ANALYZING AND SYNTHESIZING IMAGES BY EVOLVING CURVES WITH THE OSHER-SETHIAN METHOD

Numerical analysis of conservation laws plays an important role in the implementation of curve evolution equations. This paper reviews the r elevant concepts in numerical analysis and the relation between curve evolution, Hamilton-Jacobi partial differential equations, and differe ntial conservation laws. This close relation enables us to introduce f inite difference approximations, based on the theory of conservation l aws, into curve evolution. It is shown how curve evolution serves as a powerful tool for image analysis, and how these mathematical relation s enable us to construct efficient and accurate numerical schemes. Som e examples demonstrate the importance of the CFL condition as a necess ary condition for the stability of the numerical schemes.