  In this paper, we propose a learning-based framework for non-rigid shape
registration without correspondence supervision. Traditional shape registration
techniques typically rely on correspondences induced by extrinsic proximity,
therefore can fail in the presence of large intrinsic deformations. Spectral
mapping methods overcome this challenge by embedding shapes into, geometric or
learned, high-dimensional spaces, where shapes are easier to align. However,
due to the dependency on abstract, non-linear embedding schemes, the latter can
be vulnerable with respect to perturbed or alien input. In light of this, our
framework takes the best of both worlds. Namely, we deform source mesh towards
the target point cloud, guided by correspondences induced by high-dimensional
embeddings learned from deep functional maps (DFM). In particular, the
correspondences are dynamically updated according to the intermediate
registrations and filtered by consistency prior, which prominently robustify
the overall pipeline. Moreover, in order to alleviate the requirement of
extrinsically aligned input, we train an orientation regressor on a set of
aligned synthetic shapes independent of the training shapes for DFM. Empirical
results show that, with as few as dozens of training shapes of limited
variability, our pipeline achieves state-of-the-art results on several
benchmarks of non-rigid point cloud matching, but also delivers high-quality
correspondences between unseen challenging shape pairs that undergo both
significant extrinsic and intrinsic deformations, in which case neither
traditional registration methods nor intrinsic methods work. The code is
available at https://github.com/rqhuang88/DFR.
