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| The '''fast marching method''' is a numerical method for solving [[boundary_value_problem|boundary value problems]] of the [[Eikonal equation]]:
| | Ed is what people call me and my spouse doesn't like it at all. My day occupation is a journey agent. North Carolina is the place he loves most but now he is considering other choices. To play lacross is the factor I love most of all.<br><br>Also visit my web blog [http://appin.co.kr/board_Zqtv22/688025 clairvoyants] |
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| : <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.
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| The algorithm is similar to [[Dijkstra's algorithm]] and uses the fact that information only flows outward from the seeding area.
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| This problem is a special case of [[level set method]]s. More general algorithms exist but are normally slower.
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| Extensions to non-flat (triangulated) domains solving:
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| ::<math>F(x)|\nabla_S T(x)|=1,
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| \,\, \mbox{for the surface} \,\, S, \, \mbox{and} \,\, x\in S.
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| </math> | |
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| was introduced by [[Ron Kimmel]] and Sethian.
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| <gallery>
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| Image:Fast_marching_maze.png| Maze as speed function shortest path
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| Image:Fast_marching_multi_stencil_2nd_order.png|Distance map multi-stencils with random source points
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| </gallery>
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| ==See also==
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| * [[level set method]]
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| ==External links==
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| * [http://www.mit.edu/~jnt/dijkstra.html Djikstra-like Methods for the Eikonal Equation J.N. Tsitsiklis, 1995]
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| * [http://math.berkeley.edu/~sethian/ The Fast Marching Method and its Applications by James A. Sethian]
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| * [http://mecca.louisville.edu/~msabry/projects/msfm.htm Multi-Stencils Fast Marching Methods]
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| * [http://www.mathworks.com/matlabcentral/fileexchange/24531 Multi-Stencils Fast Marching Matlab Implementation]
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| * [http://www2.imm.dtu.dk/pubdb/views/edoc_download.php/841/pdf/imm841.pdf Implementation Details of the Fast Marching Methods]
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| * [http://rd.springer.com/article/10.1007/s11075-008-9183-x Generalized Fast Marching method] by Forcadel et al. [2008] for applications in image segmentation.
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| *See Chapter 8 in [http://etd.fcla.edu/CF/CFE0001159/Rumpf_Raymond_C_200608_PhD.pdf Design and Optimization of Nano-Optical Elements by Coupling Fabrication to Optical Behavior]
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| {{mathapplied-stub}}
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| [[Category:Numerical differential equations]]
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Ed is what people call me and my spouse doesn't like it at all. My day occupation is a journey agent. North Carolina is the place he loves most but now he is considering other choices. To play lacross is the factor I love most of all.
Also visit my web blog clairvoyants