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Derive the equation of contrast stretching transformation function as given in figure below.

Apply the contrast stretching transformation function on the input image F and obtain the output image R.

enter image description here

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Step 1: Derivation of Transform:

enter image description here

$S = \begin{bmatrix} αr & 0≤r≤a \ S_1+β(r-a) & a<r≤b \="" s_2+γ(r-b)="" &amp;="" b<r≤l-1="" \="" \end{bmatrix}="" $<="" p="">

When a = 8, b = 12, L – 1 = 15

S1 = 4, S2 = 8

We get, α = 0.5, β = 1, γ = 2.33

By substitution we get,

$S = \begin{bmatrix} 0.5r & 0≤r≤8 \ r-4 & 8<r≤12 \="" 8+2.33(r-12)="" &amp;="" 12<r≤15="" \="" \end{bmatrix}="" $<="" p="">

Step 2: To find output image

For r = 7, s = 3.5 = 4

r = 12, s = 8

$Output image = \begin{bmatrix} 4 & 8 & 1 & 2 & 2 \ 6 & 15 & 1 & 3 & 2 \ 8 & 2 & 3 & 15 & 8 \ 4 & 1 & 4 & 15 & 1 \ 7 & 10 & 2 & 2 & 3 \ \end{bmatrix} $

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