# Diffeomorphic Image Registration with Neural Velocity Field

arXiv: https://arxiv.org/abs/2202.12498 · HTML: https://mlsanity.com/paper/2202.12498/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- Builds on 40 of its 84 references that are in the map.
- First posted on arXiv 25 Feb 2022.

## Builds on (most cited first, 30 of 40)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [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)
- [Plenoxels: Radiance Fields without Neural Networks](https://mlsanity.com/paper/2112.05131/) (2021)
- [TransUNet: Transformers Make Strong Encoders for Medical Image Segmentation](https://mlsanity.com/paper/2102.04306/) (2021)
- [D-NeRF: Neural Radiance Fields for Dynamic Scenes](https://mlsanity.com/paper/2011.13961/) (2020)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [Learning Implicit Fields for Generative Shape Modeling](https://mlsanity.com/paper/1812.02822/) (2018)
- [UNETR: Transformers for 3D Medical Image Segmentation](https://mlsanity.com/paper/2103.10504/) (2021)
- [Neural Scene Flow Fields for Space-Time View Synthesis of Dynamic Scenes](https://mlsanity.com/paper/2011.13084/) (2020)
- [Neural Fields in Visual Computing and Beyond](https://mlsanity.com/paper/2111.11426/) (2021)
- [An Unsupervised Learning Model for Deformable Medical Image Registration](https://mlsanity.com/paper/1802.02604/) (2018)
- [Frequency Bias in Neural Networks for Input of Non-Uniform Density](https://mlsanity.com/paper/2003.04560/) (2020)
- [Large Deformation Diffeomorphic Image Registration with Laplacian Pyramid Networks](https://mlsanity.com/paper/2006.16148/) (2020)
- [Unsupervised Learning for Fast Probabilistic Diffeomorphic Registration](https://mlsanity.com/paper/1805.04605/) (2018)
- [Deep Geometric Prior for Surface Reconstruction](https://mlsanity.com/paper/1811.10943/) (2018)
- [Fast Symmetric Diffeomorphic Image Registration with Convolutional Neural Networks](https://mlsanity.com/paper/2003.09514/) (2020)
- [Recursive Cascaded Networks for Unsupervised Medical Image Registration](https://mlsanity.com/paper/1907.12353/) (2019)
- [ViT-V-Net: Vision Transformer for Unsupervised Volumetric Medical Image Registration](https://mlsanity.com/paper/2104.06468/) (2021)
- [SimCVD: Simple Contrastive Voxel-Wise Representation Distillation for Semi-Supervised Medical Image Segmentation](https://mlsanity.com/paper/2108.06227/) (2021)
- [CT Super-resolution GAN Constrained by the Identical, Residual, and Cycle Learning Ensemble(GAN-CIRCLE)](https://mlsanity.com/paper/1808.04256/) (2018)
- [DeepAtlas: Joint Semi-Supervised Learning of Image Registration and Segmentation](https://mlsanity.com/paper/1904.08465/) (2019)
- [Recurrent Mask Refinement for Few-Shot Medical Image Segmentation](https://mlsanity.com/paper/2108.00622/) (2021)
- [nnDetection: A Self-configuring Method for Medical Object Detection](https://mlsanity.com/paper/2106.00817/) (2021)
- [Conditional Deformable Image Registration with Convolutional Neural Network](https://mlsanity.com/paper/2106.12673/) (2021)
- [MADGAN: unsupervised Medical Anomaly Detection GAN using multiple adjacent brain MRI slice reconstruction](https://mlsanity.com/paper/2007.13559/) (2020)
- [Seeing Implicit Neural Representations as Fourier Series](https://mlsanity.com/paper/2109.00249/) (2021)
- [Momentum Contrastive Voxel-wise Representation Learning for Semi-supervised Volumetric Medical Image Segmentation](https://mlsanity.com/paper/2105.07059/) (2021)
- [AFTer-UNet: Axial Fusion Transformer UNet for Medical Image Segmentation](https://mlsanity.com/paper/2110.10403/) (2021)

## Built on by (most cited first, 20 of 20)

- [A survey on deep learning in medical image registration: new technologies, uncertainty, evaluation metrics, and beyond](https://mlsanity.com/paper/2307.15615/) (2023)
- [textttNePhi: Neural Deformation Fields for Approximately Diffeomorphic Medical Image Registration](https://mlsanity.com/paper/2309.07322/) (2023)
- [NAISR: A 3D Neural Additive Model for Interpretable Shape Representation](https://mlsanity.com/paper/2303.09234/) (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)
- [Neural Fields for Continuous Periodic Motion Estimation in 4D Cardiovascular Imaging](https://mlsanity.com/paper/2407.20728/) (2024)
- [Encoder-Only Image Registration](https://mlsanity.com/paper/2509.00451/) (2025)
- [The End of Reward Engineering: How LLMs Are Redefining Multi-Agent Coordination](https://mlsanity.com/paper/2601.08237/) (2026)
- [Learning Homeomorphic Image Registration via Conformal-Invariant Hyperelastic Regularisation](https://mlsanity.com/paper/2303.08113/) (2023)
- [ST-NeRP: Spatial-Temporal Neural Representation Learning with Prior Embedding for Patient-specific Imaging Study](https://mlsanity.com/paper/2410.19283/) (2024)
- [Modality-Aware Feature Matching in Visual and Vision-Language Applications: A Comprehensive Survey](https://mlsanity.com/paper/2507.22791/) (2025)
- [On-the-Fly Guidance Training for Medical Image Registration](https://mlsanity.com/paper/2308.15216/) (2023)
- [Learning Diffeomorphism for Image Registration with Time-Continuous Networks using Semigroup Regularization](https://mlsanity.com/paper/2405.18684/) (2024)
- [Stationary Velocity Fields on Matrix Groups for Deformable Image Registration](https://mlsanity.com/paper/2410.10997/) (2024)
- [Cross-Attention Fusion of MRI and Jacobian Maps for Alzheimer's Disease Diagnosis](https://mlsanity.com/paper/2503.00586/) (2025)
- [Free-Boundary Quasiconformal Maps via a Least-squares Operator in Diffeomorphism Optimization](https://mlsanity.com/paper/2511.11679/) (2025)
- [Multimodal Diffeomorphic Registration with Neural ODEs and Structural Descriptors](https://mlsanity.com/paper/2512.22689/) (2025)
- [Diffeomorphism-Equivariant Neural Networks](https://mlsanity.com/paper/2602.06695/) (2026)
- [Volumetrically Consistent Implicit Atlas Learning via Neural Diffeomorphic Flow for Placenta MRI](https://mlsanity.com/paper/2603.16078/) (2026)
- [Biophysics-Enhanced Neural Representations for Patient-Specific Respiratory Motion Modeling](https://mlsanity.com/paper/2603.22123/) (2026)

## Abstract (arXiv)

Diffeomorphic image registration, offering smooth transformation and topology preservation, is required in many medical image analysis tasks.Traditional methods impose certain modeling constraints on the space of admissible transformations and use optimization to find the optimal transformation between two images. Specifying the right space of admissible transformations is challenging: the registration quality can be poor if the space is too restrictive, while the optimization can be hard to solve if the space is too general. Recent learning-based methods, utilizing deep neural networks to learn the transformation directly, achieve fast inference, but face challenges in accuracy due to the difficulties in capturing the small local deformations and generalization ability. Here we propose a new optimization-based method named DNVF (Diffeomorphic Image Registration with Neural Velocity Field) which utilizes deep neural network to model the space of admissible transformations. A multilayer perceptron (MLP) with sinusoidal activation function is used to represent the continuous velocity field and assigns a velocity vector to every point in space, providing the flexibility of modeling complex deformations as well as the convenience of optimization. Moreover, we propose a cascaded image registration framework (Cas-DNVF) by combining the benefits of both optimization and learning based methods, where a fully convolutional neural network (FCN) is trained to predict the initial deformation, followed by DNVF for further refinement. Experiments on two large-scale 3D MR brain scan datasets demonstrate that our proposed methods significantly outperform the state-of-the-art registration methods.