# A function space perspective on stochastic shape evolution

arXiv: https://arxiv.org/abs/2302.05382 · HTML: https://mlsanity.com/paper/2302.05382/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 31 references that are in the map.
- First posted on arXiv 10 Feb 2023.

## Builds on (most cited first, 8 of 8)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Elastic shape analysis of surfaces with second-order Sobolev metrics: a comprehensive numerical framework](https://mlsanity.com/paper/2204.04238/) (2022)
- [Numerical Inversion of SRNF Maps for Elastic Shape Analysis of Genus-Zero Surfaces](https://mlsanity.com/paper/1610.04531/) (2016)
- [Shape Analysis of Surfaces Using General Elastic Metrics](https://mlsanity.com/paper/1910.02045/) (2019)
- [Diffusion bridges for stochastic Hamiltonian systems and shape evolutions](https://mlsanity.com/paper/2002.00885/) (2020)
- [A Geometric Framework for Stochastic Shape Analysis](https://mlsanity.com/paper/1703.09971/) (2017)
- [Bridge Simulation and Metric Estimation on Landmark Manifolds](https://mlsanity.com/paper/1705.10943/) (2017)

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

- [Stochastics of shapes and Kunita flows](https://mlsanity.com/paper/2512.11676/) (2025)

## Abstract (arXiv)

Modelling randomness in shape data, for example, the evolution of shapes of organisms in biology, requires stochastic models of shapes. This paper presents a new stochastic shape model based on a description of shapes as functions in a Sobolev space. Using an explicit orthonormal basis as a reference frame for the noise, the model is independent of the parameterisation of the mesh. We define the stochastic model, explore its properties, and illustrate examples of stochastic shape evolutions using the resulting numerical framework.