# HSurf-Net: Normal Estimation for 3D Point Clouds by Learning Hyper Surfaces

arXiv: https://arxiv.org/abs/2210.07158 · HTML: https://mlsanity.com/paper/2210.07158/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 57 references that are in the map.
- First posted on arXiv 13 Oct 2022.

## Builds on (most cited first, 20 of 20)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [Point Transformer](https://mlsanity.com/paper/2011.00931/) (2020)
- [PCT: Point cloud transformer](https://mlsanity.com/paper/2012.09688/) (2020)
- [Open3D: A Modern Library for 3D Data Processing](https://mlsanity.com/paper/1801.09847/) (2018)
- [Semantic3D.net: A new Large-scale Point Cloud Classification Benchmark](https://mlsanity.com/paper/1704.03847/) (2017)
- [PCPNET: Learning Local Shape Properties from Raw Point Clouds](https://mlsanity.com/paper/1710.04954/) (2017)
- [Reconstructing Surfaces for Sparse Point Clouds with On-Surface Priors](https://mlsanity.com/paper/2204.10603/) (2022)
- [3D Shape Reconstruction from 2D Images with Disentangled Attribute Flow](https://mlsanity.com/paper/2203.15190/) (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)
- [Learning Deep Implicit Functions for 3D Shapes with Dynamic Code Clouds](https://mlsanity.com/paper/2203.14048/) (2022)
- [Deep Feature-preserving Normal Estimation for Point Cloud Filtering](https://mlsanity.com/paper/2004.11563/) (2020)
- [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)
- [Latent Partition Implicit with Surface Codes for 3D Representation](https://mlsanity.com/paper/2207.08631/) (2022)
- [Normal Estimation for 3D Point Clouds via Local Plane Constraint and Multi-scale Selection](https://mlsanity.com/paper/1910.08537/) (2019)
- [Improvement of Normal Estimation for PointClouds via Simplifying Surface Fitting](https://mlsanity.com/paper/2104.10369/) (2021)

## Built on by (most cited first, 22 of 22)

- [NeAF: Learning Neural Angle Fields for Point Normal Estimation](https://mlsanity.com/paper/2211.16869/) (2022)
- [Learning Signed Distance Functions from Noisy 3D Point Clouds via Noise to Noise Mapping](https://mlsanity.com/paper/2306.01405/) (2023)
- [Rethinking the Approximation Error in 3D Surface Fitting for Point Cloud Normal Estimation](https://mlsanity.com/paper/2303.17167/) (2023)
- [Neural Gradient Learning and Optimization for Oriented Point Normal Estimation](https://mlsanity.com/paper/2309.09211/) (2023)
- [Learning Signed Hyper Surfaces for Oriented Point Cloud Normal Estimation](https://mlsanity.com/paper/2305.05873/) (2023)
- [NeuralGF: Unsupervised Point Normal Estimation by Learning Neural Gradient Function](https://mlsanity.com/paper/2311.00389/) (2023)
- [MSECNet: Accurate and Robust Normal Estimation for 3D Point Clouds by Multi-Scale Edge Conditioning](https://mlsanity.com/paper/2308.02237/) (2023)
- [CMG-Net: Robust Normal Estimation for Point Clouds via Chamfer Normal Distance and Multi-scale Geometry](https://mlsanity.com/paper/2312.09154/) (2023)
- [PFF-Net: Patch Feature Fitting for Point Cloud Normal Estimation](https://mlsanity.com/paper/2511.21365/) (2025)
- [Normal Transformer: Extracting Surface Geometry from LiDAR Points Enhanced by Visual Semantics](https://mlsanity.com/paper/2211.10580/) (2022)
- [Decodable and Sample Invariant Continuous Object Encoder](https://mlsanity.com/paper/2311.00187/) (2023)
- [Learning Normals of Noisy Points by Local Gradient-Aware Surface Filtering](https://mlsanity.com/paper/2507.03394/) (2025)
- [Surface Normal Estimation with Transformers](https://mlsanity.com/paper/2401.05745/) (2024)
- [Fast and Robust Normal Estimation for Sparse LiDAR Scans](https://mlsanity.com/paper/2404.14281/) (2024)
- [LiSu: A Dataset and Method for LiDAR Surface Normal Estimation](https://mlsanity.com/paper/2503.08601/) (2025)
- [Self-Supervised Implicit Attention Priors for Point Cloud Reconstruction](https://mlsanity.com/paper/2511.04864/) (2025)
- [PointNorm-Net: Self-Supervised Normal Prediction of 3D Point Clouds via Multi-Modal Distribution Estimation](https://mlsanity.com/paper/2304.04884/) (2023)
- [E3-Net: Efficient E(3)-Equivariant Normal Estimation Network](https://mlsanity.com/paper/2406.00347/) (2024)
- [Asymmetrical Siamese Network for Point Clouds Normal Estimation](https://mlsanity.com/paper/2406.09681/) (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)

## Abstract (arXiv)

We propose a novel normal estimation method called HSurf-Net, which can accurately predict normals from point clouds with noise and density variations. Previous methods focus on learning point weights to fit neighborhoods into a geometric surface approximated by a polynomial function with a predefined order, based on which normals are estimated. However, fitting surfaces explicitly from raw point clouds suffers from overfitting or underfitting issues caused by inappropriate polynomial orders and outliers, which significantly limits the performance of existing methods. To address these issues, we introduce hyper surface fitting to implicitly learn hyper surfaces, which are represented by multi-layer perceptron (MLP) layers that take point features as input and output surface patterns in a high dimensional feature space. We introduce a novel space transformation module, which consists of a sequence of local aggregation layers and global shift layers, to learn an optimal feature space, and a relative position encoding module to effectively convert point clouds into the learned feature space. Our model learns hyper surfaces from the noise-less features and directly predicts normal vectors. We jointly optimize the MLP weights and module parameters in a data-driven manner to make the model adaptively find the most suitable surface pattern for various points. Experimental results show that our HSurf-Net achieves the state-of-the-art performance on the synthetic shape dataset, the real-world indoor and outdoor scene datasets. The code, data and pretrained models are publicly available.