Fast marching method

Abstract: Introduction 1 Formulations of interface propagation Part I Theory and Algorithms: 2 Theory of curve and surface evolution 3 Hamilton-Jacobi equations and associated theory 4 Numerical approximations: first attempt 5 Numerical schemes for hyperbolic conservation laws 6 Algorithms for the initial and boundary value formulations 7 Efficient schemes: adaptivity 8 Triangulated versions of level set and fast marching method: extensions and variations 9 Tests of basic methods Part II Applications: 10 Geometry 11 Grid generation 12 Image denoising 13 Computer vision: shape detection and recognition 14 Fluid mechanics and materials sciences: adding physics 15 Computational geometry and computer-aided-design 16 First arrivals, optimizations, and control 17 Applications to semi-conductor manufacturing 18 Comments, conclusions, future directions References Index

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.