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In an image processing course at Coursera.org, on the section on PDE and calculus of variations, the professor gave the following as the functional to be optimized for image histogram modification:

U(I) = 0.5*∫[I(x)-0.5]2dx - 0.25*∫∫[I(x)-I(z)]dxdz

I(x) and I(z) being the new and original images, respectively

I'm not sure how to go about calculating and implementing the Euler-Lagrange for this functional. It would be great if someone gave me a few pointers.

(This is not homework, by the way, I'm just trying to implement things stated in the lectures to get a hang of things.)

Thanks in advance

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