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23
Fast approximate energy minimization via graph cuts
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 2001
"... In this paper we address the problem of minimizing a large class of energy functions that occur in early vision. The major restriction is that the energy function’s smoothness term must only involve pairs of pixels. We propose two algorithms that use graph cuts to compute a local minimum even when v ..."
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Cited by 1377 (51 self)
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In this paper we address the problem of minimizing a large class of energy functions that occur in early vision. The major restriction is that the energy function’s smoothness term must only involve pairs of pixels. We propose two algorithms that use graph cuts to compute a local minimum even when very large moves are allowed. The first move we consider is an αβswap: for a pair of labels α, β, this move exchanges the labels between an arbitrary set of pixels labeled α and another arbitrary set labeled β. Our first algorithm generates a labeling such that there is no swap move that decreases the energy. The second move we consider is an αexpansion: for a label α, this move assigns an arbitrary set of pixels the label α. Our second
Matching Hierarchical Structures Using Association Graphs
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 1998
"... this article, please send email to: tpami@computer.org, and reference IEEECS Log Number 108453 ..."
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Cited by 166 (26 self)
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this article, please send email to: tpami@computer.org, and reference IEEECS Log Number 108453
Replicator Equations, Maximal Cliques, and Graph Isomorphism
, 1999
"... We present a new energyminimization framework for the graph isomorphism problem that is based on an equivalent maximum clique formulation. The approach is centered around a fundamental result proved by Motzkin and Straus in the mid1960s, and recently expanded in various ways, which allows us to fo ..."
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Cited by 52 (11 self)
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We present a new energyminimization framework for the graph isomorphism problem that is based on an equivalent maximum clique formulation. The approach is centered around a fundamental result proved by Motzkin and Straus in the mid1960s, and recently expanded in various ways, which allows us to formulate the maximum clique problem in terms of a standard quadratic program. The attractive feature of this formulation is that a clear onetoone correspondence exists between the solutions of the quadratic program and those in the original, combinatorial problem. To solve the program we use the socalled replicator equations—a class of straightforward continuous and discretetime dynamical systems developed in various branches of theoretical biology. We show how, despite their inherent inability to escape from local solutions, they nevertheless provide experimental results that are competitive with those obtained using more elaborate meanfield annealing heuristics.
A New GraphTheoretic Approach to Clustering, with Applications to Computer Vision
, 2004
"... This work applies cluster analysis as a unified approach for a wide range of vision applications, thereby combining the research domain of computer vision and that of machine learning. Cluster analysis is the formal study of algorithms and methods for recovering the inherent structure within a given ..."
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Cited by 44 (4 self)
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This work applies cluster analysis as a unified approach for a wide range of vision applications, thereby combining the research domain of computer vision and that of machine learning. Cluster analysis is the formal study of algorithms and methods for recovering the inherent structure within a given dataset. Many problems of computer vision have precisely this goal, namely to find which visual entities belong to an inherent structure, e.g. in an image or in a database of images. For example, a meaningful structure in the context of image segmentation is a set of pixels which correspond to the same object in a scene. Clustering algorithms can be used to partition the pixels of an image into meaningful parts, which may correspond to different objects. In this work we focus on the problems of image segmentation and image database organization. The visual entities to consider are pixels and images, respectively. Our first contribution in this work is a novel partitional (flat) clustering algorithm. The algorithm uses pairwise representation, where the visual objects (pixels,
Robust point matching for nonrigid shapes by preserving local neighborhood structures
 PAMI
, 2006
"... Abstract—In previous work on point matching, a set of points is often treated as an instance of a joint distribution to exploit global relationships in the point set. For nonrigid shapes, however, the local relationship among neighboring points is stronger and more stable than the global one. In thi ..."
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Cited by 26 (4 self)
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Abstract—In previous work on point matching, a set of points is often treated as an instance of a joint distribution to exploit global relationships in the point set. For nonrigid shapes, however, the local relationship among neighboring points is stronger and more stable than the global one. In this paper, we introduce the notion of a neighborhood structure for the general point matching problem. We formulate point matching as an optimization problem to preserve local neighborhood structures during matching. Our approach has a simple graph matching interpretation, where each point is a node in the graph, and two nodes are connected by an edge if they are neighbors. The optimal match between two graphs is the one that maximizes the number of matched edges. Existing techniques are leveraged to search for an optimal solution with the shape context distance used to initialize the graph matching, followed by relaxation labeling updates for refinement. Extensive experiments show the robustness of our approach under deformation, noise in point locations, outliers, occlusion, and rotation. It outperforms the shape context and TPSRPM algorithms on most scenarios. Index Terms—Point matching, shape matching, image registration, nonrigid shapes, relaxation labeling. 1
Annealed Replication: A New Heuristic for the Maximum Clique Problem
 Discr. Appl. Math
, 2000
"... In this paper, a new heuristic for approximating the maximum clique problem is proposed, based on a detailed analysis of a class of continuous optimization models which yield a complete solution to this NPhard combinatorial problem. The idea is to alter a regularization parameter iteratively in suc ..."
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Cited by 20 (11 self)
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In this paper, a new heuristic for approximating the maximum clique problem is proposed, based on a detailed analysis of a class of continuous optimization models which yield a complete solution to this NPhard combinatorial problem. The idea is to alter a regularization parameter iteratively in such a way that an iterative procedure with the updated parameter value would avoid unwanted, inefficient local solutions, i.e., maximal cliques which contain less than the maximum possible number of vertices. The local search procedure is performed with the help of the replicator dynamics, and the regularization parameter is chosen deliberately as to render dynamical instability of the (formerly) stable solutions which we want to discard in order to get an improvement. In this respect, the proposed procedure differs from usual simulated annealing approaches which mostly use a "blackbox" cooling schedule. To demonstrate the validity of this approach, we report on the performance applied to sel...
Continuoustime Relaxation Labeling Processes
, 1998
"... We study the properties of two new relaxation labeling schemes described in terms of differential equations, and hence evolving in countinuous time. This contrasts with the customary approach to defining relaxation labeling algorithms which prefers discrete time. Continuoustime dynamical systems ar ..."
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Cited by 19 (4 self)
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We study the properties of two new relaxation labeling schemes described in terms of differential equations, and hence evolving in countinuous time. This contrasts with the customary approach to defining relaxation labeling algorithms which prefers discrete time. Continuoustime dynamical systems are particularly attractive because they can be implemented directly in hardware circuitry, and the study of their dynamical properties is simpler and more elegant. They are also more plausible as models of biological visual computation. We prove that the proposed models enjoy exactly the same dynamical properties as the classical relaxation labeling schemes, and show how they are intimately related to Hummel and Zucker's now classical theory of constraint satisfaction. In particular, we prove that, when a certain symmetry condition is met, the dynamical systems' behavior is governed by a Liapunov function which turns out to be (the negative of) a wellknown consistency measure. Moreover, we p...
Attributed Tree Matching and Maximum Weight Cliques
 In ICIAP’9910th Int. Conf. on Image Analysis and Processing
, 1999
"... A classical way of matching relational structures consists of finding a maximum clique in a derived "association graph." However, it is not clear how to apply this approach to problems where the graphs are hierarchically organized, i.e. are trees, since maximum cliques are not constrained to preserv ..."
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Cited by 9 (2 self)
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A classical way of matching relational structures consists of finding a maximum clique in a derived "association graph." However, it is not clear how to apply this approach to problems where the graphs are hierarchically organized, i.e. are trees, since maximum cliques are not constrained to preserve the partial order. We have recently provided a solution to this problem by constructing the association graph using the graphtheoretic concept of connectivity. In this paper, we extend the approach to the problem of matching attributed trees. Specifically, we show how to derive a "weighted" association graph, and prove that the attributed tree matching problem is equivalent to finding a maximum weight clique in it. We then formulate the maximum weight clique problem in terms of a continuous optimization problem, which we solve using "replicator" dynamical systems developed in theoretical biology. This formulation is attractive because it can motivate analog and biological implementations....
A GameTheoretic Approach to Hypergraph Clustering
, 2009
"... Hypergraph clustering refers to the process of extracting maximally coherent groups from a set of objects using highorder (rather than pairwise) similarities. Traditional approaches to this problem are based on the idea of partitioning the input data into a userdefined number of classes, thereby o ..."
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Cited by 8 (2 self)
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Hypergraph clustering refers to the process of extracting maximally coherent groups from a set of objects using highorder (rather than pairwise) similarities. Traditional approaches to this problem are based on the idea of partitioning the input data into a userdefined number of classes, thereby obtaining the clusters as a byproduct of the partitioning process. In this paper, we provide a radically different perspective to the problem. In contrast to the classical approach, we attempt to provide a meaningful formalization of the very notion of a cluster and we show that game theory offers an attractive and unexplored perspective that serves well our purpose. Specifically, we show that the hypergraph clustering problem can be naturally cast into a noncooperative multiplayer “clustering game”, whereby the notion of a cluster is equivalent to a classical gametheoretic equilibrium concept. From the computational viewpoint, we show that the problem of finding the equilibria of our clustering game is equivalent to locally optimizing a polynomial function over the standard simplex, and we provide a discretetime dynamics to perform this optimization. Experiments are presented which show the superiority of our approach over stateoftheart hypergraph clustering techniques.
Autoassociative Learning in Relaxation Labeling Networks
, 1997
"... We address the problem of training relaxation labeling processes, a popular class of parallel iterative procedures widely employed in pattern recognition and computer vision. The approach discussed here is based on a theory of consistency developed by Hummel and Zucker, and contrasts with a recently ..."
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Cited by 5 (3 self)
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We address the problem of training relaxation labeling processes, a popular class of parallel iterative procedures widely employed in pattern recognition and computer vision. The approach discussed here is based on a theory of consistency developed by Hummel and Zucker, and contrasts with a recently introduced learning strategy which can be regarded as heteroassociative, i.e., what is actually learned is the association between patterns rather than the patterns themselves. The proposed learning model is instead autoassociative and involves making a set of training patterns consistent, in the sense rigorously defined by Hummel and Zucker; this implies that they become local attractors of the relaxation labeling dynamical system. The learning problem is formulated in terms of solving a system of linear inequalities, and a straightforward iterative algorithm is presented to accomplish this. The learning model described here allows one to view the relaxation labeling process as a kind of ...