# Registration by Regression (RbR): a framework for interpretable and flexible atlas registration

arXiv: https://arxiv.org/abs/2404.16781 · HTML: https://mlsanity.com/paper/2404.16781/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 39 references that are in the map.
- First posted on arXiv 25 Apr 2024.

## Builds on (most cited first, 12 of 12)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [VoxelMorph: A Learning Framework for Deformable Medical Image Registration](https://mlsanity.com/paper/1809.05231/) (2018)
- [A Deep Learning Framework for Unsupervised Affine and Deformable Image Registration](https://mlsanity.com/paper/1809.06130/) (2018)
- [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 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)
- [Affine Medical Image Registration with Coarse-to-Fine Vision Transformer](https://mlsanity.com/paper/2203.15216/) (2022)
- [Learning the Effect of Registration Hyperparameters with HyperMorph](https://mlsanity.com/paper/2203.16680/) (2022)
- [A Robust and Interpretable Deep Learning Framework for Multi-modal Registration via Keypoints](https://mlsanity.com/paper/2304.09941/) (2023)
- [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)
- [Anatomy-aware and acquisition-agnostic joint registration with SynthMorph](https://mlsanity.com/paper/2301.11329/) (2023)

## Built on by (most cited first, 8 of 8)

- [MultiMorph: On-demand Atlas Construction](https://mlsanity.com/paper/2504.00247/) (2025)
- [A Modality-agnostic Multi-task Foundation Model for Human Brain Imaging](https://mlsanity.com/paper/2509.00549/) (2025)
- [Hierarchical Uncertainty Estimation for Learning-based Registration in Neuroimaging](https://mlsanity.com/paper/2410.09299/) (2024)
- [Uncertainty Estimation for Pretrained Medical Image Registration Models via Transformation Equivariance](https://mlsanity.com/paper/2509.23355/) (2025)
- [Reference-Free 3D Reconstruction of Brain Dissection Slabs via Learned Atlas Coordinates](https://mlsanity.com/paper/2503.09963/) (2025)
- [Learning to Upscale 3D Segmentations in Neuroimaging](https://mlsanity.com/paper/2505.21697/) (2025)
- [Equivariant symmetry-aware head pose estimation for fetal MRI](https://mlsanity.com/paper/2512.04890/) (2025)
- [textttDisMorph: learning to disentangle technical distortions from true biological change](https://mlsanity.com/paper/2608.08173/) (2026)

## Abstract (arXiv)

In human neuroimaging studies, atlas registration enables mapping MRI scans to a common coordinate frame, which is necessary to aggregate data from multiple subjects. Machine learning registration methods have achieved excellent speed and accuracy but lack interpretability and flexibility at test time (since their deformation model is fixed). More recently, keypoint-based methods have been proposed to tackle these issues, but their accuracy is still subpar, particularly when fitting nonlinear transforms. Here we propose Registration by Regression (RbR), a novel atlas registration framework that: is highly robust and flexible; can be trained with cheaply obtained data; and operates on a single channel, such that it can also be used as pretraining for other tasks. RbR predicts the (x, y, z) atlas coordinates for every voxel of the input scan (i.e., every voxel is a keypoint), and then uses closed-form expressions to quickly fit transforms using a wide array of possible deformation models, including affine and nonlinear (e.g., Bspline, Demons, invertible diffeomorphic models, etc.). Robustness is provided by the large number of voxels informing the registration and can be further increased by robust estimators like RANSAC. Experiments on independent public datasets show that RbR yields more accurate registration than competing keypoint approaches, over a wide range of deformation models.