Partial shape matching without point-wise correspondence

Jonathan Pokrass*, Alexander M. Bronstein, Michael M. Bronstein

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Partial similarity of shapes is 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 region-wise local 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 point clouds and meshes, and present experiments demonstrating the success of the proposed method.

Original languageEnglish
Pages (from-to)223-244
Number of pages22
JournalNumerical Mathematics
Issue number1
StatePublished - Feb 2013
Externally publishedYes


  • Deformable shapes
  • Diffusion geometry
  • Heat Kernel signature
  • Laplace-Beltrami operator
  • Mumford-Shah regularization
  • Partial correspondence
  • Partial matching
  • Partial similarity
  • Shape descriptors


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