We propose a canonical point autoencoder (CPAE) that predicts dense correspondences between 3D shapes of the same category. The autoencoder performs two key functions: (a) encoding an arbitrarily ordered point cloud to a canonical primitive, e.g., a sphere, and (b) decoding the primitive back to the original input instance shape. As being placed in the bottleneck, this primitive plays a key role to map all the unordered point clouds on the canonical surface, and to be reconstructed in an ordered…