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.

翻译：本文提出了一种用于从3D点云中学习SE(3)等变特征的卷积结构。该结构可被视为核点卷积（KPConv）的等变版本——KPConv是处理点云数据的一种广泛使用的卷积形式。与现有等变网络相比，我们的设计具有简单、轻量、快速且易于与现有任务特定点云学习流水线集成的特点。通过结合群卷积与商表示，我们实现了这些理想特性。具体而言，我们利用SO(2)作为稳定子群构建球面商特征场以节省计算，同时将SO(3)离散化为有限群以降低复杂度。我们还提出了一种置换层，用于从球面特征中恢复SO(3)特征，从而保持区分旋转的能力。实验表明，我们的方法在物体分类、姿态估计和关键点匹配等多项任务中达到相当或更优的性能，同时比现有工作消耗更少的内存并运行更快。所提方法可促进基于点云的实际应用中等变模型的发展。