  In this paper we develop the theory of parametric polynomial regression in
Riemannian manifolds and Lie groups. We show application of Riemannian
polynomial regression to shape analysis in Kendall shape space. Results are
presented, showing the power of polynomial regression on the classic rat skull
growth data of Bookstein as well as the analysis of the shape changes
associated with aging of the corpus callosum from the OASIS Alzheimer's study.
