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 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 changes in viewpoint.