Polynomial Regression on Riemannian Manifolds
This work addresses shape analysis problems in medical imaging and biology by extending regression methods to non-Euclidean spaces, though it appears incremental as it adapts existing polynomial regression to Riemannian contexts.
The paper developed parametric polynomial regression theory for Riemannian manifolds and Lie groups, applying it to shape analysis in Kendall shape space and demonstrating results on rat skull growth and corpus callosum aging data.
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.