Hausdorff point convolution with geometric priors

Developing point convolution for irregular point clouds to extract deep features remains challenging. Current methods evaluate the response by computing point set distances which account only for the spatial alignment between two point sets, but not quite for their underlying shapes. Without a shape-aware response, it is hard to characterize the 3D geometry of a point cloud efficiently with a compact set of kernels. In this paper, we advocate the use of modified Hausdorff distance as a shape-aware distance measure for calculating point convolutional responses. The technique we present, coined Hausdorff point convolution (HPC), is shape-aware. We show that HPC constitutes a powerful point feature learning with a rather compact set of only four types of geometric priors as kernels. We further develop an HPC-based deep neural network (HPC-DNN). Task-specific learning can be achieved by tuning the network weights for combining the shortest distances between the input and the kernel point sets. We also realize hierarchical feature learning by designing a multi-kernel HPC for multi-scale feature encoding. Extensive experiments demonstrate that HPC-DNN outperforms strong point convolution baselines (e.g., KPConv), achieving 2.8% mIoU performance boost on S3DIS and 1.5% on SemanticKITTI for semantic segmentation task.