A FAST MARCHING LEVEL SET METHOD FOR MONOTONICALLY ADVANCING FRONTS

A fast marching level set method is presented for monotonically advanc ing fronts, which leads to an extremely fast scheme for solving the Ei konal equation. Level set methods are numerical techniques for computi ng the position of propagating fronts. They rely on an initial value p artial differential equation for a propagating level set function and use techniques borrowed from hyperbolic conservation laws. Topological changes, corner and cusp development, and accurate determination of g eometric properties such as curvature and normal direction are natural ly obtained in this setting. This paper describes a particular case of such methods for interfaces whose speed depends only on local positio n. The technique works by coupling work on entropy conditions for inte rface motion, the theory of viscosity solutions for Hamilton-Jacobi eq uations, and fast adaptive narrow band level set methods. The techniqu e is applicable to a variety of problems, including shape-from-shading problems, lithographic development calculations in microchip manufact uring, and arrival time problems in control theory.