# NPBDREG: Uncertainty Assessment in Diffeomorphic Brain MRI Registration using a Non-parametric Bayesian Deep-Learning Based Approach

arXiv: https://arxiv.org/abs/2108.06771 · HTML: https://mlsanity.com/paper/2108.06771/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 30 references that are in the map.
- First posted on arXiv 15 Aug 2021.

## Builds on (most cited first, 15 of 15)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [Deep Exploration via Bootstrapped DQN](https://mlsanity.com/paper/1602.04621/) (2016)
- [Hands-on Bayesian Neural Networks -- a Tutorial for Deep Learning Users](https://mlsanity.com/paper/2007.06823/) (2020)
- [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)
- [Adding Gradient Noise Improves Learning for Very Deep Networks](https://mlsanity.com/paper/1511.06807/) (2015)
- [Unsupervised Learning for Fast Probabilistic Diffeomorphic Registration](https://mlsanity.com/paper/1805.04605/) (2018)
- [Quicksilver: Fast Predictive Image Registration - a Deep Learning Approach](https://mlsanity.com/paper/1703.10908/) (2017)
- [Learning Conditional Deformable Templates with Convolutional Networks](https://mlsanity.com/paper/1908.02738/) (2019)
- [A Bayesian Perspective on the Deep Image Prior](https://mlsanity.com/paper/1904.07457/) (2019)
- [On the Applicability of Registration Uncertainty](https://mlsanity.com/paper/1803.05266/) (2018)
- [ProsRegNet: A Deep Learning Framework for Registration of MRI and Histopathology Images of the Prostate](https://mlsanity.com/paper/2012.00991/) (2020)
- [Unsupervised Abnormality Detection through Mixed Structure Regularization (MSR) in Deep Sparse Autoencoders](https://mlsanity.com/paper/1902.11036/) (2019)

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

- [A review of uncertainty quantification in medical image analysis: probabilistic and non-probabilistic methods](https://mlsanity.com/paper/2310.06873/) (2023)
- [NPB-REC: A Non-parametric Bayesian Deep-learning Approach for Undersampled MRI Reconstruction with Uncertainty Estimation](https://mlsanity.com/paper/2404.04550/) (2024)
- [NPB-REC: Non-parametric Assessment of Uncertainty in Deep-learning-based MRI Reconstruction from Undersampled Data](https://mlsanity.com/paper/2208.03966/) (2022)
- [An Uncertainty Estimation Framework for Dose Accumulation in Adaptive Radiotherapy: Application to CBCT-Guided Radiotherapy for Cervical Cancer](https://mlsanity.com/paper/2606.11012/) (2026)

## Abstract (arXiv)

Quantification of uncertainty in deep-neural-networks (DNN) based image registration algorithms plays a critical role in the deployment of image registration algorithms for clinical applications such as surgical planning, intraoperative guidance, and longitudinal monitoring of disease progression or treatment efficacy as well as in research-oriented processing pipelines. Currently available approaches for uncertainty estimation in DNN-based image registration algorithms may result in sub-optimal clinical decision making due to potentially inaccurate estimation of the uncertainty of the registration stems for the assumed parametric distribution of the registration latent space. We introduce NPBDREG, a fully non-parametric Bayesian framework for uncertainty estimation in DNN-based deformable image registration by combining an Adam optimizer with stochastic gradient Langevin dynamics (SGLD) to characterize the underlying posterior distribution through posterior sampling. Thus, it has the potential to provide uncertainty estimates that are highly correlated with the presence of out of distribution data. We demonstrated the added-value of NPBDREG, compared to the baseline probabilistic VoxelMorph model (PrVXM), on brain MRI image registration using 390 image pairs from four publicly available databases: MGH10, CMUC12, ISBR18 and LPBA40. The NPBDREG shows a better correlation of the predicted uncertainty with out-of-distribution data (r>0.95 vs. r<0.5) as well as a 7.3%improvement in the registration accuracy (Dice score, 0.74 vs. 0.69, p ll 0.01), and 18% improvement in registration smoothness (percentage of folds in the deformation field, 0.014 vs. 0.017, p ll 0.01). Finally, NPBDREG demonstrated a better generalization capability for data corrupted by a mixed structure noise (Dice score of 0.73 vs. 0.69, p ll 0.01) compared to the baseline PrVXM approach.