Landmark Representation of Shapes and Fisher-Rao Geometry

We develop computational strategies to calculate geodesies and geodesic distances between plane shapes represented by mixture of Gaussians centered at landmark points with a fixed variance with respect to the information-theoretic Fisher-Rao metric. This representation and metric have been investigated recently by Peter and Rangarajan, but a feasible computational approach was not provided. The algorithms developed are applied to shape clustering and the results are compared to those obtained with other methods.