Fast marching method

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The fast marching method is introduced by James A. Sethian as a numerical method for solving boundary value problems of the form:

$F(x)|\nabla T(x)|=1.$

Typically, such a problem describes the evolution of a closed curve as a function of time $T$ with speed $F (x)$ in the normal direction at a point $x$ on the curve. The speed function is specified, and the time at which the contour crosses a point $x$ is obtained by solving the equation.

An alternative to using a fast marching method is to use a level set method. The latter is more general, but runs slower.