G-MSM: Unsupervised Multi-Shape Matching with Graph-based Affinity Priors

TL;DR

G-MSM introduces an unsupervised, graph-based approach for non-rigid shape matching that models the shape data manifold and enforces cycle-consistency, achieving state-of-the-art results on challenging benchmarks.

Contribution

It proposes a novel unsupervised multi-shape matching framework using shape graphs and cycle-consistency to learn topology-aware shape priors.

Findings

State-of-the-art performance on shape correspondence benchmarks

Effective handling of real-world 3D scan meshes with noise

Flexible framework encompassing various shape graph classes

Abstract

We present G-MSM (Graph-based Multi-Shape Matching), a novel unsupervised learning approach for non-rigid shape correspondence. Rather than treating a collection of input poses as an unordered set of samples, we explicitly model the underlying shape data manifold. To this end, we propose an adaptive multi-shape matching architecture that constructs an affinity graph on a given set of training shapes in a self-supervised manner. The key idea is to combine putative, pairwise correspondences by propagating maps along shortest paths in the underlying shape graph. During training, we enforce cycle-consistency between such optimal paths and the pairwise matches which enables our model to learn topology-aware shape priors. We explore different classes of shape graphs and recover specific settings, like template-based matching (star graph) or learnable ranking/sorting (TSP graph), as special cases in our framework. Finally, we demonstrate state-of-the-art performance on several recent shape correspondence benchmarks, including real-world 3D scan meshes with topological noise and challenging inter-class pairs.