I have been working on a practical implementation in Matlab of the algorithm Raanan Fattal suggested in the following paper.

I couldn't understand the meaning of eq. 11 on page 5:

\begin{equation}\begin{array}{llllll} U^{(i, j)}=g_{\sigma_{d}} * e^{\left(\left|D^{(i, j)}\right|-C^{(i, j)}\right)}.&&&&&(11) \end{array}\end{equation}

g is a gaussian, 1D function (See section 4.1, page 3). While in this equation no parameters are given. $D(i,j)$ is a matrix and $C(i,j)$ is a number.

Could anyone explain what it means in case it is just a writing method I don't recognize?


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    $\begingroup$ @Kaspar, Great editing. Welcome! $\endgroup$ – Royi Nov 27 '19 at 21:39
  • $\begingroup$ @Royi Thanks, in case you are wondering, it was Mathpix (mathpix.com) not manual labour. The output is very accurate, especially if the original equation was LaTex too. Even handwriting works. $\endgroup$ – KasparJohannes Nov 27 '19 at 21:47
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    $\begingroup$ @KasparJohannesSchneider, Nice! I wasn't aware of this. Learned something new. If you have feedback for my answer, I will be happy. $\endgroup$ – Royi Nov 27 '19 at 21:49

What the authors meant is to create a matrix of Weights, $ {U}^{\left( i, j \right)} $.

It is a matrix of the size of the image.
The given calculation is by the exponent of two terms (Each of them is a matrix, the calculation is element wise).
The final step is to blur it using a Gaussian Blue (2D Blur, like on an image).

In equation 10 you can see they take care of the normalization of the weights.

It would be nice if you come back and show us your results.


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