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36
A review of statistical approaches to level set segmentation: Integrating color, texture, motion and shape
 International Journal of Computer Vision
, 2007
"... Abstract. Since their introduction as a means of front propagation and their first application to edgebased segmentation in the early 90’s, level set methods have become increasingly popular as a general framework for image segmentation. In this paper, we present a survey of a specific class of reg ..."
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Cited by 163 (4 self)
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Abstract. Since their introduction as a means of front propagation and their first application to edgebased segmentation in the early 90’s, level set methods have become increasingly popular as a general framework for image segmentation. In this paper, we present a survey of a specific class of regionbased level set segmentation methods and clarify how they can all be derived from a common statistical framework. Regionbased segmentation schemes aim at partitioning the image domain by progressively fitting statistical models to the intensity, color, texture or motion in each of a set of regions. In contrast to edgebased schemes such as the classical Snakes, regionbased methods tend to be less sensitive to noise. For typical images, the respective cost functionals tend to have less local minima which makes them particularly wellsuited for local optimization methods such as the level set method. We detail a general statistical formulation for level set segmentation. Subsequently, we clarify how the integration of various low level criteria leads to a set of cost functionals and point out relations between the different segmentation schemes. In experimental results, we demonstrate how the level set function is driven to partition the image plane into domains of coherent color, texture, dynamic texture or motion. Moreover, the Bayesian formulation allows to introduce prior shape knowledge into the level set method. We briefly review a number of advances in this domain.
Dynamic texture segmentation
 In ICCV
, 2003
"... We address the problem of segmenting a sequence of images of natural scenes into disjoint regions that are characterized by constant spatiotemporal statistics. We model the spatiotemporal dynamics in each region by GaussMarkov models, and infer the model parameters as well as the boundary of the ..."
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Cited by 66 (8 self)
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We address the problem of segmenting a sequence of images of natural scenes into disjoint regions that are characterized by constant spatiotemporal statistics. We model the spatiotemporal dynamics in each region by GaussMarkov models, and infer the model parameters as well as the boundary of the regions in a variational optimization framework. Numerical results demonstrate that – in contrast to purely texturebased segmentation schemes – our method is effective in segmenting regions that differ in their dynamics even when spatial statistics are identical. 1.
Graph edit distance from spectral seriation
 IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
, 2005
"... This paper is concerned with computing graph edit distance. One of the criticisms that can be leveled at existing methods for computing graph edit distance is that they lack some of the formality and rigor of the computation of string edit distance. Hence, our aim is to convert graphs to string seq ..."
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Cited by 40 (6 self)
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This paper is concerned with computing graph edit distance. One of the criticisms that can be leveled at existing methods for computing graph edit distance is that they lack some of the formality and rigor of the computation of string edit distance. Hence, our aim is to convert graphs to string sequences so that string matching techniques can be used. To do this, we use a graph spectral seriation method to convert the adjacency matrix into a string or sequence order. We show how the serial ordering can be established using the leading eigenvector of the graph adjacency matrix. We pose the problem of graphmatching as a maximum a posteriori probability (MAP) alignment of the seriation sequences for pairs of graphs. This treatment leads to an expression in which the edit cost is the negative logarithm of the a posteriori sequence alignment probability. We compute the edit distance by finding the sequence of string edit operations which minimizes the cost of the path traversing the edit lattice. The edit costs are determined by the components of the leading eigenvectors of the adjacency matrix and by the edge densities of the graphs being matched. We demonstrate the utility of the edit distance on a number of graph clustering problems.
Disciplined convex programming
 Global Optimization: From Theory to Implementation, Nonconvex Optimization and Its Application Series
, 2006
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Implementation of a primaldual method for SDP on a shared memory parallel architecture
 Computational Optimization and Applications
, 2006
"... Primal–dual interior point methods and the HKM method in particular have been implemented in a number of software packages for semidefinite programming. These methods have performed well in practice on small to medium sized SDP’s. However, primal–dual codes have had some trouble in solving larger ..."
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Cited by 22 (0 self)
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Primal–dual interior point methods and the HKM method in particular have been implemented in a number of software packages for semidefinite programming. These methods have performed well in practice on small to medium sized SDP’s. However, primal–dual codes have had some trouble in solving larger problems because of the storage requirements and required computational effort. In this paper we describe a parallel implementation of the primaldual method on a shared memory system. Computational results are presented, including the solution of some large scale problems with over 50,000 constraints.
DSDP5: Software for semidefinite programming
 Preprint ANL/MCSP12890905, Mathematics and Computer Science Division, Argonne National Laboratory
, 2005
"... DSDP implements the dualscaling algorithm for semidefinite programming. The source code for this interiorpoint algorithm, written entirely in ANSI C, is freely available. The solver can be used as a subroutine library, as a function within the Matlab environment, or as an executable that reads and ..."
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Cited by 21 (2 self)
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DSDP implements the dualscaling algorithm for semidefinite programming. The source code for this interiorpoint algorithm, written entirely in ANSI C, is freely available. The solver can be used as a subroutine library, as a function within the Matlab environment, or as an executable that reads and writes to data files. Initiated in 1997, DSDP has developed into an efficient and robust generalpurpose solver for semidefinite programming. Its features include a convergence proof with polynomially bounded worstcase complexity, primal and dual feasible solutions when they exist, certificates of infeasibility when solutions do not exist, initial points that can be feasible or infeasible, relatively low memory requirements for an interiorpoint method, sparse and lowrank data structures, extensibility that allows applications to customize the solver and improve its performance, a subroutine library that enables it to be linked to larger applications, scalable performance for large problems on parallel architectures, and a welldocumented interface and examples of its use. The package has been used in many applications and tested for efficiency, robustness, and ease of use.
Semidefinite programming heuristics for surface reconstruction ambiguities
 In ECCV
, 2008
"... Abstract. We consider the problem of reconstructing a smooth surface under constraints that have discrete ambiguities. These problems arise in areas such as shape from texture, shape from shading, photometric stereo and shape from defocus. While the problem is computationally hard, heuristics based ..."
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Cited by 18 (1 self)
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Abstract. We consider the problem of reconstructing a smooth surface under constraints that have discrete ambiguities. These problems arise in areas such as shape from texture, shape from shading, photometric stereo and shape from defocus. While the problem is computationally hard, heuristics based on semidefinite programming may reveal the shape of the surface. 1
Solving large scale binary quadratic problems: Spectral methods vs. semidefinite programming
 In CVPR
, 2007
"... In this paper we introduce two new methods for solving binary quadratic problems. While spectral relaxation methods have been the workhorse subroutine for a wide variety of computer vision problems segmentation, clustering, image restoration to name a few it has recently been challenged by semidef ..."
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Cited by 13 (1 self)
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In this paper we introduce two new methods for solving binary quadratic problems. While spectral relaxation methods have been the workhorse subroutine for a wide variety of computer vision problems segmentation, clustering, image restoration to name a few it has recently been challenged by semidefinite programming (SDP) relaxations. In fact, it can be shown that SDP relaxations produce better lower bounds than spectral relaxations on binary problems with a quadratic objective function. On the other hand, the computational complexity for SDP increases rapidly as the number of decision variables grows making them inapplicable to large scale problems. Our methods combine the merits of both spectral and SDP relaxations better (lower) bounds than traditional spectral methods and considerably faster execution times than SDP. The first method is based on spectral subgradients and can be applied to large scale SDPs with binary decision variables and the second one is based on the trust region problem. Both algorithms have been applied to several large scale vision problems with good performance. 1 1.
Isoperimetric graph partitioning for data clustering and image segmentation
 Boston University
, 2003
"... Spectral methods of graph partitioning have been shown to provide a powerful approach to the image segmentation problem. In this paper, we adopt a different approach, based on estimating the isoperimetric constant of an image graph. Our algorithm produces the high quality segmentations and data clus ..."
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Cited by 9 (1 self)
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Spectral methods of graph partitioning have been shown to provide a powerful approach to the image segmentation problem. In this paper, we adopt a different approach, based on estimating the isoperimetric constant of an image graph. Our algorithm produces the high quality segmentations and data clustering of spectral methods, but with improved speed and stability. 1
Embedded in the Shadow of the Separator
, 2005
"... We study the problem of maximizing the second smallest eigenvalue of the Laplace matrix of a graph over all nonnegative edge weightings with bounded total weight. The optimal value is the absolute algebraic connectivity introduced by Fiedler, who proved tight connections of this value to the connect ..."
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Cited by 9 (1 self)
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We study the problem of maximizing the second smallest eigenvalue of the Laplace matrix of a graph over all nonnegative edge weightings with bounded total weight. The optimal value is the absolute algebraic connectivity introduced by Fiedler, who proved tight connections of this value to the connectivity of the graph. Using semidefinite programming techniques and exploiting optimality conditions we show that the problem is equivalent to finding an embedding of the n nodes in n−space so that their barycenter is at the origin, the distance between adjacent nodes is bounded by one and the nodes are spread as much as possible (the sum of the squared norms is maximized). For connected graphs we prove that for any separator in the graph, at least one of the two separated node sets is embedded in the shadow (with the origin being the light source) of the convex hull of the separator. In particular, the barycenters of partitions induced by separators are separated by the affine subspace spanned by the nodes of the separator. Furthermore, we show that there always exists an optimal embedding whose dimension is bounded by the tree width of the graph plus one.