Bending Graphs: Hierarchical Shape Matching Using Gated Optimal Transport

Mahdi Saleh, Shun-Cheng Wu, Luca Cosmo, Nassir Navab, Benjamin Busam, Federico Tombari; Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), 2022, pp. 11757-11767

Shape matching has been a long-studied problem for the computer graphics and vision community. The objective is to predict a dense correspondence between meshes that have a certain degree of deformation. Existing methods either consider the local description of sampled points or discover correspondences based on global shape information. In this work, we investigate a hierarchical learning design, to which we incorporate local patch-level information and global shape-level structures. This flexible representation enables correspondence prediction and provides rich features for the matching stage. Finally, we propose a novel optimal transport solver by recurrently updating features on non-confident nodes to learn globally consistent correspondences between the shapes. Our results on publicly available datasets suggest robust performance in presence of severe deformations without the need of extensive training or refinement.