An Eigendecomposition Approach to Weighted Graph Matching Problems
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This paper describes a new eigendecomposition method for weighted graph-matching. Although elegant by means of its matrix representation, the eigendecomposition method is proved notoriously susceptible to differences in the size of the graphs under consideration. In this paper we demonstrate how the method can be rendered robust to structural differences by adopting a hierarchical approach. We place the weighted graph matching problem in a probabilistic setting in which the correspondences between pairwise clusters can be used to constrain the individual correspondences. By assigning nodes to pairwise relational clusters, we compute within-cluster and between-cluster adjacency matrices. The modal co-efficients for these adjacency matrices are used to compute cluster correspondence and cluster-conditional correspondence probabilities. A sensitivity study on synthetic point-sets reveals that the method is considerably more robust than the conventional method to clutter or point-set contamination.