We give a nonparametric methodology for hypothesis testing for equality of extrinsic mean objects on a manifold embedded in a numerical spaces. The results obtained in the general setting are detailed further in the case of 3D projective shapes represented in a space of symmetric matrices via the quadratic Veronese-Whitney (VW) embedding. Large sample and nonparametric bootstrap confidence regions are derived for the common VW-mean of random projective shapes for finite 3D configurations. As an example, the VW MANOVA testing methodology is applied to the multi-sample mean problem for independent projective shapes of 3D facial configurations retrieved from digital images, via Agisoft PhotoScan technology.
@article{arxiv.1704.03106,
title = {3D mean Projective Shape Difference for Face Differentiation from Multiple Digital Camera Images},
author = {K. D. Yao and V. Patrangenaru and D. Lester},
journal= {arXiv preprint arXiv:1704.03106},
year = {2017}
}