Anti-MANOVA on Compact Manifolds with Applications to 3D Projective Shape Analysis

TL;DR

This paper develops hypothesis testing methods for extrinsic antimeans on compact manifolds, using asymptotic and bootstrap techniques, with an application to 3D shape analysis of facial images.

Contribution

It introduces new statistical tests for extrinsic antimeans on compact manifolds, applicable to both large and small samples, with practical application in 3D projective shape analysis.

Findings

Asymptotic distributions enable large-sample hypothesis testing.

Bootstrap methods provide small-sample inference.

Application demonstrates face differentiation using 3D shape data.

Abstract

Methods of hypotheses testing for equality of extrinsic antimeans on compact manifolds are unveiled in this paper. The two and multiple sample problem for antimeans on compact manifolds is addressed for large samples via asymptotic distributions, as well as for small samples using nonparametric bootstrap. An example of face differentiation using 3D VW antimean projective shape analysis for data extracted from digital camera images is also given.