Learning an Effective Equivariant 3D Descriptor Without Supervision

Establishing correspondences between 3D shapes is a fundamental task in 3D Computer Vision, typically ad- dressed by matching local descriptors. Recently, a few at- tempts 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 representa- tions 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 descrip- tors 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 re- cent innovations: spherical convolutional neural networks to learn an equivariant descriptor and plane folding de- coders to learn without supervision. The effectiveness of the proposed approach is experimentally validated by out- performing hand-crafted and learned descriptors on a stan- dard benchmark.