  Recent investigations on rotation invariance for 3D point clouds have been
devoted to devising rotation-invariant feature descriptors or learning
canonical spaces where objects are semantically aligned. Examinations of
learning frameworks for invariance have seldom been looked into. In this work,
we review rotation invariance in terms of point cloud registration and propose
an effective framework for rotation invariance learning via three sequential
stages, namely rotation-invariant shape encoding, aligned feature integration,
and deep feature registration. We first encode shape descriptors constructed
with respect to reference frames defined over different scales, e.g., local
patches and global topology, to generate rotation-invariant latent shape codes.
Within the integration stage, we propose Aligned Integration Transformer to
produce a discriminative feature representation by integrating point-wise self-
and cross-relations established within the shape codes. Meanwhile, we adopt
rigid transformations between reference frames to align the shape codes for
feature consistency across different scales. Finally, the deep integrated
feature is registered to both rotation-invariant shape codes to maximize
feature similarities, such that rotation invariance of the integrated feature
is preserved and shared semantic information is implicitly extracted from shape
codes. Experimental results on 3D shape classification, part segmentation, and
retrieval tasks prove the feasibility of our work. Our project page is released
at: https://rotation3d.github.io/.
