Matching Hierarchical Structures Using Association Graphs

?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 hierarchically organized, i.e., are trees, since maximal cliques are not constrained to preserve the partial order. Here, we provide a solution to the problem of matching two trees by constructing the association graph using the graph-theoretic concept of connectivity. We prove that, in the new formulation, there is a one-to-one correspondence between maximal cliques and maximal subtree isomorphisms. This allows us to cast the tree matching problem as an indefinite quadratic program using the MotzkinStraus theorem, and we use ?replicator? dynamical systems developed in theoretical biology to solve it. Such continuous solutions to discrete problems are attractive because they can motivate analog and biological imple...

• Type: Conference
• Year: 1998
• Where: ECCV
• Authors: Marcello Pelillo, Kaleem Siddiqi, Steven W. Zucker
• Keywords: Computer Vision, ECCV 1998, Indefinite Quadratic Program, Maximal Cliques, Maximal Subtree Isomorphisms, Tree Matching Problem, Weighted Association Graphs