# Medical Image Registration via Neural Fields

arXiv: https://arxiv.org/abs/2206.03111 · HTML: https://mlsanity.com/paper/2206.03111/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- Builds on 45 of its 86 references that are in the map.
- First posted on arXiv 7 Jun 2022.

## Builds on (most cited first, 30 of 45)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [The Lottery Ticket Hypothesis: Finding Sparse, Trainable Neural Networks](https://mlsanity.com/paper/1803.03635/) (2018)
- [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)
- [Spatial Transformer Networks](https://mlsanity.com/paper/1506.02025/) (2015)
- [VoxelMorph: A Learning Framework for Deformable Medical Image Registration](https://mlsanity.com/paper/1809.05231/) (2018)
- [Learning Continuous Image Representation with Local Implicit Image Function](https://mlsanity.com/paper/2012.09161/) (2020)
- [Neural Fields in Visual Computing and Beyond](https://mlsanity.com/paper/2111.11426/) (2021)
- [PointFlow: 3D Point Cloud Generation with Continuous Normalizing Flows](https://mlsanity.com/paper/1906.12320/) (2019)
- [Augmented Neural ODEs](https://mlsanity.com/paper/1904.01681/) (2019)
- [COIN: COmpression with Implicit Neural representations](https://mlsanity.com/paper/2103.03123/) (2021)
- [Unsupervised Learning of Probabilistic Diffeomorphic Registration for Images and Surfaces](https://mlsanity.com/paper/1903.03545/) (2019)
- [An Unsupervised Learning Model for Deformable Medical Image Registration](https://mlsanity.com/paper/1802.02604/) (2018)
- [NeRP: Implicit Neural Representation Learning with Prior Embedding for Sparsely Sampled Image Reconstruction](https://mlsanity.com/paper/2108.10991/) (2021)
- [SynthMorph: learning contrast-invariant registration without acquired images](https://mlsanity.com/paper/2004.10282/) (2020)
- [Large Deformation Diffeomorphic Image Registration with Laplacian Pyramid Networks](https://mlsanity.com/paper/2006.16148/) (2020)
- [Learn2Reg: comprehensive multi-task medical image registration challenge, dataset and evaluation in the era of deep learning](https://mlsanity.com/paper/2112.04489/) (2021)
- [Unsupervised Learning for Fast Probabilistic Diffeomorphic Registration](https://mlsanity.com/paper/1805.04605/) (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)
- [A Structured Dictionary Perspective on Implicit Neural Representations](https://mlsanity.com/paper/2112.01917/) (2021)
- [ViT-V-Net: Vision Transformer for Unsupervised Volumetric Medical Image Registration](https://mlsanity.com/paper/2104.06468/) (2021)
- [Deep Implicit Templates for 3D Shape Representation](https://mlsanity.com/paper/2011.14565/) (2020)
- [HyperMorph: Amortized Hyperparameter Learning for Image Registration](https://mlsanity.com/paper/2101.01035/) (2021)
- [CycleMorph: Cycle Consistent Unsupervised Deformable Image Registration](https://mlsanity.com/paper/2008.05772/) (2020)

## Built on by (most cited first, 19 of 19)

- [3D Vessel Reconstruction from Sparse-View Dynamic DSA Images via Vessel Probability Guided Attenuation Learning](https://mlsanity.com/paper/2405.10705/) (2024)
- [Continuous Representation Methods, Theories, and Applications: An Overview and Perspectives](https://mlsanity.com/paper/2505.15222/) (2025)
- [Neural Fields for Continuous Periodic Motion Estimation in 4D Cardiovascular Imaging](https://mlsanity.com/paper/2407.20728/) (2024)
- [Modeling the Neonatal Brain Development Using Implicit Neural Representations](https://mlsanity.com/paper/2408.08647/) (2024)
- [Encoder-Only Image Registration](https://mlsanity.com/paper/2509.00451/) (2025)
- [FLOWING: Implicit Neural Flows for Structure-Preserving Morphing](https://mlsanity.com/paper/2510.09537/) (2025)
- [The End of Reward Engineering: How LLMs Are Redefining Multi-Agent Coordination](https://mlsanity.com/paper/2601.08237/) (2026)
- [Learning Geodesics of Geometric Shape Deformations From Images](https://mlsanity.com/paper/2410.18797/) (2024)
- [DARE: A Deformable Adaptive Regularization Estimator for Learning-Based Medical Image Registration](https://mlsanity.com/paper/2510.19353/) (2025)
- [Learning Diffeomorphism for Image Registration with Time-Continuous Networks using Semigroup Regularization](https://mlsanity.com/paper/2405.18684/) (2024)
- [Neural Ordinary Differential Equation based Sequential Image Registration for Dynamic Characterization](https://mlsanity.com/paper/2404.02106/) (2024)
- [Deep End-to-end Adaptive k-Space Sampling, Reconstruction, and Registration for Dynamic MRI](https://mlsanity.com/paper/2411.18249/) (2024)
- [Dynamic PET Image Reconstruction via Non-negative INR Factorization](https://mlsanity.com/paper/2503.08025/) (2025)
- [Silhouette-to-Contour Registration: Aligning Intraoral Scan Models with Cephalometric Radiographs](https://mlsanity.com/paper/2511.14343/) (2025)
- [Multimodal Diffeomorphic Registration with Neural ODEs and Structural Descriptors](https://mlsanity.com/paper/2512.22689/) (2025)
- [Biophysics-Enhanced Neural Representations for Patient-Specific Respiratory Motion Modeling](https://mlsanity.com/paper/2603.22123/) (2026)
- [Registration-Grounded Spectral Fusion for Unregistered WLI/NBI Endoscopic Lesion Segmentation](https://mlsanity.com/paper/2607.26395/) (2026)
- [Phase-Aligned Finite-Fourier Periodic Deformation for 4D Medical Image Interpolation](https://mlsanity.com/paper/2608.24027/) (2026)
- [NEXT: Physics-Informed Neuro-Spectral Exponential Time Differencing Architectures](https://mlsanity.com/paper/2609.31539/) (2026)

## Abstract (arXiv)

Image registration is an essential step in many medical image analysis tasks. Traditional methods for image registration are primarily optimization-driven, finding the optimal deformations that maximize the similarity between two images. Recent learning-based methods, trained to directly predict transformations between two images, run much faster, but suffer from performance deficiencies due to model generalization and the inefficiency in handling individual image specific deformations. Here we present a new neural net based image registration framework, called NIR (Neural Image Registration), which is based on optimization but utilizes deep neural nets to model deformations between image pairs. NIR represents the transformation between two images with a continuous function implemented via neural fields, receiving a 3D coordinate as input and outputting the corresponding deformation vector. NIR provides two ways of generating deformation field: directly output a displacement vector field for general deformable registration, or output a velocity vector field and integrate the velocity field to derive the deformation field for diffeomorphic image registration. The optimal registration is discovered by updating the parameters of the neural field via stochastic gradient descent. We describe several design choices that facilitate model optimization, including coordinate encoding, sinusoidal activation, coordinate sampling, and intensity sampling. Experiments on two 3D MR brain scan datasets demonstrate that NIR yields state-of-the-art performance in terms of both registration accuracy and regularity, while running significantly faster than traditional optimization-based methods.