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If I have the histogram of an input image as Gaussian probability density function of the form:

$$P_r(r)=\dfrac{1}{\sqrt{2\pi}\sigma}e^{-\dfrac{(r-\mu)^2}{2\sigma^2}} $$

where: $\mu$ and $\sigma$ are the mean and standard deviation of the Gaussian PDF respectively.

The approach is to let $\mu$ and $\sigma$ be the measures of average grey level and contrast of a given image. What is the transformation function that can be used for histogram equalization?

Now, I found that I have to take small value for sigma and make some integration. So any help to do that please?

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  • $\begingroup$ Is there a reason you need to have a theoretical solution? There are lots of numerical techniques for accomplishing this, and that should be sufficient for any real application. $\endgroup$ – John Sep 5 '14 at 17:02
  • $\begingroup$ any techniques would you advise me to use?@John $\endgroup$ – Lana Joe Sep 9 '14 at 8:30

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