Sparse modeling of intrinsic correspondences

We present a novel sparse modeling approach to non-rigid shape match-ing using only the ability to detect repeatable regions. As the input to our algorithm, we are given only two sets of regions in two shapes; no descriptors are provided so the correspondence between the regions is not know, nor we know how many regions correspond in the two shapes. We show that even with such scarce information, it is possible to estab-lish very accurate correspondence between the shapes by using methods from the field of sparse modeling, being this, the first non-trivial use of sparse models in shape correspondence. We formulate the problem of per-muted sparse coding, in which we solve simultaneously for an unknown permutation ordering the regions on two shapes and for an unknown cor-respondence in functional representation. We also propose a robust vari-ant capable of handling incomplete matches. Numerically, the problem is solved efficiently by alternating the solution of a linear assignment and a sparse coding problem. The proposed methods are evaluated qualitatively and quantitatively on standard benchmarks containing both synthetic and scanned objects.