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94
Geodesic Active Regions and Level Set Methods for Supervised Texture Segmentation
- INTERNATIONAL JOURNAL OF COMPUTER VISION
, 2002
"... This paper presents a novel variational framework to deal with frame partition problems in Computer Vision. This framework exploits boundary and region-based segmentation modules under a curve-based optimization objective function. The task of supervised texture segmentation is considered to demonst ..."
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Cited by 312 (9 self)
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This paper presents a novel variational framework to deal with frame partition problems in Computer Vision. This framework exploits boundary and region-based segmentation modules under a curve-based optimization objective function. The task of supervised texture segmentation is considered to demonstrate the potentials of the proposed framework. The textured feature space is generated by filtering the given textured images using isotropic and anisotropic filters, and analyzing their responses as multi-component conditional probability density functions. The texture segmentation is obtained by unifying region and boundary-based information as an improved Geodesic Active Contour Model. The defined objective function is minimized using a gradient-descent method where a level set approach is used to implement the obtained PDE. According to this PDE, the curve propagation towards the final solution is guided by boundary and region-based segmentation forces, and is constrained by a regularity force. The level set implementation is performed using a fast front propagation algorithm where topological changes are naturally handled. The performance of our method is demonstrated on a variety of synthetic and real textured frames.
Mathematical Models for Local Nontexture Inpaintings
- SIAM J. Appl. Math
, 2002
"... Inspired by the recent work of Bertalmio et al. on digital inpaintings [SIGGRAPH 2000], we develop general mathematical models for local inpaintings of nontexture images. On smooth regions, inpaintings are connected to the harmonic and biharmonic extensions, and inpainting orders are analyzed. For i ..."
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Cited by 214 (29 self)
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Inspired by the recent work of Bertalmio et al. on digital inpaintings [SIGGRAPH 2000], we develop general mathematical models for local inpaintings of nontexture images. On smooth regions, inpaintings are connected to the harmonic and biharmonic extensions, and inpainting orders are analyzed. For inpaintings involving the recovery of edges, we study a variational model that is closely connected to the classical total variation (TV) denoising model of Rudin, Osher, and Fatemi [PhSG D, 60 (1992), pp. 259--268]. Other models are also discussed based on the Mumford--Shah regularity [Comm. Pure Appl. Mathq XLII (1989), pp. 577--685] and curvature driven di#usions (CDD) of Chan and Shen [J. Visual Comm. Image Rep., 12 (2001)]. The broad applications of the inpainting models are demonstrated through restoring scratched old photos, disocclusion in vision analysis, text removal, digital zooming, and edge-based image coding.
Diffusion snakes: introducing statistical shape knowledge into the Mumford-Shah functional
- J. OF COMPUTER VISION
, 2002
"... We present a modification of the Mumford-Shah functional and its cartoon limit which facilitates the incorporation of a statistical prior on the shape of the segmenting contour. By minimizing a single energy functional, we obtain a segmentation process which maximizes both the grey value homogeneit ..."
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Cited by 130 (16 self)
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We present a modification of the Mumford-Shah functional and its cartoon limit which facilitates the incorporation of a statistical prior on the shape of the segmenting contour. By minimizing a single energy functional, we obtain a segmentation process which maximizes both the grey value homogeneity in the separated regions and the similarity of the contour with respect to a set of training shapes. We propose a closed-form, parameter-free solution for incorporating invariance with respect to similarity transformations in the variational framework. We show segmentation results on artificial and real-world images with and without prior shape information. In the cases of noise, occlusion or 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.
Using prior shapes in geometric active contours in a variational framework
- IJCV
, 2002
"... Abstract. 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 ..."
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Cited by 113 (3 self)
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Abstract. 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.
Digital inpainting based on the Mumford-Shah-Euler image model
- EUROPEAN J. APPL. MATH
, 2002
"... Image inpainting is an image restoration problem, in which image models play a critical role, as demonstrated by Chan, Kang and Shen’s recent inpainting schemes based on the bounded variation [10] and the elastica [9] image models. In the present paper, we propose two novel inpainting models based ..."
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Cited by 81 (23 self)
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Image inpainting is an image restoration problem, in which image models play a critical role, as demonstrated by Chan, Kang and Shen’s recent inpainting schemes based on the bounded variation [10] and the elastica [9] image models. In the present paper, we propose two novel inpainting models based on the Mumford-Shah image model [37], and its high order correction — the Mumford-Shah-Euler image model. We also present their efficient numerical realization based on the ¡ and De Giorgi [18].
Level set based shape prior segmentation
- In Proc. CVPR’05
, 2005
"... We propose a level set based variational approach that incorporates shape priors into Chan-Vese’s model [3] for the shape prior segmentation problem. In our model, besides the level set function for segmentation, as in Cremers’ work [5], we introduce another labelling level set function to indicate ..."
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Cited by 52 (2 self)
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We propose a level set based variational approach that incorporates shape priors into Chan-Vese’s model [3] for the shape prior segmentation problem. In our model, besides the level set function for segmentation, as in Cremers’ work [5], we introduce another labelling level set function to indicate the regions on which the prior shape should be compared. Our model can segment an object, whose shape is similar to the given prior shape, from a background where there are several objects. Moreover, we provide a proof for a fast solution principle, which was mentioned [7] and similar to the one proposed in [19], for minimizing Chan-Vese’s segmentation model without length term. We extend the principle to the minimization of our prescribed functionals. 1.
Variational PDE models in image processing
, 2002
"... This paper is based on a plenary presentation given by Tony F. Chan at the 2002 Joint Mathematical Meeting, San Diego, and has been supported in part by NSF under grant numbers DMS-9973341 (Chan), DMS-0202565 (Shen), and ITR-0113439 (Vese), by ONR under N00014-02-1-0015 (Chan), and by NIH under NIH- ..."
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Cited by 45 (11 self)
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This paper is based on a plenary presentation given by Tony F. Chan at the 2002 Joint Mathematical Meeting, San Diego, and has been supported in part by NSF under grant numbers DMS-9973341 (Chan), DMS-0202565 (Shen), and ITR-0113439 (Vese), by ONR under N00014-02-1-0015 (Chan), and by NIH under NIH-P20MH65166 (Chan and Vese). For the preprints and reprints mentioned in this paper, please visit our web site at: www.math.ucla.edu/~imagers. Chan and Vese are with the Department of Mathematics, UCLA, Los Angeles, CA 90095, fchan, lveseg@math.ucla.edu; Shen is with the School of Mathematics, University of Minnesota, Minneapolis, MN 55455, jhshen@math.umn.edu
Towards Recognition-Based Variational Segmentation Using Shape Priors and Dynamic Labeling
- Isle of Skye
, 2003
"... We propose a novel variational approach based on a level set formulation of the Mumford-Shah functional and shape priors. We extend the functional by a labeling function which indicates image regions in which the shape prior is enforced. By minimizing the proposed functional with respect to both ..."
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Cited by 30 (6 self)
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We propose a novel variational approach based on a level set formulation of the Mumford-Shah functional and shape priors. We extend the functional by a labeling function which indicates image regions in which the shape prior is enforced. By minimizing the proposed functional with respect to both the level set function and the labeling function, the algorithm selects image regions where it is favorable to enforce the shape prior. By this, the approach permits to segment multiple independent objects in an image, and to discriminate familiar objects from unfamiliar ones by means of the labeling function. Numerical results demonstrate the performance of our approach.
Composite Finite Elements for 3D Image Based Computing
- COMPUTING AND VISUALIZATION IN SCIENCE 12
, 2009
"... We present an algorithmical concept for modeling and simulation with partial differential equations (PDEs) in image based computing where the computational geometry is defined through previously segmented image data. Such problems occur in applications from biology and medicine where the underlying ..."
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Cited by 28 (4 self)
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We present an algorithmical concept for modeling and simulation with partial differential equations (PDEs) in image based computing where the computational geometry is defined through previously segmented image data. Such problems occur in applications from biology and medicine where the underlying image data has been acquired through, e.g. computed tomography (CT), magnetic resonance imaging (MRI) or electron microscopy (EM). Based on a level-set description of the computational domain, our approach is capable of automatically providing suitable composite finite element functions that resolve the complicated shapes in the medical/biological data set. It is efficient in the sense that the traversal of the grid (and thus assembling matrices for finite element computations) inherits the efficiency of uniform grids away from complicated structures. The method’s efficiency heavily depends on precomputed lookup tables in the vicinity of the domain boundary or interface. A suitable multigrid method is used for an efficient solution of the systems of equations resulting from the composite finite element discretization. The paper focuses on both algorithmical and implementational details. Scalar and vector valued model problems as well as real applications underline the usability of our approach.
