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Perona-Malik Diffusion Equation

  1. Dec 7, 2011 #1
    1. The problem statement, all variables and given/known data
    Implement the non-linear de-noising algorithm of Perona-Malik. Consider a noisy image, u, with pixel values referenced by u(i,j). Non-linear de-noising can be achieved by solving the following non-linear diffusion equation:

    ∇ · (g(∇u)∇u) = 0

    with g(s) = ((K^2)v) / ((K^2) + |s|)

    where v and K are parameters controlling the amount of diffusion.

    Write down the linear system associated with this discretization.

    My question is how do I do this? How can I take the gradient of a pixel? It isn't a function so how can I do partial derivative with respect to x and y to it?
    1. The problem statement, all variables and given/known data

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
  3. Dec 7, 2011 #2
    I have no idea what to do here. If I could have shown work I would have, but I have no work done. I just need a nudge in the right direction here.
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