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36
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 283 (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...
Algorithms for the Satisfiability (SAT) Problem: A Survey
 DIMACS Series in Discrete Mathematics and Theoretical Computer Science
, 1996
"... . The satisfiability (SAT) problem is a core problem in mathematical logic and computing theory. In practice, SAT is fundamental in solving many problems in automated reasoning, computeraided design, computeraided manufacturing, machine vision, database, robotics, integrated circuit design, compute ..."
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Cited by 125 (3 self)
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. The satisfiability (SAT) problem is a core problem in mathematical logic and computing theory. In practice, SAT is fundamental in solving many problems in automated reasoning, computeraided design, computeraided manufacturing, machine vision, database, robotics, integrated circuit design, computer architecture design, and computer network design. Traditional methods treat SAT as a discrete, constrained decision problem. In recent years, many optimization methods, parallel algorithms, and practical techniques have been developed for solving SAT. In this survey, we present a general framework (an algorithm space) that integrates existing SAT algorithms into a unified perspective. We describe sequential and parallel SAT algorithms including variable splitting, resolution, local search, global optimization, mathematical programming, and practical SAT algorithms. We give performance evaluation of some existing SAT algorithms. Finally, we provide a set of practical applications of the sat...
Flexible Syntactic Matching of Curves and its Application to Automatic Hierarchical Classification of Silhouettes
 IEEE Transactions on Pattern Analysis and Machine Intelligence
"... Curve matching is one instance of the fundamental correspondence problem. Our exible algorithm is designed to match curves under substantial deformations and arbitrary large scaling and rigid transformations. A syntactic representation is constructed for both curves, and an edit transformation which ..."
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Cited by 113 (2 self)
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Curve matching is one instance of the fundamental correspondence problem. Our exible algorithm is designed to match curves under substantial deformations and arbitrary large scaling and rigid transformations. A syntactic representation is constructed for both curves, and an edit transformation which maps one curve to the other is found using dynamic programming. We present extensive...
ShapeBased Retrieval: A Case Study with Trademark Image Databases
 Pattern Recognition
, 1998
"... Retrieval efficiency and accuracy are two important issues in designing a contentbased database retrieval system. We propose a method for trademark image database retrieval based on object shape information that would supplement traditional textbased retrieval systems. This system achieves both th ..."
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Cited by 101 (0 self)
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Retrieval efficiency and accuracy are two important issues in designing a contentbased database retrieval system. We propose a method for trademark image database retrieval based on object shape information that would supplement traditional textbased retrieval systems. This system achieves both the desired efficiency and accuracy using a twostage hierarchy: in the first stage, simple and easily computable shape features are used to quickly browse through the database to generate a moderate number of plausible retrievals when a query is presented; in the second stage, the candidates from the first stage are screened using a deformable template matching process to discard spurious matches. We have tested the algorithm using hand drawn queries on a trademark database containing 1; 100 images. Each retrieval takes a reasonable amount of computation time (¸ 45 seconds on a Sun Sparc 20 workstation). The top most image retrieved by the system agrees with that obtained by human subjects, ...
Dot pattern processing using voronoi neighborhoods
 IEEE Transactzons on Pattern Analyszs and Machzne Intellzgence
, 1982
"... AbstractA sound notion of the neighborhood of a point is essential for analyzing dot patterns. The past work in this direction has concentrated on identifying pairs of points that are neighbors. Examples of such methods include those based on a fixed radius, knearest neighbors, minimal spanning tr ..."
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Cited by 42 (5 self)
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AbstractA sound notion of the neighborhood of a point is essential for analyzing dot patterns. The past work in this direction has concentrated on identifying pairs of points that are neighbors. Examples of such methods include those based on a fixed radius, knearest neighbors, minimal spanning tree, relative neighborhood graph, and the Gabriel graph. This correspondence considers the use of the region enclosed by a point's Voronoi polygon as its neighborhood. It is argued that the Voronoi polygons possess intuitively appealing characteristics, as would be expected from the neighborhood of a point. Geometrical characteristics of the Voronoi neighborhood are used as features in dot pattern processing. Procedures for segmentation, matching, and perceptual border extraction using the Voronoi neighborhood are outlined. Extensions of the Voronoi definition to other domains are discussed. Index TermsClustering, computational complexity, dot patterns, Gabriel graph, knearest neighbors, matching, minimal spanning tree, neighborhood, neighbors, perceptual boundary extraction, relative neighborhood graph, Voronoi tessellation.
Matching: Invariant to Translations, Rotations and Scale Changes
 Pattern Recognition
, 1992
"... We present an approach to invariant matching. In this approach, an object or a pattern is invariantly represented by an objectcentered description called an attributed relational structure (ARS) embedding invariant properties and relations between the primitives of the pattern such as line segments ..."
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Cited by 39 (5 self)
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We present an approach to invariant matching. In this approach, an object or a pattern is invariantly represented by an objectcentered description called an attributed relational structure (ARS) embedding invariant properties and relations between the primitives of the pattern such as line segments and points. Noise effect is taken into account such that a scene can consist of noisy subparts of a model. The matching is then to find the optimal mapping between the ARSs of the scene and the model. A gain functional is formulated to measure the goodness of fit and is to be maximized by using the relaxation labeling method. Experiments are shown to illustrate the matching algorithm and to demonstrate that the approach is truly invariant to arbitrary translations, rotations, and scale changes under noise. Index terms  Attributed relational structures, invariance, pattern recognition, relaxation labeling, subgraph matching. Pattern Recognition, 25(6):583594, June 1992 2 Contents 1...
Recognition by Prototypes
 International Journal of Computer Vision
, 1992
"... A scheme for recognizing 3D objects from single 2D images is introduced. The scheme proceeds in two stages. In the first stage, the categorization stage, the image is compared to prototype objects. For each prototype, the view that most resembles the image is recovered, and, if the view is found t ..."
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Cited by 30 (1 self)
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A scheme for recognizing 3D objects from single 2D images is introduced. The scheme proceeds in two stages. In the first stage, the categorization stage, the image is compared to prototype objects. For each prototype, the view that most resembles the image is recovered, and, if the view is found to be similar to the image, the class identity of the object is determined. In the second stage, the identification stage, the observed object is compared to the individual models of its class, where classes are expected to contain objects with relatively similar shapes. For each model, a view that matches the image is sought.
Graphical models and point pattern matching
 IEEE Trans. PAMI
, 2006
"... Abstract—This paper describes a novel solution to the rigid point pattern matching problem in Euclidean spaces of any dimension. Although we assume rigid motion, jitter is allowed. We present a noniterative, polynomial time algorithm that is guaranteed to find an optimal solution for the noiseless c ..."
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Cited by 30 (5 self)
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Abstract—This paper describes a novel solution to the rigid point pattern matching problem in Euclidean spaces of any dimension. Although we assume rigid motion, jitter is allowed. We present a noniterative, polynomial time algorithm that is guaranteed to find an optimal solution for the noiseless case. First, we model point pattern matching as a weighted graph matching problem, where weights correspond to Euclidean distances between nodes. We then formulate graph matching as a problem of finding a maximum probability configuration in a graphical model. By using graph rigidity arguments, we prove that a sparse graphical model yields equivalent results to the fully connected model in the noiseless case. This allows us to obtain an algorithm that runs in polynomial time and is provably optimal for exact matching between noiseless point sets. For inexact matching, we can still apply the same algorithm to find approximately optimal solutions. Experimental results obtained by our approach show improvements in accuracy over current methods, particularly when matching patterns of different sizes. Index Terms—Point pattern matching, graph matching, graphical models, Markov random fields, junction tree algorithm. 1
A Lagrangian Relaxation Network for Graph Matching
 IEEE Trans. Neural Networks
, 1996
"... A Lagrangian relaxation network for graph matching is presented. The problem is formulated as follows: given graphs G and g, find a permutation matrix M that brings the two sets of vertices into correspondence. Permutation matrix constraints are formulated in the framework of deterministic annealing ..."
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Cited by 26 (7 self)
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A Lagrangian relaxation network for graph matching is presented. The problem is formulated as follows: given graphs G and g, find a permutation matrix M that brings the two sets of vertices into correspondence. Permutation matrix constraints are formulated in the framework of deterministic annealing. Our approach is in the same spirit as a Lagrangian decomposition approach in that the row and column constraints are satisfied separately with a Lagrange multiplier used to equate the two "solutions." Due to the unavoidable symmetries in graph isomorphism (resulting in multiple global minima), we add a symmetrybreaking selfamplification term in order to obtain a permutation matrix. With the application of a fixpoint preserving algebraic transformation to both the distance measure and selfamplification terms, we obtain a Lagrangian relaxation network. The network performs minimization with respect to the Lagrange parameters and maximization with respect to the permutation matrix variable...