Riemannian Analysis of Probability Density Functions with Applications in Vision

Applications in computer vision involve statistically analyzing an important class of constrained, non-negative functions, including probability density functions (in texture analysis), dynamic time-warping functions (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 metric that provides closed-form expressions for geodesies and distances, and allows fast computation of sample statistics. To demonstrate this approach, we present an application in planar shape classification.