A hierarchical framework for modal correspondence matching

The modal correspondence method of L.S. Shapiro and J.M. Brady (see Image and Vision Computing, vol.10, p.283-8, 1992) aims to match point-sets by comparing the eigenvectors of a pairwise point proximity matrix. Although elegant by means of its matrix representation, the method is notoriously susceptible to differences in the relational structure of the point-sets under consideration. We demonstrate how the method can be rendered robust to structural differences by adopting a hierarchical approach. We place the modal matching problem in a probabilistic setting in which the arrangement of pairwise clusters can be used to constrain the individual point correspondences. We commence by using an iterative pairwise clustering method which can be applied to locate the main structure in the point-sets under study. Once we have located point clusters, we compute within-cluster and between-cluster proximity matrices. The modal coefficients for these two sets of proximity matrices are used to compute the probabilities that the detected cluster-centres are in correspondence and also the probabilities that individual points are in correspondence. We develop an evidence-combining framework which draws on these two sets of probabilities to locate point correspondences. In this way, the arrangement of the cluster-centre correspondences constrain the individual point correspondences.