Fast marching method: Difference between revisions

Revision as of 03:45, 11 April 2017

Revision as of 12:21, 9 July 2017

Line 4:

: <math>u(x) = 0 \text{ for } x \in \partial\Omega</math>

Typically, such a problem describes the evolution of a closed surface as a function of time <math>u</math> with speed <math>f(x)</math> in the normal direction at a point <math>x</math> on the propagating surface. The speed function is specified, and the time at which the contour crosses a point <math>x</math> is obtained by solving the equation. Alternatively, <math>u(x)</math> can be thought of as the minimum amount of time it would take to reach <math>\partial\Omega</math> starting from the point <math>x</math>. The fast marching method takes advantage of this [[optimal control]] interpretation of the problem in order to build a solution outwards starting from the "known information", i.e. the boundary values.

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 method]]s. [[Eikonal equation#Computational algorithms|More general algorithms exist]] but are normally slower.