  In this paper one develops nonparametric inference procedures for comparing
two extrinsic antimeans on compact manifolds. Based on recent Central limit
theorems for extrinsic sample antimeans w.r.t. an arbitrary embedding of a
compact manifold in a Euclidean space, one derives an asymptotic chi square
test for the equality of two extrinsic antimeans. Applications are given to
distributions on complex projective space $CP^{k-2}$ w.r.t. the
Veronese-Whitney embedding, that is a submanifold representation for the
Kendall planar shape space. Two medical imaging analysis applications are also
given.
