Polynomial regression on riemannian manifolds

Authors:
Jacob Hinkle;Prasanna Muralidharan;P. Thomas Fletcher;Sarang Joshi
Affiliations:
SCI Institute, University of Utah, Salt Lake City, UT;SCI Institute, University of Utah, Salt Lake City, UT;SCI Institute, University of Utah, Salt Lake City, UT;SCI Institute, University of Utah, Salt Lake City, UT
Venue:
ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part III
Year:
2012

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Abstract

In this paper we develop the theory of parametric polynomial regression in Riemannian manifolds. The theory enables parametric analysis in a wide range of applications, including rigid and non-rigid kinematics as well as shape change of organs due to growth and aging. 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 and the analysis of the shape changes associated with aging of the corpus callosum from the OASIS Alzheimer's study.