Learning Polynomial-Based Separable Convolution for 3D Point Cloud Analysis

Shape classification and segmentation of point cloud data are two of the most demanding tasks in photogrammetry and remote sensing applications, which aim to recognize object categories or point labels. Point convolution is an essential operation when designing a network on point clouds for these tasks, which helps to explore 3D local points for feature learning. In this paper, we propose a novel point convolution (PSConv) using separable weights learned with polynomials for 3D point cloud analysis. Specifically, we generalize the traditional convolution defined on the regular data to a 3D point cloud by learning the point convolution kernels based on the polynomials of transformed local point coordinates. We further propose a separable assumption on the convolution kernels to reduce the parameter size and computational cost for our point convolution. Using this novel point convolution, a hierarchical network (PSNet) defined on the point cloud is proposed for 3D shape analysis tasks such as 3D shape classification and segmentation. Experiments are conducted on standard datasets, including synthetic and real scanned ones, and our PSNet achieves state-of-the-art accuracies for shape classification, as well as competitive results for shape segmentation compared with previous methods.