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I'm not sure if this is an appropriate question for stack overflow or for math overflow, so please point me in the right direction if I'm in the wrong place.

I am trying to implement shadow removal based on the methods of Drs. Drew, Finlayson, and Fredembach, and my question is a math one. Here are the papers I've reviewed:

  1. Entropy Minimization Shadow Removal
  2. Hamiltonian Path Based Shadow Removal
  3. Piecewise Shadow Removal

I have successfully created an edge map using the methods from 1 and 2 above. Now I am trying to reintegrate to recover the shadow-free color image.

There are 2 things I don't understand about paper 3:

  1. How do you add the constant back to grad(log(I)) when you have both grad_x and grad_y to consider? (Adding back to the magnitude of the gradient does not work)

  2. Do you not need to perform integration, or are you simply adding the constant back to the shadow region? (The derivatives inside the shadow are not zero. Per the papers, We set the derivative at the shadow edge to zero, but not inside the shadow.)

Any help would be MUCH appreciated! I can gladly paste code. Thank you.

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