Polynomial Regression on Riemannian Manifolds

2012/01/11 by Jacob Hinkle, Prasanna Muralidharan, Hinkle, Jacob +5 · 2 citations
Mathematics · Medicine · #Clusterin in disease pathology #Computer Vision and Pattern Recognition (cs.CV) #Differential Geometry (math.DG) #FOS: Computer and information sciences #FOS: Mathematics #Morphological variations and asymmetry #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.1201.2395

openalex publication_date 2012/01/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Citations

• Shape Manifolds, Procrustean Metrics, and Complex Projective Spaces

Cited by

• DFNN: A Deep Fréchet Neural Network Framework for Learning Metric-Space-Valued Responses
• Local Fr'echet Regression via RKHS embedding and Its Applications to Data Analysis on Manifolds

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