A fast marching level set method for monotonically advancing fronts.

TLDR

Level set methods numerically compute propagating front positions using an initial value PDE and techniques from hyperbolic conservation laws. The paper presents a fast marching level set method for monotonically advancing fronts, aiming to solve the Eikonal equation efficiently for interfaces whose speed depends only on local position. The method couples entropy conditions for interface motion, viscosity solution theory for Hamilton–Jacobi equations, and fast adaptive narrow‑band level set techniques, and applies to problems such as shape‑from‑shading, lithographic development, and control‑theory arrival times. Topological changes, corner and cusp development, and accurate determination of geometric properties such as curvature and normal direction are naturally obtained in this setting.

Abstract

A fast marching level set method is presented for monotonically advancing fronts, which leads to an extremely fast scheme for solving the Eikonal equation. Level set methods are numerical techniques for computing the position of propagating fronts. They rely on an initial value partial 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 geometric properties such as curvature and normal direction are naturally obtained in this setting. This paper describes a particular case of such methods for interfaces whose speed depends only on local position. The technique works by coupling work on entropy conditions for interface motion, the theory of viscosity solutions for Hamilton-Jacobi equations, and fast adaptive narrow band level set methods. The technique is applicable to a variety of problems, including shape-from-shading problems, lithographic development calculations in microchip manufacturing, and arrival time problems in control theory.