  Learning to predict reliable characteristic orientations of 3D point clouds
is an important yet challenging problem, as different point clouds of the same
class may have largely varying appearances. In this work, we introduce a novel
method to decouple the shape geometry and semantics of the input point cloud to
achieve both stability and consistency. The proposed method integrates
shape-geometry-based SO(3)-equivariant learning and shape-semantics-based
SO(3)-invariant residual learning, where a final characteristic orientation is
obtained by calibrating an SO(3)-equivariant orientation hypothesis using an
SO(3)-invariant residual rotation. In experiments, the proposed method not only
demonstrates superior stability and consistency but also exhibits
state-of-the-art performances when applied to point cloud part segmentation,
given randomly rotated inputs.
