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In image processing \ computer vision It is known that some filtering operations can be formalized as

$$ E(u)=\int_{\Omega} \lVert u - f \rVert^2 + \lambda \lVert \nabla u\rVert^2 d\Omega $$

Suppose $\lambda = \lambda(x,y)$, where $(x,y)$ are coordinates in image space. I'm looking for implementing a particular filter in special region of an image, according to some paper I read the features I need to smooth/remove can be detected using a Gabor filter.

I haven't implemented the filter yet, but I'll that soon. In a more general setting I do wonder however if there's some research showing how to properly set the $\lambda$ function based on features being detected.

Can you suggest any reading on this subject? if there's any.

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