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This paper proposes a convolution structure for learning SE(3)-equivariantfeatures from 3D point clouds. It can be viewed as an equivariant version ofkernel point convolutions (KPConv), a widely used convolution form to processpoint cloud data. Compared with existing equivariant networks, our design issimple, lightweight, fast, and easy to be integrated with existingtask-specific point cloud learning pipelines. We achieve these desirableproperties by combining group convolutions and quotient representations.Specifically, we discretize SO(3) to finite groups for their simplicity whileusing SO(2) as the stabilizer subgroup to form spherical quotient featurefields to save computations. We also propose a permutation layer to recoverSO(3) features from spherical features to preserve the capacity to distinguishrotations. Experiments show that our method achieves comparable or superiorperformance in various tasks, including object classification, pose estimation,and keypoint-matching, while consuming much less memory and running faster thanexisting work. The proposed method can foster the development of equivariantmodels for real-world applications based on point clouds.

E2PN: Efficient SE(3)-Equivariant Point Network