Ramona) — This Contours dataset, published at 1:24000 (1in=2000ft) scale, was produced all or in part from Other information as of 2009. It is described as 'contour 500 ft'....
Contours, contour 50 ft, Published in 2009, 1:24000 (1in=2000ft) scale, Washington County.
NSGIC GIS Inventory (aka Ramona) — This Contours dataset, published at 1:24000 (1in=2000ft) scale, was produced all or in part from Other information as of 2009. It is described as 'contour 50 ft'....
Contours, contour 10 ft, Published in 2009, 1:24000 (1in=2000ft) scale, Washington County.
NSGIC GIS Inventory (aka Ramona) — This Contours dataset, published at 1:24000 (1in=2000ft) scale, was produced all or in part from Other information as of 2009. It is described as 'contour 10 ft'....
Contour Estimation by Array Processing Methods
Directory of Open Access Journals (Sweden)
Bourennane Salah
2006-01-01
Full Text Available This work is devoted to the estimation of rectilinear and distorted contours in images by high-resolution methods. In the case of rectilinear contours, it has been shown that it is possible to transpose this image processing problem to an array processing problem. The existing straight line characterization method called subspace-based line detection (SLIDE leads to models with orientations and offsets of straight lines as the desired parameters. Firstly, a high-resolution method of array processing leads to the orientation of the lines. Secondly, their offset can be estimated by either the well-known method of extension of the Hough transform or another method, namely, the variable speed propagation scheme, that belongs to the array processing applications field. We associate it with the method called "modified forward-backward linear prediction" (MFBLP. The signal generation process devoted to straight lines retrieval is retained for the case of distorted contours estimation. This issue is handled for the first time thanks to an inverse problem formulation and a phase model determination. The proposed method is initialized by means of the SLIDE algorithm.
Waterline extraction in optical images and InSAR coherence maps based on the geodesic time concept
Soares, Fernando; Nico, Giovanni
2010-10-01
An algorithm for waterline extraction from SAR images is presented based on the estimation of the geodesic path, or minimal path (MP) between two pixels on the waterline. For two given pixels, geodesic time is determined in terms of the time shortest path, between them. The MP is determined by estimating the mean value for all pairs of neighbor pixels that can be part of a possible path connecting the initial given pixels. A MP is computed as the sum of those two geodesic image functions. In general, a MP is obtained with the knowledge of two end pixels. Based on the 2-dimensional spreading of the estimated geodesic time function, the concepts of propagation energy and strong pixels are introduced and tested for the waterline extraction by marking only one pixel in the image.
VT 10 ft Contour Lines generated from bare earth lidar - Chittenden
Vermont Center for Geographic Information — (Link to Metadata) ElevationContours_CN10T (10ft contours) was extracted from ElevationContours_CN2T (2ft contours), which was generated by USGS from the 2004...
Context modulates the ERP signature of contour integration.
Directory of Open Access Journals (Sweden)
Bart Machilsen
Full Text Available We investigated how the electrophysiological signature of contour integration is changed by the context in which a contour is embedded. Specifically, we manipulated the orientations of Gabor elements surrounding an embedded shape outline. The amplitudes of early visual components over posterior scalp regions were changed by the presence of a contour, and by the orientation of elements surrounding the contour. Differences in context type had an effect on the early P1 and N1 components, but not on the later P2 component. The presence of a contour had an effect on the N1 and P2 components, but not on the earlier P1 component. A modulatory effect of context on contour integration was observed on the N1 component. These results highlight the importance of the context in which contour integration takes place.
Soroushfar, Saheb; Kazempour, Sobhan; Grunau, Saskia; Kunz, Jutta
2016-01-01
We study the geodesic equations in the space time of a rotating charged black hole in $f(R)$ gravity. We derive the equations of motion for test particles and light rays and present their solutions in terms of the Weierstrass $\\wp$, $\\zeta$ and $\\sigma$ functions as well as the Kleinian $\\sigma$ function. With the help of parametric diagrams and effective potentials we analyze the geodesic motion and classify the possible orbit types.
On the behaviour of non-radial null geodesics in self-similar Tolman-Bondi collapse
Ortiz, Néstor; Zannias, Thomas
2015-01-01
Motivated by recent work on the structure of the singularity in inhomogeneous Tolman-Bondi collapse models, we investigate the behaviour of null geodesics in the particular case where the collapse is self-similar. The presence of the homothetic Killing vector field implies that the geodesic equation can be described by an integrable Hamiltonian system, and exploiting this fact we provide a full qualitative picture for its phase flow.
Three-dimensional adult male head and skull contours.
Lee, Calvin; Loyd, Andre M; Nightingale, Roger; Myers, Barry S; Damon, Andrew; Bass, Cameron R
2014-01-01
Traumatic brain injury (TBI) is a major public health issue, affecting millions of people annually. Anthropomorphic test devices (ATDs) and finite element models (FEMs) provide a means of understanding factors leading to TBI, potentially reducing the occurrence. Thus, there is a need to ensure that these tools accurately model humans. For example, the Hybrid III was not based on 3-dimensional human head shape data. The objective of this study is to produce average head and skull contours for an average U.S. male that can be used for ATDs and FEMs. Computed tomography (CT) scans of adult male heads were obtained from a database provided by the University of Virginia Center for Applied Biomechanics. An orthographic viewer was used to extract head and skull contours from the CT scans. Landmarks were measured graphically using HyperMesh (Altair, HyperWorks). To determine the head occipital condyle (OC) centroid, surface meshes of the OCs were made and the centroid of the surfaces was calculated. The Hybrid III contour was obtained using a MicroScribe Digitizer (Solution Technologies, Inc., Oella, MD). Comparisons of the average male and ATD contours were performed using 2 methods: (1) the midsagittal and midcoronal ATD contours relative to the OC centroid were compared to the corresponding 1 SD range of the average male contours; (2) the ATD sagittal contour was translated relative to the average male sagittal contour to minimize the area between the 2 contours. Average male head and skull contours were created. Landmark measurements were made for the dorsum sellae, nasion skin, nasion bone, infraorbital foramen, and external auditory meatus, all relative to the OC centroid. The Hybrid III midsagittal contour was outside the 1 SD range for 15.2 percent of the average male head contour but only by a maximum distance of 1.5 mm, whereas the Hybrid III midcoronal head contour was outside the 1 SD range for 12.2 percent of the average male head contour by a maximum distance
Detailed study of null and time-like geodesics in the Alcubierre Warp spacetime
Müller, Thomas
2011-01-01
The Alcubierre warp spacetime yields a fascinating chance for comfortable interstellar travel between arbitrary distant places without the time dilation effect as in special relativistic flights. Even though the warp spacetime needs exotic matter for its construction and is thus far from being physically feasible, it offers a rich playground for studying geodesics in the general theory of relativity. This paper is addressed to graduate students who have finished a first course in general relativity to give them a deeper inside in the calculation of non-affinely parametrized null and time-like geodesics and a straightforward approach to determine the gravitational lensing effect due to curved spacetime by means of the Jacobi equation. Both topics are necessary for a thorough discussion of the visual effects as observed by a traveller inside the warp bubble or a person looking from outside. The visual effects of the traveller can be reproduced with an interactive Java application.
Geodesic-length functions and the Weil-Petersson curvature tensor
Wolpert, Scott A
2010-01-01
An expansion is developed for the Weil-Petersson Riemann curvature tensor in the thin region of the Teichm\\"{u}ller and moduli spaces. The tensor is evaluated on the gradients of geodesic-lengths for disjoint geodesics. A precise lower bound for sectional curvature in terms of the systole is presented. The curvature tensor expansion is applied to establish continuity properties at the frontier strata of the augmented Teichm\\"{u}ller space. The curvature tensor has the asymptotic product structure already observed for the metric and covariant derivative. The product structure is combined with the earlier negative sectional curvature results to establish a classification of asymptotic flats. Furthermore, tangent subspaces of more than half the dimension of Teichm\\"{u}ller space contain sections with a definite amount of negative curvature. Proofs combine estimates for uniformization group exponential-distance sums and potential theory bounds.
Vacuum non-expanding horizons and shear-free null geodesic congruences
Adamo, T M
2009-01-01
We investigate the geometry of a particular class of null surfaces in space-time called vacuum Non-Expanding Horizons (NEHs). Using the spin-coefficient equation, we provide a complete description of the horizon geometry, as well as fixing a canonical choice of null tetrad and coordinates on a NEH. By looking for particular classes of null geodesic congruences which live exterior to NEHs but have the special property that their shear vanishes at the intersection with the horizon, a good cut formalism for NEHs is developed which closely mirrors asymptotic theory. In particular, we show that such null geodesic congruences are generated by arbitrary choice of a complex world-line in a complex four dimensional space, each such choice induces a CR structure on the horizon, and a particular world-line (and hence CR structure) may be chosen by transforming to a privileged tetrad frame.
Singh, Nikhil; Hinkle, Jacob; Joshi, Sarang; Fletcher, P Thomas
2013-04-01
This paper presents a novel approach for diffeomorphic image regression and atlas estimation that results in improved convergence and numerical stability. We use a vector momenta representation of a diffeomorphism's initial conditions instead of the standard scalar momentum that is typically used. The corresponding variational problem results in a closed-form update for template estimation in both the geodesic regression and atlas estimation problems. While we show that the theoretical optimal solution is equivalent to the scalar momenta case, the simplification of the optimization problem leads to more stable and efficient estimation in practice. We demonstrate the effectiveness of our method for atlas estimation and geodesic regression using synthetically generated shapes and 3D MRI brain scans.
Geodesic mode instability driven by electron and ion fluxes in tokamaks
Energy Technology Data Exchange (ETDEWEB)
Elfimov, A. G., E-mail: elfimov@if.usp.br; Camilo de Souza, F.; Galvão, R. M. O. [Institute of Physics, University of São Paulo, São Paulo 05508-090 (Brazil)
2015-11-15
The effect of the parallel electron current and plasma flux on Geodesic Acoustic Modes (GAM) in a tokamak is analyzed by kinetic theory taking into the account the ion Landau damping and diamagnetic drifts. It is shown that the electron current and plasma flow, modeled by shifted Maxwell distributions of electrons and ions, may overcome the ion Landau damping generating the GAM instability when the parallel electron current velocity is larger than the effective parallel GAM phase velocity of sidebands, Rqω. The instability is driven by the electron current and the parallel ion flux cross term. Possible applications to tokamak experiments are discussed. The existence of the geodesic ion sound mode due to plasma flow is shown.
Hackmann, Eva
2015-01-01
The complete set of analytic solutions of the geodesic equation in a Schwarzschild--(anti-)de Sitter space--time is presented. The solutions are derived from the Jacobi inversion problem restricted to the set of zeros of the theta function, called the theta divisor. In its final form the solutions can be expressed in terms of derivatives of Kleinian sigma functions. The different types of the resulting orbits are characterized in terms of the conserved energy and angular momentum as well as the cosmological constant. Using the analytical solution, the question whether the cosmological constant could be a cause of the Pioneer Anomaly is addressed. The periastron shift and its post--Schwarzschild limit is derived. The developed method can also be applied to the geodesic equation in higher dimensional Schwarzschild space--times.
Geodesic least squares regression for scaling studies in magnetic confinement fusion
Energy Technology Data Exchange (ETDEWEB)
Verdoolaege, Geert [Department of Applied Physics, Ghent University, Ghent, Belgium and Laboratory for Plasma Physics, Royal Military Academy, Brussels (Belgium)
2015-01-13
In regression analyses for deriving scaling laws that occur in various scientific disciplines, usually standard regression methods have been applied, of which ordinary least squares (OLS) is the most popular. However, concerns have been raised with respect to several assumptions underlying OLS in its application to scaling laws. We here discuss a new regression method that is robust in the presence of significant uncertainty on both the data and the regression model. The method, which we call geodesic least squares regression (GLS), is based on minimization of the Rao geodesic distance on a probabilistic manifold. We demonstrate the superiority of the method using synthetic data and we present an application to the scaling law for the power threshold for the transition to the high confinement regime in magnetic confinement fusion devices.
Equatorial geodesics of dyonic Kerr-Newman black hole pierced by a cosmic string
Sharif, M.; Iftikhar, Sehrish
2016-12-01
This paper is devoted to study the circular geodesics of the dyonic Kerr-Newman black hole with a cosmic string passing through it. We investigate circular geodesics of null and timelike particle. In this context, we find the circular photon orbit as well as the innermost stable circular orbit. The angular velocity and time period for the timelike particle are calculated. The effect of electric and magnetic charge as well as of the cosmic string parameter on the effective potential is analyzed numerically. Finally, we discuss the role of these parameters on the energy extraction by the Penrose process. We conclude that the string parameter does not affect the gain energy of the particle but it decreases with respect to charge.
AdS/CFT prescription for angle-deficit space and winding geodesics
Aref'eva, Irina Ya
2016-01-01
We present the holographic computation of the boundary two-point correlator using the GKPW prescription for a scalar field in the AdS$_3$ space with a conical defect. Generally speaking, a conical defect breaks conformal invariance in the dual theory, however we calculate the classical Green functions for a scalar field in the bulk with conical defect and use them to compute the two-point correlator in the boundary theory. We compare the obtained general expression with previous studies based on the geodesic approximation. They are in good agreement for short correlators, and main discrepancy comes in the region of long correlations. Meanwhile, in case of $\\mathbb{Z}_r$-orbifold, the GKPW result coincides with the one obtained via geodesic images prescription and with the general result for the boundary theory, which is conformal in this special case.
Single Past Null Geodesic in the Lemaitre-Tolman-Bondi Cosmology
Nogueira, Felipe A M G
2013-01-01
This work provides a general discussion of the spatially inhomogeneous Lema\\^itre-Tolman-Bondi (LTB) cosmology, as well as its basic properties and many useful relevant quantities, such as the cosmological distances. We apply the concept of the single null geodesic to produce some simple analytical solutions for observational quantities such as the redshift. As an application of the single null geodesic technique, we carry out a fractal approach to the parabolic LTB model, comparing it to the spatially homogeneous Einstein-de Sitter cosmology. The results obtained indicate that the standard model, in this case represented by the Einstein-de Sitter cosmology, can be equivalently described by a fractal distribution of matter, as we found that different single fractal dimensions describe different scale ranges of the parabolic LTB matter distribution. It is shown that at large ranges the parabolic LTB model with fractal dimension equal to 0.5 approximates the matter distribution of the Einstein-de Sitter univers...
The Differential of the Exponential Map, Jacobi Fields and Exact Principal Geodesic Analysis
Sommer, Stefan; Nielsen, Mads
2010-01-01
The importance of manifolds and Riemannian geometry in mathematics is spreading to applied fields in which the need to model non-linear structure has spurred wide-spread interest in geometry. The transfer of interest has created demand for methods for computing classical constructs of geometry on manifolds occurring in practical applications. This paper develops initial value problems for the computation of the differential of the exponential map and Jacobi fields on parametrically and implicitly represented manifolds. It is shown how the solution to these problems allow for determining sectional curvatures and provides upper bounds for injectivity radii. In addition, when combined with the second derivative of the exponential map, the initial value problems allow for solving the problem of computing Principal Geodesic Analysis, a non-linear version of the Principal Component Analysis procedure for estimating variability in datasets. The paper develops algorithms for computing Principal Geodesic Analysis with...
Models of rotating boson stars and geodesics around them: New type of orbits
Grandclément, Philippe; Somé, Claire; Gourgoulhon, Eric
2014-07-01
We have developed a highly accurate numerical code capable of solving the coupled Einstein-Klein-Gordon system, in order to construct rotating boson stars in general relativity. Free fields and self-interacting fields, with quartic and sextic potentials, are considered. In particular, we present the first numerical solutions of rotating boson stars with rotational quantum number k=3 and k=4, as well as the first determination of the maximum mass of free-field boson stars with k=2. We have also investigated timelike geodesics in the spacetime generated by a rotating boson star for k=1, 2 and 3. A numerical integration of the geodesic equation has enabled us to identify a peculiar type of orbit: the zero-angular-momentum ones. These orbits pass very close to the center and are qualitatively different from orbits around a Kerr black hole. Should such orbits be observed, they would put stringent constraints on astrophysical compact objects like the Galactic center.
Higher dimensional spacetimes with a geodesic, shearfree, twistfree and expanding null congruence
Ortaggio, M
2007-01-01
We present the complete family of higher dimensional spacetimes that admit a geodesic, shearfree, twistfree and expanding null congruence, thus extending the well-known D=4 class of Robinson-Trautman solutions. Einstein's equations are solved for empty space with an arbitrary cosmological constant and for aligned pure radiation. Main differences with respect to the D=4 case (such as the absence of type III/N solutions, related to ``violations'' of the Goldberg-Sachs theorem in D>4) are pointed out, also in connection with other recent works. A formal analogy with electromagnetic fields is briefly discussed in an appendix, where we demonstrate that multiple principal null directions of null Maxwell fields are necessarily geodesic, and that in D>4 they are also shearing if expanding.
Models of rotating boson stars and geodesics around them: new type of orbits
Grandclement, Philippe; Gourgoulhon, Eric
2014-01-01
We have developed a highly accurate numerical code capable of solving the coupled Einstein-Klein-Gordon system, in order to construct rotating boson stars in general relativity. Free fields and self-interacting fields, with quartic and sextic potentials, are considered. In particular, we present the first numerical solutions of rotating boson stars with rotational quantum number $k=3$ and $k=4$, as well as the first determination of the maximum mass of free-field boson stars with $k=2$. We have also investigated timelike geodesics in the spacetime generated by a rotating boson star for $k=1$, $2$ and $3$. A numerical integration of the geodesic equation has enabled us to identify a peculiar type of orbits: the zero-angular-momentum ones. These orbits pass very close to the center and are qualitatively different from orbits around a Kerr black hole. Should such orbits be observed, they would put stringent constraints on astrophysical compact objects like the Galactic center.
On the determination of shifting operators along geodesics on a surface
Directory of Open Access Journals (Sweden)
Drašković Zoran
2013-01-01
Full Text Available A procedure to obtain a closed form of the shifting operators along a known geodesic line on a surface as a solution of a system of linear algebraic equations is proposed. Its correctness is numerically demonstrated in the case of a helicoid surface and a spherical one. The future use of these operators in finite element approximations of tensor fields in non-Euclidean spaces is announced.
Action-angle variables for geodesic motions in Sasaki-Einstein spaces $Y^{p,q}$
Visinescu, Mihai
2016-01-01
We use the action-angle variables to describe the geodesic motions in the $5$-dimensional Sasaki-Einstein spaces $Y^{p,q}$. This formulation allows us to study thoroughly the complete integrability of the system. We find that the Hamiltonian involves a reduced number of action variables. Therefore one of the fundamental frequency is zero indicating a chaotic behavior when the system is perturbed.
Multi-focal spherical media and geodesic lenses in geometrical optics
Sarbort, Martin
2013-01-01
This paper presents a general approach to designing the isotropic spherical media with complex spatial structure that provide different types of imaging for different light rays. It is based on equivalence of the spherical medium and the corresponding geodesic lens. We use this approach to design multi-focal gradient- index lenses embedded into an optically homogeneous region and multi-focal absolute instruments that provide perfect imaging of three-dimensional domains.
Physical infeasibility of geodesic dissipative dust as a source of gravitational radiation
Herrera, L; Ospino, J
2015-01-01
Using a framework based on the 1+3 formalism, we show that a source represented by a geodesic, dissipative, rotational dust, endowed with axial and reflection symmetry, violates regularity conditions at the center of the fluid distribution, unless the dissipative flux vanishes. In this latter case the vorticity also must vanish, and the resulting spacetime is Friedman--Robertson--Walker (FRW). Therefore it does not produce gravitational radiation.
Space-time Geodesics of the 5D Schwarzschild field and its deformation retract
Ahmed, Nasr
2014-01-01
In this article we introduce some types of the deformtion retracts of the $5D$ Schwarzchild space making use of Lagrangian equations. The retraction of this space into itself and into geodesics has been presented. The relation between folding and deformation retract of this space has been achieved. A relation for energy conservation similar to the one obtained in four dimensions has been obtained for the five dimensional case.
Dimensional Reduction of the 5D Kaluza-Klein Geodesic Deviation Equation
Lacquaniti, V; Vietri, F; 10.1007/s10714-009-0853-3
2009-01-01
In the work of Kerner et al. (2001) the problem of the geodesic deviation in a 5D Kaluza Klein background is faced. The 4D space-time projection of the resulting equation coincides with the usual geodesic deviation equation in the presence of the Lorenz force, provided that the fifth component of the deviation vector satisfies an extra constraint which takes into account the $q/m$ conservation along the path. The analysis was performed setting as a constant the scalar field which appears in Kaluza-Klein model. Here we focus on the extension of such a work to the model where the presence of the scalar field is considered. Our result coincides with that of Kerner et al. when the minimal case $\\phi=1$ is considered, while it shows some departures in the general case. The novelty due to the presence of $\\phi$ is that the variation of the $q/m$ between the two geodesic lines is not conserved during the motion; an exact law for such a behaviour has been derived.
Geodesic motions of test particles in a relativistic core-shell spacetime
Liu, Lei; Wu, Xin; Huang, Guoqing
2017-02-01
In this paper, we discuss the geodesic motions of test particles in the intermediate vacuum between a monopolar core and an exterior shell of dipoles, quadrupoles and octopoles. The radii of the innermost stable circular orbits at the equatorial plane depend only on the quadrupoles. A given oblate quadrupolar leads to the existence of two innermost stable circular orbits, and their radii are larger than in the Schwarzschild spacetime. However, a given prolate quadrupolar corresponds to only one innermost stable circular orbit, and its radius is smaller than in the Schwarzschild spacetime. As to the general geodesic orbits, one of the recently developed extended phase space fourth order explicit symplectic-like methods is efficiently applicable to them although the Hamiltonian of the relativistic core-shell system is not separable. With the aid of both this fast integrator without secular growth in the energy errors and gauge invariant chaotic indicators, the effect of these shell multipoles on the geodesic dynamics of order and chaos is estimated numerically.
A triangulation-invariant method for anisotropic geodesic map computation on surface meshes.
Yoo, Sang Wook; Seong, Joon-Kyung; Sung, Min-Hyuk; Shin, Sung Yo; Cohen, Elaine
2012-10-01
This paper addresses the problem of computing the geodesic distance map from a given set of source vertices to all other vertices on a surface mesh using an anisotropic distance metric. Formulating this problem as an equivalent control theoretic problem with Hamilton-Jacobi-Bellman partial differential equations, we present a framework for computing an anisotropic geodesic map using a curvature-based speed function. An ordered upwind method (OUM)-based solver for these equations is available for unstructured planar meshes. We adopt this OUM-based solver for surface meshes and present a triangulation-invariant method for the solver. Our basic idea is to explore proximity among the vertices on a surface while locally following the characteristic direction at each vertex. We also propose two speed functions based on classical curvature tensors and show that the resulting anisotropic geodesic maps reflect surface geometry well through several experiments, including isocontour generation, offset curve computation, medial axis extraction, and ridge/valley curve extraction. Our approach facilitates surface analysis and processing by defining speed functions in an application-dependent manner.