Affine-invariant geodesic geometry of deformable 3D shapes

Dan Raviv*, Alexander M. Bronstein, Michael M. Bronstein, Ron Kimmel, Nir Sochen

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Natural objects can be subject to various transformations yet still preserve properties that we refer to as invariants. Here, we use definitions of affine-invariant arclength for surfaces in R3 in order to extend the set of existing non-rigid shape analysis tools. We show that by re-defining the surface metric as its equi-affine version, the surface with its modified metric tensor can be treated as a canonical Euclidean object on which most classical Euclidean processing and analysis tools can be applied. The new definition of a metric is used to extend the fast marching method technique for computing geodesic distances on surfaces, where now, the distances are defined with respect to an affine-invariant arclength. Applications of the proposed framework demonstrate its invariance, efficiency, and accuracy in shape analysis.

Original languageEnglish
Pages (from-to)692-697
Number of pages6
JournalComputers and Graphics
Issue number3
StatePublished - Jun 2011


  • Affine
  • Equi-affine
  • Geodesics


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