Shock Graphs and Shape Matching

  • Authors:
  • Kaleem Siddiqi;Ali Shokoufandeh;Sven J. Dickinson;Steven W. Zucker

  • Affiliations:
  • School of Computer Science and Center for Intelligent Machines, McGill University, 3480 University Street, Montréal, PQ, Canada H3A 2A7;Department of Computer Science and Center for Cognitive Science, Rutgers University, New Brunswick, NJ 08903, USA;Department of Computer Science and Center for Cognitive Science, Rutgers University, New Brunswick, NJ 08903, USA;Departments of Computer Science and Electrical Enginnering and Center for Computational Vision and Control, Yale University, New Haven, CT 06520-8285, USA

  • Venue:
  • International Journal of Computer Vision
  • Year:
  • 1999

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Abstract

We have been developing a theory for the generic representation of2-D shape, where structural descriptions are derived from theshocks (singularities) of a curve evolution process, acting on boundingcontours. We now apply the theory to the problem of shape matching. The shocksare organized into a directed, acyclic shock graph, and complexity ismanaged by attending to the most significant (central) shape componentsfirst. The space of all such graphs is highly structured and can becharacterized by the rules of a shock graph grammar. The grammarpermits a reduction of a shock graph to a unique rooted shock tree. Weintroduce a novel tree matching algorithm which finds the best set ofcorresponding nodes between two shock trees in polynomial time. Using adiverse database of shapes, we demonstrate our system‘s performance underarticulation, occlusion, and moderate changes in viewpoint.