  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.
