  Establishing correspondences between 3D shapes is a fundamental task in 3D
Computer Vision, typically addressed by matching local descriptors. Recently, a
few attempts at applying the deep learning paradigm to the task have shown
promising results. Yet, the only explored way to learn rotation invariant
descriptors has been to feed neural networks with highly engineered and
invariant representations provided by existing hand-crafted descriptors, a path
that goes in the opposite direction of end-to-end learning from raw data so
successfully deployed for 2D images. In this paper, we explore the benefits of
taking a step back in the direction of end-to-end learning of 3D descriptors by
disentangling the creation of a robust and distinctive rotation equivariant
representation, which can be learned from unoriented input data, and the
definition of a good canonical orientation, required only at test time to
obtain an invariant descriptor. To this end, we leverage two recent
innovations: spherical convolutional neural networks to learn an equivariant
descriptor and plane folding decoders to learn without supervision. The
effectiveness of the proposed approach is experimentally validated by
outperforming hand-crafted and learned descriptors on a standard benchmark.
