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.