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International Journal of Computer Vision

, Volume 35, Issue 1, pp 13–32 | Cite as

Shock Graphs and Shape Matching

  • Kaleem Siddiqi
  • Ali Shokoufandeh
  • Sven J. Dickinson
  • Steven W. Zucker
Article

Abstract

We have been developing a theory for the generic representation of 2-D shape, where structural descriptions are derived from the shocks (singularities) of a curve evolution process, acting on bounding contours. We now apply the theory to the problem of shape matching. The shocks are organized into a directed, acyclic shock graph, and complexity is managed by attending to the most significant (central) shape components first. The space of all such graphs is highly structured and can be characterized by the rules of a shock graph grammar. The grammar permits a reduction of a shock graph to a unique rooted shock tree. We introduce a novel tree matching algorithm which finds the best set of corresponding nodes between two shock trees in polynomial time. Using a diverse database of shapes, we demonstrate our system's performance under articulation, occlusion, and moderate changes in viewpoint.

shape representation shape matching shock graph shock graph grammar subgraph isomorphism 

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Copyright information

© Kluwer Academic Publishers 1999

Authors and Affiliations

  • Kaleem Siddiqi
    • 1
  • Ali Shokoufandeh
    • 2
  • Sven J. Dickinson
    • 2
  • Steven W. Zucker
    • 3
  1. 1.School of Computer Science and Center for Intelligent MachinesMcGill UniversityMontréal, PQCanada
  2. 2.Department of Computer Science and Center for Cognitive ScienceRutgers UniversityNew BrunswickUSA
  3. 3.Departments of Computer Science and Electrical Enginnering and Center for Computational Vision and ControlYale UniversityNew HavenUSA

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