# Normal Estimation for 3D Point Clouds via Local Plane Constraint and Multi-scale Selection

arXiv: https://arxiv.org/abs/1910.08537 · HTML: https://mlsanity.com/paper/1910.08537/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Oct 2019.

## Built on by (most cited first, 20 of 20)

- [NeAF: Learning Neural Angle Fields for Point Normal Estimation](https://mlsanity.com/paper/2211.16869/) (2022)
- [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)
- [CPSeg: Cluster-free Panoptic Segmentation of 3D LiDAR Point Clouds](https://mlsanity.com/paper/2111.01723/) (2021)
- [Rethinking the Approximation Error in 3D Surface Fitting for Point Cloud Normal Estimation](https://mlsanity.com/paper/2303.17167/) (2023)
- [Improvement of Normal Estimation for PointClouds via Simplifying Surface Fitting](https://mlsanity.com/paper/2104.10369/) (2021)
- [PCDNF: Revisiting Learning-based Point Cloud Denoising via Joint Normal Filtering](https://mlsanity.com/paper/2209.00798/) (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)
- [Fast and Accurate Normal Estimation for Point Cloud via Patch Stitching](https://mlsanity.com/paper/2103.16066/) (2021)
- [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)
- [Surface Normal Estimation with Transformers](https://mlsanity.com/paper/2401.05745/) (2024)
- [Unsupervised Segmentation for Terracotta Warrior with Seed-Region-Growing CNN (SRG-Net)](https://mlsanity.com/paper/2107.13167/) (2021)
- [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)

## Abstract (arXiv)

In this paper, we propose a normal estimation method for unstructured 3D point clouds. In this method, a feature constraint mechanism called Local Plane Features Constraint (LPFC) is used and then a multi-scale selection strategy is introduced. The LPEC can be used in a single-scale point network architecture for a more stable normal estimation of the unstructured 3D point clouds. In particular, it can partly overcome the influence of noise on a large sampling scale compared to the other methods which only use regression loss for normal estimation. For more details, a subnetwork is built after point-wise features extracted layers of the network and it gives more constraints to each point of the local patch via a binary classifier in the end. Then we use multi-task optimization to train the normal estimation and local plane classification tasks simultaneously.Also, to integrate the advantages of multi-scale results, a scale selection strategy is adopted, which is a data-driven approach for selecting the optimal scale around each point and encourages subnetwork specialization. Specifically, we employed a subnetwork called Scale Estimation Network to extract scale weight information from multi-scale features. More analysis is given about the relations between noise levels, local boundary, and scales in the experiment. These relationships can be a better guide to choosing particular scales for a particular model. Besides, the experimental result shows that our network can distinguish the points on the fitting plane accurately and this can be used to guide the normal estimation and our multi-scale method can improve the results well. Compared to some state-of-the-art surface normal estimators, our method is robust to noise and can achieve competitive results.