# AdaFit: Rethinking Learning-based Normal Estimation on Point Clouds

arXiv: https://arxiv.org/abs/2108.05836 · HTML: https://mlsanity.com/paper/2108.05836/

## Key facts

- Cited by 29 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 38 references that are in the map.
- First posted on arXiv 12 Aug 2021.

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

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [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)
- [Semantic3D.net: A new Large-scale Point Cloud Classification Benchmark](https://mlsanity.com/paper/1704.03847/) (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)
- [EC-Net: an Edge-aware Point set Consolidation Network](https://mlsanity.com/paper/1807.06010/) (2018)
- [Total Denoising: Unsupervised Learning of 3D Point Cloud Cleaning](https://mlsanity.com/paper/1904.07615/) (2019)
- [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, 29 of 29)

- [NeAF: Learning Neural Angle Fields for Point Normal Estimation](https://mlsanity.com/paper/2211.16869/) (2022)
- [IterativePFN: True Iterative Point Cloud Filtering](https://mlsanity.com/paper/2304.01529/) (2023)
- [HSurf-Net: Normal Estimation for 3D Point Clouds by Learning Hyper Surfaces](https://mlsanity.com/paper/2210.07158/) (2022)
- [GraphFit: Learning Multi-scale Graph-Convolutional Representation for Point Cloud Normal Estimation](https://mlsanity.com/paper/2207.11484/) (2022)
- [Fast Learning of Signed Distance Functions from Noisy Point Clouds via Noise to Noise Mapping](https://mlsanity.com/paper/2407.14225/) (2024)
- [Rethinking the Approximation Error in 3D Surface Fitting for Point Cloud Normal Estimation](https://mlsanity.com/paper/2303.17167/) (2023)
- [Contrastive Learning for Joint Normal Estimation and Point Cloud Filtering](https://mlsanity.com/paper/2208.06811/) (2022)
- [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)
- [Semi-signed prioritized neural fitting for surface reconstruction from unoriented point clouds](https://mlsanity.com/paper/2206.06715/) (2022)
- [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)
- [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)
- [Weighted Point Cloud Normal Estimation](https://mlsanity.com/paper/2305.04007/) (2023)
- [Surface Normal Estimation with Transformers](https://mlsanity.com/paper/2401.05745/) (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)
- [GLASS: Geometry-aware Local Alignment and Structure Synchronization Network for 2D-3D Registration](https://mlsanity.com/paper/2603.26262/) (2026)
- [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)
- [CNS-Edit++: Category-Agnostic 3D Editing with Coupled Neural Shape Representation](https://mlsanity.com/paper/2607.16577/) (2026)

## Abstract (arXiv)

This paper presents a neural network for robust normal estimation on point clouds, named AdaFit, that can deal with point clouds with noise and density variations. Existing works use a network to learn point-wise weights for weighted least squares surface fitting to estimate the normals, which has difficulty in finding accurate normals in complex regions or containing noisy points. By analyzing the step of weighted least squares surface fitting, we find that it is hard to determine the polynomial order of the fitting surface and the fitting surface is sensitive to outliers. To address these problems, we propose a simple yet effective solution that adds an additional offset prediction to improve the quality of normal estimation. Furthermore, in order to take advantage of points from different neighborhood sizes, a novel Cascaded Scale Aggregation layer is proposed to help the network predict more accurate point-wise offsets and weights. Extensive experiments demonstrate that AdaFit achieves state-of-the-art performance on both the synthetic PCPNet dataset and the real-word SceneNN dataset.