  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,
Point-wise 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. Spherical Voxel Convolution and Point Re-sampling are proposed to
extract rotation invariant features for each point. In addition, we extend PRIN
to a sparse version called SPRIN, which directly operates on sparse point
clouds. Both PRIN and SPRIN can be applied to tasks ranging from object
classification, part segmentation, to 3D feature matching and label alignment.
Results show that, on the dataset with randomly rotated point clouds, SPRIN
demonstrates better performance than state-of-the-art methods without any data
augmentation. We also provide thorough theoretical proof and analysis for
point-wise rotation invariance achieved by our methods. Our code is available
on https://github.com/qq456cvb/SPRIN.
