Alpha geodesic distances for clustering of shapes

According to Information Geometry, we represent landmarks of a complex shape, as probability densities in a statistical manifold where geometric structures from -connections are considered. In particular the 0-connection is the Riemannian connection with respect to the Fisher metric. In the setting of shapes clustering, we compare the discriminative power of different shapes distances induced by geodesic distances derived from alpha-connections. The methodology is analyzed in an application to a data set of aeroplane shapes.