  This paper introduces GenCorres, a novel unsupervised joint shape matching
(JSM) approach. Our key idea is to learn a mesh generator to fit an unorganized
deformable shape collection while constraining deformations between adjacent
synthetic shapes to preserve geometric structures such as local rigidity and
local conformality. GenCorres presents three appealing advantages over existing
JSM techniques. First, GenCorres performs JSM among a synthetic shape
collection whose size is much bigger than the input shapes and fully leverages
the datadriven power of JSM. Second, GenCorres unifies consistent shape
matching and pairwise matching (i.e., by enforcing deformation priors between
adjacent synthetic shapes). Third, the generator provides a concise encoding of
consistent shape correspondences. However, learning a mesh generator from an
unorganized shape collection is challenging, requiring a good initialization.
GenCorres addresses this issue by learning an implicit generator from the input
shapes, which provides intermediate shapes between two arbitrary shapes. We
introduce a novel approach for computing correspondences between adjacent
implicit surfaces, which we use to regularize the implicit generator. Synthetic
shapes of the implicit generator then guide initial fittings (i.e., via
template-based deformation) for learning the mesh generator. Experimental
results show that GenCorres considerably outperforms state-of-the-art JSM
techniques. The synthetic shapes of GenCorres also achieve salient performance
gains against state-of-the-art deformable shape generators.
