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A fast marching level set method for monotonically advancing fronts. (English) Zbl 0852.65055
The level set method is a numerical technique for computing the position of propagating fronts. This method is used for monotonically advancing fronts, which leads to an extremely fast scheme for solving the eikonal equation. This method relies on an initial value partial differential equation for a propagating level set function and uses techniques borrowed from hyperbolic conservation laws. Topological changes, corner and cusp development, and accurate and normal direction are naturally obtained in this setting.
The paper describes a particular case of such methods for interfaces whose speed depends only on the local position. The suggested technique is applicable to a variety of problems, including shape-from-shading problems, lithographic development calculation, microship manufacturing, and arrival time problem in control theory.

MSC:
65K10 Numerical optimization and variational techniques
65D18 Numerical aspects of computer graphics, image analysis, and computational geometry
49J20 Existence theories for optimal control problems involving partial differential equations
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