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

  • Marcello Pelillo
  • Kaleem Siddiqi
  • Steven W. Zucker
Part of the Nonconvex Optimization and Its Applications book series (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.

Keywords

Maximum clique quadratic programming replicator dynamics shape recognition. 

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Copyright information

© Springer Science+Business Media Dordrecht 2000

Authors and Affiliations

  • Marcello Pelillo
    • 1
  • Kaleem Siddiqi
    • 2
  • Steven W. Zucker
    • 3
  1. 1.Dipartimento di InformaticaUniversità Ca’ Foscari di VeneziaItaly
  2. 2.Center for Intelligent MachinesMcGill UniversityCanada
  3. 3.Center for Computational Vision and ControlYale UniversityUSA

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