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We formulate the problem of high order structural matching by applying dominant cluster analysis (DCA) to a direct product hypergraph (DPH). For brevity we refer to the resulting algorithm as DPH-DCA. The DPH-DCA can be considered as an extension of the game theoretic algorithms presented in [8] from clustering to matching, and also as a reduced version of reduced version of the method of ensembles of affinity relations presented in [6]. The starting point for our method is to construct a K-uniform direct product hypergraph for the two sets of higher-order features to be matched. Each vertex in the direct product hypergraph represents a potential correspondence and the weight on each hyperedge represents the agreement between two K-tuples drawn from the two feature sets. Vertices representing correct assignment tend to form a strongly intra-connected cluster, i.e. a dominant cluster. We evaluate the association of each vertex belonging to the dominant cluster by maximizing an objective function which maintains the K-tuple agreements. The potential correspondences with nonzero association weights are more likely to belong to the dominant cluster than the remaining zeroweighted ones. They are thus selected as correct matchings subject to the one-to-one correspondence constraint. Furthermore, we present a route to improving the matching accuracy by invoking prior knowledge. An experimental evaluation shows that our method outperforms the state-of-the-art high order structural matching methods[10][3].

High Order Structural Matching Using Dominant Cluster Analysis