  We propose a local-to-global representation learning algorithm for 3D point
cloud data, which is appropriate to handle various geometric transformations,
especially rotation, without explicit data augmentation with respect to the
transformations. Our model takes advantage of multi-level abstraction based on
graph convolutional neural networks, which constructs a descriptor hierarchy to
encode rotation-invariant shape information of an input object in a bottom-up
manner. The descriptors in each level are obtained from a neural network based
on a graph via stochastic sampling of 3D points, which is effective in making
the learned representations robust to the variations of input data. The
proposed algorithm presents the state-of-the-art performance on the
rotation-augmented 3D object recognition and segmentation benchmarks, and we
further analyze its characteristics through comprehensive ablative experiments.
