# E3-Net: Efficient E(3)-Equivariant Normal Estimation Network

arXiv: https://arxiv.org/abs/2406.00347 · HTML: https://mlsanity.com/paper/2406.00347/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 35 of its 63 references that are in the map.
- First posted on arXiv 1 Jun 2024.

## Builds on (most cited first, 30 of 35)

- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds](https://mlsanity.com/paper/1802.08219/) (2018)
- [SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networks](https://mlsanity.com/paper/2006.10503/) (2020)
- [Vector Neurons: A General Framework for SO(3)-Equivariant Networks](https://mlsanity.com/paper/2104.12229/) (2021)
- [Equivariant Flows: Exact Likelihood Generative Learning for Symmetric Densities](https://mlsanity.com/paper/2006.02425/) (2020)
- [Learning SO(3) Equivariant Representations with Spherical CNNs](https://mlsanity.com/paper/1711.06721/) (2017)
- [PU-Net: Point Cloud Upsampling Network](https://mlsanity.com/paper/1801.06761/) (2018)
- [Frame Averaging for Invariant and Equivariant Network Design](https://mlsanity.com/paper/2110.03336/) (2021)
- [Points2Surf: Learning Implicit Surfaces from Point Cloud Patches](https://mlsanity.com/paper/2007.10453/) (2020)
- [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)
- [Score-Based Point Cloud Denoising](https://mlsanity.com/paper/2107.10981/) (2021)
- [Equivariant Point Network for 3D Point Cloud Analysis](https://mlsanity.com/paper/2103.14147/) (2021)
- [FAENet: Frame Averaging Equivariant GNN for Materials Modeling](https://mlsanity.com/paper/2305.05577/) (2023)
- [A Rotation-Invariant Framework for Deep Point Cloud Analysis](https://mlsanity.com/paper/2003.07238/) (2020)
- [Differentiable Manifold Reconstruction for Point Cloud Denoising](https://mlsanity.com/paper/2007.13551/) (2020)
- [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)
- [Learning Graph-Convolutional Representations for Point Cloud Denoising](https://mlsanity.com/paper/2007.02578/) (2020)
- [NeAF: Learning Neural Angle Fields for Point Normal Estimation](https://mlsanity.com/paper/2211.16869/) (2022)
- [Globally Consistent Normal Orientation for Point Clouds by Regularizing the Winding-Number Field](https://mlsanity.com/paper/2304.11605/) (2023)
- [AdaFit: Rethinking Learning-based Normal Estimation on Point Clouds](https://mlsanity.com/paper/2108.05836/) (2021)
- [IterativePFN: True Iterative Point Cloud Filtering](https://mlsanity.com/paper/2304.01529/) (2023)
- [VN-Transformer: Rotation-Equivariant Attention for Vector Neurons](https://mlsanity.com/paper/2206.04176/) (2022)
- [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)
- [Normal Estimation for 3D Point Clouds via Local Plane Constraint and Multi-scale Selection](https://mlsanity.com/paper/1910.08537/) (2019)
- [GraphFit: Learning Multi-scale Graph-Convolutional Representation for Point Cloud Normal Estimation](https://mlsanity.com/paper/2207.11484/) (2022)

## Abstract (arXiv)

Point cloud normal estimation is a fundamental task in 3D geometry processing. While recent learning-based methods achieve notable advancements in normal prediction, they often overlook the critical aspect of equivariance. This results in inefficient learning of symmetric patterns. To address this issue, we propose E3-Net to achieve equivariance for normal estimation. We introduce an efficient random frame method, which significantly reduces the training resources required for this task to just 1/8 of previous work and improves the accuracy. Further, we design a Gaussian-weighted loss function and a receptive-aware inference strategy that effectively utilizes the local properties of point clouds. Our method achieves superior results on both synthetic and real-world datasets, and outperforms current state-of-the-art techniques by a substantial margin. We improve RMSE by 4% on the PCPNet dataset, 2.67% on the SceneNN dataset, and 2.44% on the FamousShape dataset.