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Histogram Equalization. Obtain a plot of original as well as Equalized Histogram
Grey levels 0 1 2 3 4 5 6 7
No of pixels 100 90 50 20 0 0 0 0
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Histogram Equalization Transformation function is defined as:

$S_k =\sum_{j=0}^k P_r r_j$

where $r_k$ and $s_k$ are normalized input and output gray values

Input gray value Normalized input Frequency $N_{rk}$ PDF $P_r = N_{rk}/N$ CDF $S_k = \sum P_r$ Output gray value,$S_k$(CDFx7)
0 0 100 0.384 0.84 0.2688=3
1 1/7 90 0.346 0.73 5.11=5
2 2/7 50 0.192 0.922 6.944=7
3 3/7 20 0.077 1 7
4 4/7 0 0 1 7
5 5/7 0 0 1 7
6 6/7 0 0 1 7
7 1 0 0 1 7
- - N = 260 - - -

Histogram of input image:

enter image description here

Histogram of output image:

enter image description here

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