  Recent interest in point cloud analysis has led rapid progress in designing
deep learning methods for 3D models. However, state-of-the-art models are not
robust to rotations, which remains an unknown prior to real applications and
harms the model performance. In this work, we introduce a novel Patch-wise
Rotation-invariant network (PaRot), which achieves rotation invariance via
feature disentanglement and produces consistent predictions for samples with
arbitrary rotations. Specifically, we design a siamese training module which
disentangles rotation invariance and equivariance from patches defined over
different scales, e.g., the local geometry and global shape, via a pair of
rotations. However, our disentangled invariant feature loses the intrinsic pose
information of each patch. To solve this problem, we propose a
rotation-invariant geometric relation to restore the relative pose with
equivariant information for patches defined over different scales. Utilising
the pose information, we propose a hierarchical module which implements
intra-scale and inter-scale feature aggregation for 3D shape learning.
Moreover, we introduce a pose-aware feature propagation process with the
rotation-invariant relative pose information embedded. Experiments show that
our disentanglement module extracts high-quality rotation-robust features and
the proposed lightweight model achieves competitive results in rotated 3D
object classification and part segmentation tasks. Our project page is released
at: https://patchrot.github.io/.
