International Journal of Computer Vision

, Volume 24, Issue 1, pp 37–55

Analyzing and Synthesizing Images by Evolving Curves with the Osher-Sethian Method

  • Ron Kimmel
  • Nahum Kiryati
  • Alfred M. Bruckstein

DOI: 10.1023/A:1007970107971

Cite this article as:
Kimmel, R., Kiryati, N. & Bruckstein, A.M. International Journal of Computer Vision (1997) 24: 37. doi:10.1023/A:1007970107971


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.

shape from shadinghalftoningoffsetsdistance mapsminimal geodesicssegmentationnumerical methods

Copyright information

© Kluwer Academic Publishers 1997

Authors and Affiliations

  • Ron Kimmel
    • 1
  • Nahum Kiryati
    • 2
  • Alfred M. Bruckstein
    • 3
  1. 1.Lawrence Berkeley LaboratoryUniversity of CaliforniaBerkeley
  2. 2.Electrical Engineering DepartmentTECHNIONHaifaIsrael
  3. 3.Computer Science DepartmentTECHNIONHaifaIsrael