Recently, plenty of deep learning methods have been proposed to handle point clouds. Almost all of them input the entire point cloud and ignore the information redundancy lying in point clouds. This paper addresses this problem by extracting the Reeb graph from point clouds, which is a much more informative and compact representation of point clouds, and then filter the graph with deep graph convolution. To be able to classify or segment point clouds well, we propose (1) Graph Normalization to transform various graphs into a canonical graph space; (2) Normalized Similarity Distance to better identify the graph structure;(3) Reeb Graph Guided Node Pooling in order to aggregate high-level features from kNN graphs. Besides, our method naturally fits into the problem of classifying point clouds with unknown orientations. In the results, we show that our method gives a competitive performance to the state-of-the-art methods and outperforms previous methods by a large margin on handling point clouds with unknown orientations.

最近，已经提出了许多深度学习方法来处理点云。他们几乎都输入了整个点云，而忽略了点云中的信息冗余。本文通过从点云中提取Reeb图来解决此问题，该图是点云的一种更为有用和紧凑的表示形式，然后使用深度图卷积对该图进行过滤。为了能够很好地对点云进行分类或分割，我们提出：（1）图归一化将各种图转换为规范图空间；（2）归一化相似距离以更好地识别图结构;（3）Reeb图引导节点池化，以便从kNN图中聚合高级特征。此外，我们的方法自然适用于对方向未知的点云进行分类的问题。在结果中