Cyclic Functional Mapping: Self-supervised correspondence between non-isometric deformable shapes

TL;DR

This paper introduces a self-supervised neural network that learns dense correspondences between non-isometric 3D shapes using cyclic mappings, achieving state-of-the-art results without labeled data.

Contribution

The first self-supervised approach for dense correspondence of non-isometric shapes using cyclic metric space mappings, eliminating the need for labeled training data.

Findings

Achieves state-of-the-art accuracy on shape correspondence tasks.

Operates effectively without labeled training data.

Handles complex non-isometric deformations robustly.

Abstract

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.