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

TL;DR

This paper develops nonparametric tests for comparing two extrinsic antimeans on shape spaces, with applications in medical imaging, using recent CLTs and chi-square tests on embedded manifolds.

Contribution

It introduces a new asymptotic chi-square test for extrinsic antimeans on compact manifolds, applicable to shape analysis and medical imaging.

Findings

Derived an asymptotic chi-square test for extrinsic antimeans.

Applied the test to complex projective space and Kendall shape space.

Demonstrated applications in medical imaging analysis.

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.