  Various recent methods attempt to implement rotation-invariant 3D deep
learning by replacing the input coordinates of points with relative distances
and angles. Due to the incompleteness of these low-level features, they have to
undertake the expense of losing global information. In this paper, we propose
the CRIN, namely Centrifugal Rotation-Invariant Network. CRIN directly takes
the coordinates of points as input and transforms local points into
rotation-invariant representations via centrifugal reference frames. Aided by
centrifugal reference frames, each point corresponds to a discrete rotation so
that the information of rotations can be implicitly stored in point features.
Unfortunately, discrete points are far from describing the whole rotation
space. We further introduce a continuous distribution for 3D rotations based on
points. Furthermore, we propose an attention-based down-sampling strategy to
sample points invariant to rotations. A relation module is adopted at last for
reinforcing the long-range dependencies between sampled points and predicts the
anchor point for unsupervised rotation estimation. Extensive experiments show
that our method achieves rotation invariance, accurately estimates the object
rotation, and obtains state-of-the-art results on rotation-augmented
classification and part segmentation. Ablation studies validate the
effectiveness of the network design.
