  We present a new deep learning approach for matching deformable shapes by
introducing {\it Shape Deformation Networks} which jointly encode 3D shapes and
correspondences. This is achieved by factoring the surface representation into
(i) a template, that parameterizes the surface, and (ii) a learnt global
feature vector that parameterizes the transformation of the template into the
input surface. By predicting this feature for a new shape, we implicitly
predict correspondences between this shape and the template. We show that these
correspondences can be improved by an additional step which improves the shape
feature by minimizing the Chamfer distance between the input and transformed
template. We demonstrate that our simple approach improves on state-of-the-art
results on the difficult FAUST-inter challenge, with an average correspondence
error of 2.88cm. We show, on the TOSCA dataset, that our method is robust to
many types of perturbations, and generalizes to non-human shapes. This
robustness allows it to perform well on real unclean, meshes from the the SCAPE
dataset.
