# Spatial regularisation for improved accuracy and interpretability in keypoint-based registration

arXiv: https://arxiv.org/abs/2503.04499 · HTML: https://mlsanity.com/paper/2503.04499/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 38 references that are in the map.
- First posted on arXiv 6 Mar 2025.

## Builds on (most cited first, 16 of 16)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Understanding Contrastive Representation Learning through Alignment and Uniformity on the Hypersphere](https://mlsanity.com/paper/2005.10242/) (2020)
- [VoxelMorph: A Learning Framework for Deformable Medical Image Registration](https://mlsanity.com/paper/1809.05231/) (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)
- [Weakly-Supervised Convolutional Neural Networks for Multimodal Image Registration](https://mlsanity.com/paper/1807.03361/) (2018)
- [Numerical Coordinate Regression with Convolutional Neural Networks](https://mlsanity.com/paper/1801.07372/) (2018)
- [A survey on deep learning in medical image registration: new technologies, uncertainty, evaluation metrics, and beyond](https://mlsanity.com/paper/2307.15615/) (2023)
- [Real-time Deep Pose Estimation with Geodesic Loss for Image-to-Template Rigid Registration](https://mlsanity.com/paper/1803.05982/) (2018)
- [Image-and-Spatial Transformer Networks for Structure-Guided Image Registration](https://mlsanity.com/paper/1907.09200/) (2019)
- [BIRNet: Brain Image Registration Using Dual-Supervised Fully Convolutional Networks](https://mlsanity.com/paper/1802.04692/) (2018)
- [A Robust and Interpretable Deep Learning Framework for Multi-modal Registration via Keypoints](https://mlsanity.com/paper/2304.09941/) (2023)
- [Equivariant Filters for Efficient Tracking in 3D Imaging](https://mlsanity.com/paper/2103.10255/) (2021)
- [SE(3)-Equivariant and Noise-Invariant 3D Rigid Motion Tracking in Brain MRI](https://mlsanity.com/paper/2312.13534/) (2023)

## Built on by (most cited first, 1 of 1)

- [PointExplainer: Towards Transparent Parkinson's Disease Diagnosis](https://mlsanity.com/paper/2505.03833/) (2025)

## Abstract (arXiv)

Unsupervised registration strategies bypass requirements in ground truth transforms or segmentations by optimising similarity metrics between fixed and moved volumes. Among these methods, a recent subclass of approaches based on unsupervised keypoint detection stand out as very promising for interpretability. Specifically, these methods train a network to predict feature maps for fixed and moving images, from which explainable centres of mass are computed to obtain point clouds, that are then aligned in closed-form. However, the features returned by the network often yield spatially diffuse patterns that are hard to interpret, thus undermining the purpose of keypoint-based registration. Here, we propose a three-fold loss to regularise the spatial distribution of the features. First, we use the KL divergence to model features as point spread functions that we interpret as probabilistic keypoints. Then, we sharpen the spatial distributions of these features to increase the precision of the detected landmarks. Finally, we introduce a new repulsive loss across keypoints to encourage spatial diversity. Overall, our loss considerably improves the interpretability of the features, which now correspond to precise and anatomically meaningful landmarks. We demonstrate our three-fold loss in foetal rigid motion tracking and brain MRI affine registration tasks, where it not only outperforms state-of-the-art unsupervised strategies, but also bridges the gap with state-of-the-art supervised methods. Our code is available at https://github.com/BenBillot/spatial_regularisation.