# Nesti-Net: Normal Estimation for Unstructured 3D Point Clouds using Convolutional Neural Networks

arXiv: https://arxiv.org/abs/1812.00709 · HTML: https://mlsanity.com/paper/1812.00709/

## Key facts

- Cited by 44 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Dec 2018.

## Built on by (most cited first, 30 of 44)

- [Shape As Points: A Differentiable Poisson Solver](https://mlsanity.com/paper/2106.03452/) (2021)
- [DiGS : Divergence guided shape implicit neural representation for unoriented point clouds](https://mlsanity.com/paper/2106.10811/) (2021)
- [CAP-UDF: Learning Unsigned Distance Functions Progressively from Raw Point Clouds with Consistency-Aware Field Optimization](https://mlsanity.com/paper/2210.02757/) (2022)
- [NeAF: Learning Neural Angle Fields for Point Normal Estimation](https://mlsanity.com/paper/2211.16869/) (2022)
- [Learning a More Continuous Zero Level Set in Unsigned Distance Fields through Level Set Projection](https://mlsanity.com/paper/2308.11441/) (2023)
- [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)
- [GraphFit: Learning Multi-scale Graph-Convolutional Representation for Point Cloud Normal Estimation](https://mlsanity.com/paper/2207.11484/) (2022)
- [SketchSampler: Sketch-based 3D Reconstruction via View-dependent Depth Sampling](https://mlsanity.com/paper/2208.06880/) (2022)
- [Neural Geometry Processing via Spherical Neural Surfaces](https://mlsanity.com/paper/2407.07755/) (2024)
- [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)
- [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)
- [Neural Experts: Mixture of Experts for Implicit Neural Representations](https://mlsanity.com/paper/2410.21643/) (2024)
- [Fast and Accurate Normal Estimation for Point Cloud via Patch Stitching](https://mlsanity.com/paper/2103.16066/) (2021)
- [Point Cloud Upsampling and Normal Estimation using Deep Learning for Robust Surface Reconstruction](https://mlsanity.com/paper/2102.13391/) (2021)
- [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)
- [Fine-Grained VR Sketching: Dataset and Insights](https://mlsanity.com/paper/2209.10008/) (2022)
- [Deep Point Cloud Normal Estimation via Triplet Learning](https://mlsanity.com/paper/2110.10494/) (2021)
- [A review of laser scanning for geological and geotechnical applications in underground mining](https://mlsanity.com/paper/2211.11181/) (2022)
- [Procedural Generation of 3D Maize Plant Architecture from LIDAR Data](https://mlsanity.com/paper/2501.13963/) (2025)
- [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)
- [Learning Normals of Noisy Points by Local Gradient-Aware Surface Filtering](https://mlsanity.com/paper/2507.03394/) (2025)

## Abstract (arXiv)

In this paper, we propose a normal estimation method for unstructured 3D point clouds. This method, called Nesti-Net, builds on a new local point cloud representation which consists of multi-scale point statistics (MuPS), estimated on a local coarse Gaussian grid. This representation is a suitable input to a CNN architecture. The normals are estimated using a mixture-of-experts (MoE) architecture, which relies on a data-driven approach for selecting the optimal scale around each point and encourages sub-network specialization. Interesting insights into the network's resource distribution are provided. The scale prediction significantly improves robustness to different noise levels, point density variations and different levels of detail. We achieve state-of-the-art results on a benchmark synthetic dataset and present qualitative results on real scanned scenes.