A New Closed-Form Information Metric for Shape Analysis

Abstract

Shape matching plays a prominent role in the analysis of medical and biological structures. Recently, a unifying framework was introduced for shape matching that uses mixture-models to couple both the shape representation and deformation. Essentially, shape distances were defined as geodesics induced by the Fisher-Rao metric on the manifold of mixture-model represented shapes. A fundamental drawback of the Fisher-Rao metric is that it is NOT available in closed-form for the mixture model. Consequently, shape comparisons are computationally very expensive. Here, we propose a new Riemannian metric based on generalized phi-entropy measures. In sharp contrast to the Fisher-Rao metric, our new metric is available in closed-form. Geodesic computations using the new metric are considerably more efficient. Discriminative capabilities of this new metric are studied by pairwise matching of corpus callosum shapes. Comparisons are conducted with the Fisher-Rao metric and the thin-plate spline bending energy.