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Matching Free Trees, Maximal Cliques, and Monotone Game Dynamics

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Energy Minimization Methods in Computer Vision and Pattern Recognition (EMMCVPR 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2134))

Abstract

It is well known that the problem of matching two relational structures can be posed as an equivalent problem of finding a maximal clique in a (derived) association graph. However, it is not clear how to apply this approach to computer vision problems where the graphs are connected and acyclic, i.e. are free trees, since maximal cliques are not constrained to preserve connectedness. Motivated by our recent work on rooted tree matching, in this paper we provide a solution to the problem of matching two free trees by constructing an association graph whose maximal cliques are in one-to-one correspondence with maximal subtree isomorphisms. We then solve the problem using simple payoff-monotonic dynamics from evolutionary game theory. We illustrate the power of the approach by matching articulated and deformed shapes described by shape-axis trees. Experiments on hundreds of larger (random) trees are also presented. The results are impressive: despite the inherent inability of these simple dynamics to escape from local optima, they always returned a globally optimal solution.

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Author information

Authors and Affiliations

  1. Dipartimento di Informatica, Universitá Ca’ Foscari di Venezia, Via Torino 155, 30172, Venezia Mestre, Italy

    Marcello Pelillo

Authors
  1. Marcello Pelillo
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Editor information

Editors and Affiliations

  1. Instituto de Telecomunicacoes and Instituto Superior Tecnico, 1049-001, Lisboa, Portugal

    Mário Figueiredo

  2. INRIA, 2004 Route des Lucioles, 06902 Sophia-Antipolis cedex, France

    Josiane Zerubia

  3. Department of Computer Science and Engineering, Michigan State University, East Lansing, MI, 48824, USA

    Anil K. Jain

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© 2001 Springer-Verlag Berlin Heidelberg

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Pelillo, M. (2001). Matching Free Trees, Maximal Cliques, and Monotone Game Dynamics. In: Figueiredo, M., Zerubia, J., Jain, A.K. (eds) Energy Minimization Methods in Computer Vision and Pattern Recognition. EMMCVPR 2001. Lecture Notes in Computer Science, vol 2134. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44745-8_28

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  • DOI: https://doi.org/10.1007/3-540-44745-8_28

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42523-6

  • Online ISBN: 978-3-540-44745-0

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