# Learning Homeomorphic Image Registration via Conformal-Invariant Hyperelastic Regularisation

arXiv: https://arxiv.org/abs/2303.08113 · HTML: https://mlsanity.com/paper/2303.08113/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 72 references that are in the map.
- First posted on arXiv 14 Mar 2023.

## Builds on (most cited first, 26 of 26)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Fully Convolutional Networks for Semantic Segmentation](https://mlsanity.com/paper/1411.4038/) (2014)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [3D U-Net: Learning Dense Volumetric Segmentation from Sparse Annotation](https://mlsanity.com/paper/1606.06650/) (2016)
- [VoxelMorph: A Learning Framework for Deformable Medical Image Registration](https://mlsanity.com/paper/1809.05231/) (2018)
- [FlowNet3D: Learning Scene Flow in 3D Point Clouds](https://mlsanity.com/paper/1806.01411/) (2018)
- [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)
- [Large Deformation Diffeomorphic Image Registration with Laplacian Pyramid Networks](https://mlsanity.com/paper/2006.16148/) (2020)
- [Recursive Cascaded Networks for Unsupervised Medical Image Registration](https://mlsanity.com/paper/1907.12353/) (2019)
- [CycleMorph: Cycle Consistent Unsupervised Deformable Image Registration](https://mlsanity.com/paper/2008.05772/) (2020)
- [DeepAtlas: Joint Semi-Supervised Learning of Image Registration and Segmentation](https://mlsanity.com/paper/1904.08465/) (2019)
- [Unsupervised 3D End-to-End Medical Image Registration with Volume Tweening Network](https://mlsanity.com/paper/1902.05020/) (2019)
- [Closing the Gap between Deep and Conventional Image Registration using Probabilistic Dense Displacement Networks](https://mlsanity.com/paper/1907.10931/) (2019)
- [BIRNet: Brain Image Registration Using Dual-Supervised Fully Convolutional Networks](https://mlsanity.com/paper/1802.04692/) (2018)
- [CNN-based Lung CT Registration with Multiple Anatomical Constraints](https://mlsanity.com/paper/2011.14372/) (2020)
- [Unsupervised Deformable Image Registration Using Cycle-Consistent CNN](https://mlsanity.com/paper/1907.01319/) (2019)
- [Diffeomorphic Image Registration with Neural Velocity Field](https://mlsanity.com/paper/2202.12498/) (2022)
- [Landmark and Intensity Based Registration with Large Deformations via Quasi-conformal Maps](https://mlsanity.com/paper/1310.1710/) (2013)
- [Probabilistic Multilayer Regularization Network for Unsupervised 3D Brain Image Registration](https://mlsanity.com/paper/1907.01922/) (2019)
- [3D Convolutional Neural Networks Image Registration Based on Efficient Supervised Learning from Artificial Deformations](https://mlsanity.com/paper/1908.10235/) (2019)
- [PC-SwinMorph: Patch Representation for Unsupervised Medical Image Registration and Segmentation](https://mlsanity.com/paper/2203.05684/) (2022)
- [Rethinking Medical Image Reconstruction via Shape Prior, Going Deeper and Faster: Deep Joint Indirect Registration and Reconstruction](https://mlsanity.com/paper/1912.07648/) (2019)
- [Predicting respiratory motion for real-time tumour tracking in radiotherapy](https://mlsanity.com/paper/1508.00749/) (2015)
- [Fast Predictive Multimodal Image Registration](https://mlsanity.com/paper/1703.10902/) (2017)

## Built on by (most cited first, 2 of 2)

- [Enhancing Fourier Neural Operators with Local Spatial Features](https://mlsanity.com/paper/2503.17797/) (2025)
- [EADReg: Probabilistic Correspondence Generation with Efficient Autoregressive Diffusion Model for Outdoor Point Cloud Registration](https://mlsanity.com/paper/2411.15271/) (2024)

## Abstract (arXiv)

Deformable image registration is a fundamental task in medical image analysis and plays a crucial role in a wide range of clinical applications. Recently, deep learning-based approaches have been widely studied for deformable medical image registration and achieved promising results. However, existing deep learning image registration techniques do not theoretically guarantee topology-preserving transformations. This is a key property to preserve anatomical structures and achieve plausible transformations that can be used in real clinical settings. We propose a novel framework for deformable image registration. Firstly, we introduce a novel regulariser based on conformal-invariant properties in a nonlinear elasticity setting. Our regulariser enforces the deformation field to be smooth, invertible and orientation-preserving. More importantly, we strictly guarantee topology preservation yielding to a clinical meaningful registration. Secondly, we boost the performance of our regulariser through coordinate MLPs, where one can view the to-be-registered images as continuously differentiable entities. We demonstrate, through numerical and visual experiments, that our framework is able to outperform current techniques for image registration.