Matching Hierarchical Structures Using Association Graphs
IEEE Transactions on Pattern Analysis and Machine Intelligence
Shock Graphs and Shape Matching
International Journal of Computer Vision
A tree-edit-distance algorithm for comparing simple, closed shapes
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Ligature instabilities in the perceptual organization of shape
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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
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Matching Free Trees, Maximal Cliques, and Monotone Game Dynamics
EMMCVPR '01 Proceedings of the Third International Workshop on Energy Minimization Methods in Computer Vision and Pattern Recognition
A Complementary Pivoting Approach to Graph Matching
EMMCVPR '01 Proceedings of the Third International Workshop on Energy Minimization Methods in Computer Vision and Pattern Recognition
Pattern Recognition Letters - Special issue: In memoriam Azriel Rosenfeld
Matching Hierarchies of Deformable Shapes
GbRPR '09 Proceedings of the 7th IAPR-TC-15 International Workshop on Graph-Based Representations in Pattern Recognition
GbRPR '09 Proceedings of the 7th IAPR-TC-15 International Workshop on Graph-Based Representations in Pattern Recognition
From region based image representation to object discovery and recognition
SSPR&SPR'10 Proceedings of the 2010 joint IAPR international conference on Structural, syntactic, and statistical pattern recognition
Many-to-many graph matching via metric embedding
CVPR'03 Proceedings of the 2003 IEEE computer society conference on Computer vision and pattern recognition
Graph-based quadratic optimization: A fast evolutionary approach
Computer Vision and Image Understanding
Object categorization using bone graphs
Computer Vision and Image Understanding
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The matching of hierarchical relational structures is of significant interest in computer vision and pattern recognition. We have recently introduced a new solution to this problem, based on a maximum clique formulation in a (derived) "association graph." This allows us to exploit the full arsenal of clique finding algorithms developed in the algorithms community. However, thus far we have focussed on one-to-one correspondences (isomorphisms), and many-to-one correspondences (homomorphisms). In this paper we present a general solution for the case of many-to-many correspondences (morphisms) which is of particular interest when the underlying trees reflect real-world data and are likely to contain structural alterations. We define a notion of an Ɛ-morphism between attributed trees, and provide a method of constructing a weighted association graph where maximal weight cliques are in one-to-one correspondence with maximal similarity subtree morphisms. We then solve the problem by using replicator dynamical systems from evolutionary game theory. We illustrate the power of the approach by matching articulated and deformed shapes described by shock trees.