  We present a novel rotation invariant architecture operating directly on
point cloud data. We demonstrate how rotation invariance can be injected into a
recently proposed point-based PCNN architecture, at all layers of the network,
achieving invariance to both global shape transformations, and to local
rotations on the level of patches or parts, useful when dealing with non-rigid
objects. We achieve this by employing a spherical harmonics based kernel at
different layers of the network, which is guaranteed to be invariant to rigid
motions. We also introduce a more efficient pooling operation for PCNN using
space-partitioning data-structures. This results in a flexible, simple and
efficient architecture that achieves accurate results on challenging shape
analysis tasks including classification and segmentation, without requiring
data-augmentation, typically employed by non-invariant approaches.
