  We propose a novel unsupervised learning approach to 3D shape correspondence
that builds a multiscale matching pipeline into a deep neural network. This
approach is based on smooth shells, the current state-of-the-art axiomatic
correspondence method, which requires an a priori stochastic search over the
space of initial poses. Our goal is to replace this costly preprocessing step
by directly learning good initializations from the input surfaces. To that end,
we systematically derive a fully differentiable, hierarchical matching pipeline
from entropy regularized optimal transport. This allows us to combine it with a
local feature extractor based on smooth, truncated spectral convolution
filters. Finally, we show that the proposed unsupervised method significantly
improves over the state-of-the-art on multiple datasets, even in comparison to
the most recent supervised methods. Moreover, we demonstrate compelling
generalization results by applying our learned filters to examples that
significantly deviate from the training set.
