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

Area of Science:

• Computer Vision
• 3D Geometry Processing
• Machine Learning

Background:

• Point cloud normal estimation is vital for 3D applications.
• Existing learning methods lack equivariance, hindering symmetric pattern learning.
• E3-Net addresses the need for equivariant normal estimation.

Purpose of the Study:

• To propose an equivariant neural network, E3-Net, for accurate point cloud normal estimation.
• To reduce computational resources for normal estimation.
• To improve the learning of symmetric patterns in geometric data.

Main Methods:

• Developed E3-Net, a novel neural network architecture with inherent equivariance.
• Introduced an efficient random frame method reducing training resources by 8x.
• Designed a Gaussian-weighted loss function and receptive-aware inference strategy.

Main Results:

• E3-Net demonstrated superior performance on synthetic and real-world datasets.
• Achieved significant RMSE improvements: 4% on PCPNet, 2.67% on SceneNN, 2.44% on FamousShape.
• The method shows robustness and scalability in diverse environments.

Conclusions:

• E3-Net offers a highly accurate and resource-efficient solution for point cloud normal estimation.
• The proposed equivariant approach effectively leverages geometric data properties.
• E3-Net represents a significant advancement in 3D geometry processing and computer vision.