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1st ieee workshop on variational and level set methods in computer vision

作者： Goldenberg, R Kimmel, R Rivlin, E Rudzsky, M Technion Israel Inst Technol Dept Comp Sci IL-32000 Haifa Israel

ISBN: (纸本)076951278X

An automatic cortical gray matter segmentation from a three-dimensional brain images (MR or CT) is a well known problem in medical image processing. In this paper we formulate it as geometric variational problem for propagation of two coupled bounding surfaces. An efficient numerical scheme is used to implement the geodesic active surface model. Experimental results of cortex segmentation on real three-dimensional MR data are provided.

关键词： Image segmentation

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Total Variation minimization by the Fast level sets Transform

Total Variation minimization by the Fast Level Sets Transfor...

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1st ieee workshop on variational and level set methods in computer vision

作者： Dibos, F Koepfler, G Univ Paris 09 CEREMADE CNRS 7534 UMR F-75775 Paris France

ISBN: (纸本)076951278X

The minimization of the Total Variation is an important toot of image processing. A lot of authors have addressed the problem and developed algorithms for image denoising. In a previous paper we gave an alternative approach of the Total Variation minimization problem based on the Coarea formula. The aim of this paper is to present a new efficient algorithm for the Coarea formula approach, based on the Fast level sets Transform.

关键词： Image denoising

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Diffusion-snakes:: Combining statistical shape knowledge and image information in a variational framework

Diffusion-snakes:: Combining statistical shape knowledge and...

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1st ieee workshop on variational and level set methods in computer vision

作者： Cremers, D Schnörr, C Weickert, J Univ Mannheim Dept Math & Comp Sci Comp Vis Graph & Pattern Recognit Grp D-68131 Mannheim Germany

ISBN: (纸本)076951278X

We present a modification of the Mumford-Shah Junctional and its cartoon limit which allows the incorporation of statistical shape knowledge in a single energy functional. We show segmentation results on artificial and real-world images with and without prior shape information. In the case of occlusion and strongly cluttered background the shape prior significantly improves segmentation. Finally we compare our results to those obtained by, a level-set implementation of geodesic active contours.

关键词： image segmentation shape recognition statistical learning variational methods diffusion geodesic active contours diffusion-snake

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A self-referencing level-set method for image reconstruction from sparse Fourier samples

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INTERNATIONAL JOURNAL OF computer vision 2002年第3期50卷 253-270页

作者： Ye, JC Philips Res USA Briarcliff Manor NY 10510 USA Univ Illinois Coordinated Sci Lab Urbana IL 61801 USA

We address an ill-posed inverse problem of image estimation from sparse samples of its Fourier transform. The problem is formulated as joint estimation of the supports of unknown sparse objects in the image, and pixel values on these supports. The domain and the pixel values are alternately estimated using the level-set method and the conjugate gradient method, respectively. Our level-set evolution shows a unique switching behavior, which stabilizes the level-set evolution. Furthermore, the trade-off between the stability and the speed of evolution can be easily controlled by the number of the conjugate gradient steps, thus avoiding the re-initialization steps in conventional level set approaches.

关键词： inverse problems Fourier imaging medical imaging partial-data level-set geometry-driven diffusion

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On smoothness measures of active contours and surfaces

On smoothness measures of active contours and surfaces

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1st ieee workshop on variational and level set methods in computer vision

作者： Delingette, H INRIA Projet Epidaure F-06902 Sophia Antipolis France

ISBN: (纸本)076951278X

In this paper we propose to study different smoothness measures of planar contours or surfaces. We first define a smoothness measure as a functional that follows three types of invariance : invariance to changes of contour parameterization, invariance to contour rotations and translations and invariance to the contour sizes. We then introduce different smoothness measures that can be classified into local or global functionals but also that can be of geometric or algebraic nature. We finally discuss their implementation by observing the advantages and disadvantages of explicit and implicit Contour representations.

关键词： Numerical methods

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A variational approach for the segmentation of the left ventricle in MR cardiac images

A variational approach for the segmentation of the left vent...

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1st ieee workshop on variational and level set methods in computer vision

作者： Paragios, N Siemens Corp Res Princeton NJ 08540 USA

ISBN: (纸本)076951278X

This paper proposes a new front propagation method to segment MR cardiac images. This framework is based on the Geodesic Active Region Model, refers to a coupled propagation of two curves (inner and outer cardiac contours) and integrates boundary and region-based segmentation modules. The boundary information is introduced to the objective function rising the gradient vector flow framework while the region information using continuous probability density functions. The defined objective function is minimized rising a gradient descent method and the obtained motion equations are implemented using a level set approach. A recently introduced numerical approximation scheme with fast convergence rate and stable behavior is used to implement the level set motion equations. Finally, according to the application the propagations of the level set contours are coupled rising their relative di. stances. Encouraging experimental results are provided using real data.

关键词： Equations of motion

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A new variational image restoration applied to 3D angiographies

A new variational image restoration applied to 3D angiograph...

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1st ieee workshop on variational and level set methods in computer vision

作者： Krissian, K Univ Palmas Gran Canaria Dept Informat & Sistemas Las Palmas Gran Canaria 35017 Spain

ISBN: (纸本)076951278X

In this paper, we propose a new variational restoration method. We express the energy as the sum of a data attachment term, a contour smoothing term and an enhancement term. The contour smoothing is acheived by minimizing the square of the derivative of the intensity in the contour direction. The enhancement is obtained by minimizing the square of the gradient norm in each estimated region, and acts like shock filters. The minimization of the energy is then done using the conjugate gradient algorithm. We present an algorithm which allows to compute easily the gradient of the energy in the discrete case, without calculating the Euler-Lagrange equations. Experiments have been carried out on both synthetic and real images applied to 3D angiographies.

关键词： restoration variational approach 3D angiographies segmentation

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variational problems and PDE's on implicit surfaces

Variational problems and PDE's on implicit surfaces

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1st ieee workshop on variational and level set methods in computer vision

作者： Bertalmío, M Sapiro, G Cheng, LT Osher, S Univ Minnesota Minneapolis MN 55455 USA

ISBN: (纸本)076951278X

A novel framework for solving variational problems and partial differential equations for scalar and vector-valued data defined on surfaces is introduced in this paper The key idea is to implicitly represent the surface as the level set of a higher dimensional function, and solve the surface equations in a fixed Cartesian coordinate system using this new embedding function. The equations are then both intrinsic to the surface and defined in the embedding space. This approach thereby eliminates the need for performing complicated and not-accurate computations on triangulated surfaces, as it is commonly done in the literature. We describe the framework and present examples in computer graphics and image processing applications, including texture synthesis, flowfield visualization, as well as image and vector field intrinsic regularization for data defined on 3D surfaces.

关键词： variational problems Partial Differential Equations level-set method implicit surfaces Image Processing computer Graphics flow visualization regularization pattern formation texture synthesis

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A level set algorithm for minimizing the Mumford-Shah functional in image processing

A level set algorithm for minimizing the Mumford-Shah functi...

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1st ieee workshop on variational and level set methods in computer vision

作者： Chan, TF Vese, LA Univ Calif Los Angeles Dept Math Los Angeles CA 90095 USA

ISBN: (纸本)076951278X

We show how the piecewise-smooth Mumford-Shah segmentation problem [25] can be solved using the level set method of S. Osher and J. sethian [26]. The obtained algorithm can be simultaneously used to denoise, segment, detect-extract edges, and perform active contours. The proposed model is also a generalization of a previous active contour model without edges, proposed by the authors in [12], and of its extension to the case with more than two segments for piecewise-constant segmentation [11]. Based on the Four Color Theorem, we can assume that in general, at most two level set functions are sufficient to detect and represent distinct objects of distinct intensities, with triple junctions, or T-junctions.

关键词： Numerical methods

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A multiphase level set framework for image segmentation using the Mumford and Shah model

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INTERNATIONAL JOURNAL OF computer vision 2002年第3期50卷 271-293页

作者： Vese, LA Chan, TF Univ Calif Los Angeles Dept Math Los Angeles CA 90024 USA

We propose a new multiphase level set framework for image segmentation using the Mumford and Shah model, for piecewise constant and piecewise smooth optimal approximations. The proposed method is also a generalization of an active contour model without edges based 2-phase segmentation, developed by the authors earlier in T. Chan and L. Vese (1999. In Scale-Space'99, M. Nilsen et al. (Eds.), LNCS, vol. 1682, pp. 141-151) and T. Chan and L. Vese (2001. ieee-IP, 10(2):266-277). The multiphase level set formulation is new and of interest on its own: by construction, it automatically avoids the problems of vacuum and overlap;it needs only log n level set functions for n phases in the piecewise constant case;it can represent boundaries with complex topologies, including triple junctions;in the piecewise smooth case, only two level set functions formally suffice to represent any partition, based on The Four-Color Theorem. Finally, we validate the proposed models by numerical results for signal and image denoising and segmentation, implemented using the Osher and sethian level set method.

关键词： energy minimization multi-phase motion image segmentation level sets curvature PDE's denoising edge detection active contours

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