Issue No. 11 - November (2002 vol. 24)
<p><b>Abstract</b>—Motivated by our recent work on rooted tree matching, in this paper we provide a solution to the problem of matching two free (i.e., unrooted) trees by constructing an association graph whose maximal cliques are in one-to-one correspondence with maximal common subtrees. 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, uniformly 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.</p>
Graph matching, combinatorial optimization, quadratic programming, dynamical systems, evolutionary game theory, shape recognition.
Marcello Pelillo, "Matching Free Trees, Maximal Cliques, and Monotone Game Dynamics", IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 24, no. , pp. 1535-1541, November 2002, doi:10.1109/TPAMI.2002.1046176