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Fast marching method
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Fast marching method : ウィキペディア英語版
Fast marching method
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 \,\, S, \, \mbox \,\, x\in S.


was introduced by Ron Kimmel and James Sethian.

Image:Fast_marching_maze.png| Maze as speed function shortest path
Image:Fast_marching_multi_stencil_2nd_order.png|Distance map multi-stencils with random source points

==See also==

* Level set method

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
ウィキペディアで「Fast marching method」の詳細全文を読む



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