Analyzing and synthesizing images by evolving curves with the Osher-Sethian method

Ron Kimmel, Nahum Kiryati, Alfred M. Bruckstein

Research output: Contribution to journalArticlepeer-review


Numerical analysis of conservation laws plays an important role in the implementation of curve evolution equations. This paper reviews the relevant concepts in numerical analysis and the relation between curve evolution, Hamilton-Jacobi partial differential equations, and differential conservation laws. This close relation enables us to introduce finite difference approximations, based on the theory of conservation laws, into curve evolution. It is shown how curve evolution serves as a powerful tool for image analysis, and how these mathematical relations enable us to construct efficient and accurate numerical schemes. Some examples demonstrate the importance of the CFL condition as a necessary condition for the stability of the numerical schemes.

Original languageEnglish
Pages (from-to)37-55
Number of pages19
JournalInternational Journal of Computer Vision
Issue number1
StatePublished - 1997
Externally publishedYes


  • Distance maps
  • Halftoning
  • Minimal geodesics
  • Numerical methods
  • Offsets
  • Segmentation
  • Shape from shading


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