Introduction to algorithms
Relaxation labeling networks for the maximum clique problem
Journal of Artificial Neural Networks - Special issue: neural networks for optimization
Feasible and infeasible maxima in a quadratic program for maximum clique
Journal of Artificial Neural Networks - Special issue: neural networks for optimization
FORMS: a flexible object recognition and modeling system
International Journal of Computer Vision
Matching Hierarchical Structures Using Association Graphs
IEEE Transactions on Pattern Analysis and Machine Intelligence
Computer Vision
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Evolution towards the Maximum Clique
Journal of Global Optimization
Many-to-many Matching of Attributed Trees Using Association Graphs and Game Dynamics
IWVF-4 Proceedings of the 4th International Workshop on Visual Form
Representation and Self-Similarity of Shapes
ICCV '98 Proceedings of the Sixth International Conference on Computer Vision
Replicator Equations, Maximal Cliques, and Graph Isomorphism
Neural Computation
A versatile computer-controlled assembly system
IJCAI'73 Proceedings of the 3rd international joint conference on Artificial intelligence
Approximating the maximum weight clique using replicator dynamics
IEEE Transactions on Neural Networks
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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.