Sparse Models for Intrinsic Shape Correspondence

  • Jonathan Pokrass
  • Alexander M. BronsteinEmail author
  • Michael M. Bronstein
  • Pablo Sprechmann
  • Guillermo Sapiro
Conference paper
Part of the Mathematics and Visualization book series (MATHVISUAL)


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 do 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.


Sparse Code Iterative Close Point Sparse Modeling Proximal Operator Pursuit Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



Work partially supported by GIF, ISF, and BSF. M.B. is supported by the ERC Starting grant No. 307047. A.B. is supported by the ERC Starting Grant No. 335491.


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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Jonathan Pokrass
    • 1
  • Alexander M. Bronstein
    • 1
    Email author
  • Michael M. Bronstein
    • 2
  • Pablo Sprechmann
    • 3
  • Guillermo Sapiro
    • 3
  1. 1.School of Electrical EngineeringTel Aviv UniversityTel AvivIsrael
  2. 2.Faculty of InformaticsInstitute of Computational Science University of LuganoLuganoSwitzerland
  3. 3.School of Electrical and Computer EngineeringDuke UniversityDurhamUSA

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