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Continuous-based Heuristics for Graph and Tree Isomorphisms, with Application to Computer Vision

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Approximation and Complexity in Numerical Optimization

Part of the book series: Nonconvex Optimization and Its Applications ((NOIA,volume 42))

Abstract

We present a new (continuous) quadratic programming approach for graph- and tree-isomorphism problems which is based on an equivalent maximum clique formulation. The approach is centered around a fundamental result proved by Motzkin and Straus in the mid-1960s, 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 one-to-one correspondence exists between the solutions of the quadratic programs and those in the original, combinatorial problems. To approximately solve the program we use the so-called “replicator” equations, a class of straightforward continuous- and discrete-time 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 which are competitive with those obtained using more sophisticated mean-field annealing heuristics. Application of this approach to shape matching problems arising in computer vision and pattern recognition are also presented.

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Author information

Authors and Affiliations

  1. Dipartimento di Informatica, Università Ca’ Foscari di Venezia, Italy

    Marcello Pelillo

  2. Center for Intelligent Machines, McGill University, Canada

    Kaleem Siddiqi

  3. Center for Computational Vision and Control, Yale University, USA

    Steven W. Zucker

Authors
  1. Marcello Pelillo
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  2. Kaleem Siddiqi
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  3. Steven W. Zucker
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Editor information

Editors and Affiliations

  1. Center for Applied Optimization, Department of Industrial and Systems Engineering, University of Florida, USA

    Panos M. Pardalos

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Pelillo, M., Siddiqi, K., Zucker, S.W. (2000). Continuous-based Heuristics for Graph and Tree Isomorphisms, with Application to Computer Vision. In: Pardalos, P.M. (eds) Approximation and Complexity in Numerical Optimization. Nonconvex Optimization and Its Applications, vol 42. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-3145-3_25

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  • DOI: https://doi.org/10.1007/978-1-4757-3145-3_25

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4419-4829-8

  • Online ISBN: 978-1-4757-3145-3

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