# Improvement of Normal Estimation for PointClouds via Simplifying Surface Fitting

arXiv: https://arxiv.org/abs/2104.10369 · HTML: https://mlsanity.com/paper/2104.10369/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 41 references that are in the map.
- First posted on arXiv 21 Apr 2021.

## Builds on (most cited first, 13 of 13)

- [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)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [OctNet: Learning Deep 3D Representations at High Resolutions](https://mlsanity.com/paper/1611.05009/) (2016)
- [Volumetric and Multi-View CNNs for Object Classification on 3D Data](https://mlsanity.com/paper/1604.03265/) (2016)
- [Escape from Cells: Deep Kd-Networks for the Recognition of 3D Point Cloud Models](https://mlsanity.com/paper/1704.01222/) (2017)
- [PointCleanNet: Learning to Denoise and Remove Outliers from Dense Point Clouds](https://mlsanity.com/paper/1901.01060/) (2019)
- [PCPNET: Learning Local Shape Properties from Raw Point Clouds](https://mlsanity.com/paper/1710.04954/) (2017)
- [Pointfilter: Point Cloud Filtering via Encoder-Decoder Modeling](https://mlsanity.com/paper/2002.05968/) (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)
- [Deep Feature-preserving Normal Estimation for Point Cloud Filtering](https://mlsanity.com/paper/2004.11563/) (2020)
- [Normal Estimation for 3D Point Clouds via Local Plane Constraint and Multi-scale Selection](https://mlsanity.com/paper/1910.08537/) (2019)

## Built on by (most cited first, 12 of 12)

- [NeAF: Learning Neural Angle Fields for Point Normal Estimation](https://mlsanity.com/paper/2211.16869/) (2022)
- [HSurf-Net: Normal Estimation for 3D Point Clouds by Learning Hyper Surfaces](https://mlsanity.com/paper/2210.07158/) (2022)
- [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)
- [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)
- [Surface Normal Estimation with Transformers](https://mlsanity.com/paper/2401.05745/) (2024)
- [Fast, Accurate and Object Boundary-Aware Surface Normal Estimation from Depth Maps](https://mlsanity.com/paper/2209.08241/) (2022)
- [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)

## Abstract (arXiv)

With the burst development of neural networks in recent years, the task of normal estimation has once again become a concern. By introducing the neural networks to classic methods based on problem-specific knowledge, the adaptability of the normal estimation algorithm to noise and scale has been greatly improved. However, the compatibility between neural networks and the traditional methods has not been considered. Similar to the principle of Occam's razor, that is, the simpler is better. We observe that a more simplified process of surface fitting can significantly improve the accuracy of the normal estimation. In this paper, two simple-yet-effective strategies are proposed to address the compatibility between the neural networks and surface fitting process to improve normal estimation. Firstly, a dynamic top-k selection strategy is introduced to better focus on the most critical points of a given patch, and the points selected by our learning method tend to fit a surface by way of a simple tangent plane, which can dramatically improve the normal estimation results of patches with sharp corners or complex patterns. Then, we propose a point update strategy before local surface fitting, which smooths the sharp boundary of the patch to simplify the surface fitting process, significantly reducing the fitting distortion and improving the accuracy of the predicted point normal. The experiments analyze the effectiveness of our proposed strategies and demonstrate that our method achieves SOTA results with the advantage of higher estimation accuracy over most existed approaches.