E$^3$-Net: Efficient E(3)-Equivariant Normal Estimation Network

TL;DR

E$^3$-Net introduces an efficient E(3)-equivariant neural network for point cloud normal estimation, significantly reducing training resources and improving accuracy by leveraging equivariance, a local property, and novel loss strategies.

Contribution

The paper presents E$^3$-Net, a novel equivariant network with a random frame method, Gaussian-weighted loss, and receptive-aware inference for superior normal estimation.

Findings

Reduces training resources to 1/8 of previous methods.

Achieves 4% RMSE improvement on PCPNet dataset.

Outperforms state-of-the-art techniques on multiple datasets.

Abstract

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.