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

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.

External links

• The Fast Marching Method and its Applications by James A. Sethian
• Multi-Stencils Fast Marching Methods