# Topology-Preserving Shape Reconstruction and Registration via Neural Diffeomorphic Flow

arXiv: https://arxiv.org/abs/2203.08652 · HTML: https://mlsanity.com/paper/2203.08652/

## Key facts

- Cited by 38 papers in the map (data through 14 Oct 2026).
- Builds on 43 of its 69 references that are in the map.
- First posted on arXiv 16 Mar 2022.

## Builds on (most cited first, 30 of 43)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (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)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [Learning Implicit Fields for Generative Shape Modeling](https://mlsanity.com/paper/1812.02822/) (2018)
- [VoxelMorph: A Learning Framework for Deformable Medical Image Registration](https://mlsanity.com/paper/1809.05231/) (2018)
- [Pixel2Mesh: Generating 3D Mesh Models from Single RGB Images](https://mlsanity.com/paper/1804.01654/) (2018)
- [AtlasNet: A Papier-Mach'e Approach to Learning 3D Surface Generation](https://mlsanity.com/paper/1802.05384/) (2018)
- [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)
- [Local Implicit Grid Representations for 3D Scenes](https://mlsanity.com/paper/2003.08981/) (2020)
- [DISN: Deep Implicit Surface Network for High-quality Single-view 3D Reconstruction](https://mlsanity.com/paper/1905.10711/) (2019)
- [Deep Local Shapes: Learning Local SDF Priors for Detailed 3D Reconstruction](https://mlsanity.com/paper/2003.10983/) (2020)
- [Learning Shape Templates with Structured Implicit Functions](https://mlsanity.com/paper/1904.06447/) (2019)
- [Unsupervised Learning of Probabilistic Diffeomorphic Registration for Images and Surfaces](https://mlsanity.com/paper/1903.03545/) (2019)
- [Modulated Periodic Activations for Generalizable Local Functional Representations](https://mlsanity.com/paper/2104.03960/) (2021)
- [Deformed Implicit Field: Modeling 3D Shapes with Learned Dense Correspondence](https://mlsanity.com/paper/2011.13650/) (2020)
- [Unsupervised Learning for Fast Probabilistic Diffeomorphic Registration](https://mlsanity.com/paper/1805.04605/) (2018)
- [Learning elementary structures for 3D shape generation and matching](https://mlsanity.com/paper/1908.04725/) (2019)
- [NPMs: Neural Parametric Models for 3D Deformable Shapes](https://mlsanity.com/paper/2104.00702/) (2021)
- [BAE-NET: Branched Autoencoder for Shape Co-Segmentation](https://mlsanity.com/paper/1903.11228/) (2019)
- [Deep Implicit Templates for 3D Shape Representation](https://mlsanity.com/paper/2011.14565/) (2020)
- [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)
- [DualSDF: Semantic Shape Manipulation using a Two-Level Representation](https://mlsanity.com/paper/2004.02869/) (2020)
- [PatchNets: Patch-Based Generalizable Deep Implicit 3D Shape Representations](https://mlsanity.com/paper/2008.01639/) (2020)
- [Recurrent Mask Refinement for Few-Shot Medical Image Segmentation](https://mlsanity.com/paper/2108.00622/) (2021)
- [Learning a Probabilistic Model for Diffeomorphic Registration](https://mlsanity.com/paper/1812.07460/) (2018)

## Built on by (most cited first, 30 of 38)

- [A survey on deep learning in medical image registration: new technologies, uncertainty, evaluation metrics, and beyond](https://mlsanity.com/paper/2307.15615/) (2023)
- [Medical Image Registration via Neural Fields](https://mlsanity.com/paper/2206.03111/) (2022)
- [SDF4CHD: Generative Modeling of Cardiac Anatomies with Congenital Heart Defects](https://mlsanity.com/paper/2311.00332/) (2023)
- [4D Myocardium Reconstruction with Decoupled Motion and Shape Model](https://mlsanity.com/paper/2308.14083/) (2023)
- [DeepMesh: Mesh-based Cardiac Motion Tracking using Deep Learning](https://mlsanity.com/paper/2309.14306/) (2023)
- [Neural Deformable Models for 3D Bi-Ventricular Heart Shape Reconstruction and Modeling from 2D Sparse Cardiac Magnetic Resonance Imaging](https://mlsanity.com/paper/2307.07693/) (2023)
- [Common3D: Self-Supervised Learning of 3D Morphable Models for Common Objects in Neural Feature Space](https://mlsanity.com/paper/2504.21749/) (2025)
- [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)
- [CanFields: Consolidating Diffeomorphic Flows for Non-Rigid 4D Interpolation from Arbitrary-Length Sequences](https://mlsanity.com/paper/2406.18582/) (2024)
- [Hybrid Neural Diffeomorphic Flow for Shape Representation and Generation via Triplane](https://mlsanity.com/paper/2307.01957/) (2023)
- [RFNet-4D++: Joint Object Reconstruction and Flow Estimation from 4D Point Clouds with Cross-Attention Spatio-Temporal Features](https://mlsanity.com/paper/2203.16482/) (2022)
- [Fast Point Cloud to Mesh Reconstruction for Deformable Object Tracking](https://mlsanity.com/paper/2311.02749/) (2023)
- [Molecular Representations in Implicit Functional Space via Hyper-Networks](https://mlsanity.com/paper/2601.22327/) (2026)
- [Hybrid-CSR: Coupling Explicit and Implicit Shape Representation for Cortical Surface Reconstruction](https://mlsanity.com/paper/2307.12299/) (2023)
- [BrainMRDiff: A Diffusion Model for Anatomically Consistent Brain MRI Synthesis](https://mlsanity.com/paper/2504.04532/) (2025)
- [From Pixels to Polygons: A Survey of Deep Learning Approaches for Medical Image-to-Mesh Reconstruction](https://mlsanity.com/paper/2505.03599/) (2025)
- [Implicit Modeling of Non-rigid Objects with Cross-Category Signals](https://mlsanity.com/paper/2312.10246/) (2023)
- [Deformable registration and generative modelling of aortic anatomies by auto-decoders and neural ODEs](https://mlsanity.com/paper/2506.00947/) (2025)
- [FLOWING: Implicit Neural Flows for Structure-Preserving Morphing](https://mlsanity.com/paper/2510.09537/) (2025)
- [Shape-Graph Matching Network (SGM-net): Registration for Statistical Shape Analysis](https://mlsanity.com/paper/2308.06869/) (2023)
- [Learning Geodesics of Geometric Shape Deformations From Images](https://mlsanity.com/paper/2410.18797/) (2024)
- [GenMed: A Pairwise Generative Reformulation of Medical Diagnostic Tasks](https://mlsanity.com/paper/2605.10645/) (2026)
- [Learning Volumetric Neural Deformable Models to Recover 3D Regional Heart Wall Motion from Multi-Planar Tagged MRI](https://mlsanity.com/paper/2411.15233/) (2024)
- [MorphiNet: A Graph Subdivision Network for Adaptive Bi-ventricle Surface Reconstruction](https://mlsanity.com/paper/2412.10985/) (2024)
- [Latent Diffeomorphic Co-Design of End-Effectors for Deformable and Fragile Object Manipulation](https://mlsanity.com/paper/2602.17921/) (2026)
- [Automatic classification of deformable shapes](https://mlsanity.com/paper/2211.02530/) (2022)
- [Generative Prior-Guided Neural Interface Reconstruction for 3D Electrical Impedance Tomography](https://mlsanity.com/paper/2505.16487/) (2025)
- [Posterior shape models revisited: Improving 3D reconstructions from partial data using target specific models](https://mlsanity.com/paper/2509.05776/) (2025)

## Abstract (arXiv)

Deep Implicit Functions (DIFs) represent 3D geometry with continuous signed distance functions learned through deep neural nets. Recently DIFs-based methods have been proposed to handle shape reconstruction and dense point correspondences simultaneously, capturing semantic relationships across shapes of the same class by learning a DIFs-modeled shape template. These methods provide great flexibility and accuracy in reconstructing 3D shapes and inferring correspondences. However, the point correspondences built from these methods do not intrinsically preserve the topology of the shapes, unlike mesh-based template matching methods. This limits their applications on 3D geometries where underlying topological structures exist and matter, such as anatomical structures in medical images. In this paper, we propose a new model called Neural Diffeomorphic Flow (NDF) to learn deep implicit shape templates, representing shapes as conditional diffeomorphic deformations of templates, intrinsically preserving shape topologies. The diffeomorphic deformation is realized by an auto-decoder consisting of Neural Ordinary Differential Equation (NODE) blocks that progressively map shapes to implicit templates. We conduct extensive experiments on several medical image organ segmentation datasets to evaluate the effectiveness of NDF on reconstructing and aligning shapes. NDF achieves consistently state-of-the-art organ shape reconstruction and registration results in both accuracy and quality. The source code is publicly available at https://github.com/Siwensun/Neural_Diffeomorphic_Flow--NDF.