Despite the recent active research on processing point clouds with deep networks, few attention has been on the sensitivity of the networks to rotations. In this paper, we propose a deep learning architecture that achieves discrete $\mathbf{SO}(2)$/$\mathbf{SO}(3)$ rotation equivariance for point cloud recognition. Specifically, the rotation of an input point cloud with elements of a rotation group is similar to shuffling the feature vectors generated by our approach. The equivariance is easily reduced to invariance by eliminating the permutation with operations such as maximum or average. Our method can be directly applied to any existing point cloud based networks, resulting in significant improvements in their performance for rotated inputs. We show state-of-the-art results in the classification tasks with various datasets under both $\mathbf{SO}(2)$ and $\mathbf{SO}(3)$ rotations. In addition, we further analyze the necessary conditions of applying our approach to PointNet based networks. Source codes at https://github.com/lijx10/rot-equ-net

该论文提出了一种深度学习架构，能够在点云识别中实现离散的SO（2）/SO（3）旋转等变性，通过消除置换并进行操作，提升了任何现有点云网络的性能，并在各种旋转下，展示了分类任务的最新成果。

点云识别的离散旋转等变性