  Graph matching aims to establish correspondences between vertices of graphs
such that both the node and edge attributes agree. Various learning-based
methods were recently proposed for finding correspondences between image key
points based on deep graph matching formulations. While these approaches mainly
focus on learning node and edge attributes, they completely ignore the 3D
geometry of the underlying 3D objects depicted in the 2D images. We fill this
gap by proposing a trainable framework that takes advantage of graph neural
networks for learning a deformable 3D geometry model from inhomogeneous image
collections, i.e. a set of images that depict different instances of objects
from the same category. Experimentally we demonstrate that our method
outperforms recent learning-based approaches for graph matching considering
both accuracy and cycle-consistency error, while we in addition obtain the
underlying 3D geometry of the objects depicted in the 2D images.
