3D mean Projective Shape Difference for Face Differentiation from Multiple Digital Camera Images

TL;DR

This paper introduces a nonparametric hypothesis testing method for 3D projective shape comparison, specifically applied to facial configurations from digital images, using a manifold embedding and bootstrap techniques.

Contribution

It develops a novel nonparametric framework for testing equality of 3D projective shape means on a manifold, with applications to facial shape analysis from digital images.

Findings

Derived bootstrap confidence regions for 3D shape means.

Applied VW MANOVA to facial shape data from digital images.

Validated methodology with real 3D facial configuration data.

Abstract

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.