Hi,

Does anyone know what calculations should be used to minimize an energy functional (level set and active contour method):

$\displaystyle E(\phi)=\mu\int p(|grad(\phi)|)dx+\lambda\int g\delta(\phi)|grad(\phi)|dx+\alpha \int gH(-\phi)dx$ (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:

$\displaystyle \frac{\partial \phi}{\partial t}=\mu div(dp(|grad(\phi)|)grad(\phi))+\lambda\delta (\phi)div(g\frac{grad(\phi)}{|grad(\phi)|})+\alpha g \delta (\phi)$ (II)

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

Where:

$\displaystyle \delta$ is a Dirac delta function

$\displaystyle H$ is a Heavside function

$\displaystyle dp(x)=\frac{p'(x)}{x}$

Thanks