In this article we develop a nonparametric methodology for estimating the mean change for matched samples on a Lie group. We then notice that for k ≥ 5, a manifold of projective shapes k-ads in 3D has a structure of 3k − 15 dimensional Lie group that is equivariantly embedded in an Euclidean space, therefore testing for mean change amounts to a one sample test for extrinsic means on this Lie gr...
