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28
A Graduated Assignment Algorithm for Graph Matching
, 1996
"... A graduated assignment algorithm for graph matching is presented which is fast and accurate even in the presence of high noise. By combining graduated nonconvexity, twoway (assignment) constraints, and sparsity, large improvements in accuracy and speed are achieved. Its low order computational comp ..."
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Cited by 305 (15 self)
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A graduated assignment algorithm for graph matching is presented which is fast and accurate even in the presence of high noise. By combining graduated nonconvexity, twoway (assignment) constraints, and sparsity, large improvements in accuracy and speed are achieved. Its low order computational complexity [O(lm), where l and m are the number of links in the two graphs] and robustness in the presence of noise offer advantages over traditional combinatorial approaches. The algorithm, not restricted to any special class of graph, is applied to subgraph isomorphism, weighted graph matching, and attributed relational graph matching. To illustrate the performance of the algorithm, attributed relational graphs derived from objects are matched. Then, results from twentyfive thousand experiments conducted on 100 node random graphs of varying types (graphs with only zeroone links, weighted graphs, and graphs with node attributes and multiple link types) are reported. No comparable results have...
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 182 (26 self)
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this article, please send email to: tpami@computer.org, and reference IEEECS Log Number 108453
THIRTY YEARS OF GRAPH MATCHING IN PATTERN RECOGNITION
, 2004
"... A recent paper posed the question: "Graph Matching: What are we really talking about?". Far from providing a definite answer to that question, in this paper we will try to characterize the role that graphs play within the Pattern Recognition field. To this aim two taxonomies are presented ..."
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Cited by 137 (1 self)
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A recent paper posed the question: "Graph Matching: What are we really talking about?". Far from providing a definite answer to that question, in this paper we will try to characterize the role that graphs play within the Pattern Recognition field. To this aim two taxonomies are presented and discussed. The first includes almost all the graph matching algorithms proposed from the late seventies, and describes the different classes of algorithms. The second taxonomy considers the types of common applications of graphbased techniques in the Pattern Recognition and Machine Vision field.
Symmetrybased Indexing of Image Databases
 J. VISUAL COMMUNICATION AND IMAGE REPRESENTATION
, 1998
"... The use of shape as a cue for indexing into pictorial databases has been traditionally based on global invariant statistics and deformable templates, on the one hand, and local edge correlation on the other. This paper proposes an intermediate approach based on a characterization of the symmetry in ..."
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Cited by 83 (6 self)
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The use of shape as a cue for indexing into pictorial databases has been traditionally based on global invariant statistics and deformable templates, on the one hand, and local edge correlation on the other. This paper proposes an intermediate approach based on a characterization of the symmetry in edge maps. The use of symmetry matching as a joint correlation measure between pairs of edge elements further constrains the comparison of edge maps. In addition, a natural organization of groups of symmetry into a hierarchy leads to a graphbased representation of relational structure of components of shape that allows for deformations by changing attributes of this relational graph. A graduate assignment graph matching algorithm is used to match symmetry structure in images to stored prototypes or sketches. The results of matching sketches and greyscale images against a small database consisting of a variety of fish, planes, tools, etc., are depicted.
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 54 (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 Novel Optimizing Network Architecture with Applications
 Neural Computation
, 1996
"... We present a novel optimizing network architecture with applications in vision, learning, pattern recognition and combinatorial optimization. This architecture is constructed by combining the following techniques: (i) deterministic annealing, (ii) selfamplification, (iii) algebraic transformations, ..."
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Cited by 36 (16 self)
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We present a novel optimizing network architecture with applications in vision, learning, pattern recognition and combinatorial optimization. This architecture is constructed by combining the following techniques: (i) deterministic annealing, (ii) selfamplification, (iii) algebraic transformations, (iv) clocked objectives and (v) softassign. Deterministic annealing in conjunction with selfamplification avoids poor local minima and ensures that a vertex of the hypercube is reached. Algebraic transformations and clocked objectives help partition the relaxation into distinct phases. The problems considered have doubly stochastic matrix constraints or minor variations thereof. We introduce a new technique, softassign, which is used to satisfy this constraint. Experimental results on different problems are presented and discussed. 1
Learning With Preknowledge: Clustering With Point and Graph Matching Distance Measures
 Neural Computation
, 1996
"... Prior knowledge constraints are imposed upon a learning problem in the form of distance measures. Prototypical 2D point sets and graphs are learned by clustering with point matching and graph matching distance measures. The point matching distance measure is approx. invariant under affine transform ..."
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Cited by 28 (10 self)
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Prior knowledge constraints are imposed upon a learning problem in the form of distance measures. Prototypical 2D point sets and graphs are learned by clustering with point matching and graph matching distance measures. The point matching distance measure is approx. invariant under affine transformationstranslation, rotation, scale and shearand permutations. It operates between noisy images with missing and spurious points. The graph matching distance measure operates on weighted graphs and is invariant under permutations. Learning is formulated as an optimization problem. Large objectives so formulated (¸ million variables) are efficiently minimized using a combination of optimization techniquessoftassign, algebraic transformations, clocked objectives, and deterministic annealing. 1 Introduction While few biologists today would subscribe to Locke's description of the nascent mind as a tabula rasa, the nature of the inherent constraintsKant's preknowledgethat helps org...
Softmax to Softassign: Neural Network Algorithms for Combinatorial Optimization
 Journal of Artificial Neural Networks
, 1995
"... A new technique termed softassign is applied to three combinatorial optimization problems  weighted graph matching, the travelling salesman problem and graph partitioning. Softassign, which has emerged from the recurrent neural network/ statistical physics framework, enforces twoway (assignment) c ..."
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Cited by 13 (3 self)
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A new technique termed softassign is applied to three combinatorial optimization problems  weighted graph matching, the travelling salesman problem and graph partitioning. Softassign, which has emerged from the recurrent neural network/ statistical physics framework, enforces twoway (assignment) constraints without the use of penalty terms in the energy functions. The softassign can also be generalised from twoway winnertakeall constraints to multiple membership constraints which are required for graph partitioning. The softassign technique is compared to softmax (Potts glass) dynamics. Within the statistical physics framework, softmax and a penalty term has been a widely used method for enforcing the twoway constraints common to many combinatorial optimization problems. The benchmarks present evidence that softassign has clear advantages in accuracy, speed, parallelizability and algorithmic simplicity over softmax and a penalty term in optimization problems with twoway constraints.
A Dynamical Systems Approach to Weighted Graph Matching
, 2006
"... Graph matching is a fundamental problem that arises frequently in the areas of distributed control, computer vision, and facility allocation. In this paper, we consider the optimal graph matching problem for weighted graphs, which is computationally challenging due the combinatorial nature of the se ..."
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Cited by 12 (3 self)
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Graph matching is a fundamental problem that arises frequently in the areas of distributed control, computer vision, and facility allocation. In this paper, we consider the optimal graph matching problem for weighted graphs, which is computationally challenging due the combinatorial nature of the set of permutations. Contrary to optimizationbased relaxations to this problem, in this paper we develop a novel relaxation by constructing dynamical systems on the manifold of orthogonal matrices. In particular, since permutation matrices are orthogonal matrices with nonnegative elements, we define two gradient flows in the space of orthogonal matrices. The first minimizes the cost of weighted graph matching over orthogonal matrices, whereas the second minimizes the distance of an orthogonal matrix from the finite set of all permutations. The combination of the two dynamical systems converges to a permutation matrix which, provides a suboptimal solution to the weighted graph matching problem. Finally, our approach is shown to be promising by illustrating it on nontrivial problems.
Monte Carlo EM for data association and its applications in computer vision
, 2001
"... Estimating geometry from images is at the core of many computer vision applications, whether it concerns the imaging geometry, the geometry of the scene, or both. Examples include image mosaicking, pose estimation, multibaseline stereo, and structure from motion. All these problems can be modeled pr ..."
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Cited by 10 (4 self)
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Estimating geometry from images is at the core of many computer vision applications, whether it concerns the imaging geometry, the geometry of the scene, or both. Examples include image mosaicking, pose estimation, multibaseline stereo, and structure from motion. All these problems can be modeled probabilistically and translate into wellunderstood statistical estimation problems, provided the correspondence between measurements in the different images is known. I will show that, if the correspondence is not known, the statistically optimal estimate for the geometry can be obtained using the expectationmaximization (EM) algorithm. In contrast to existing techniques, the EM algorithm avoids the estimation bias associated with computing a single “best ” set of correspondences, but rather considers the distribution over all possible correspondences consistent with the data. While the latter computation is intractable in general, I show that it can be approximated well in practice using Markov chain