# Fast Symmetric Diffeomorphic Image Registration with Convolutional Neural Networks

arXiv: https://arxiv.org/abs/2003.09514 · HTML: https://mlsanity.com/paper/2003.09514/

## Key facts

- Cited by 107 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Mar 2020.

## Built on by (most cited first, 30 of 107)

- [Breaking the Dilemma of Medical Image-to-image Translation](https://mlsanity.com/paper/2110.06465/) (2021)
- [Conditional Deformable Image Registration with Convolutional Neural Network](https://mlsanity.com/paper/2106.12673/) (2021)
- [DiffuseMorph: Unsupervised Deformable Image Registration Using Diffusion Model](https://mlsanity.com/paper/2112.05149/) (2021)
- [uniGradICON: A Foundation Model for Medical Image Registration](https://mlsanity.com/paper/2403.05780/) (2024)
- [A survey on deep learning in medical image registration: new technologies, uncertainty, evaluation metrics, and beyond](https://mlsanity.com/paper/2307.15615/) (2023)
- [U-Net vs Transformer: Is U-Net Outdated in Medical Image Registration?](https://mlsanity.com/paper/2208.04939/) (2022)
- [Correlation-aware Coarse-to-fine MLPs for Deformable Medical Image Registration](https://mlsanity.com/paper/2406.00123/) (2024)
- [Affine Medical Image Registration with Coarse-to-Fine Vision Transformer](https://mlsanity.com/paper/2203.15216/) (2022)
- [NODEO: A Neural Ordinary Differential Equation Based Optimization Framework for Deformable Image Registration](https://mlsanity.com/paper/2108.03443/) (2021)
- [DeepTag: An Unsupervised Deep Learning Method for Motion Tracking on Cardiac Tagging Magnetic Resonance Images](https://mlsanity.com/paper/2103.02772/) (2021)
- [Learning a Model-Driven Variational Network for Deformable Image Registration](https://mlsanity.com/paper/2105.12227/) (2021)
- [Fourier-Net: Fast Image Registration with Band-limited Deformation](https://mlsanity.com/paper/2211.16342/) (2022)
- [Deep Learning in Medical Image Registration: Magic or Mirage?](https://mlsanity.com/paper/2408.05839/) (2024)
- [Diffeomorphic Image Registration with Neural Velocity Field](https://mlsanity.com/paper/2202.12498/) (2022)
- [Medical Image Registration via Neural Fields](https://mlsanity.com/paper/2206.03111/) (2022)
- [FSDiffReg: Feature-wise and Score-wise Diffusion-guided Unsupervised Deformable Image Registration for Cardiac Images](https://mlsanity.com/paper/2307.12035/) (2023)
- [Modality-Agnostic Structural Image Representation Learning for Deformable Multi-Modality Medical Image Registration](https://mlsanity.com/paper/2402.18933/) (2024)
- [Nesterov Accelerated ADMM for Fast Diffeomorphic Image Registration](https://mlsanity.com/paper/2109.12688/) (2021)
- [multiGradICON: A Foundation Model for Multimodal Medical Image Registration](https://mlsanity.com/paper/2408.00221/) (2024)
- [Unsupervised Deformable Image Registration with Absent Correspondences in Pre-operative and Post-Recurrence Brain Tumor MRI Scans](https://mlsanity.com/paper/2206.03900/) (2022)
- [ResNet-LDDMM: Advancing the LDDMM Framework using Deep Residual Networks](https://mlsanity.com/paper/2102.07951/) (2021)
- [Enhancing Medical Image Registration via Appearance Adjustment Networks](https://mlsanity.com/paper/2103.05213/) (2021)
- [Inverse Consistency by Construction for Multistep Deep Registration](https://mlsanity.com/paper/2305.00087/) (2023)
- [Beyond the LUMIR challenge: The pathway to foundational registration models](https://mlsanity.com/paper/2505.24160/) (2025)
- [Embedding Gradient-based Optimization in Image Registration Networks](https://mlsanity.com/paper/2112.03915/) (2021)
- [Residual Aligner Network](https://mlsanity.com/paper/2203.04290/) (2022)
- [Symmetric Transformer-based Network for Unsupervised Image Registration](https://mlsanity.com/paper/2204.13575/) (2022)
- [Recent Progress in Transformer-based Medical Image Analysis](https://mlsanity.com/paper/2208.06643/) (2022)
- [Robust Image Registration with Absent Correspondences in Pre-operative and Follow-up Brain MRI Scans of Diffuse Glioma Patients](https://mlsanity.com/paper/2210.11045/) (2022)
- [SAME++: A Self-supervised Anatomical eMbeddings Enhanced medical image registration framework using stable sampling and regularized transformation](https://mlsanity.com/paper/2311.14986/) (2023)

## Abstract (arXiv)

Diffeomorphic deformable image registration is crucial in many medical image studies, as it offers unique, special properties including topology preservation and invertibility of the transformation. Recent deep learning-based deformable image registration methods achieve fast image registration by leveraging a convolutional neural network (CNN) to learn the spatial transformation from the synthetic ground truth or the similarity metric. However, these approaches often ignore the topology preservation of the transformation and the smoothness of the transformation which is enforced by a global smoothing energy function alone. Moreover, deep learning-based approaches often estimate the displacement field directly, which cannot guarantee the existence of the inverse transformation. In this paper, we present a novel, efficient unsupervised symmetric image registration method which maximizes the similarity between images within the space of diffeomorphic maps and estimates both forward and inverse transformations simultaneously. We evaluate our method on 3D image registration with a large scale brain image dataset. Our method achieves state-of-the-art registration accuracy and running time while maintaining desirable diffeomorphic properties.