  Point cloud analysis without pose priors is very challenging in real
applications, as the orientations of point clouds are often unknown. In this
paper, we propose a brand new point-set learning framework PRIN, namely,
Pointwise Rotation-Invariant Network, focusing on rotation-invariant feature
extraction in point clouds analysis. We construct spherical signals by Density
Aware Adaptive Sampling to deal with distorted point distributions in spherical
space. In addition, we propose Spherical Voxel Convolution and Point
Re-sampling to extract rotation-invariant features for each point. Our network
can be applied to tasks ranging from object classification, part segmentation,
to 3D feature matching and label alignment. We show that, on the dataset with
randomly rotated point clouds, PRIN demonstrates better performance than
state-of-the-art methods without any data augmentation. We also provide
theoretical analysis for the rotation-invariance achieved by our methods.
