# Uncertainty quantification in non-rigid image registration via stochastic gradient Markov chain Monte Carlo

arXiv: https://arxiv.org/abs/2110.13289 · HTML: https://mlsanity.com/paper/2110.13289/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 60 references that are in the map.
- First posted on arXiv 25 Oct 2021.

## Builds on (most cited first, 18 of 18)

- [VoxelMorph: A Learning Framework for Deformable Medical Image Registration](https://mlsanity.com/paper/1809.05231/) (2018)
- [Stochastic Gradient Descent as Approximate Bayesian Inference](https://mlsanity.com/paper/1704.04289/) (2017)
- [Cyclical Stochastic Gradient MCMC for Bayesian Deep Learning](https://mlsanity.com/paper/1902.03932/) (2019)
- [Unsupervised Learning of Probabilistic Diffeomorphic Registration for Images and Surfaces](https://mlsanity.com/paper/1903.03545/) (2019)
- [A Deep Learning Framework for Unsupervised Affine and Deformable Image Registration](https://mlsanity.com/paper/1809.06130/) (2018)
- [An Unsupervised Learning Model for Deformable Medical Image Registration](https://mlsanity.com/paper/1802.02604/) (2018)
- [Learning Non-Convergent Non-Persistent Short-Run MCMC Toward Energy-Based Model](https://mlsanity.com/paper/1904.09770/) (2019)
- [Unsupervised Learning for Fast Probabilistic Diffeomorphic Registration](https://mlsanity.com/paper/1805.04605/) (2018)
- [Learning a Probabilistic Model for Diffeomorphic Registration](https://mlsanity.com/paper/1812.07460/) (2018)
- [Closing the Gap between Deep and Conventional Image Registration using Probabilistic Dense Displacement Networks](https://mlsanity.com/paper/1907.10931/) (2019)
- [Image-and-Spatial Transformer Networks for Structure-Guided Image Registration](https://mlsanity.com/paper/1907.09200/) (2019)
- [Metric Learning for Image Registration](https://mlsanity.com/paper/1904.09524/) (2019)
- [Region-specific Diffeomorphic Metric Mapping](https://mlsanity.com/paper/1906.00139/) (2019)
- [Bridging the Gap between Stochastic Gradient MCMC and Stochastic Optimization](https://mlsanity.com/paper/1512.07962/) (2015)
- [On the Applicability of Registration Uncertainty](https://mlsanity.com/paper/1803.05266/) (2018)
- [Probabilistic Multilayer Regularization Network for Unsupervised 3D Brain Image Registration](https://mlsanity.com/paper/1907.01922/) (2019)
- [Probabilistic Diffeomorphic Registration: Representing Uncertainty](https://mlsanity.com/paper/1701.03266/) (2017)
- [Unsupervised Deep-Learning Based Deformable Image Registration: A Bayesian Framework](https://mlsanity.com/paper/2008.03949/) (2020)

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

- [PULPo: Probabilistic Unsupervised Laplacian Pyramid Registration](https://mlsanity.com/paper/2407.10567/) (2024)
- [Structured SIR: Efficient and Expressive Importance-Weighted Inference for High-Dimensional Image Registration](https://mlsanity.com/paper/2603.17415/) (2026)
- [BINDER: A Latent Variable Model for Probabilistic Medical Image Registration](https://mlsanity.com/paper/2609.19875/) (2026)

## Abstract (arXiv)

We develop a new Bayesian model for non-rigid registration of three-dimensional medical images, with a focus on uncertainty quantification. Probabilistic registration of large images with calibrated uncertainty estimates is difficult for both computational and modelling reasons. To address the computational issues, we explore connections between the Markov chain Monte Carlo by backpropagation and the variational inference by backpropagation frameworks, in order to efficiently draw samples from the posterior distribution of transformation parameters. To address the modelling issues, we formulate a Bayesian model for image registration that overcomes the existing barriers when using a dense, high-dimensional, and diffeomorphic transformation parametrisation. This results in improved calibration of uncertainty estimates. We compare the model in terms of both image registration accuracy and uncertainty quantification to VoxelMorph, a state-of-the-art image registration model based on deep learning.