đ¤ AI Summary
This work addresses the lack of effective support for Kendallâs 3D shape space in existing Python librariesâsuch as Geomstatsâwhich has hindered the practical application of Riemannian geometry in three-dimensional shape analysis. We present the first systematic implementation of an efficient and user-friendly Python toolkit tailored specifically to Kendallâs 3D shape space, enabling scale-, position-, and orientation-invariant shape modeling and statistical analysis. By providing a ready-to-use, open-source solution for shape statistics on manifolds, this contribution fills a critical software gap in advanced 3D shape analysis, substantially lowering the barrier to entry for researchers, improving computational efficiency, and enhancing the reproducibility of results.
đ 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.