Fisher Information Geometry for Shape Analysis

The aim of this study is to model shapes from complex systems using Information Geometry tools. It is well-known that the Fisher information endows the statistical manifold, defined by a family of probability distributions, with a Riemannian metric, called the Fisher-Rao metric. With respect to this, geodesic paths are determined, minimizing information in Fisher sense. Under the hypothesis that it is possible to extract from the shape a finite number of representing points, called landmarks, we propose to model each of them with a probability distribution, as for example a multivariate Gaussian distribution. Then using the geodesic distance, induced by the Fisher-Rao metric, we can define a shape metric which enables us to quantify differences between shapes. The discriminative power of the proposed shape metric is tested performing a cluster analysis on the shapes of three different groups of specimens corresponding to three species of flatfish. Results show a better ability in recovering the true cluster structure with respect to other existing shape distances.