  Analyzing the geometric and semantic properties of 3D point clouds through
the deep networks is still challenging due to the irregularity and sparsity of
samplings of their geometric structures. This paper presents a new method to
define and compute convolution directly on 3D point clouds by the proposed
annular convolution. This new convolution operator can better capture the local
neighborhood geometry of each point by specifying the (regular and dilated)
ring-shaped structures and directions in the computation. It can adapt to the
geometric variability and scalability at the signal processing level. We apply
it to the developed hierarchical neural networks for object classification,
part segmentation, and semantic segmentation in large-scale scenes. The
extensive experiments and comparisons demonstrate that our approach outperforms
the state-of-the-art methods on a variety of standard benchmark datasets (e.g.,
ModelNet10, ModelNet40, ShapeNet-part, S3DIS, and ScanNet).
