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88
Region Competition: Unifying Snakes, Region Growing, and Bayes/MDL for Multiband Image Segmentation
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 1996
"... We present a novel statistical and variational approach to image segmentation based on a new algorithm named region competition. This algorithm is derived by minimizing a generalized Bayes/MDL criterion using the variational principle. The algorithm is guaranteed to converge to a local minimum and c ..."
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Cited by 778 (21 self)
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We present a novel statistical and variational approach to image segmentation based on a new algorithm named region competition. This algorithm is derived by minimizing a generalized Bayes/MDL criterion using the variational principle. The algorithm is guaranteed to converge to a local minimum and combines aspects of snakes/balloons and region growing. Indeed the classic snakes/balloons and region growing algorithms can be directly derived from our approach. We provide theoretical analysis of region competition including accuracy of boundary location, criteria for initial conditions, and the relationship to edge detection using filters. It is straightforward to generalize the algorithm to multiband segmentation and we demonstrate it on grey level images, color images and texture images. The novel color model allows us to eliminate intensity gradients and shadows, thereby obtaining segmentation based on the albedos of objects. It also helps detect highlight regions. 1 Division of Appli...
A Multiphase Level Set Framework for Image Segmentation Using the Mumford and Shah Model
 INTERNATIONAL JOURNAL OF COMPUTER VISION
, 2002
"... 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 2phase segmentation, developed by ..."
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Cited by 493 (21 self)
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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 2phase segmentation, developed by the authors earlier in T. Chan and L. Vese (1999. In ScaleSpace'99, M. Nilsen et al. (Eds.), LNCS, vol. 1682, pp. 141151) and T. Chan and L. Vese (2001. IEEEIP, 10(2):266277). 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 FourColor 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.
Contour Detection and Hierarchical Image Segmentation
 IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
, 2010
"... This paper investigates two fundamental problems in computer vision: contour detection and image segmentation. We present stateoftheart algorithms for both of these tasks. Our contour detector combines multiple local cues into a globalization framework based on spectral clustering. Our segmentati ..."
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Cited by 383 (23 self)
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This paper investigates two fundamental problems in computer vision: contour detection and image segmentation. We present stateoftheart algorithms for both of these tasks. Our contour detector combines multiple local cues into a globalization framework based on spectral clustering. Our segmentation algorithm consists of generic machinery for transforming the output of any contour detector into a hierarchical region tree. In this manner, we reduce the problem of image segmentation to that of contour detection. Extensive experimental evaluation demonstrates that both our contour detection and segmentation methods significantly outperform competing algorithms. The automatically generated hierarchical segmentations can be interactively refined by userspecified annotations. Computation at multiple image resolutions provides a means of coupling our system to recognition applications.
Image Segmentation by Data Driven Markov Chain Monte Carlo
, 2001
"... This paper presents a computational paradigm called Data Driven Markov Chain Monte Carlo (DDMCMC) for image segmentation in the Bayesian statistical framework. The paper contributes to image segmentation in three aspects. Firstly, it designs effective and well balanced Markov Chain dynamics to exp ..."
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Cited by 281 (32 self)
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This paper presents a computational paradigm called Data Driven Markov Chain Monte Carlo (DDMCMC) for image segmentation in the Bayesian statistical framework. The paper contributes to image segmentation in three aspects. Firstly, it designs effective and well balanced Markov Chain dynamics to explore the solution space and makes the split and merge process reversible at a middle level vision formulation. Thus it achieves globally optimal solution independent of initial segmentations. Secondly, instead of computing a single maximum a posteriori solution, it proposes a mathematical principle for computing multiple distinct solutions to incorporates intrinsic ambiguities in image segmentation. A kadventurers algorithm is proposed for extracting distinct multiple solutions from the Markov chain sequence. Thirdly, it utilizes datadriven (bottomup) techniques, such as clustering and edge detection, to compute importance proposal probabilities, which eectively drive the Markov chain dynamics and achieve tremendous speedup in comparison to traditional jumpdiffusion method[4]. Thus DDMCMC paradigm provides a unifying framework where the role of existing segmentation algorithms, such as, edge detection, clustering, region growing, splitmerge, SNAKEs, region competition, are revealed as either realizing Markov chain dynamics or computing importance proposal probabilities. We report some results on color and grey level image segmentation in this paper and refer to a detailed report and a web site for extensive discussion.
Modeling Textures with Total Variation Minimization and Oscillating Patterns in Image Processing
 JOURNAL OF SCIENTIFIC COMPUTING
, 2002
"... This paper is devoted to the modeling of real textured images by functional minimization and partial differential equations. Following the ideas of Yves Meyer in a total variation minimization framework of L. Rudin, S. Osher and E. Fatemi, we decompose a given (possible textured) image f into a su ..."
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Cited by 201 (25 self)
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This paper is devoted to the modeling of real textured images by functional minimization and partial differential equations. Following the ideas of Yves Meyer in a total variation minimization framework of L. Rudin, S. Osher and E. Fatemi, we decompose a given (possible textured) image f into a sum of two functions u + v, where u E BV is a function of bounded variation (a cartoon or sketchy approximation of f), while v is a function representing the texture or noise. To model v we use the space of oscillating functions introduced by Yves Meyer, which is in some sense the dual of the BV space. The new algorithm is very simple, making use of differential equations and is easily solved in practice. Finally, we implement the method by finite differences, and we present various numerical results on real textured images, showing the obtained decomposition u + v, but we also show how the method can be used for texture discrimination and texture segmentation.
Active Contours without Edges for VectorValued Images
 Journal of Visual Communication and Image Representation
, 2000
"... this paper, we propose an active contour algorithm for object detection in vectorvalued images (such as RGB or multispectral). The model is an extension of the scalar ChanVese algorithm to the vectorvalued case [1]. The model minimizes a MumfordShah functional over the length of the contour, ..."
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Cited by 106 (12 self)
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this paper, we propose an active contour algorithm for object detection in vectorvalued images (such as RGB or multispectral). The model is an extension of the scalar ChanVese algorithm to the vectorvalued case [1]. The model minimizes a MumfordShah functional over the length of the contour, plus the sum of the fitting error over each component of the vectorvalued image. Like the ChanVese model, our vectorvalued model can detect edges both with or without gradient. We show examples where our model detects vectorvalued objects which are undetectable in any scalar representation. For instance, objects with different missing parts in different channels are completely detected (such as occlusion). Also, in color images, objects which are invisible in each channel or in intensity can be detected by our algorithm. Finally, the model is robust with respect to noise, requiring no a priori denoising step. C 2000 Academic Press Key Words: vectorvalued images; active contours; level sets; segmentation; PDEs; object detection
A level set algorithm for minimizing the MumfordShah functional in image processing
 IEEE WORKSHOP ON VARIATIONAL AND LEVEL SET METHODS
, 2001
"... We show how the piecewisesmooth MumfordShah 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, detectextract edges, and perform active contours. The proposed model is also a gen ..."
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Cited by 93 (11 self)
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We show how the piecewisesmooth MumfordShah 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, detectextract 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 piecewiseconstant 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 Tjunctions.
Geodesic Active Regions: A new framework to deal with frame partition problems in Computer Vision
, 2002
"... This paper presents a novel variational framework for dealing with frame partition problems in Computer Vision by the propagation of curves. This framework integrates boundary and regionbased frame partition modules under a curvebased energy framework, which aims at finding a set of minimal le ..."
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Cited by 84 (10 self)
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This paper presents a novel variational framework for dealing with frame partition problems in Computer Vision by the propagation of curves. This framework integrates boundary and regionbased frame partition modules under a curvebased energy framework, which aims at finding a set of minimal length curves that preserve three main properties: (i) they are regular and smooth, (ii) they are attracted by the boundary points (boundarybased information), (ii) and they create a partition that is optimal according to the expected region properties of the different hypotheses (regionbased information). The defined objective function is minimized using a gradient descent method. According to the obtained motion equations, the set of initial curves is propagated towards the best partition under the influence of boundary and regionbased forces, and being constrained by a regularity force. The changes of topology are naturally handled thanks to the level set implementation. Furthermore, a coupled multiphase propagation is proposed that imposes the idea of mutually exclusive propagating curves, and increases the robustness as well as the convergence rate. The proposed framework has been validated using three important applications in Computer Vision, the tasks of image and supervised texture segmentation in lowlevel vision and the task of motion estimation and tracking in motion analysis
Image denoising and decomposition with total variation minimization and oscillatory functions
 J. Math. Imaging Vision
, 2004
"... Abstract. In this paper, we propose a new variational model for image denoising and decomposition, witch combines the total variation minimization model of Rudin, Osher and Fatemi from image restoration, with spaces of oscillatory functions, following recent ideas introduced by Meyer. The spaces int ..."
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Cited by 44 (7 self)
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Abstract. In this paper, we propose a new variational model for image denoising and decomposition, witch combines the total variation minimization model of Rudin, Osher and Fatemi from image restoration, with spaces of oscillatory functions, following recent ideas introduced by Meyer. The spaces introduced here are appropriate to model oscillatory patterns of zero mean, such as noise or texture. Numerical results of image denoising, image decomposition and texture discrimination are presented, showing that the new models decompose better a given image, possible noisy, into cartoon and oscillatory pattern of zero mean, than the standard ones. The present paper develops further the models previously introduced by the authors in Vese and Osher (Modeling textures with total variation minimization and oscillating patterns in image processing, UCLA CAM Report 0219, May 2002, to appear in Journal of Scientific Computing, 2003). Other recent and related image decomposition models are also discussed.
Image Segmentation and Edge Enhancement with Stabilized Inverse Diffusion Equations.
 IEEE Transactions on Image Processing
, 1999
"... We introduce a family of firstorder multidimensional ordinary differential equations (ODEs) with discontinuous righthand sides and demonstrate their applicability in image processing. An equation belonging to this family is an inverse diffusion everywhere except at local extrema, where some stabil ..."
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Cited by 41 (10 self)
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We introduce a family of firstorder multidimensional ordinary differential equations (ODEs) with discontinuous righthand sides and demonstrate their applicability in image processing. An equation belonging to this family is an inverse diffusion everywhere except at local extrema, where some stabilization is introduced. For this reason, we call these equations "stabilized inverse diffusion equations" ("SIDEs"). Existence and uniqueness of solutions, as well as stability, are proven for SIDEs. A SIDE in one spatial dimension may be interpreted as a limiting case of a semidiscretized PeronaMalik equation [14], [15]. In an experimental section, SIDEs are shown to suppress noise while sharpening edges present in the input signal. Their application to image segmentation is also demonstrated.