Analyzing and Synthesizing Images by Evolving Curves with theOsher-Sethian Method

Authors:
Ron Kimmel;Nahum Kiryati;Alfred M. Bruckstein
Affiliations:
Mail-Stop 50A-2152, Lawrence Berkeley Laboratory, University of California, Berkeley, CA 94720. E-mail: ron@math.lbl.gov;TECHNION, Electrical Engineering Department, Haifa 32000, Israel. E-mail: nk@tx.technion.ac.il;TECHNION, Computer Science Department, Haifa 32000, Israel. E-mail: freddy@cs.technion.ac.il
Venue:
International Journal of Computer Vision
Year:
1997

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Abstract

Numerical analysis of conservation laws plays an important role inthe implementation of curve evolution equations. This paper reviewsthe relevant concepts in numerical analysis and the relation betweencurve evolution, Hamilton-Jacobi partial differential equations, anddifferential conservation laws. This close relation enables us tointroduce finite difference approximations, based on the theory ofconservation laws, into curve evolution. It is shown how curveevolution serves as a powerful tool for image analysis, and how thesemathematical relations enable us to construct efficient and accuratenumerical schemes. Some examples demonstrate the importance of theCFL condition as a necessary condition for the stability of thenumerical schemes.