Fast marching method

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The fast marching method is a numerical method for solving boundary value problems of the Eikonal equation:

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.

The algorithm is similar to Dijkstra's algorithm and uses the fact that information only flows outward from the seeding area.

This problem is a special case of level set methods. More general algorithms exist but are normally slower.

Extensions to non-flat (triangulated) domains solving:

F(x)|\nabla_S T(x)|=1,
   \,\, \mbox{for the surface} \,\, S, \, \mbox{and} \,\, x\in S.

was introduced by Ron Kimmel and Sethian.

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