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

arXiv: https://arxiv.org/abs/2406.10437 · HTML: https://mlsanity.com/paper/2406.10437/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Jun 2024.

## Built on by (most cited first, 1 of 1)

- [TAGTorch: A PyTorch Library for Geometry, Topology, and Symmetry-Aware Machine Learning](https://mlsanity.com/paper/2607.28755/) (2026)

## Abstract (arXiv)

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.