The Experts below are selected from a list of 46176 Experts worldwide ranked by ideXlab platform
Allen Tannenbaum - One of the best experts on this subject based on the ideXlab platform.
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on the computation of the affine skeletons of planar Curves and the detection of skew symmetry
Pattern Recognition, 2001Co-Authors: S Betelu, Allen Tannenbaum, Guillermo Sapiro, Peter GiblinAbstract:Abstract In this paper we discuss a new approach to compute discrete skeletons of planar shapes which is based on affine distances, being therefore affine invariant. The method works with generic Curves that may contain concave sections. A dynamical interpretation of the affine skeleton construction, based on Curve Evolution, is discussed as well. We propose an efficient implementation of the method and give examples. We also demonstrate how to use this method to detect affine skew symmetry in real images.
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conformal curvature flows from phase transitions to active vision
Archive for Rational Mechanics and Analysis, 1996Co-Authors: Satyanad Kichenassamy, Allen Tannenbaum, Peter J Olver, Arun Kumar, Anthony YezziAbstract:In this paper, we analyze geometric active contour models from a Curve Evolution point of view and propose some modifications based on gradient flows relative to certain new feature-based Riemannian metrics. This leads to a novel edge-detection paradigm in which the feature of interest may be considered to lie at the bottom of a potential well. Thus an edge-seeking Curve is attracted very naturally and efficiently to the desired feature. Comparison with the Allen-Cahn model clarifies some of the choices made in these models, and suggests inhomogeneous models which may in return be useful in phase transitions. We also consider some 3-dimensional active surface models based on these ideas. The justification of this model rests on the careful study of the viscosity solutions of Evolution equations derived from a level-set approach.
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optical flow a Curve Evolution approach
IEEE Transactions on Image Processing, 1996Co-Authors: Aditya Kumar, Allen Tannenbaum, Gary J BalasAbstract:A novel approach for the computation of optical flow based on an L/sup 1/ type minimization is presented. It is shown that the approach has inherent advantages since it does not smooth the flow-velocity across the edges and hence preserves edge information. A numerical approach based on computation of evolving Curves is proposed for computing the optical flow field. Computations are carried out on a number of real image sequences in order to illustrate the theory as well as the numerical approach.
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optical flow a Curve Evolution approach
International Conference on Image Processing, 1995Co-Authors: Aditya Kumar, Allen Tannenbaum, Gary J BalasAbstract:A novel approach for the computation of optical flow based on an L/sup 1/ type minimization is presented. It is shown that the approach has inherent advantages since it does not smooth the flow-velocity across the edges and hence preserves edge information. A numerical approach based on computation of evolving Curves is proposed for computing the optical flow field and results of experiments are presented.
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gradient flows and geometric active contour models
International Conference on Computer Vision, 1995Co-Authors: Satyanad Kichenassamy, Allen Tannenbaum, Ashish Kumar, Peter J Olver, Anthony YezziAbstract:In this paper, we analyze the geometric active contour models discussed previously from a Curve Evolution point of view and propose some modifications based on gradient flows relative to certain new feature-based Riemannian metrics. This leads to a novel snake paradigm in which the feature of interest may be considered to lie at the bottom of a potential well. Thus the snake is attracted very naturally and efficiently to the desired feature. Moreover, we consider some 3-D active surface models based on these ideas. >
Anthony Yezzi - One of the best experts on this subject based on the ideXlab platform.
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localized principal component analysis based Curve Evolution a divide and conquer approach
International Conference on Computer Vision, 2011Co-Authors: Vikram Appia, Anthony Yezzi, Balaji Ganapathy, Tracy L FaberAbstract:We propose a novel localized principal component analysis (PCA) based Curve Evolution approach which evolves the segmenting Curve semi-locally within various target regions (divisions) in an image and then combines these locally accurate segmentation Curves to obtain a global segmentation. The training data for our approach consists of training shapes and associated auxiliary (target) masks. The masks indicate the various regions of the shape exhibiting highly correlated variations locally which may be rather independent of the variations in the distant parts of the global shape. Thus, in a sense, we are clustering the variations exhibited in the training data set. We then use a parametric model to implicitly represent each localized segmentation Curve as a combination of the local shape priors obtained by representing the training shapes and the masks as a collection of signed distance functions. We also propose a parametric model to combine the locally evolved segmentation Curves into a single hybrid (global) segmentation. Finally, we combine the Evolution of these semi-local and global parameters to minimize an objective energy function. The resulting algorithm thus provides a globally accurate solution, which retains the local variations in shape. We present some results to illustrate how our approach performs better than the traditional approach with fully global PCA.
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a nonparametric statistical method for image segmentation using information theory and Curve Evolution
IEEE Transactions on Image Processing, 2005Co-Authors: Junmo Kim, Anthony Yezzi, John W Fisher, Mujdat Cetin, Alan S WillskyAbstract:In this paper, we present a new information-theoretic approach to image segmentation. We cast the segmentation problem as the maximization of the mutual information between the region labels and the image pixel intensities, subject to a constraint on the total length of the region boundaries. We assume that the probability densities associated with the image pixel intensities within each region are completely unknown a priori, and we formulate the problem based on nonparametric density estimates. Due to the nonparametric structure, our method does not require the image regions to have a particular type of probability distribution and does not require the extraction and use of a particular statistic. We solve the information-theoretic optimization problem by deriving the associated gradient flows and applying Curve Evolution techniques. We use level-set methods to implement the resulting Evolution. The experimental results based on both synthetic and real images demonstrate that the proposed technique can solve a variety of challenging image segmentation problems. Furthermore, our method, which does not require any training, performs as good as methods based on training.
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a shape based approach to the segmentation of medical imagery using level sets
IEEE Transactions on Medical Imaging, 2003Co-Authors: Andy Tsai, Anthony Yezzi, William M Wells, Clare M Tempany, D Tucker, Ayres Fan, W E L Grimson, Alan S WillskyAbstract:We propose a shape-based approach to Curve Evolution for the segmentation of medical images containing known object types. In particular, motivated by the work of Leventon, Grimson, and Faugeras (2000), we derive a parametric model for an implicit representation of the segmenting Curve by applying principal component analysis to a collection of signed distance representations of the training data. The parameters of this representation are then manipulated to minimize an objective function for segmentation. The resulting algorithm is able to handle multidimensional data, can deal with topological changes of the Curve, is robust to noise and initial contour placements, and is computationally efficient. At the same time, it avoids the need for point correspondences during the training phase of the algorithm. We demonstrate this technique by applying it to two medical applications; two-dimensional segmentation of cardiac magnetic resonance imaging (MRI) and three-dimensional segmentation of prostate MRI.
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nonparametric methods for image segmentation using information theory and Curve Evolution
International Conference on Image Processing, 2002Co-Authors: Junmo Kim, Anthony Yezzi, John W Fisher, Mujdat Cetin, Alan S WillskyAbstract:We present a novel information theoretic approach to image segmentation. We cast the segmentation problem as the maximization of the mutual information between the region labels and the image pixel intensities, subject to a constraint on the total length of the region boundaries. We assume that the probability densities associated with the image pixel intensities within each region are completely unknown a priori, and we formulate the problem based on nonparametric density estimates. Due to the nonparametric structure, our method does not require the image regions to have a particular type of probability distribution, and does not require the extraction and use of a particular statistic. We solve the information-theoretic optimization problem by deriving the associated gradient flows and applying Curve Evolution techniques. We use fast level set methods to implement the resulting Evolution The Evolution equations are based on nonparametric statistics, and have an intuitive appeal. The experimental results based on both synthetic and real images demonstrate that the proposed technique can solve a variety of challenging image segmentation problems.
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a fully global approach to image segmentation via coupled Curve Evolution equations
Journal of Visual Communication and Image Representation, 2002Co-Authors: Anthony Yezzi, Andy Tsai, Alan S WillskyAbstract:In this paper, we develop a novel region-based approach to snakes designed to optimally separate the values of certain image statistics over a known number of region types. Multiple sets of contours deform according to a coupled set of Curve Evolution equations derived from a single global cost functional. The resulting active contour model, in contrast to many other edge and region based models, is fully global in that the Evolution of each Curve depends at all times upon every pixel in the image and is directly coupled to the Evolution of every other Curve regardless of their mutual proximity. As such evolving contours enjoy a very wide “field of view,” endowing the algorithm with a robustness to initial contour placement above and beyond the significant improvement exhibited by other region based snakes over earlier edge based snakes.
Alan S Willsky - One of the best experts on this subject based on the ideXlab platform.
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mcmc Curve sampling for image segmentation
Medical Image Computing and Computer-Assisted Intervention, 2007Co-Authors: Ayres Fan, Iii John W Fisher, Iii William M Wells, James J Levitt, Alan S WillskyAbstract:We present an algorithm to generate samples from probability distributions on the space of Curves. We view a traditional Curve Evolution energy functional as a negative log probability distribution and sample from it using a Markov chain Monte Carlo (MCMC) algorithm. We define a proposal distribution by generating smooth perturbations to the normal of the Curve and show how to compute the transition probabilities to ensure that the samples come from the posterior distribution. We demonstrate some advantages of sampling methods such as robustness to local minima, better characterization of multi-modal distributions, access to some measures of estimation error, and ability to easily incorporate constraints on the Curve.
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a nonparametric statistical method for image segmentation using information theory and Curve Evolution
IEEE Transactions on Image Processing, 2005Co-Authors: Junmo Kim, Anthony Yezzi, John W Fisher, Mujdat Cetin, Alan S WillskyAbstract:In this paper, we present a new information-theoretic approach to image segmentation. We cast the segmentation problem as the maximization of the mutual information between the region labels and the image pixel intensities, subject to a constraint on the total length of the region boundaries. We assume that the probability densities associated with the image pixel intensities within each region are completely unknown a priori, and we formulate the problem based on nonparametric density estimates. Due to the nonparametric structure, our method does not require the image regions to have a particular type of probability distribution and does not require the extraction and use of a particular statistic. We solve the information-theoretic optimization problem by deriving the associated gradient flows and applying Curve Evolution techniques. We use level-set methods to implement the resulting Evolution. The experimental results based on both synthetic and real images demonstrate that the proposed technique can solve a variety of challenging image segmentation problems. Furthermore, our method, which does not require any training, performs as good as methods based on training.
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a shape based approach to the segmentation of medical imagery using level sets
IEEE Transactions on Medical Imaging, 2003Co-Authors: Andy Tsai, Anthony Yezzi, William M Wells, Clare M Tempany, D Tucker, Ayres Fan, W E L Grimson, Alan S WillskyAbstract:We propose a shape-based approach to Curve Evolution for the segmentation of medical images containing known object types. In particular, motivated by the work of Leventon, Grimson, and Faugeras (2000), we derive a parametric model for an implicit representation of the segmenting Curve by applying principal component analysis to a collection of signed distance representations of the training data. The parameters of this representation are then manipulated to minimize an objective function for segmentation. The resulting algorithm is able to handle multidimensional data, can deal with topological changes of the Curve, is robust to noise and initial contour placements, and is computationally efficient. At the same time, it avoids the need for point correspondences during the training phase of the algorithm. We demonstrate this technique by applying it to two medical applications; two-dimensional segmentation of cardiac magnetic resonance imaging (MRI) and three-dimensional segmentation of prostate MRI.
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nonparametric methods for image segmentation using information theory and Curve Evolution
International Conference on Image Processing, 2002Co-Authors: Junmo Kim, Anthony Yezzi, John W Fisher, Mujdat Cetin, Alan S WillskyAbstract:We present a novel information theoretic approach to image segmentation. We cast the segmentation problem as the maximization of the mutual information between the region labels and the image pixel intensities, subject to a constraint on the total length of the region boundaries. We assume that the probability densities associated with the image pixel intensities within each region are completely unknown a priori, and we formulate the problem based on nonparametric density estimates. Due to the nonparametric structure, our method does not require the image regions to have a particular type of probability distribution, and does not require the extraction and use of a particular statistic. We solve the information-theoretic optimization problem by deriving the associated gradient flows and applying Curve Evolution techniques. We use fast level set methods to implement the resulting Evolution The Evolution equations are based on nonparametric statistics, and have an intuitive appeal. The experimental results based on both synthetic and real images demonstrate that the proposed technique can solve a variety of challenging image segmentation problems.
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a fully global approach to image segmentation via coupled Curve Evolution equations
Journal of Visual Communication and Image Representation, 2002Co-Authors: Anthony Yezzi, Andy Tsai, Alan S WillskyAbstract:In this paper, we develop a novel region-based approach to snakes designed to optimally separate the values of certain image statistics over a known number of region types. Multiple sets of contours deform according to a coupled set of Curve Evolution equations derived from a single global cost functional. The resulting active contour model, in contrast to many other edge and region based models, is fully global in that the Evolution of each Curve depends at all times upon every pixel in the image and is directly coupled to the Evolution of every other Curve regardless of their mutual proximity. As such evolving contours enjoy a very wide “field of view,” endowing the algorithm with a robustness to initial contour placement above and beyond the significant improvement exhibited by other region based snakes over earlier edge based snakes.
Guillermo Sapiro - One of the best experts on this subject based on the ideXlab platform.
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on the computation of the affine skeletons of planar Curves and the detection of skew symmetry
Pattern Recognition, 2001Co-Authors: S Betelu, Allen Tannenbaum, Guillermo Sapiro, Peter GiblinAbstract:Abstract In this paper we discuss a new approach to compute discrete skeletons of planar shapes which is based on affine distances, being therefore affine invariant. The method works with generic Curves that may contain concave sections. A dynamical interpretation of the affine skeleton construction, based on Curve Evolution, is discussed as well. We propose an efficient implementation of the method and give examples. We also demonstrate how to use this method to detect affine skew symmetry in real images.
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geodesic active contours
International Conference on Computer Vision, 1995Co-Authors: Vicent Caselles, Ron Kimmel, Guillermo SapiroAbstract:A novel scheme for the detection of object boundaries is presented. The technique is based on active contours deforming according to intrinsic geometric measures of the image. The evolving contours naturally split and merge, allowing the simultaneous detection of several objects and both interior and exterior boundaries. The proposed approach is based on the relation between active contours and the computation of geodesics or minimal distance Curves. The minimal distance Curve lays in a Riemannian space whose metric as defined by the image content. This geodesic approach for object segmentation allows to connect classical "snakes" based on energy minimization and geometric active contours based on the theory of Curve Evolution. Previous models of geometric active contours are improved as showed by a number of examples. Formal results concerning existence, uniqueness, stability, and correctness of the Evolution are presented as well. >
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on affine plane Curve Evolution
Journal of Functional Analysis, 1994Co-Authors: Guillermo Sapiro, Allen TannenbaumAbstract:Abstract An affine invariant Curve Evolution process is presented in this work. The Evolution studied is the affine analogue of the Euclidean Curve Shortening flow. Evolution equations, for both affine and Euclidean invariants, are developed. An affine version of the classical (Euclidean) isoperimetric inequality is proved. This inequality is used to show that in the case of affine Evolution of convex plane Curves, the affine isoperimetric ratio is a non-decreasing function of time. Convergence of this affine isoperimetric ratio to the ellipse′s value (8π 2 ), as well as convergence, in the Hausdorff metric, of the evolving Curve to an ellipse, is also proved.
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implementing continuous scale morphology via Curve Evolution
Pattern Recognition, 1993Co-Authors: Guillermo Sapiro, Ron Kimmel, Doron Shaked, Benjamin B Kimia, Alfred M BrucksteinAbstract:Abstract A new approach to digital implementation of continuous-scale mathematical morphology is presented. The approach is based on discretization of Evolution equations associated with continuous multiscale morphological operations. Those equations, and their corresponding numerical implementation, can be derived either directly from mathematical morphology definitions or from Curve Evolution theory. The advantages of the proposed approach over the classical discrete morphology are demonstrated.
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affine invariant scale space
International Journal of Computer Vision, 1993Co-Authors: Guillermo Sapiro, Allen TannenbaumAbstract:A newaffine invariant scale-space for planar Curves is presented in this work. The scale-space is obtained from the solution of a novel nonlinear Curve Evolution equation which admits affine invariant solutions. This flow was proved to be the affine analogue of the well knownEuclidean shortening flow. The Evolution also satisfies properties such ascausality, which makes it useful in defining a scale-space. Using an efficient numerical algorithm for Curve Evolution, this continuous affine flow is implemented, and examples are presented. The affine-invariant progressive smoothing property of the Evolution equation is demonstrated as well.
Andy Tsai - One of the best experts on this subject based on the ideXlab platform.
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a shape based approach to the segmentation of medical imagery using level sets
IEEE Transactions on Medical Imaging, 2003Co-Authors: Andy Tsai, Anthony Yezzi, William M Wells, Clare M Tempany, D Tucker, Ayres Fan, W E L Grimson, Alan S WillskyAbstract:We propose a shape-based approach to Curve Evolution for the segmentation of medical images containing known object types. In particular, motivated by the work of Leventon, Grimson, and Faugeras (2000), we derive a parametric model for an implicit representation of the segmenting Curve by applying principal component analysis to a collection of signed distance representations of the training data. The parameters of this representation are then manipulated to minimize an objective function for segmentation. The resulting algorithm is able to handle multidimensional data, can deal with topological changes of the Curve, is robust to noise and initial contour placements, and is computationally efficient. At the same time, it avoids the need for point correspondences during the training phase of the algorithm. We demonstrate this technique by applying it to two medical applications; two-dimensional segmentation of cardiac magnetic resonance imaging (MRI) and three-dimensional segmentation of prostate MRI.
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a fully global approach to image segmentation via coupled Curve Evolution equations
Journal of Visual Communication and Image Representation, 2002Co-Authors: Anthony Yezzi, Andy Tsai, Alan S WillskyAbstract:In this paper, we develop a novel region-based approach to snakes designed to optimally separate the values of certain image statistics over a known number of region types. Multiple sets of contours deform according to a coupled set of Curve Evolution equations derived from a single global cost functional. The resulting active contour model, in contrast to many other edge and region based models, is fully global in that the Evolution of each Curve depends at all times upon every pixel in the image and is directly coupled to the Evolution of every other Curve regardless of their mutual proximity. As such evolving contours enjoy a very wide “field of view,” endowing the algorithm with a robustness to initial contour placement above and beyond the significant improvement exhibited by other region based snakes over earlier edge based snakes.
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model based Curve Evolution technique for image segmentation
Computer Vision and Pattern Recognition, 2001Co-Authors: Andy Tsai, Anthony Yezzi, William M Wells, Clare M Tempany, D Tucker, Ayres Fan, W E L Grimson, Alan S WillskyAbstract:We propose a model-based Curve Evolution technique for segmentation of images containing known object types. In particular, motivated by the work of Leventon et al. (2000), we derive a parametric model for an implicit representation of the segmenting Curve by applying principal component analysis to a collection of signed distance representations of the training data, The parameters of this representation are then calculated to minimize an objective function for segmentation. We found the resulting algorithm to be computationally efficient, able to handle multidimensional data, robust to noise and initial contour placements, while at the same time, avoiding the need for point correspondences during the training phase of the algorithm. We demonstrate this technique by applying it to two medical applications.
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Curve Evolution implementation of the mumford shah functional for image segmentation denoising interpolation and magnification
IEEE Transactions on Image Processing, 2001Co-Authors: Andy Tsai, Anthony Yezzi, Alan S WillskyAbstract:We first address the problem of simultaneous image segmentation and smoothing by approaching the Mumford-Shah (1989) paradigm from a Curve Evolution perspective. In particular, we let a set of deformable contours define the boundaries between regions in an image where we model the data via piecewise smooth functions and employ a gradient flow to evolve these contours. Each gradient step involves solving an optimal estimation problem for the data within each region, connecting Curve Evolution and the Mumford-Shah functional with the theory of boundary-value stochastic processes. The resulting active contour model offers a tractable implementation of the original Mumford-Shah model (i.e., without resorting to elliptic approximations which have traditionally been favored for greater ease in implementation) to simultaneously segment and smoothly reconstruct the data within a given image in a coupled manner. Various implementations of this algorithm are introduced to increase its speed of convergence. We also outline a hierarchical implementation of this algorithm to handle important image features such as triple points and other multiple junctions. Next, by generalizing the data fidelity term of the original Mumford-Shah functional to incorporate a spatially varying penalty, we extend our method to problems in which data quality varies across the image and to images in which sets of pixel measurements are missing. This more general model leads us to a novel PDE-based approach for simultaneous image magnification, segmentation, and smoothing, thereby extending the traditional applications of the Mumford-Shah functional which only considers simultaneous segmentation and smoothing.
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a Curve Evolution approach to smoothing and segmentation using the mumford shah functional
Computer Vision and Pattern Recognition, 2000Co-Authors: Andy Tsai, Anthony Yezzi, Alan S WillskyAbstract:In this work, we approach the classic Mumford-Shah problem from a Curve Evolution perspective. In particular we let a given family of Curves define the boundaries between regions in an image within which the data are modeled by piecewise smooth functions plus noise as in the standard Mumford-Shah functional. The gradient descent equation of this functional is then used to evolve the Curve. Each gradient descent step involves solving a corresponding optimal estimation problem which connects the Mumford-Shah functional and our Curve Evolution implementation with the theory of boundary-value stochastic processes. The resulting active contour model, therefore, inherits the attractive ability of the Mumford-Shah technique to generate, in a coupled Mumford-Shah a smooth reconstruction of the image and a segmentation as well. We demonstrate applications of our method to problems in which data quality is spatially varying and to problems in which sets of pixel measurements are missing. Finally, we demonstrate a hierarchical implementation of our model which leads to a fast and efficient algorithm capable of dealing with important image features such as triple points.
