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63
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 285 (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...
A New Method for Mapping Optimization Problems onto Neural Networks
 International Journal of Neural Systems
, 1989
"... : A novel modified method for obtaining approximate solutions to difficult optimization problems within the neural network paradigm is presented. We consider the graph partition and the travelling salesman problems. The key new ingredient is a reduction of solution space by one dimension by using gr ..."
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Cited by 149 (18 self)
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: A novel modified method for obtaining approximate solutions to difficult optimization problems within the neural network paradigm is presented. We consider the graph partition and the travelling salesman problems. The key new ingredient is a reduction of solution space by one dimension by using graded neurons, thereby avoiding the destructive redundancy that has plagued these problems when using straightforward neural network techniques. This approach maps the problems onto Potts glass rather than spin glass theories. A systematic prescription is given for estimating the phase transition temperatures in advance, which facilitates the choice of optimal parameters. This analysis, which is performed for both serial and synchronous updating of the mean field theory equations, makes it possible to consistently avoid chaotic bahaviour. When exploring this new technique numerically we find the results very encouraging
LargeStep Markov Chains for the Traveling Salesman Problem
 Complex Systems
, 1991
"... We introduce a new class of Markov chain Monte Carlo search procedures, leading to more powerful optimization methods than simulated annealing. The main idea is to embed deterministic local search techniques into stochastic algorithms. The Monte Carlo explores only local optima, and it is able to ma ..."
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Cited by 92 (6 self)
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We introduce a new class of Markov chain Monte Carlo search procedures, leading to more powerful optimization methods than simulated annealing. The main idea is to embed deterministic local search techniques into stochastic algorithms. The Monte Carlo explores only local optima, and it is able to make large, global changes, even at low temperatures, thus overcoming large barriers in configuration space. We test these procedures in the case of the Traveling Salesman Problem. The embedded local searches we use are 3opt and LinKernighan. The large change or step consists of a special kind of 4change followed by localopt minimization. We test this algorithm on a number of instances. The power of the method is illustrated by solving to optimality some large problems such as the LIN318, the AT&T532, and the RAT783 problems. For even larger instances with randomly distributed cities, the Markov chain procedure improves 3opt by over 1.6%, and LinKernighan by 1.3%, leading to a new best h...
New Algorithms for 2D and 3D Point Matching: Pose Estimation and Correspondence
"... A fundamental open problem in computer visiondetermining pose and correspondence between two sets of points in spaceis solved with a novel, fast [O(nm)], robust and easily implementable algorithm. The technique works on noisy 2D or 3D point sets that may be of unequal sizes and may differ by n ..."
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Cited by 85 (19 self)
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A fundamental open problem in computer visiondetermining pose and correspondence between two sets of points in spaceis solved with a novel, fast [O(nm)], robust and easily implementable algorithm. The technique works on noisy 2D or 3D point sets that may be of unequal sizes and may differ by nonrigid transformations. Using a combination of optimization techniques such as deterministic annealing and the softassign, which have recently emerged out of the recurrent neural network/statistical physics framework, analog objective functions describing the problems are minimized. Over thirty thousand experiments, on randomly generated points sets with varying amounts of noise and missing and spurious points, and on handwritten character sets demonstrate the robustness of the algorithm. Keywords: Pointmatching, pose estimation, correspondence, neural networks, optimization, softassign, deterministic annealing, affine. 1 Introduction Matching the representations of two images has long...
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 76 (5 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.
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 35 (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
Parallel Distributed Approaches to Combinatorial Optimization  Benchmark Studies on Traveling Salesman Problem
, 1990
"... We present and summarize the results from 50, 100 and 200city TSP benchmarks presented at the 1989 NIPS postconference workshop using neural network, elastic net, genetic algorithm and simulated annealing approaches. These results are also compared with a stateoftheart hybrid approach consist ..."
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Cited by 31 (7 self)
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We present and summarize the results from 50, 100 and 200city TSP benchmarks presented at the 1989 NIPS postconference workshop using neural network, elastic net, genetic algorithm and simulated annealing approaches. These results are also compared with a stateoftheart hybrid approach consisting of greedy solution, simulated annealing, and exhaustive search.
The Dynamics of Nonlinear Relaxation Labeling Processes
, 1997
"... We present some new results which definitively explain the behavior of the classical, heuristic nonlinear relaxation labeling algorithm of Rosenfeld, Hummel, and Zucker in terms of the HummelZucker consistency theory and dynamical systems theory. In particular, it is shown that, when a certain symm ..."
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Cited by 31 (10 self)
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We present some new results which definitively explain the behavior of the classical, heuristic nonlinear relaxation labeling algorithm of Rosenfeld, Hummel, and Zucker in terms of the HummelZucker consistency theory and dynamical systems theory. In particular, it is shown that, when a certain symmetry condition is met, the algorithm possesses a Liapunov function which turns out to be (the negative of) a wellknown consistency measure. This follows almost immediately from a powerful result of Baum and Eagon developed in the context of Markov chain theory. Moreover, it is seen that most of the essential dynamical properties of the algorithm are retained when the symmetry restriction is relaxed. These properties are also shown to naturally generalize to higherorder relaxation schemes. Some applications and implications of the presented results are finally outlined.
Connectionist Inference Systems
, 1991
"... This paper presents a survey of connectionist inference systems. ..."
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Cited by 25 (6 self)
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This paper presents a survey of connectionist inference systems.
Computational Complexity Of Neural Networks: A Survey
, 1994
"... . We survey some of the central results in the complexity theory of discrete neural networks, with pointers to the literature. Our main emphasis is on the computational power of various acyclic and cyclic network models, but we also discuss briefly the complexity aspects of synthesizing networks fr ..."
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Cited by 22 (6 self)
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. We survey some of the central results in the complexity theory of discrete neural networks, with pointers to the literature. Our main emphasis is on the computational power of various acyclic and cyclic network models, but we also discuss briefly the complexity aspects of synthesizing networks from examples of their behavior. CR Classification: F.1.1 [Computation by Abstract Devices]: Models of Computationneural networks, circuits; F.1.3 [Computation by Abstract Devices ]: Complexity Classescomplexity hierarchies Key words: Neural networks, computational complexity, threshold circuits, associative memory 1. Introduction The currently again very active field of computation by "neural" networks has opened up a wealth of fascinating research topics in the computational complexity analysis of the models considered. While much of the general appeal of the field stems not so much from new computational possibilities, but from the possibility of "learning", or synthesizing networks...