A Python implementation of some geometric tools on Kendall 3D shape space for practical applications

TL;DR

This paper introduces a Python library that implements geometric tools for Kendall's 3D shape space, facilitating practical shape analysis by translating complex Riemannian geometry into accessible computational methods.

Contribution

The work provides new Python utilities specifically designed for 3D shape analysis within Kendall's shape space, filling a gap in existing manifold-based statistical tools.

Findings

Developed efficient algorithms for 3D shape analysis

Enhanced accessibility of Riemannian geometric methods

Enabled practical applications in shape analysis research

Abstract

This work addresses the challenge of analyzing geometric structures using Kendall's 3D Shape Space. While Riemannian geometry provides a robust framework for shape analysis (independent of scale, position, and orientation) the transition from theoretical manifolds to practical computational workflows remains difficult. Although Geomstats is currently the leading Python library for manifold-based statistics, it lacks specific utilities required for advanced 3D shape analysis. This article introduces tools designed to bridge this gap, translating complex mathematical abstractions into efficient, accessible software solutions for researchers.