A shape distance based on the Fisher–Rao metric and its application for shapes clustering

In the clustering of shapes, which is a longstanding challenge in the framework of geometric morphometrics and shape analysis, is crucial the selection and application of a suitable and appropriate measurement of distance among observations (i.e. individuals). 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. The geodesic distance induced by the Fisher–Rao metric can be used to define a shape metric which enables us to quantify differences between shapes. The discriminative power of the proposed Fisher–Rao distance is tested in the context of shapes clustering on both simulated and real data sets. Results show a better ability in recovering the true cluster structure with respect to the standard Kendall’s shape metric.