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Energy minimization (level set)

  1. Jul 10, 2012 #1
    Hi
    Does anyone know what calculations should be used to minimize an energy functional (level set and active contour method):

    [itex]E(\phi)=\mu\int p(|grad(\phi)|)dx+\lambda\int g\delta(\phi)|grad(\phi)|dx+\alpha \int gH(-\phi)dx[/itex] (I)

    According to Chunming Li and Chenyang Xu "Distance Regularized Level Set Evolution and Its Application to Image Segmentation" this energy functional can be minimized by solving the gradient flow equation:

    [itex]\frac{\partial \phi}{\partial t}=\mu div(dp(|grad(\phi)|)grad(\phi))+\lambda\delta (\phi)div(g\frac{grad(\phi)}{|grad(\phi)|})+\alpha g \delta (\phi)[/itex] (II)

    But how to obtain (II) from (I) ?

    [itex]\delta[/itex] is a Dirac delta function

    [itex]H[/itex] is a Heavside function, and

    [itex]dp(x)=\frac{p'(x)}{x}[/itex]

    Thanks !
     
  2. jcsd
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