# Interpretable deformable image registration: A geometric deep learning perspective

arXiv: https://arxiv.org/abs/2412.13294 · HTML: https://mlsanity.com/paper/2412.13294/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 45 references that are in the map.
- First posted on arXiv 17 Dec 2024.

## Builds on (most cited first, 19 of 19)

- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [PWC-Net: CNNs for Optical Flow Using Pyramid, Warping, and Cost Volume](https://mlsanity.com/paper/1709.02371/) (2017)
- [VoxelMorph: A Learning Framework for Deformable Medical Image Registration](https://mlsanity.com/paper/1809.05231/) (2018)
- [SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networks](https://mlsanity.com/paper/2006.10503/) (2020)
- [Large Deformation Diffeomorphic Image Registration with Laplacian Pyramid Networks](https://mlsanity.com/paper/2006.16148/) (2020)
- [Deep Learning in Medical Image Registration: A Survey](https://mlsanity.com/paper/1903.02026/) (2019)
- [Unsupervised Learning for Fast Probabilistic Diffeomorphic Registration](https://mlsanity.com/paper/1805.04605/) (2018)
- [Recursive Cascaded Networks for Unsupervised Medical Image Registration](https://mlsanity.com/paper/1907.12353/) (2019)
- [Conditional Deformable Image Registration with Convolutional Neural Network](https://mlsanity.com/paper/2106.12673/) (2021)
- [Dual-Stream Pyramid Registration Network](https://mlsanity.com/paper/1909.11966/) (2019)
- [A Point-Cloud Deep Learning Framework for Prediction of Fluid Flow Fields on Irregular Geometries](https://mlsanity.com/paper/2010.09469/) (2020)
- [U-Net vs Transformer: Is U-Net Outdated in Medical Image Registration?](https://mlsanity.com/paper/2208.04939/) (2022)
- [Accurate Point Cloud Registration with Robust Optimal Transport](https://mlsanity.com/paper/2111.00648/) (2021)
- [ModeT: Learning Deformable Image Registration via Motion Decomposition Transformer](https://mlsanity.com/paper/2306.05688/) (2023)
- [Coordinate Translator for Learning Deformable Medical Image Registration](https://mlsanity.com/paper/2203.03626/) (2022)
- [Non-iterative Coarse-to-fine Registration based on Single-pass Deep Cumulative Learning](https://mlsanity.com/paper/2206.12596/) (2022)
- [Recurrent Registration Neural Networks for Deformable Image Registration](https://mlsanity.com/paper/1906.09988/) (2019)
- [Deep learning based geometric registration for medical images: How accurate can we get without visual features?](https://mlsanity.com/paper/2103.00885/) (2021)

## Abstract (arXiv)

Deformable image registration poses a challenging problem where, unlike most deep learning tasks, a complex relationship between multiple coordinate systems has to be considered. Although data-driven methods have shown promising capabilities to model complex non-linear transformations, existing works employ standard deep learning architectures assuming they are general black-box solvers. We argue that understanding how learned operations perform pattern-matching between the features in the source and target domains is the key to building robust, data-efficient, and interpretable architectures. We present a theoretical foundation for designing an interpretable registration framework: separated feature extraction and deformation modeling, dynamic receptive fields, and a data-driven deformation functions awareness of the relationship between both spatial domains. Based on this foundation, we formulate an end-to-end process that refines transformations in a coarse-to-fine fashion. Our architecture employs spatially continuous deformation modeling functions that use geometric deep-learning principles, therefore avoiding the problematic approach of resampling to a regular grid between successive refinements of the transformation. We perform a qualitative investigation to highlight interesting interpretability properties of our architecture. We conclude by showing significant improvement in performance metrics over state-of-the-art approaches for both mono- and multi-modal inter-subject brain registration, as well as the challenging task of longitudinal retinal intra-subject registration. We make our code publicly available