On the use of Gromov-Hausdorff Distances for Shape Comparison

Abstract

It is the purpose of this paper to propose and discuss certain modifications of the ideas concerning Gromov- Hausdorff distances in order to tackle the problems of shape matching and comparison. These reformulations render these distances more amenable to practical computations without sacrificing theoretical underpinnings. A second goal of this paper is to establish links to several other practical methods proposed in the literature for comparing/matching shapes in precise terms. Connections with the Quadratic Assignment Problem (QAP) are also established, and computational examples are presented.