Structured Prediction of Dense Maps between Geometric Domains

We introduce a new framework for learning dense correspondence between deformable geometric domains such as polygonal meshes and point clouds. Existing learning based approaches model correspondence as a labelling problem, where each point of a query domain receives a label identifying a point on some reference domain; the correspondence is then constructed a posteriori by composing the label predictions of two input geometries. We propose a paradigm shift and design a structured prediction model in the space of functional maps, linear operators that provide a compact representation of the correspondence. We model the learning process via a deep residual network which takes dense descriptor fields as input, and outputs a soft map between the two given objects. The resulting correspondence is shown to be accurate on several challenging shape correspondence benchmarks.