How is Weighted Thresholded Histogram Equalization different from Gamma Correction Image enhancement

In case of Weighted Thresholded Histogram Equalization we use:-

calculate, the Weighted Probablity Density Function for Image using,

$$P_{wt}(k) = \left( \frac{P(k)-P_l}{P_u-P_l} \right)^r P_u$$

Where $P_u$ is the highest probability of a intensity in a Image. $P_l$ is the lowest probability of a intensity in a Image. $P(k)$ is the Probability Density Function for the Image,i.e. the number of pixels having the intensity $k$ in a image.

Then perform Histogram Equalization on the image using, calculating Cumulative Distribution Function

$$C_{wt}(k) = \sum_{m=0}^k P_{wt}(m)$$ $$Im(i,j) = W_{out} C_{wt}\left(F(i,j)\right)$$

For $r<1$ the Power Law Transformation function will give a higher weight to the low probabilities in the PDF than the high probabilities.

How is this procedure conceptually different from the Gamma Correction technique, explain if similar how much similarity is there or if something is different, Explain where does it deviate from Gamma Correction method for Single Image Enhancement.

Does this Procedure Passes for Being Called as Gamma Correction in some Aspect OR Do some Changes are Required.

Answer

This Method can very well pass for being Gamma Correction Technique as We are Increasing the Weight of the Less probable Intensities in the Image by the Exponential Factor r So that the Less Clear Details may be Visible upon the increase in their Weight thus Providing a Enhanced Image , On the Similiar Note the Gamma Correction Function Does this by using Power Law Transformation.