# Neural Gradient Learning and Optimization for Oriented Point Normal Estimation

arXiv: https://arxiv.org/abs/2309.09211 · HTML: https://mlsanity.com/paper/2309.09211/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 70 references that are in the map.
- First posted on arXiv 17 Sep 2023.

## Builds on (most cited first, 26 of 26)

- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [Implicit Geometric Regularization for Learning Shapes](https://mlsanity.com/paper/2002.10099/) (2020)
- [SAL: Sign Agnostic Learning of Shapes from Raw Data](https://mlsanity.com/paper/1911.10414/) (2019)
- [Neural Unsigned Distance Fields for Implicit Function Learning](https://mlsanity.com/paper/2010.13938/) (2020)
- [Shape As Points: A Differentiable Poisson Solver](https://mlsanity.com/paper/2106.03452/) (2021)
- [Neural-Pull: Learning Signed Distance Functions from Point Clouds by Learning to Pull Space onto Surfaces](https://mlsanity.com/paper/2011.13495/) (2020)
- [SALD: Sign Agnostic Learning with Derivatives](https://mlsanity.com/paper/2006.05400/) (2020)
- [PCPNET: Learning Local Shape Properties from Raw Point Clouds](https://mlsanity.com/paper/1710.04954/) (2017)
- [Controlling Neural Level Sets](https://mlsanity.com/paper/1905.11911/) (2019)
- [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)
- [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)
- [NeAF: Learning Neural Angle Fields for Point Normal Estimation](https://mlsanity.com/paper/2211.16869/) (2022)
- [Globally Consistent Normal Orientation for Point Clouds by Regularizing the Winding-Number Field](https://mlsanity.com/paper/2304.11605/) (2023)
- [Deep Feature-preserving Normal Estimation for Point Cloud Filtering](https://mlsanity.com/paper/2004.11563/) (2020)
- [Orienting Point Clouds with Dipole Propagation](https://mlsanity.com/paper/2105.01604/) (2021)
- [AdaFit: Rethinking Learning-based Normal Estimation on Point Clouds](https://mlsanity.com/paper/2108.05836/) (2021)
- [Refine-Net: Normal Refinement Neural Network for Noisy Point Clouds](https://mlsanity.com/paper/2203.12514/) (2022)
- [HSurf-Net: Normal Estimation for 3D Point Clouds by Learning Hyper Surfaces](https://mlsanity.com/paper/2210.07158/) (2022)
- [Normal Estimation for 3D Point Clouds via Local Plane Constraint and Multi-scale Selection](https://mlsanity.com/paper/1910.08537/) (2019)
- [GraphFit: Learning Multi-scale Graph-Convolutional Representation for Point Cloud Normal Estimation](https://mlsanity.com/paper/2207.11484/) (2022)
- [Improvement of Normal Estimation for PointClouds via Simplifying Surface Fitting](https://mlsanity.com/paper/2104.10369/) (2021)
- [Point normal orientation and surface reconstruction by incorporating isovalue constraints to Poisson equation](https://mlsanity.com/paper/2209.15619/) (2022)

## Built on by (most cited first, 11 of 11)

- [A Lightweight UDF Learning Framework for 3D Reconstruction Based on Local Shape Functions](https://mlsanity.com/paper/2407.01330/) (2024)
- [Consistent Point Orientation for Manifold Surfaces via Boundary Integration](https://mlsanity.com/paper/2407.03165/) (2024)
- [PFF-Net: Patch Feature Fitting for Point Cloud Normal Estimation](https://mlsanity.com/paper/2511.21365/) (2025)
- [Learning Normals of Noisy Points by Local Gradient-Aware Surface Filtering](https://mlsanity.com/paper/2507.03394/) (2025)
- [LiSu: A Dataset and Method for LiDAR Surface Normal Estimation](https://mlsanity.com/paper/2503.08601/) (2025)
- [A Divide-and-Conquer Approach for Global Orientation of Non-Watertight Scene-Level Point Clouds Using 0-1 Integer Optimization](https://mlsanity.com/paper/2505.23469/) (2025)
- [E3-Net: Efficient E(3)-Equivariant Normal Estimation Network](https://mlsanity.com/paper/2406.00347/) (2024)
- [Refining 3D Point Cloud Normal Estimation via Sample Selection](https://mlsanity.com/paper/2406.18541/) (2024)
- [OCMG-Net: Neural Oriented Normal Refinement for Unstructured Point Clouds](https://mlsanity.com/paper/2409.01100/) (2024)
- [MambaH-Fit: Rethinking Hyper-surface Fitting-based Point Cloud Normal Estimation via State Space Modelling](https://mlsanity.com/paper/2510.09088/) (2025)
- [SharpNet: Enhancing MLPs to Represent Functions with Controlled Non-differentiability](https://mlsanity.com/paper/2601.19683/) (2026)

## Abstract (arXiv)

We propose Neural Gradient Learning (NGL), a deep learning approach to learn gradient vectors with consistent orientation from 3D point clouds for normal estimation. It has excellent gradient approximation properties for the underlying geometry of the data. We utilize a simple neural network to parameterize the objective function to produce gradients at points using a global implicit representation. However, the derived gradients usually drift away from the ground-truth oriented normals due to the lack of local detail descriptions. Therefore, we introduce Gradient Vector Optimization (GVO) to learn an angular distance field based on local plane geometry to refine the coarse gradient vectors. Finally, we formulate our method with a two-phase pipeline of coarse estimation followed by refinement. Moreover, we integrate two weighting functions, i.e., anisotropic kernel and inlier score, into the optimization to improve the robust and detail-preserving performance. Our method efficiently conducts global gradient approximation while achieving better accuracy and generalization ability of local feature description. This leads to a state-of-the-art normal estimator that is robust to noise, outliers and point density variations. Extensive evaluations show that our method outperforms previous works in both unoriented and oriented normal estimation on widely used benchmarks. The source code and pre-trained models are available at https://github.com/LeoQLi/NGLO.