Convex multi-region segmentation on manifolds

Delaunoy, Amaël; Fundana, Ketut; Prados, Emmanuel; Heyden, Anders

doi:10.1109/iccv.2009.5459174

Cited by 17 publications

(17 citation statements)

References 33 publications

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“…To find u that minimizes the functional (11), a gradient descent method [Delaunoy et al 2009] may be used. However, explicit schemes often lead to numerical instability, slow convergence for large meshes, and insufficient control over global behavior.…”

Section: Fast Primal-dual Methodsmentioning

confidence: 99%

Variational mesh decomposition

Zhang

Zheng

et al. 2012

ACM Trans. Graph.

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The problem of decomposing a 3D mesh into meaningful segments (or parts) is of great practical importance in computer graphics. This article presents a variational mesh decomposition algorithm that can efficiently partition a mesh into a prescribed number of segments. The algorithm extends the Mumford-Shah model to 3D meshes that contains a data term measuring the variation within a segment using eigenvectors of a dual Laplacian matrix whose weights are related to the dihedral angle between adjacent triangles and a regularization term measuring the length of the boundary between segments. Such a formulation simultaneously handles segmentation and boundary smoothing, which are usually two separate processes in most previous work. The efficiency is achieved by solving the Mumford-Shah model through a saddle-point problem that is solved by a fast primal-dual method. A preprocess step is also proposed to determine the number of segments that the mesh should be decomposed into. By incorporating this preprocessing step, the proposed algorithm can automatically segment a mesh into meaningful parts. Furthermore, user interaction is allowed by incorporating the user's inputs into the variational model to reflect the user's special intention. Experimental results show that the proposed algorithm outperforms competitive segmentation methods when evaluated on the Princeton Segmentation Benchmark.

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Section: Fast Primal-dual Methodsmentioning

confidence: 99%

Variational mesh decomposition

Zhang

Zheng

et al. 2012

ACM Trans. Graph.

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“…This model has been proposed in 2D planar image segmentation recently in [38,42] and extended to data segmentation on triangulated manifolds in [52]. We suppose that the N-channel (either single or multiple channels) data d on M are to be partitioned to M segments.…”

Section: Multi-region Segmentation On Triangulated Surfacesmentioning

confidence: 99%

“…Due to these successes, TV based restoration and segmentation models have been extended to data processing on triangulated manifolds [50][51][52] via gradient descent method. When this paper was nearly finished, we got to know the technical report [53] released, which is, to the best of our knowledge, the only paper discussing fast convex optimization techniques for these problems.…”

Section: Introductionmentioning

confidence: 99%

Augmented Lagrangian Method for Total Variation Based Image Restoration and Segmentation Over Triangulated Surfaces

Wu¹,

Zhang

Duan

et al. 2011

J Sci Comput

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Recently total variation (TV) regularization has been proven very successful in image restoration and segmentation. In image restoration, TV based models offer a good edge preservation property. In image segmentation, TV (or vectorial TV) helps to obtain convex formulations of the problems and thus provides global minimizations. Due to these advantages, TV based models have been extended to image restoration and data segmentation on manifolds. However, TV based restoration and segmentation models are difficult to solve, due to the nonlinearity and non-differentiability of the TV term. Inspired by the success of operator splitting and the augmented Lagrangian method (ALM) in 2D planar image processing, we extend the method to TV and vectorial TV based image restoration and segmentation on triangulated surfaces, which are widely used in computer graphics and computer vision. In particular, we will focus on the following problems. First, several Hilbert spaces will be given to describe TV and vectorial TV based variational models in the discrete setting. Second, we present ALM applied to TV and vectorial TV image restoration on mesh surfaces, leading to efficient algorithms for both gray and color image restoration. Third, we discuss ALM for vectorial TV based multi-region image segmentation, which also works for both gray and color images. The proposed method benefits from fast solvers for

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“…In particular, in this paper we are interested in region based methods [11], which aim at partitioning an image into homogenous regions by grouping together the basic image elements (e.g., superpixels) with similar appearances. Many etlorts have been devoted to this topic (e.g., [8,19,31,32]). However, some critical problems remain unsolved.…”

Section: Introductionmentioning

confidence: 99%

Multi-task low-rank affinity pursuit for image segmentation

Cheng

Liu

Wang

et al. 2011

2011 International Conference on Computer Vision

170

111

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This paper investigates how to boost region-based im age segmentation by pursuing a new solution to fuse multi ple types of image features . A collaborative image segmen tation framework, called multi-task low-rank affinity pur suit, is presented for such a purpose . Given an image de scribed with multiple types of features, we aim at inferring a unified affinity matrix that implicitly encodes the segmen tation of the image . This is achieved by seeking the sparsity consistent low-rank affinities from the joint decompositions of multiple feature matrices into pairs of sparse and low rank matrices, the latter of which is expressed as the pro duction of the image feature matrix and its corresponding image affinity matrix . The inference process is formulated as a constrained nuclear norm and t'2,1-norm minimization problem, which is convex and can be solved efficiently with the Augmented Lagrange Multiplier method . Compared to previous methods, which are usually based on a single type of features, the proposed method seamlessly integrates mul tiple types of features to jointly produce the affinity matrix within a single inference step, and produces more accu rate and reliable segmentation results . Experiments on the MSRC dataset and Berkeley segmentation dataset well val idate the superiority of using multiple features over single feature and also the superiority of our method over conven tional methods for feature fusion . Moreover, our method is shown to be very competitive while comparing to other state-of-the-art methods .

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Convex multi-region segmentation on manifolds

Cited by 17 publications

References 33 publications

Variational mesh decomposition

Variational mesh decomposition

Augmented Lagrangian Method for Total Variation Based Image Restoration and Segmentation Over Triangulated Surfaces

Multi-task low-rank affinity pursuit for image segmentation

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