# textttNePhi: Neural Deformation Fields for Approximately Diffeomorphic Medical Image Registration arXiv: https://arxiv.org/abs/2309.07322 ยท HTML: https://mlsanity.com/paper/2309.07322/ ## Key facts - Cited by 8 papers in the map (data through 14 Oct 2026). - Builds on 35 of its 69 references that are in the map. - First posted on arXiv 13 Sep 2023. ## Builds on (most cited first, 30 of 35) - [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) - [D-NeRF: Neural Radiance Fields for Dynamic Scenes](https://mlsanity.com/paper/2011.13961/) (2020) - [Nerfies: Deformable Neural Radiance Fields](https://mlsanity.com/paper/2011.12948/) (2020) - [Neural Scene Flow Fields for Space-Time View Synthesis of Dynamic Scenes](https://mlsanity.com/paper/2011.13084/) (2020) - [VoxelMorph: A Learning Framework for Deformable Medical Image Registration](https://mlsanity.com/paper/1809.05231/) (2018) - [Non-Rigid Neural Radiance Fields: Reconstruction and Novel View Synthesis of a Dynamic Scene From Monocular Video](https://mlsanity.com/paper/2012.12247/) (2020) - [Dynamic View Synthesis from Dynamic Monocular Video](https://mlsanity.com/paper/2105.06468/) (2021) - [Animatable Neural Radiance Fields for Modeling Dynamic Human Bodies](https://mlsanity.com/paper/2105.02872/) (2021) - [I M Avatar: Implicit Morphable Head Avatars from Videos](https://mlsanity.com/paper/2112.07471/) (2021) - [SNARF: Differentiable Forward Skinning for Animating Non-Rigid Neural Implicit Shapes](https://mlsanity.com/paper/2104.03953/) (2021) - [Neural Head Avatars from Monocular RGB Videos](https://mlsanity.com/paper/2112.01554/) (2021) - [Unsupervised Learning of Probabilistic Diffeomorphic Registration for Images and Surfaces](https://mlsanity.com/paper/1903.03545/) (2019) - [H-NeRF: Neural Radiance Fields for Rendering and Temporal Reconstruction of Humans in Motion](https://mlsanity.com/paper/2110.13746/) (2021) - [An Unsupervised Learning Model for Deformable Medical Image Registration](https://mlsanity.com/paper/1802.02604/) (2018) - [Modulated Periodic Activations for Generalizable Local Functional Representations](https://mlsanity.com/paper/2104.03960/) (2021) - [Large Deformation Diffeomorphic Image Registration with Laplacian Pyramid Networks](https://mlsanity.com/paper/2006.16148/) (2020) - [Quicksilver: Fast Predictive Image Registration - a Deep Learning Approach](https://mlsanity.com/paper/1703.10908/) (2017) - [Fast Symmetric Diffeomorphic Image Registration with Convolutional Neural Networks](https://mlsanity.com/paper/2003.09514/) (2020) - [DeVRF: Fast Deformable Voxel Radiance Fields for Dynamic Scenes](https://mlsanity.com/paper/2205.15723/) (2022) - [CaDeX: Learning Canonical Deformation Coordinate Space for Dynamic Surface Representation via Neural Homeomorphism](https://mlsanity.com/paper/2203.16529/) (2022) - [DoubleField: Bridging the Neural Surface and Radiance Fields for High-fidelity Human Reconstruction and Rendering](https://mlsanity.com/paper/2106.03798/) (2021) - [Networks for Joint Affine and Non-parametric Image Registration](https://mlsanity.com/paper/1903.08811/) (2019) - [textttGradICON: Approximate Diffeomorphisms via Gradient Inverse Consistency](https://mlsanity.com/paper/2206.05897/) (2022) - [Fast 3D registration with accurate optimisation and little learning for Learn2Reg 2021](https://mlsanity.com/paper/2112.03053/) (2021) - [Topologically-Aware Deformation Fields for Single-View 3D Reconstruction](https://mlsanity.com/paper/2205.06267/) (2022) - [ICON: Learning Regular Maps Through Inverse Consistency](https://mlsanity.com/paper/2105.04459/) (2021) - [Diffeomorphic Image Registration with Neural Velocity Field](https://mlsanity.com/paper/2202.12498/) (2022) - [Learning Deformable Image Registration from Optimization: Perspective, Modules, Bilevel Training and Beyond](https://mlsanity.com/paper/2004.14557/) (2020) ## Built on by (most cited first, 8 of 8) - [Implicit Neural Representations of Intramyocardial Motion and Strain](https://mlsanity.com/paper/2509.09004/) (2025) - [Learning Diffeomorphism for Image Registration with Time-Continuous Networks using Semigroup Regularization](https://mlsanity.com/paper/2405.18684/) (2024) - [Implicit Neural Representations for Registration of Left Ventricle Myocardium During a Cardiac Cycle](https://mlsanity.com/paper/2501.07248/) (2025) - [Uncertainty Estimation for Pretrained Medical Image Registration Models via Transformation Equivariance](https://mlsanity.com/paper/2509.23355/) (2025) - [Multimodal Diffeomorphic Registration with Neural ODEs and Structural Descriptors](https://mlsanity.com/paper/2512.22689/) (2025) - [Don't Mind the Gaps: Implicit Neural Representations for Resolution-Agnostic Retinal OCT Analysis](https://mlsanity.com/paper/2601.02447/) (2026) - [DrivenMorph: Bridging Attention Mechanism and Variational Image Registration via Difference Modeling](https://mlsanity.com/paper/2606.30183/) (2026) - [Two-Parameter Flow Map Learning for Continuous-Time Diffeomorphic Image Registration](https://mlsanity.com/paper/2609.10789/) (2026) ## Abstract (arXiv) This work proposes NePhi, a generalizable neural deformation model which results in approximately diffeomorphic transformations. In contrast to the predominant voxel-based transformation fields used in learning-based registration approaches, NePhi represents deformations functionally, leading to great flexibility within the design space of memory consumption during training and inference, inference time, registration accuracy, as well as transformation regularity. Specifically, NePhi 1) requires less memory compared to voxel-based learning approaches, 2) improves inference speed by predicting latent codes, compared to current existing neural deformation based registration approaches that only rely on optimization, 3) improves accuracy via instance optimization, and 4) shows excellent deformation regularity which is highly desirable for medical image registration. We demonstrate the performance of NePhi on a 2D synthetic dataset as well as for real 3D medical image datasets (e.g., lungs and brains). Our results show that NePhi can match the accuracy of voxel-based representations in a single-resolution registration setting. For multi-resolution registration, our method matches the accuracy of current SOTA learning-based registration approaches with instance optimization while reducing memory requirements by a factor of five. Our code is available at https://github.com/uncbiag/NePhi.