  Recently, many deep neural networks were designed to process 3D point clouds,
but a common drawback is that rotation invariance is not ensured, leading to
poor generalization to arbitrary orientations. In this paper, we introduce a
new low-level purely rotation-invariant representation to replace common 3D
Cartesian coordinates as the network inputs. Also, we present a network
architecture to embed these representations into features, encoding local
relations between points and their neighbors, and the global shape structure.
To alleviate inevitable global information loss caused by the
rotation-invariant representations, we further introduce a region relation
convolution to encode local and non-local information. We evaluate our method
on multiple point cloud analysis tasks, including shape classification, part
segmentation, and shape retrieval. Experimental results show that our method
achieves consistent, and also the best performance, on inputs at arbitrary
orientations, compared with the state-of-the-arts.
