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We give a nonparametric methodology for hypothesis testing for equality ofextrinsic mean objects on a manifold embedded in a numerical spaces. Theresults obtained in the general setting are detailed further in the case of 3Dprojective shapes represented in a space of symmetric matrices via thequadratic Veronese-Whitney (VW) embedding. Large sample and nonparametricbootstrap confidence regions are derived for the common VW-mean of randomprojective shapes for finite 3D configurations. As an example, the VW MANOVAtesting methodology is applied to the multi-sample mean problem for independentprojective shapes of $3D$ facial configurations retrieved from digital images,via Agisoft PhotoScan technology.

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