Self-supervised non-rigid correspondence by geodesic distortion minimization using the deformation field

Geodesic distortion minimization has been demonstrated as an effective approach for self-supervised non-rigid correspondence; see "Unsupervised learning of dense shape correspondence‏" (CVPR 2019).

There, shape descriptors were represented by a deep network, and the network was optimized to minimize the geodesic distortion criteria of the correspondence, resulting through the Functional Maps pipeline.

A novel method to differentiate the geodesic distortion with respect to the deformation field was introduced later in the paper "Limp: Learning latent shape representations with metric preservation priors" (ECCV 2020).

The proposed project aims at combining the observations in both mentioned publications. The goal is to represent the deformation field using a deep network and to optimize it to admit the following requirements:

1) Geodesic distance preservation of the deformation field 

2) Overlapping between the deformed source shape and the target shape.

Project timezone: C