# Learning a Probabilistic Model for Diffeomorphic Registration

arXiv: https://arxiv.org/abs/1812.07460 · HTML: https://mlsanity.com/paper/1812.07460/

## Key facts

- Cited by 62 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Dec 2018.

## Built on by (most cited first, 30 of 62)

- [HyperMorph: Amortized Hyperparameter Learning for Image Registration](https://mlsanity.com/paper/2101.01035/) (2021)
- [A survey on deep learning in medical image registration: new technologies, uncertainty, evaluation metrics, and beyond](https://mlsanity.com/paper/2307.15615/) (2023)
- [Topology-Preserving Shape Reconstruction and Registration via Neural Diffeomorphic Flow](https://mlsanity.com/paper/2203.08652/) (2022)
- [Correlation-aware Coarse-to-fine MLPs for Deformable Medical Image Registration](https://mlsanity.com/paper/2406.00123/) (2024)
- [Learning the Effect of Registration Hyperparameters with HyperMorph](https://mlsanity.com/paper/2203.16680/) (2022)
- [Generative Adversarial Registration for Improved Conditional Deformable Templates](https://mlsanity.com/paper/2105.04349/) (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)
- [A Robust and Interpretable Deep Learning Framework for Multi-modal Registration via Keypoints](https://mlsanity.com/paper/2304.09941/) (2023)
- [Generative Myocardial Motion Tracking via Latent Space Exploration with Biomechanics-informed Prior](https://mlsanity.com/paper/2206.03830/) (2022)
- [Anatomy-aware and acquisition-agnostic joint registration with SynthMorph](https://mlsanity.com/paper/2301.11329/) (2023)
- [A Deep Discontinuity-Preserving Image Registration Network](https://mlsanity.com/paper/2107.04440/) (2021)
- [MulViMotion: Shape-aware 3D Myocardial Motion Tracking from Multi-View Cardiac MRI](https://mlsanity.com/paper/2208.00034/) (2022)
- [ResNet-LDDMM: Advancing the LDDMM Framework using Deep Residual Networks](https://mlsanity.com/paper/2102.07951/) (2021)
- [MultiMorph: On-demand Atlas Construction](https://mlsanity.com/paper/2504.00247/) (2025)
- [Registration by Regression (RbR): a framework for interpretable and flexible atlas registration](https://mlsanity.com/paper/2404.16781/) (2024)
- [SITReg: Multi-resolution architecture for symmetric, inverse consistent, and topology preserving image registration](https://mlsanity.com/paper/2303.10211/) (2023)
- [RDA-INR: Riemannian Diffeomorphic Autoencoding via Implicit Neural Representations](https://mlsanity.com/paper/2305.12854/) (2023)
- [Diffeomorphic Mesh Deformation via Efficient Optimal Transport for Cortical Surface Reconstruction](https://mlsanity.com/paper/2305.17555/) (2023)
- [IGCN: Image-to-graph Convolutional Network for 2D/3D Deformable Registration](https://mlsanity.com/paper/2111.00484/) (2021)
- [AutoFuse: Automatic Fusion Networks for Deformable Medical Image Registration](https://mlsanity.com/paper/2309.05271/) (2023)
- [CorticalFlow: A Diffeomorphic Mesh Deformation Module for Cortical Surface Reconstruction](https://mlsanity.com/paper/2206.02374/) (2022)
- [Medical image registration using unsupervised deep neural network: A scoping literature review](https://mlsanity.com/paper/2208.01825/) (2022)
- [Unsupervised Echocardiography Registration through Patch-based MLPs and Transformers](https://mlsanity.com/paper/2211.11687/) (2022)
- [Joint segmentation and discontinuity-preserving deformable registration: Application to cardiac cine-MR images](https://mlsanity.com/paper/2211.13828/) (2022)
- [CartiMorph: a framework for automated knee articular cartilage morphometrics](https://mlsanity.com/paper/2308.01981/) (2023)
- [Continuous 3D Myocardial Motion Tracking via Echocardiography](https://mlsanity.com/paper/2310.02792/) (2023)
- [Decoder-Only Image Registration](https://mlsanity.com/paper/2402.03585/) (2024)
- [Hierarchical Uncertainty Estimation for Learning-based Registration in Neuroimaging](https://mlsanity.com/paper/2410.09299/) (2024)
- [MICS : Multi-steps, Inverse Consistency and Symmetric deep learning registration network](https://mlsanity.com/paper/2111.12123/) (2021)

## Abstract (arXiv)

We propose to learn a low-dimensional probabilistic deformation model from data which can be used for registration and the analysis of deformations. The latent variable model maps similar deformations close to each other in an encoding space. It enables to compare deformations, generate normal or pathological deformations for any new image or to transport deformations from one image pair to any other image. Our unsupervised method is based on variational inference. In particular, we use a conditional variational autoencoder (CVAE) network and constrain transformations to be symmetric and diffeomorphic by applying a differentiable exponentiation layer with a symmetric loss function. We also present a formulation that includes spatial regularization such as diffusion-based filters. Additionally, our framework provides multi-scale velocity field estimations. We evaluated our method on 3-D intra-subject registration using 334 cardiac cine-MRIs. On this dataset, our method showed state-of-the-art performance with a mean DICE score of 81.2% and a mean Hausdorff distance of 7.3mm using 32 latent dimensions compared to three state-of-the-art methods while also demonstrating more regular deformation fields. The average time per registration was 0.32s. Besides, we visualized the learned latent space and show that the encoded deformations can be used to transport deformations and to cluster diseases with a classification accuracy of 83% after applying a linear projection.