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

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. © 2009 Springer Science+Business Media, LLC.

Full Text

Duke Authors

Cited Authors

  • Bronstein, AM; Bronstein, MM; Kimmel, R; Mahmoudi, M; Sapiro, G

Published Date

  • 2010

Published In

Volume / Issue

  • 89 / 2-3

Start / End Page

  • 266 - 286

International Standard Serial Number (ISSN)

  • 0920-5691

Digital Object Identifier (DOI)

  • 10.1007/s11263-009-0301-6

Citation Source

  • SciVal