# Hierarchical Uncertainty Estimation for Learning-based Registration in Neuroimaging

arXiv: https://arxiv.org/abs/2410.09299 · HTML: https://mlsanity.com/paper/2410.09299/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 68 references that are in the map.
- First posted on arXiv 11 Oct 2024.

## Builds on (most cited first, 29 of 29)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Spatial Transformer Networks](https://mlsanity.com/paper/1506.02025/) (2015)
- [A Review of Uncertainty Quantification in Deep Learning: Techniques, Applications and Challenges](https://mlsanity.com/paper/2011.06225/) (2020)
- [A Survey of Uncertainty in Deep Neural Networks](https://mlsanity.com/paper/2107.03342/) (2021)
- [VoxelMorph: A Learning Framework for Deformable Medical Image Registration](https://mlsanity.com/paper/1809.05231/) (2018)
- [Predictive Uncertainty Estimation via Prior Networks](https://mlsanity.com/paper/1802.10501/) (2018)
- [SynthSeg: Segmentation of brain MRI scans of any contrast and resolution without retraining](https://mlsanity.com/paper/2107.09559/) (2021)
- [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)
- [Bayesian Convolutional Neural Networks with Bernoulli Approximate Variational Inference](https://mlsanity.com/paper/1506.02158/) (2015)
- [SynthMorph: learning contrast-invariant registration without acquired images](https://mlsanity.com/paper/2004.10282/) (2020)
- [Quicksilver: Fast Predictive Image Registration - a Deep Learning Approach](https://mlsanity.com/paper/1703.10908/) (2017)
- [Learning in an Uncertain World: Representing Ambiguity Through Multiple Hypotheses](https://mlsanity.com/paper/1612.00197/) (2016)
- [Learning Conditional Deformable Templates with Convolutional Networks](https://mlsanity.com/paper/1908.02738/) (2019)
- [Learning a Probabilistic Model for Diffeomorphic Registration](https://mlsanity.com/paper/1812.07460/) (2018)
- [Multi-Atlas Segmentation of Biomedical Images: A Survey](https://mlsanity.com/paper/1412.3421/) (2014)
- [Bayesian Image Quality Transfer with CNNs: Exploring Uncertainty in dMRI Super-Resolution](https://mlsanity.com/paper/1705.00664/) (2017)
- [A Robust and Interpretable Deep Learning Framework for Multi-modal Registration via Keypoints](https://mlsanity.com/paper/2304.09941/) (2023)
- [Unsupervised Probabilistic Deformation Modeling for Robust Diffeomorphic Registration](https://mlsanity.com/paper/1804.07172/) (2018)
- [Joint Progressive and Coarse-to-fine Registration of Brain MRI via Deformation Field Integration and Non-Rigid Feature Fusion](https://mlsanity.com/paper/2109.12384/) (2021)
- [On the Applicability of Registration Uncertainty](https://mlsanity.com/paper/1803.05266/) (2018)
- [Heteroscedastic Uncertainty Estimation Framework for Unsupervised Registration](https://mlsanity.com/paper/2312.00836/) (2023)
- [Registration by Regression (RbR): a framework for interpretable and flexible atlas registration](https://mlsanity.com/paper/2404.16781/) (2024)
- [Are Registration Uncertainty and Error Monotonically Associated](https://mlsanity.com/paper/1908.07709/) (2019)
- [LiftReg: Limited Angle 2D/3D Deformable Registration](https://mlsanity.com/paper/2203.05565/) (2022)
- [From Registration Uncertainty to Segmentation Uncertainty](https://mlsanity.com/paper/2403.05111/) (2024)

## Built on by (most cited first, 5 of 5)

- [A Modality-agnostic Multi-task Foundation Model for Human Brain Imaging](https://mlsanity.com/paper/2509.00549/) (2025)
- [UNSURF: Uncertainty Quantification for Cortical Surface Reconstruction of Clinical Brain MRIs](https://mlsanity.com/paper/2506.00498/) (2025)
- [Uncertainty Estimation for Pretrained Medical Image Registration Models via Transformation Equivariance](https://mlsanity.com/paper/2509.23355/) (2025)
- [Learning to Upscale 3D Segmentations in Neuroimaging](https://mlsanity.com/paper/2505.21697/) (2025)
- [Uncertainty-Aware Cortical Surface Reconstruction and Spherical Registration for Heterogeneous Brain MRI](https://mlsanity.com/paper/2610.16595/) (2026)

## Abstract (arXiv)

Over recent years, deep learning based image registration has achieved impressive accuracy in many domains, including medical imaging and, specifically, human neuroimaging with magnetic resonance imaging (MRI). However, the uncertainty estimation associated with these methods has been largely limited to the application of generic techniques (e.g., Monte Carlo dropout) that do not exploit the peculiarities of the problem domain, particularly spatial modeling. Here, we propose a principled way to propagate uncertainties (epistemic or aleatoric) estimated at the level of spatial location by these methods, to the level of global transformation models, and further to downstream tasks. Specifically, we justify the choice of a Gaussian distribution for the local uncertainty modeling, and then propose a framework where uncertainties spread across hierarchical levels, depending on the choice of transformation model. Experiments on publicly available data sets show that Monte Carlo dropout correlates very poorly with the reference registration error, whereas our uncertainty estimates correlate much better. Crucially, the results also show that uncertainty-aware fitting of transformations improves the registration accuracy of brain MRI scans. Finally, we illustrate how sampling from the posterior distribution of the transformations can be used to propagate uncertainties to downstream neuroimaging tasks. Code is available at: https://github.com/HuXiaoling/Regre4Regis.