Two Sample Test for Extrinsic Antimeans on Planar Kendall Shape Spaces with an Application to Medical Imaging

Abstract: In this paper one develops nonparametric inference procedures for comparing two extrinsic antimeans on compact manifolds. Based on recent Central limit theorems for extrinsic sample antimeans w.r.t. an arbitrary embedding of a compact manifold in a Euclidean space, one derives an asymptotic chi square test for the equality of two extrinsic antimeans. Applications are given to distributions on complex projective space $CP^{k-2}$ w.r.t. the Veronese-Whitney embedding, that is a submanifold representation for the Kendall planar shape space. Two medical imaging analysis applications are also given.