Multilayer matching of metric structures using hierarchically well-separated trees

Abstract

We consider the matching problem between two metric distributions where establishing a one-to-one matching of features may not always be possible. Although many-to-many graph matching techniques achieve the desired multi map between features, they ignore the spatial structure of the nodes. We propose a novel technique, multilayer matching, for solving the matching problem which utilizes both the individual node features and the clustering information of nodes. Our method uses the hierarchically well-separated trees (HSTs) to represent the metric distribution such that non-leaf nodes in the tree representation corresponds to a constellation of features in the original structure. By using HSTs in a linear programming setup, we obtain a matching between features through finding a mapping between non-leaf nodes among the two HSTs. We further provide a primal-dual approximation algorithm for the multilayer matching which runs several order of magnitudes faster while achieving comparable success rates. Application of the method to the image matching problem is also presented in the paper. Empirical evaluation of the method and its primal-dual extension on a set of recognition tests show the robustness and efficiency of the overall approach.