# Unsupervised Deep-Learning Based Deformable Image Registration: A Bayesian Framework

arXiv: https://arxiv.org/abs/2008.03949 · HTML: https://mlsanity.com/paper/2008.03949/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Aug 2020.

## Built on by (most cited first, 2 of 2)

- [Uncertainty quantification in non-rigid image registration via stochastic gradient Markov chain Monte Carlo](https://mlsanity.com/paper/2110.13289/) (2021)
- [NPB-REC: Non-parametric Assessment of Uncertainty in Deep-learning-based MRI Reconstruction from Undersampled Data](https://mlsanity.com/paper/2208.03966/) (2022)

## Abstract (arXiv)

Unsupervised deep-learning (DL) models were recently proposed for deformable image registration tasks. In such models, a neural-network is trained to predict the best deformation field by minimizing some dissimilarity function between the moving and the target images. After training on a dataset without reference deformation fields available, such a model can be used to rapidly predict the deformation field between newly seen moving and target images. Currently, the training process effectively provides a point-estimate of the network weights rather than characterizing their entire posterior distribution. This may result in a potential over-fitting which may yield sub-optimal results at inference phase, especially for small-size datasets, frequently present in the medical imaging domain. We introduce a fully Bayesian framework for unsupervised DL-based deformable image registration. Our method provides a principled way to characterize the true posterior distribution, thus, avoiding potential over-fitting. We used stochastic gradient Langevin dynamics (SGLD) to conduct the posterior sampling, which is both theoretically well-founded and computationally efficient. We demonstrated the added-value of our Basyesian unsupervised DL-based registration framework on the MNIST and brain MRI (MGH10) datasets in comparison to the VoxelMorph unsupervised DL-based image registration framework. Our experiments show that our approach provided better estimates of the deformation field by means of improved mean-squared-error (0.0063 vs. 0.0065) and Dice coefficient (0.73 vs. 0.71) for the MNIST and the MGH10 datasets respectively. Further, our approach provides an estimate of the uncertainty in the deformation-field by characterizing the true posterior distribution.