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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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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 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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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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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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variational methods for multimodal image matching

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INTERNATIONAL JOURNAL OF computer vision 2002年第3期50卷 329-343页

作者： Hermosillo, G Chefd'Hotel, C Faugeras, O INRIA Sophia Antipolis Odyssee Lab Sophia Antipolis France

Matching images of different modalities can be achieved by the maximization of suitable statistical similarity measures within a given class of geometric transformations. Handling complex, nonrigid deformations in this context turns out to be particularly difficult and has attracted much attention in the last few years. The thrust of this paper is that many of the existing methods for nonrigid monomodal registration that use simple criteria for comparing the intensities (e. g. SSD) can be extended to the multimodal case where more complex intensity similarity measures are necessary. To this end, we perform a formal computation of the variational gradient of a hierarchy of statistical similarity measures, and use the results to generalize a recently proposed and very effective optical flow algorithm (L. Alvarez, J. Weickert, and J. Sanchez, 2000, Technical Report, and IJCV 39(1):41-56) to the case of multimodal image registration. Our method readily extends to the case of locally computed similarity measures, thus providing the flexibility to cope with spatial non-stationarities in the way the intensities in the two images are related. The well posedness of the resulting equations is proved in a complementary work (O.D. Faugeras and G. Hermosillo, 2001, Technical Report 4235, INRIA) using well established techniques in functional analysis. We briefly describe our numerical implementation of these equations and show results on real and synthetic data.

关键词： image matching cross correlation correlation ratio mutual information partial differential equations regularization variational methods

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Flame front matching and tracking in PLIF images using geodesic paths and level sets

Flame front matching and tracking in PLIF images using geode...

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

作者： Abu-Gharbieh, R Kaminski, C Gustavsson, T Hamarneh, G Chalmers Univ Technol Dept Signals & Syst S-41296 Gothenburg Sweden

ISBN: (纸本)076951278X

This paper treats the problem of tracking contours of flames captured by PLIF imaging using geodesic paths and level sets. Successive images of the combustion process captured in controlled experiments are smoothed by, non-linear diffusion filtering then active contour models are used to obtain the curves that most accurately describe the flame boundary. These curves are matched using the concept of shortest path (geodesic) computation on a cost surface. level set representation is employed so that complex curve evolutions including those with topological changes in their structures could be handled. A critical point detection algorithm is used to identify important curve landmarks that are then used to modify the cost surface so as to improve the quality and stability of the matching. Accordingly, the propagation of curves representing successive flame contours within a sequence is obtained and used for studying the flame dynamics.

关键词： Geodesy

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Using prior shapes in geometric active contours in a variational framework

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INTERNATIONAL JOURNAL OF computer vision 2002年第3期50卷 315-328页

作者： Chen, YM Tagare, HD Thiruvenkadam, S Huang, F Wilson, D Gopinath, KS Briggs, RW Geiser, EA Univ Florida Dept Math Gainesville FL 32611 USA Yale Univ Dept Diagnost Radiol New Haven CT 06520 USA Yale Univ Dept Elect Engn New Haven CT 06520 USA Univ Florida Dept Radiol Gainesville FL 32611 USA Univ Florida Dept Med Div Cardiol Gainesville FL 32610 USA

In this paper, we report an active contour algorithm that is capable of using prior shapes. The energy functional of the contour is modified so that the energy depends on the image gradient as well as the prior shape. The model provides the segmentation and the transformation that maps the segmented contour to the prior shape. The active contour is able to find boundaries that are similar in shape to the prior, even when the entire boundary is not visible in the image (i.e., when the boundary has gaps). A level set formulation of the active contour is presented. The existence of the solution to the energy minimization is also established. We also report experimental results of the use of this contour on 2d synthetic images, ultrasound images and fMRI images. Classical active contours cannot be used in many of these images.

关键词： segmentation registration shape prior active contour variational method

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A summary of geometric level-set analogues for a general class of parametric active contour and surface models

A summary of geometric level-set analogues for a general cla...

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

作者： Xu, CY Yezzi, A Prince, JL Johns Hopkins Univ Baltimore MD 21218 USA

ISBN: (纸本)076951278X

Geometric active contours (GACs) and surfaces (GASs) implemented via level set techniques enjoy many advantages over parametric active contours (PACs) and surfaces (PASs), such as computational stability and the ability to change topology during deformation. While many capabilities of earlier PACs and PASs have been reproduced by various GACs and GASs, and while relationships have been discussed for a variety of specific cases, a comprehensive accounting of the connections between these two worlds (particularly regarding rigid forces) has not been consolidated thus far. In this paper we present the precise mathematical relationships between the two for an extensive family of both active contour and surface models, encompassing spatially varying coefficients, both tension and rigidity, and both conservative and non-conservative external forces. The result is a very general geometric formulation for which the intuitive design principles of PACs and PASs can be applied. We also point out which type of PAC and PAS methodologies cannot be adapted to the geometric level set framework. We conclude by demonstrating several geometric adaptations of specific PACs and PASs in several simulations.

关键词： Numerical methods

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Piecewise constant level set method for 3D image segmentation

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1st International Conference on Scale Space and variational methods in computer vision

作者： Losnegard, Are Christiansen, Oddvar Tai, Xue-Cheng Univ Bergen Dept Math Johannes Brunsgate 12 N-5007 Bergen Norway

ISBN: (纸本)9783540728221

level set methods have been proven to be efficient tools for tracing interface problems. Recently;some variants of the Osher- sethian level set methods, which are called the Piecewise Constant level set methods (PCLSM), have been proposed for some interface problems. The methods need to minimize a smooth cost functional under some special constraints. In this paper a PCLSM for 3D image segmentation is tested. The algorithm uses the gradient descent method combined with a Quasi-Newton method to minimize an augmented Lagrangian functional. Experiments for medical image segmentation are shown on synthetic three dimensional MR brain images. The efficiency of the algorithm and the quality of the obtained images are demonstrated.

关键词： Image segmentation

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