Nonparametric statistics on manifolds with applications to shape spaces

TL;DR

This paper introduces recent methods and new results for analyzing probability distributions on manifolds, with a focus on 2-D shape spaces of landmarks, advancing statistical tools for complex geometric data.

Contribution

It develops novel nonparametric statistical techniques specifically tailored for shape spaces, expanding the analytical capabilities for geometric and shape data.

Findings

New methodologies for probability distributions on manifolds

Application to 2-D shape space of landmarks

Enhanced statistical analysis tools for shape data

Abstract

This article presents certain recent methodologies and some new results for the statistical analysis of probability distributions on manifolds. An important example considered in some detail here is the 2-D shape space of k-ads, comprising all configurations of $k$ planar landmarks ($k>2$)-modulo translation, scaling and rotation.