  This paper proposes a convolution structure for learning SE(3)-equivariant
features from 3D point clouds. It can be viewed as an equivariant version of
kernel point convolutions (KPConv), a widely used convolution form to process
point cloud data. Compared with existing equivariant networks, our design is
simple, lightweight, fast, and easy to be integrated with existing
task-specific point cloud learning pipelines. We achieve these desirable
properties by combining group convolutions and quotient representations.
Specifically, we discretize SO(3) to finite groups for their simplicity while
using SO(2) as the stabilizer subgroup to form spherical quotient feature
fields to save computations. We also propose a permutation layer to recover
SO(3) features from spherical features to preserve the capacity to distinguish
rotations. Experiments show that our method achieves comparable or superior
performance in various tasks, including object classification, pose estimation,
and keypoint-matching, while consuming much less memory and running faster than
existing work. The proposed method can foster the development of equivariant
models for real-world applications based on point clouds.
