Supervised Descriptor Learning for Non-Rigid Shape Matching

We present a novel method for computing correspondences between pairs of non-rigid shapes. Unlike the majority of existing techniques that assume a deformation model, such as intrinsic isometries, a priori and use a pre-defined set of point or part descriptors, we consider the problem of learning a correspondence model given a collection of reference pairs with known mappings between them. Our formulation is purely intrinsic and does not rely on a consistent parametrization or spatial positions of vertices on the shapes. Instead, we consider the problem of finding the optimal set of descriptors that can be jointly used to reproduce the given reference maps. We show how this problem can be formalized and solved for efficiently by using the recently proposed functional maps framework. Moreover, we demonstrate how to extract the functional subspaces that can be mapped reliably across shapes. This gives us a way to not only obtain better functional correspondences, but also to associate a confidence value to the different parts of the mappings. We demonstrate the efficiency and usefulness of the proposedapproach on a variety of challenging shape matching tasks.