  We present the first utterly self-supervised network for dense correspondence
mapping between non-isometric shapes. The task of alignment in non-Euclidean
domains is one of the most fundamental and crucial problems in computer vision.
As 3D scanners can generate highly complex and dense models, the mission of
finding dense mappings between those models is vital. The novelty of our
solution is based on a cyclic mapping between metric spaces, where the distance
between a pair of points should remain invariant after the full cycle. As the
same learnable rules that generate the point-wise descriptors apply in both
directions, the network learns invariant structures without any labels while
coping with non-isometric deformations. We show here state-of-the-art-results
by a large margin for a variety of tasks compared to known self-supervised and
supervised methods.
