3D points distribute in a continuous 3D space irregularly, thus directly adapting 2D image convolution to 3D points is not an easy job. Previous works often artificially divide the space into regular grids, yet it could be suboptimal to learn geometry. In this paper, we propose SPCNN, namely, Space Probing Convolutional Neural Network, which naturally generalizes image CNN to deal with point clouds. The key idea of SPCNN is learning to probe the 3D space in an adaptive manner. Specifically, we define a pool of learnable convolutional weights, and let each point in the local region learn to choose a suitable convolutional weight from the pool. This is achieved by constructing a geometry guided index-mapping function that implicitly establishes a correspondence between convolutional weights and some local regions in the neighborhood (Fig. 1). In this way, the index-mapping function learns to adaptively partition nearby space for local geometry pattern recognition. With this convolution as a basic operator, SPCNN, a hierarchical architecture can be developed for effective point cloud analysis. Extensive experiments on challenging benchmarks across three tasks demonstrate that SPCNN achieves the state-of-the-art or has competitive performance.

We propose Spherical Hierarchical modeling of 3D point cloud. Inspired by Shape Context, we design a receptive field on each 3D point by placing a spherical coordinate on it. We sample points using the furthest point method and creating overlapping balls of points. For each ball, we divide the space into radial, polar angular and azimuthal angular bins on which we form a Spherical Hierarchy. We apply 1x1 CNN convolution on points to start the initial feature extraction. Repeated 3D CNN and max pooling over the Spherical bins propagate contextual information until all the information is condensed in the center bin. Extensive experiments on five datasets strongly evidence that our method outperform current models on various Point Cloud Learning tasks, including 2D/3D shape classification, 3D part segmentation and 3D semantic segmentation.