Fast marching method: Difference between revisions

Revision as of 13:12, 8 August 2016

Revision as of 15:55, 13 September 2016

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# Assign every node <math>x_i</math> the value of <math>U_i=+\infty</math> and label them as ''far''; for all nodes <math>x_i \in \partial\Omega</math> set <math>U_i = 0</math> and label <math>x_i</math> as ''accepted''.

# For every acceptedfar node <math>x_i</math>, use the [[Eikonal equation#Numerical Approximation|Eikonal update formula]] to calculate a new value for <math>\tilde{U}</math>. If <math>\tilde{U} < U_i</math> then set <math>U_i = \tilde{U}</math> and label <math>x_i</math> as ''considered''.

# Let <math>\tilde{x}</math> be the considered node with the smallest value <math>U</math>. Label <math>\tilde{x}</math> as ''accepted''.

# For every neighbor <math>x_i</math> of <math>\tilde{x}</math> that is not-accepted, calculate a tentative value <math>\tilde{U}</math>.