# Moment evolution equations and moment matching for stochastic image EPDiff

arXiv: https://arxiv.org/abs/2110.03337 · HTML: https://mlsanity.com/paper/2110.03337/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 45 references that are in the map.
- First posted on arXiv 7 Oct 2021.

## Builds on (most cited first, 6 of 6)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Metric Learning for Image Registration](https://mlsanity.com/paper/1904.09524/) (2019)
- [Region-specific Diffeomorphic Metric Mapping](https://mlsanity.com/paper/1906.00139/) (2019)
- [A Geometric Framework for Stochastic Shape Analysis](https://mlsanity.com/paper/1703.09971/) (2017)
- [String Methods for Stochastic Image and Shape Matching](https://mlsanity.com/paper/1805.06038/) (2018)
- [Stochastic Image Deformation in Frequency Domain and Parameter Estimation using Moment Evolutions](https://mlsanity.com/paper/1812.05537/) (2018)

## Abstract (arXiv)

Models of stochastic image deformation allow study of time-continuous stochastic effects transforming images by deforming the image domain. Applications include longitudinal medical image analysis with both population trends and random subject specific variation. Focusing on a stochastic extension of the LDDMM models with evolutions governed by a stochastic EPDiff equation, we use moment approximations of the corresponding Ito diffusion to construct estimators for statistical inference in the full stochastic model. We show that this approach, when efficiently implemented with automatic differentiation tools, can successfully estimate parameters encoding the spatial correlation of the noise fields on the image.