# Shape spaces: From geometry to biological plausibility

arXiv: https://arxiv.org/abs/2205.01237 · HTML: https://mlsanity.com/paper/2205.01237/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 May 2022.

## Built on by (most cited first, 3 of 3)

- [BaRe-ESA: A Riemannian Framework for Unregistered Human Body Shapes](https://mlsanity.com/paper/2211.13185/) (2022)
- [Basis restricted elastic shape analysis on the space of unregistered surfaces](https://mlsanity.com/paper/2311.04382/) (2023)
- [Automatic classification of deformable shapes](https://mlsanity.com/paper/2211.02530/) (2022)

## Abstract (arXiv)

This paper reviews several Riemannian metrics and evolution equations in the context of diffeomorphic shape analysis. After a short review of of various approaches at building Riemannian spaces of shapes, with a special focus on the foundations of the large deformation diffeomorphic metric mapping algorithm, the attention is turned to elastic metrics, and to growth models that can be derived from it. In the latter context, a new class of metrics, involving the optimization of a growth tensor, is introduced and some of its properties are studied.