# 4Deform: Neural Surface Deformation for Robust Shape Interpolation

arXiv: https://arxiv.org/abs/2502.20208 · HTML: https://mlsanity.com/paper/2502.20208/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 59 references that are in the map.
- First posted on arXiv 27 Feb 2025.

## Builds on (most cited first, 30 of 31)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Implicit Geometric Regularization for Learning Shapes](https://mlsanity.com/paper/2002.10099/) (2020)
- [GRAB: A Dataset of Whole-Body Human Grasping of Objects](https://mlsanity.com/paper/2008.11200/) (2020)
- [3D Menagerie: Modeling the 3D shape and pose of animals](https://mlsanity.com/paper/1611.07700/) (2016)
- [BEHAVE: Dataset and Method for Tracking Human Object Interactions](https://mlsanity.com/paper/2204.06950/) (2022)
- [NeuralRecon: Real-Time Coherent 3D Reconstruction from Monocular Video](https://mlsanity.com/paper/2104.00681/) (2021)
- [Deep Geometric Functional Maps: Robust Feature Learning for Shape Correspondence](https://mlsanity.com/paper/2003.14286/) (2020)
- [LoopReg: Self-supervised Learning of Implicit Surface Correspondences, Pose and Shape for 3D Human Mesh Registration](https://mlsanity.com/paper/2010.12447/) (2020)
- [Learning Smooth Neural Functions via Lipschitz Regularization](https://mlsanity.com/paper/2202.08345/) (2022)
- [Unsupervised Deep Learning for Structured Shape Matching](https://mlsanity.com/paper/1812.03794/) (2018)
- [NeuroMorph: Unsupervised Shape Interpolation and Correspondence in One Go](https://mlsanity.com/paper/2106.09431/) (2021)
- [Unsupervised Learning of Robust Spectral Shape Matching](https://mlsanity.com/paper/2304.14419/) (2023)
- [LIMP: Learning Latent Shape Representations with Metric Preservation Priors](https://mlsanity.com/paper/2003.12283/) (2020)
- [4D-DRESS: A 4D Dataset of Real-world Human Clothing with Semantic Annotations](https://mlsanity.com/paper/2404.18630/) (2024)
- [A Level Set Theory for Neural Implicit Evolution under Explicit Flows](https://mlsanity.com/paper/2204.07159/) (2022)
- [Motion2VecSets: 4D Latent Vector Set Diffusion for Non-rigid Shape Reconstruction and Tracking](https://mlsanity.com/paper/2401.06614/) (2024)
- [FARM: Functional Automatic Registration Method for 3D Human Bodies](https://mlsanity.com/paper/1807.10517/) (2018)
- [Spectral Meets Spatial: Harmonising 3D Shape Matching and Interpolation](https://mlsanity.com/paper/2402.18920/) (2024)
- [NICP: Neural ICP for 3D Human Registration at Scale](https://mlsanity.com/paper/2312.14024/) (2023)
- [Neural Implicit Surface Evolution](https://mlsanity.com/paper/2201.09636/) (2022)
- [Hybrid Functional Maps for Crease-Aware Non-Isometric Shape Matching](https://mlsanity.com/paper/2312.03678/) (2023)
- [Hamiltonian Dynamics for Real-World Shape Interpolation](https://mlsanity.com/paper/2004.05199/) (2020)
- [Gradient-SDF: A Semi-Implicit Surface Representation for 3D Reconstruction](https://mlsanity.com/paper/2111.13652/) (2021)
- [Revisiting Map Relations for Unsupervised Non-Rigid Shape Matching](https://mlsanity.com/paper/2310.11420/) (2023)
- [DiscoMatch: Fast Discrete Optimisation for Geometrically Consistent 3D Shape Matching](https://mlsanity.com/paper/2310.08230/) (2023)
- [Divergence-Free Shape Interpolation and Correspondence](https://mlsanity.com/paper/1806.10417/) (2018)
- [DiffCD: A Symmetric Differentiable Chamfer Distance for Neural Implicit Surface Fitting](https://mlsanity.com/paper/2407.17058/) (2024)
- [Implicit Neural Surface Deformation with Explicit Velocity Fields](https://mlsanity.com/paper/2501.14038/) (2025)
- [Bayesian 3D Reconstruction of Complex Scenes from Single-Photon Lidar Data](https://mlsanity.com/paper/1810.11633/) (2018)

## Built on by (most cited first, 7 of 7)

- [BiMotion: B-spline Motion for Text-guided Dynamic 3D Character Generation](https://mlsanity.com/paper/2602.18873/) (2026)
- [TwoSquared: 4D Generation from 2D Image Pairs](https://mlsanity.com/paper/2504.12825/) (2025)
- [FLOWING: Implicit Neural Flows for Structure-Preserving Morphing](https://mlsanity.com/paper/2510.09537/) (2025)
- [ArtHOI: Articulated Human-Object Interaction Synthesis by 4D Reconstruction from Video Priors](https://mlsanity.com/paper/2603.04338/) (2026)
- [3DMorph: Single-Image-Guided Local 3D Shape Editing and Morphing](https://mlsanity.com/paper/2606.07115/) (2026)
- [GrowFields: Compositional 4D Neural Fields for Topology-Changing Plant Growth](https://mlsanity.com/paper/2607.03330/) (2026)
- [NeuralSRNF: Neural Square Root Normal Fields for the Statistical Shape Analysis and Generation of Nonrigid 3D and 4D Objects](https://mlsanity.com/paper/2609.27728/) (2026)

## Abstract (arXiv)

Generating realistic intermediate shapes between non-rigidly deformed shapes is a challenging task in computer vision, especially with unstructured data (e.g., point clouds) where temporal consistency across frames is lacking, and topologies are changing. Most interpolation methods are designed for structured data (i.e., meshes) and do not apply to real-world point clouds. In contrast, our approach, 4Deform, leverages neural implicit representation (NIR) to enable free topology changing shape deformation. Unlike previous mesh-based methods that learn vertex-based deformation fields, our method learns a continuous velocity field in Euclidean space. Thus, it is suitable for less structured data such as point clouds. Additionally, our method does not require intermediate-shape supervision during training; instead, we incorporate physical and geometrical constraints to regularize the velocity field. We reconstruct intermediate surfaces using a modified level-set equation, directly linking our NIR with the velocity field. Experiments show that our method significantly outperforms previous NIR approaches across various scenarios (e.g., noisy, partial, topology-changing, non-isometric shapes) and, for the first time, enables new applications like 4D Kinect sequence upsampling and real-world high-resolution mesh deformation.