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

Point cloud normal estimation is a fundamental task in 3D geometry processing, playing a crucial role in applications such as 3D reconstruction, object recognition, and surface analysis. While recent learning-based methods achieve notable advancements in normal prediction, they often overlook the critical aspect of equivariance. This oversight leads to inefficient learning of symmetric patterns inherent in geometric data. To address this issue, we propose E$^{3}$3-Net, an innovative neural network architecture designed to inherently achieve equivariance for normal estimation. We introduce an efficient random frame method, which significantly reduces the training resources required for this task to just 1/8 of previous work, while simultaneously enhancing prediction accuracy. Furthermore, we design a Gaussian-weighted loss function and a receptive-aware inference strategy that effectively leverage the local properties of point clouds, ensuring more precise and reliable normal estimation. Our method demonstrates superior performance across both synthetic and real-world datasets, consistently outperforming current state-of-the-art techniques by a substantial margin. Specifically, we achieve a 4% improvement in RMSE on the PCPNet dataset, 2.67% on the SceneNN dataset, and 2.44% on the FamousShape dataset, highlighting the robustness and scalability of E$^{3}$3-Net in diverse environments.