# DiGS : Divergence guided shape implicit neural representation for unoriented point clouds

arXiv: https://arxiv.org/abs/2106.10811 · HTML: https://mlsanity.com/paper/2106.10811/

## Key facts

- Cited by 77 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 47 references that are in the map.
- First posted on arXiv 21 Jun 2021.

## Builds on (most cited first, 27 of 27)

- [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)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (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)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [Scene Representation Networks: Continuous 3D-Structure-Aware Neural Scene Representations](https://mlsanity.com/paper/1906.01618/) (2019)
- [Convolutional Occupancy Networks](https://mlsanity.com/paper/2003.04618/) (2020)
- [Implicit Geometric Regularization for Learning Shapes](https://mlsanity.com/paper/2002.10099/) (2020)
- [AtlasNet: A Papier-Mach'e Approach to Learning 3D Surface Generation](https://mlsanity.com/paper/1802.05384/) (2018)
- [SAL: Sign Agnostic Learning of Shapes from Raw Data](https://mlsanity.com/paper/1911.10414/) (2019)
- [Local Implicit Grid Representations for 3D Scenes](https://mlsanity.com/paper/2003.08981/) (2020)
- [Neural RGB-D Surface Reconstruction](https://mlsanity.com/paper/2104.04532/) (2021)
- [State of the Art on Neural Rendering](https://mlsanity.com/paper/2004.03805/) (2020)
- [Octree Generating Networks: Efficient Convolutional Architectures for High-resolution 3D Outputs](https://mlsanity.com/paper/1703.09438/) (2017)
- [Shape As Points: A Differentiable Poisson Solver](https://mlsanity.com/paper/2106.03452/) (2021)
- [SDFDiff: Differentiable Rendering of Signed Distance Fields for 3D Shape Optimization](https://mlsanity.com/paper/1912.07109/) (2019)
- [SALD: Sign Agnostic Learning with Derivatives](https://mlsanity.com/paper/2006.05400/) (2020)
- [Deep Geometric Prior for Surface Reconstruction](https://mlsanity.com/paper/1811.10943/) (2018)
- [PCPNET: Learning Local Shape Properties from Raw Point Clouds](https://mlsanity.com/paper/1710.04954/) (2017)
- [Geometry-Consistent Neural Shape Representation with Implicit Displacement Fields](https://mlsanity.com/paper/2106.05187/) (2021)
- [Neural Splines: Fitting 3D Surfaces with Infinitely-Wide Neural Networks](https://mlsanity.com/paper/2006.13782/) (2020)
- [Nesti-Net: Normal Estimation for Unstructured 3D Point Clouds using Convolutional Neural Networks](https://mlsanity.com/paper/1812.00709/) (2018)
- [DeepFit: 3D Surface Fitting via Neural Network Weighted Least Squares](https://mlsanity.com/paper/2003.10826/) (2020)
- [Phase Transitions, Distance Functions, and Implicit Neural Representations](https://mlsanity.com/paper/2106.07689/) (2021)
- [DPDist : Comparing Point Clouds Using Deep Point Cloud Distance](https://mlsanity.com/paper/2004.11784/) (2020)

## Built on by (most cited first, 30 of 77)

- [Advances in 3D Generation: A Survey](https://mlsanity.com/paper/2401.17807/) (2024)
- [Reconstructing Surfaces for Sparse Point Clouds with On-Surface Priors](https://mlsanity.com/paper/2204.10603/) (2022)
- [Surface Reconstruction from Point Clouds by Learning Predictive Context Priors](https://mlsanity.com/paper/2204.11015/) (2022)
- [Towards Better Gradient Consistency for Neural Signed Distance Functions via Level Set Alignment](https://mlsanity.com/paper/2305.11601/) (2023)
- [Learning a More Continuous Zero Level Set in Unsigned Distance Fields through Level Set Projection](https://mlsanity.com/paper/2308.11441/) (2023)
- [Neural-Singular-Hessian: Implicit Neural Representation of Unoriented Point Clouds by Enforcing Singular Hessian](https://mlsanity.com/paper/2309.01793/) (2023)
- [LODE: Locally Conditioned Eikonal Implicit Scene Completion from Sparse LiDAR](https://mlsanity.com/paper/2302.14052/) (2023)
- [Unsupervised Inference of Signed Distance Functions from Single Sparse Point Clouds without Learning Priors](https://mlsanity.com/paper/2303.14505/) (2023)
- [Learning Signed Distance Functions from Noisy 3D Point Clouds via Noise to Noise Mapping](https://mlsanity.com/paper/2306.01405/) (2023)
- [StEik: Stabilizing the Optimization of Neural Signed Distance Functions and Finer Shape Representation](https://mlsanity.com/paper/2305.18414/) (2023)
- [Latent Partition Implicit with Surface Codes for 3D Representation](https://mlsanity.com/paper/2207.08631/) (2022)
- [VisCo Grids: Surface Reconstruction with Viscosity and Coarea Grids](https://mlsanity.com/paper/2303.14569/) (2023)
- [Unsupervised Occupancy Learning from Sparse Point Cloud](https://mlsanity.com/paper/2404.02759/) (2024)
- [Fast Learning of Signed Distance Functions from Noisy Point Clouds via Noise to Noise Mapping](https://mlsanity.com/paper/2407.14225/) (2024)
- [Neural-IMLS: Self-supervised Implicit Moving Least-Squares Network for Surface Reconstruction](https://mlsanity.com/paper/2109.04398/) (2021)
- [Mixing-Denoising Generalizable Occupancy Networks](https://mlsanity.com/paper/2311.12125/) (2023)
- [Geometry-Informed Neural Networks](https://mlsanity.com/paper/2402.14009/) (2024)
- [NeurCADRecon: Neural Representation for Reconstructing CAD Surfaces by Enforcing Zero Gaussian Curvature](https://mlsanity.com/paper/2404.13420/) (2024)
- [GridPull: Towards Scalability in Learning Implicit Representations from 3D Point Clouds](https://mlsanity.com/paper/2308.13175/) (2023)
- [Neural Vector Fields for Implicit Surface Representation and Inference](https://mlsanity.com/paper/2204.06552/) (2022)
- [Robustifying Generalizable Implicit Shape Networks with a Tunable Non-Parametric Model](https://mlsanity.com/paper/2311.12967/) (2023)
- [Accurate Differential Operators for Hybrid Neural Fields](https://mlsanity.com/paper/2312.05984/) (2023)
- [NeurCross: A Neural Approach to Computing Cross Fields for Quad Mesh Generation](https://mlsanity.com/paper/2405.13745/) (2024)
- [Neural Experts: Mixture of Experts for Implicit Neural Representations](https://mlsanity.com/paper/2410.21643/) (2024)
- [Semi-signed prioritized neural fitting for surface reconstruction from unoriented point clouds](https://mlsanity.com/paper/2206.06715/) (2022)
- [Point normal orientation and surface reconstruction by incorporating isovalue constraints to Poisson equation](https://mlsanity.com/paper/2209.15619/) (2022)
- [p-Poisson surface reconstruction in curl-free flow from point clouds](https://mlsanity.com/paper/2310.20095/) (2023)
- [HotSpot: Signed Distance Function Optimization with an Asymptotically Sufficient Condition](https://mlsanity.com/paper/2411.14628/) (2024)
- [GridFormer: Point-Grid Transformer for Surface Reconstruction](https://mlsanity.com/paper/2401.02292/) (2024)
- [CanFields: Consolidating Diffeomorphic Flows for Non-Rigid 4D Interpolation from Arbitrary-Length Sequences](https://mlsanity.com/paper/2406.18582/) (2024)

## Abstract (arXiv)

Shape implicit neural representations (INRs) have recently shown to be effective in shape analysis and reconstruction tasks. Existing INRs require point coordinates to learn the implicit level sets of the shape. When a normal vector is available for each point, a higher fidelity representation can be learned, however normal vectors are often not provided as raw data. Furthermore, the method's initialization has been shown to play a crucial role for surface reconstruction. In this paper, we propose a divergence guided shape representation learning approach that does not require normal vectors as input. We show that incorporating a soft constraint on the divergence of the distance function favours smooth solutions that reliably orients gradients to match the unknown normal at each point, in some cases even better than approaches that use ground truth normal vectors directly. Additionally, we introduce a novel geometric initialization method for sinusoidal INRs that further improves convergence to the desired solution. We evaluate the effectiveness of our approach on the task of surface reconstruction and shape space learning and show SOTA performance compared to other unoriented methods. Code and model parameters available at our project page https://chumbyte.github.io/DiGS-Site/.