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Shock Graphs and Shape Matching

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 have now begun to 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 the reduction of a shock graph to a unique rooted shock tree. We have introduced 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 have demonstrated our system's performance under articulation, occlusion, and moderate changes in viewpoint. Representative results are shown in Fig. 5.4.

K. Siddiqi, A. Shokoufandeh (Rutgers University), S. J. Dickinson (Rutgers University), S. W. Zucker (Yale University) [

Figure 5.4: Similarity between database shapes and class prototypes. In each row, a box is drawn around the most similar shape.

Annual Report

Mon Jun 26 21:22:20 GMT 2000