Scale invariant geometry for nonrigid shapes

Yonathan Aflalo, Ron Kimmel, Dan Raviv

Research output: Contribution to journalArticlepeer-review


In nature, different animals of the same species frequently exhibit local variations in scale. New developments in shape matching research thus increasingly provide us with the tools to answer such fascinating questions as the following: How should we measure the discrepancy between a small dog with large ears and a large one with small ears? Are there geometric structures common to both an elephant and a giraffe? What is the morphometric similarity between a blue whale and a dolphin? Currently, there are only two methods that allow us to quantify similarities between surfaces which are insensitive to deformations in size: scale invariant local descriptors and global normalization methods. Here, we propose a new tool for shape exploration. We introduce a scale invariant metric for surfaces that allows us to analyze nonrigid shapes, generate locally invariant features, produce scale invariant geodesics, embed one surface into another despite changes in local and global size, and assist in the computational study of intrinsic symmetries where size is insignificant.

Original languageEnglish
Pages (from-to)1579-1597
Number of pages19
JournalSIAM Journal on Imaging Sciences
Issue number3
StatePublished - 2013
Externally publishedYes


  • Laplace-Beltrami
  • Scale invariant
  • Shape analysis


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