Bending Graphs: Hierarchical Shape Matching using Gated Optimal Transport

TL;DR

This paper introduces a hierarchical shape matching method that combines local and global shape information using a novel optimal transport solver, achieving robust correspondence predictions even with severe deformations.

Contribution

It proposes a hierarchical learning framework with a new optimal transport solver that updates features iteratively for globally consistent shape correspondences.

Findings

Robust performance on datasets with severe deformations

No extensive training or refinement needed

Effective integration of local and global shape features

Abstract

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 for extensive training or refinement.