Level Set Methods

The level set method was devised by Osher and Sethian in [56] as a simple and versatile method for computing and analyzing the motion of an interface in two or three dimensions. bounds a (possibly multiply connected) region The goal is to compute and analyze the subsequent motion of under a velocity field ~v. This velocity can depend on position, time, the geometry of the interface and the external physics. The interface is captured for later time as the zero level set of a smooth (at least Lipschitz continuous) function '(~x; t), i.e., (t) = f~xj'(~x; t) = 0g. ' is positive inside negative outside and is zero on (t). Topological merging and breaking are well defined and easily performed. In this review article we discuss recent variants and extensions, including the motion of curves in three dimensions, the Dynamic Surface Extension method, fast methods for steady state problems, diffusion generated motion and the variational level set approach. We also give a user's gui..