Learning from landmarks, curves, surfaces, and shapes in Geomstats

TL;DR

The paper introduces the shape module of Geomstats, a Python package that provides tools for analyzing and performing statistical operations on shapes represented as landmarks, curves, and surfaces using Riemannian geometry.

Contribution

It presents a comprehensive implementation of shape spaces and geometric structures in Geomstats, enabling advanced shape analysis and machine learning applications.

Findings

Implementation of shape spaces like Kendall and elastic spaces

Tools for comparing, averaging, and interpolating shapes

Application examples demonstrating shape analysis capabilities

Abstract

We introduce the shape module of the Python package Geomstats to analyze shapes of objects represented as landmarks, curves and surfaces across fields of natural sciences and engineering. The shape module first implements widely used shape spaces, such as the Kendall shape space, as well as elastic spaces of discrete curves and surfaces. The shape module further implements the abstract mathematical structures of group actions, fiber bundles, quotient spaces and associated Riemannian metrics which allow users to build their own shape spaces. The Riemannian geometry tools enable users to compare, average, interpolate between shapes inside a given shape space. These essential operations can then be leveraged to perform statistics and machine learning on shape data. We present the object-oriented implementation of the shape module along with illustrative examples and show how it can be used to perform statistics and machine learning on shape spaces.