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. More 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 while consuming much less memory and running faster than existing work. The proposed method can foster the adoption of equivariant feature learning in practical applications based on point clouds and inspire future developments of equivariant feature learning for real-world applications.

翻译：本文建议了从 3D 点云中学习 SE(3) 等离异特性的演进结构。 它可以被看作用于处理点云数据的一种广泛使用的演进形式( KPConv) 内点变异( KPConv) 的变异版本。 与现有的等异网络相比, 我们的设计简单、 轻量、 快速、 容易与现有任务特定点云学习管道结合。 我们通过组合变异和商数表达方式实现这些理想特性。 更具体地说, 我们将SO(3) 分解为限制组, 以简单为目的, 同时使用 SO(2) 作为稳定器分组, 形成球点点点点点点点点数特性域以保存计算。 我们还建议一个变异层, 将SO(3) 特性从球状特性中恢复出来, 以保持辨别旋转的能力。 实验表明, 我们的方法在各种任务中取得了相似或优异性性, 同时消耗的记忆和运行速度要快得多。 拟议的方法可以促进在基于点点云的实用应用中采用等异特性学习方法, 并激励未来在现实应用中进行等异特性学习。