Riemannian analysis of probability density functions with applications in vision

Applications in computer vision involve statisti-cally analyzing an important class of constrained, non-negative functions, including probability density func-tions (in texture analysis), dynamic time-warping func-tions (in activity analysis), and re-parametrization or non-rigid registration functions (in shape analysis of curves). For this one needs to impose a Riemannian structure on the spaces formed by these functions. We propose a “spherical ” version of the Fisher-Rao met-ric that provides closed-form expressions for geodesics and distances, and allows fast computation of sample statistics. To demonstrate this approach, we present an application in planar shape classification. 1