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The '''fast marching method''' is introduced by [[James Sethian|James A. Sethian]] as a numerical method for solving [[boundary_value_problem|boundary value problems]] of the form:
: <math>F(x)|\nabla T(x)|=1</math>.
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Typically, such a problem describes the evolution of a closed curve as a function of time <math>T</math> with speed <math>F(x)</math> in the normal direction at a point <math>x</math> on the curve. The speed function is specified, and the time at which the contour crosses a point <math>x</math> is obtained by solving the equation.
The algorithm is similar to [[Dijkstra's_algorithm|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 method|level set methods]]. More general algorithms exist but are normally slower
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