Cyclic Functional Mapping: Self-supervised Correspondence Between Non-isometric Deformable Shapes

Abstract

We present the first spatial-spectral joint consistency network for self-supervised 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.