# Gonzalez question solution

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?

• 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. – John Sep 5 '14 at 17:02
• any techniques would you advise me to use?@John – Lana Joe Sep 9 '14 at 8:30