Publications

Sparse Modeling of Intrinsic Correspondences
J. Pokrass, A. M. Bronstein, M. M. Bronstein, P. Sprechmann, G. Sapiro
Eurographics: Computer Graphics Forum, 2013.

Abstract: We present a novel sparse modeling approach to non-rigid shape matching 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 establish 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 permuted sparse coding, in which we solve simultaneously for an unknown permutation ordering the regions on two shapes and for an unknown correspondence in functional representation. We also propose a robust variant 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.

Partial shape matching without point-wise correspondence

J. Pokrass, A. M. Bronstein, M. M. Bronstein

Numerical Mathematics: Theory, Methods and Applications (NM-TMA), 2012.

 

Abstract: Partial similarity of shapes in a challenging problem arising in many important applications in computer vision, shape analysis, and graphics, e.g. when one has to deal with partial information and acquisition artifacts. The problem is especially hard when the underlying shapes are non-rigid and are given up to a deformation. Partial matching is usually approached by computing local descriptors on a pair of shapes and then establishing a point-wise non-bijective correspondence between the two, taking into account possibly different parts. In this paper, we introduce an alternative correspondence-less approach to matching fragments to an entire shape undergoing a non-rigid deformation. We use diffusion geometric descriptors and optimize over the integration domains on which the integral descriptors of the two parts match. The problem is regularized using the Mumford-Shah functional. We show an efficient discretization based on the Ambrosio-Tortorelli approximation generalized to triangular meshes and point clouds, and present experiments demonstrating the success of the proposed method.

A correspondence-less approach to matching of deformable shapes

J. Pokrass, A. M. Bronstein, M. M. Bronstein

Proc. Conf. on Scale Space and Variational Methods in Computer Vision (SSVM), 2011 

Abstract: Finding a match between partially available deformable shapes is a challenging problem with numerous applications. The problem is usually approached by computing local descriptors on a pair of shapes and then establishing a point-wise correspondence between the two. In this paper, we introduce an alternative correspondence-less approach to matching fragments to an entire shape undergoing a non-rigid deformation. We use diffusion geometric descriptors and optimize over the integration domains on which the integral descriptors of the two parts match. The problem is regularized using the Mumford-Shah functional.We show an efficient discretization based on the Ambrosio-Tortorelli approximation generalized to triangular meshes. Experiments demonstrating the success of the proposed method are presented.