A gromov-hausdorff framework with diffusion geometry for topologically-robust non-rigid shape matching

Alexander M. Bronstein, Michael M. Bronstein, Ron Kimmel, Mona Mahmoudi, Guillermo Sapiro*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


In this paper, the problem of non-rigid shape recognition is studied from the perspective of metric geometry. In particular, we explore the applicability of diffusion distances within the Gromov-Hausdorff framework. While the traditionally used geodesic distance exploits the shortest path between points on the surface, the diffusion distance averages all paths connecting the points. The diffusion distance constitutes an intrinsic metric which is robust, in particular, to topological changes. Such changes in the form of shortcuts, holes, and missing data may be a result of natural non-rigid deformations as well as acquisition and representation noise due to inaccurate surface construction. The presentation of the proposed framework is complemented with examples demonstrating that in addition to the relatively low complexity involved in the computation of the diffusion distances between surface points, its recognition and matching performances favorably compare to the classical geodesic distances in the presence of topological changes between the non-rigid shapes.

Original languageEnglish
Pages (from-to)266-286
Number of pages21
JournalInternational Journal of Computer Vision
Issue number2-3
StatePublished - Sep 2010
Externally publishedYes


  • Diffusion geometry
  • Gromov-Hausdorff distance
  • Missing data
  • Non-rigid shape matching
  • Partiality
  • Topology


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