We address the problem of segmenting a sequence of images of natural scenes into disjoint regions that are characterized by constant spatio-temporal statistics. We model the spatio-temporal dynamics in each region by Gauss-Markov 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 texture-based segmentation schemes -- our method is effective in segmenting regions that differ in their dynamics even when spatial statistics are identical.

Abstract. Since their introduction as a means of front propagation and their first application to edge-based 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 region-based level set segmentation methods and clarify how they can all be derived from a common statistical framework. Region-based 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 edge-based schemes such as the classical Snakes, region-based 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 well-suited 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.

Abstract—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 graph-matching 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. Index Terms—Graph edit distance, graph seriation, maximum a posteriori probability (MAP), graph-spectral methods. 1

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this paper. They show, however, that DSDP is a competitive solver on a broad set of SDP problems. Of 108 tests, DSDP solved 102 and exhausted the 4 GB of memory on the other six problems. In most of the examples b#/#b# 10 -6 , and the objective is correct to at least six digits of precision, although solutions whose norm is very large usually exhibited less precision

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

Primal–dual interior point methods and the HKM method in particu-lar have been implemented in a number of software packages for semidef-inite 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 require-ments and required computational effort. In this paper we describe a parallel implementation of the primal-dual method on a shared memory system. Computational results are presented, including the solution of some large scale problems with over 50,000 constraints.

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.

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

Abstract. Image segmentation based on graph representations has been a very active field of research recently. One major reason is that pairwise similarities (encoded by a graph) are also applicable in general situations where prototypical image descriptors as partitioning cues are no longer adequate. In this context, we recently proposed a novel convex programming approach for segmentation in terms of optimal graph cuts which compares favorably with alternative methods in several aspects. In this paper we present a fully elaborated version of this approach along several directions: first, an image preprocessing method is proposed to reduce the problem size by several orders of magnitude. Furthermore, we argue that the hierarchical partition tree is a natural data structure as opposed to enforcing multiway cuts directly. In this context, we address various aspects regarding the fully automatic computation of the final segmentation. Experimental results illustrate the encouraging performance of our approach for unsupervised image segmentation. 1