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 geodesics and distances, and allows an
efficient computation of statistics. We compare this metric with
some previously used metrics and present an application in planar
shape classification.