Matching Free Trees, Maximal Cliques, and Monotone Game Dynamics

Abstract

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 connected and acyclic, i.e. are free trees, since maximal cliques are not constrained to preserve connectedness. Motivated by our recent work on rooted tree matching, in this paper we provide a solution to the problem of matching two free trees by constructing an association graph whose maximal cliques are in one-to-one correspondence with maximal subtree isomorphisms. We then solve the problem using simple payoff-monotonic dynamics from evolutionary game theory. We illustrate the power of the approach by matching articulated and deformed shapes described by shape-axis trees. Experiments on hundreds of larger (random) trees are also presented. The results are impressive: despite the inherent inability of these simple dynamics to escape from local optima, they always returned a globally optimal solution.KeywordsMaximal CliqueReplicator DynamicEvolutionary Game TheoryFree TreeMaximum Clique ProblemThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.