# Probabilistic Diffeomorphic Registration: Representing Uncertainty

arXiv: https://arxiv.org/abs/1701.03266 · HTML: https://mlsanity.com/paper/1701.03266/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Jan 2017.

## Built on by (most cited first, 4 of 4)

- [Deep Decomposition for Stochastic Normal-Abnormal Transport](https://mlsanity.com/paper/2111.14777/) (2021)
- [Uncertainty quantification in non-rigid image registration via stochastic gradient Markov chain Monte Carlo](https://mlsanity.com/paper/2110.13289/) (2021)
- [Nonparametric Multi-shape Modeling with Uncertainty Quantification](https://mlsanity.com/paper/2206.09127/) (2022)
- [A practical probabilistic framework for deformable image registration uncertainty in radiotherapy dose propagation](https://mlsanity.com/paper/2606.09253/) (2026)

## Abstract (arXiv)

This paper presents a novel mathematical framework for representing uncertainty in large deformation diffeomorphic image registration. The Bayesian posterior distribution over the deformations aligning a moving and a fixed image is approximated via a variational formulation. A stochastic differential equation (SDE) modeling the deformations as the evolution of a time-varying velocity field leads to a prior density over deformations in the form of a Gaussian process. This permits estimating the full posterior distribution in order to represent uncertainty, in contrast to methods in which the posterior is approximated via Monte Carlo sampling or maximized in maximum a-posteriori (MAP) estimation. The frame-work is demonstrated in the case of landmark-based image registration, including simulated data and annotated pre and intra-operative 3D images.