  3D point clouds deep learning is a promising field of research that allows a
neural network to learn features of point clouds directly, making it a robust
tool for solving 3D scene understanding tasks. While recent works show that
point cloud convolutions can be invariant to translation and point permutation,
investigations of the rotation invariance property for point cloud convolution
has been so far scarce. Some existing methods perform point cloud convolutions
with rotation-invariant features, existing methods generally do not perform as
well as translation-invariant only counterpart. In this work, we argue that a
key reason is that compared to point coordinates, rotation-invariant features
consumed by point cloud convolution are not as distinctive. To address this
problem, we propose a simple yet effective convolution operator that enhances
feature distinction by designing powerful rotation invariant features from the
local regions. We consider the relationship between the point of interest and
its neighbors as well as the internal relationship of the neighbors to largely
improve the feature descriptiveness. Our network architecture can capture both
local and global context by simply tuning the neighborhood size in each
convolution layer. We conduct several experiments on synthetic and real-world
point cloud classifications, part segmentation, and shape retrieval to evaluate
our method, which achieves the state-of-the-art accuracy under challenging
rotations.
