The Experts below are selected from a list of 793227 Experts worldwide ranked by ideXlab platform
Chunming Li - One of the best experts on this subject based on the ideXlab platform.
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distance regularized level Set evolution and its application to image segmentation
IEEE Transactions on Image Processing, 2010Co-Authors: Chunming Li, Chenyang XuAbstract:Level Set methods have been widely used in image processing and computer vision. In conventional level Set formulations, the level Set Function typically develops irregularities during its evolution, which may cause numerical errors and eventually destroy the stability of the evolution. Therefore, a numerical remedy, called reinitialization, is typically applied to periodically replace the degraded level Set Function with a signed distance Function. However, the practice of reinitialization not only raises serious problems as when and how it should be performed, but also affects numerical accuracy in an undesirable way. This paper proposes a new variational level Set formulation in which the regularity of the level Set Function is intrinsically maintained during the level Set evolution. The level Set evolution is derived as the gradient flow that minimizes an energy Functional with a distance regularization term and an external energy that drives the motion of the zero level Set toward desired locations. The distance regularization term is defined with a potential Function such that the derived level Set evolution has a unique forward-and-backward (FAB) diffusion effect, which is able to maintain a desired shape of the level Set Function, particularly a signed distance profile near the zero level Set. This yields a new type of level Set evolution called distance regularized level Set evolution (DRLSE). The distance regularization effect eliminates the need for reinitialization and thereby avoids its induced numerical errors. In contrast to complicated implementations of conventional level Set formulations, a simpler and more efficient finite difference scheme can be used to implement the DRLSE formulation. DRLSE also allows the use of more general and efficient initialization of the level Set Function. In its numerical implementation, relatively large time steps can be used in the finite difference scheme to reduce the number of iterations, while ensuring sufficient numerical accuracy. To demonstrate the effectiveness of the DRLSE formulation, we apply it to an edge-based active contour model for image segmentation, and provide a simple narrowband implementation to greatly reduce computational cost.
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minimization of region scalable fitting energy for image segmentation
IEEE Transactions on Image Processing, 2008Co-Authors: Chunming Li, John C Gore, Chiuyen Kao, Zhaohua DingAbstract:Intensity inhomogeneities often occur in real-world images and may cause considerable difficulties in image segmentation. In order to overcome the difficulties caused by intensity inhomogeneities, we propose a region-based active contour model that draws upon intensity information in local regions at a controllable scale. A data fitting energy is defined in terms of a contour and two fitting Functions that locally approximate the image intensities on the two sides of the contour. This energy is then incorporated into a variational level Set formulation with a level Set regularization term, from which a curve evolution equation is derived for energy minimization. Due to a kernel Function in the data fitting term, intensity information in local regions is extracted to guide the motion of the contour, which thereby enables our model to cope with intensity inhomogeneity. In addition, the regularity of the level Set Function is intrinsically preserved by the level Set regularization term to ensure accurate computation and avoids expensive reinitialization of the evolving level Set Function. Experimental results for synthetic and real images show desirable performances of our method.
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level Set evolution without re initialization a new variational formulation
Computer Vision and Pattern Recognition, 2005Co-Authors: Chunming Li, Chenyang XuAbstract:In this paper, we present a new variational formulation for geometric active contours that forces the level Set Function to be close to a signed distance Function, and therefore completely eliminates the need of the costly re-initialization procedure. Our variational formulation consists of an internal energy term that penalizes the deviation of the level Set Function from a signed distance Function, and an external energy term that drives the motion of the zero level Set toward the desired image features, such as object boundaries. The resulting evolution of the level Set Function is the gradient flow that minimizes the overall energy Functional. The proposed variational level Set formulation has three main advantages over the traditional level Set formulations. First, a significantly larger time step can be used for numerically solving the evolution partial differential equation, and therefore speeds up the curve evolution. Second, the level Set Function can be initialized with general Functions that are more efficient to construct and easier to use in practice than the widely used signed distance Function. Third, the level Set evolution in our formulation can be easily implemented by simple finite difference scheme and is computationally more efficient. The proposed algorithm has been applied to both simulated and real images with promising results.
W A Mulder - One of the best experts on this subject based on the ideXlab platform.
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salt reconstruction in full waveform inversion with a parametric level Set method
IEEE Transactions on Computational Imaging, 2017Co-Authors: Ajinkya Kadu, Tristan Van Leeuwen, W A MulderAbstract:Seismic full-waveform inversion tries to estimate subsurface medium parameters from seismic data. Areas with subsurface salt bodies are of particular interest because they often have hydrocarbon reservoirs on their sides or underneath. Accurate reconstruction of their geometry is a challenge for current techniques. This paper presents a parametric level-Set method for the reconstruction of salt-bodies in seismic full-waveform inversion. We split the subsurface model in two parts: a background velocity model and a salt body with known velocity but undetermined shape. The salt geometry is represented by a level-Set Function that evolves during the inversion. We choose radial basis Functions to represent the level-Set Function, leading to an optimization problem with a modest number of parameters. A common problem with level-Set methods is to fine-tune the width of the level-Set boundary for optimal sensitivity. We propose a robust algorithm that dynamically adapts the width of the level-Set boundary to ensure faster convergence. Tests on a suite of idealized salt geometries show that the proposed method is stable against a modest amount of noise. We also extend the method to joint inversion of both the background velocity model and the salt geometry.
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salt reconstruction in full waveform inversion with a parametric level Set method
arXiv: Computational Engineering Finance and Science, 2016Co-Authors: Ajinkya Kadu, Tristan Van Leeuwen, W A MulderAbstract:Seismic full-waveform inversion tries to estimate subsurface medium parameters from seismic data. Areas with subsurface salt bodies are of particular interest because they often have hydrocarbon reservoirs on their sides or underneath. Accurate reconstruction of their geometry is a challenge for current techniques. This paper presents a parametric level-Set method for the reconstruction of salt-bodies in seismic full-waveform inversion. We split the subsurface model in two parts: a background velocity model and the salt body with known velocity but undetermined shape. The salt geometry is represented by a level-Set Function that evolves during the inversion. We choose radial basis Functions to represent the level-Set Function, leading to an optimization problem with a modest number of parameters. A common problem with level-Set methods is to fine tune the width of the level-Set boundary for optimal sensitivity. We propose a robust algorithm that dynamically adapts the width of the level-Set boundary to ensure faster convergence. Tests on a suite of idealized salt geometries show that the proposed method is stable against a modest amount of noise. We also extend the method to joint inversion of both the background velocity model and the salt-geometry.
Chenyang Xu - One of the best experts on this subject based on the ideXlab platform.
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distance regularized level Set evolution and its application to image segmentation
IEEE Transactions on Image Processing, 2010Co-Authors: Chunming Li, Chenyang XuAbstract:Level Set methods have been widely used in image processing and computer vision. In conventional level Set formulations, the level Set Function typically develops irregularities during its evolution, which may cause numerical errors and eventually destroy the stability of the evolution. Therefore, a numerical remedy, called reinitialization, is typically applied to periodically replace the degraded level Set Function with a signed distance Function. However, the practice of reinitialization not only raises serious problems as when and how it should be performed, but also affects numerical accuracy in an undesirable way. This paper proposes a new variational level Set formulation in which the regularity of the level Set Function is intrinsically maintained during the level Set evolution. The level Set evolution is derived as the gradient flow that minimizes an energy Functional with a distance regularization term and an external energy that drives the motion of the zero level Set toward desired locations. The distance regularization term is defined with a potential Function such that the derived level Set evolution has a unique forward-and-backward (FAB) diffusion effect, which is able to maintain a desired shape of the level Set Function, particularly a signed distance profile near the zero level Set. This yields a new type of level Set evolution called distance regularized level Set evolution (DRLSE). The distance regularization effect eliminates the need for reinitialization and thereby avoids its induced numerical errors. In contrast to complicated implementations of conventional level Set formulations, a simpler and more efficient finite difference scheme can be used to implement the DRLSE formulation. DRLSE also allows the use of more general and efficient initialization of the level Set Function. In its numerical implementation, relatively large time steps can be used in the finite difference scheme to reduce the number of iterations, while ensuring sufficient numerical accuracy. To demonstrate the effectiveness of the DRLSE formulation, we apply it to an edge-based active contour model for image segmentation, and provide a simple narrowband implementation to greatly reduce computational cost.
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level Set evolution without re initialization a new variational formulation
Computer Vision and Pattern Recognition, 2005Co-Authors: Chunming Li, Chenyang XuAbstract:In this paper, we present a new variational formulation for geometric active contours that forces the level Set Function to be close to a signed distance Function, and therefore completely eliminates the need of the costly re-initialization procedure. Our variational formulation consists of an internal energy term that penalizes the deviation of the level Set Function from a signed distance Function, and an external energy term that drives the motion of the zero level Set toward the desired image features, such as object boundaries. The resulting evolution of the level Set Function is the gradient flow that minimizes the overall energy Functional. The proposed variational level Set formulation has three main advantages over the traditional level Set formulations. First, a significantly larger time step can be used for numerically solving the evolution partial differential equation, and therefore speeds up the curve evolution. Second, the level Set Function can be initialized with general Functions that are more efficient to construct and easier to use in practice than the widely used signed distance Function. Third, the level Set evolution in our formulation can be easily implemented by simple finite difference scheme and is computationally more efficient. The proposed algorithm has been applied to both simulated and real images with promising results.
Zoltan Szigeti - One of the best experts on this subject based on the ideXlab platform.
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partition constrained covering of a symmetric crossing supermodular Function by a graph
SIAM Journal on Discrete Mathematics, 2017Co-Authors: Attila Bernath, Roland Grappe, Zoltan SzigetiAbstract:We are given a symmetric crossing supermodular Set Function $p$ on $V$ and a partition $\mathcal{P}$ of $V$. We solve the problem of finding a graph with vertex Set $V$ having edges only between the classes of $\mathcal{P}$ such that for every subSet $X$ of $V$ the cut of the graph defined by $X$ contains at least $p(X)$ edges. The objective is to minimize the number of edges of the graph. This problem is a common generalization of the global edge-connectivity augmentation of a graph with partition constraints, which was solved by Bang-Jensen et al. [SIAM J. Discrete Math., 12 (1999), pp. 160--207] and the problem of covering a symmetric crossing supermodular Set Function solved by Benczur and Frank [Math. Program., 84 (1999), pp. 483--503]. Our problem can be considered as an abstract form of the problem of global edge-connectivity augmentation of a hypergraph with partition constraints, which was earlier solved by the authors [J. Graph Theory, 72 (2013), pp. 291--312].
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partition constrained covering of a symmetric crossing supermodular Function by a graph
Symposium on Discrete Algorithms, 2010Co-Authors: Attila Bernath, Roland Grappe, Zoltan SzigetiAbstract:Given a symmetric crossing supermodular Set Function p on V and a partition ρ of V, we solve the problem of finding a graph with ground Set V having edges only between the classes of ρ such that for every subSet X of V the cut of the graph defined by X contains at least p(X) edges. The objective is to minimize the number of edges of the graph. This problem is a common generalization of the global edge-connectivity augmentation of a graph with partition constraints, which was solved by Bang-Jensen, Gabow, Jordan and Szigeti [1] and the problem of covering a symmetric crossing supermodular Set Function solved by Benczur and Frank [3]. Our problem can be considered as an abstract form of the problem of global edge-connectivity augmentation of a hypergraph by a multipartite graph, which was earlier solved by the authors [5].
Ron Kimmel - One of the best experts on this subject based on the ideXlab platform.
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multi region active contours with a single level Set Function
IEEE Transactions on Pattern Analysis and Machine Intelligence, 2015Co-Authors: Anastasia Dubrovinakarni, Guy Rosman, Ron KimmelAbstract:Segmenting an image into an arbitrary number of coherent regions is at the core of image understanding. Many formulations of the segmentation problem have been suggested over the past years. These formulations include, among others, axiomatic Functionals, which are hard to implement and analyze, and graph-based alternatives, which impose a non-geometric metric on the problem. We propose a novel method for segmenting an image into an arbitrary number of regions using an axiomatic variational approach. The proposed method allows to incorporate various generic region appearance models, while avoiding metrication errors. In the suggested framework, the segmentation is performed by level Set evolution. Yet, contrarily to most existing methods, here, multiple regions are represented by a single non-negative level Set Function. The level Set Function evolution is efficiently executed through the Voronoi Implicit Interface Method for multi-phase interface evolution. The proposed approach is shown to obtain accurate segmentation results for various natural 2D and 3D images, comparable to state-of-the-art image segmentation algorithms.
