Methods of Information Geometry to model complex shapes

Abstract

In this paper, a new statistical method to model patterns emerging in complex systems is proposed. A framework for shape analysis of 2− dimensional landmark data is introduced, in which each landmark is represented by a bivariate Gaussian distribution. From Information Geometry we know that Fisher-Rao metric endows the statistical manifold of parameters of a family of probability distributions with a Riemannian metric. Thus this approach allows to reconstruct the intermediate steps in the evolution between observed shapes by computing the geodesic, with respect to the Fisher-Rao metric, between the corresponding distributions. Furthermore, the geodesic path can be used for shape predictions. As application, we study the evolution of the rat skull shape. A future application in Ophthalmology is introduced.