Abstract

The modal correspondence method of Shapiro and Brady aims to match point-sets by comparing the eigenvectors of a pairwise point proximity matrix. Although elegant by means of its matrix repre- sentation, the method is notoriously susceptible to difierences in the re- lational structure of the point-sets under consideration. In this paper we demonstrate how the method can be rendered robust to structural difier- ences by adopting a hierarchical approach. We place the modal matching problem in a probabilistic setting in which the correspondences between pairwise clusters can be used to constrain the individual point corre- spondences. To meet this goal we commence by describing an iterative method which can be applied to the point proximity matrix to identify the locations of pairwise modal clusters. Once we have assigned points to clusters, we compute within-cluster and between-cluster proximity ma- trices. The modal co-eficients for these two sets of proximity matrices are used to compute cluster correspondence and cluster-conditional point correspondence probabilities. A sensitivity study on synthetic point-sets reveals that the method is considerably more robust than the conven- tional method to clutter or point-set contamination.