  Finding correspondences between 3D shapes is a crucial problem in computer
vision and graphics, which is for example relevant for tasks like shape
interpolation, pose transfer, or texture transfer. An often neglected but
essential property of matchings is geometric consistency, which means that
neighboring triangles in one shape are consistently matched to neighboring
triangles in the other shape. Moreover, while in practice one often has only
access to partial observations of a 3D shape (e.g. due to occlusion, or
scanning artifacts), there do not exist any methods that directly address
geometrically consistent partial shape matching. In this work we fill this gap
by proposing to integrate state-of-the-art deep shape features into a novel
integer linear programming partial shape matching formulation. Our optimization
yields a globally optimal solution on low resolution shapes, which we then
refine using a coarse-to-fine scheme. We show that our method can find more
reliable results on partial shapes in comparison to existing geometrically
consistent algorithms (for which one first has to fill missing parts with a
dummy geometry). Moreover, our matchings are substantially smoother than
learning-based state-of-the-art shape matching methods.
