Localizing Region-Based Active Contours

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MatLab

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I am working in Lankton paper Localizing Region-Based Active Contours(here[^]) that has to do with localized active contours and especially in mean separation energy part.I am stuck in a point that i can not understand how is implemented.The equation (17) in this paper is Equation link[^]

I download the matlab code for this part from here

The equation (17) from paper is transformed in matlab code to

F = -((u-v).*((I(idx)-u)./Ain+(I(idx)-v)./Aout));

where Ain=Au and Aout=Aυ. Can anyone help me with the mathematics and how (17) is transformed to this code part. Thank you in advance.