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Determine the output image using power law transformations

s=$(r)^2$

Given

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Step 1: Find normalized input image pixel value (r)

$Normalized pixel value = \frac{Input pixel value}{Max pixel value(10)}$

By Normalization we get,

$\begin{bmatrix} 2 & 3 & 5 & 10 \ 4 & 6 & 4 & 10 \ 7 & 1 & 3 & 3 \ \end{bmatrix}$ = $\begin{bmatrix} 0.2 & 0.3 & 0.5 & 1 \ 0.4 & 0.6 & 0.4 & 1 \ 0.7 & 0.1 & 0.3 & 0.3 \ \end{bmatrix}$

Step 2: Find normalized output pixel value (s) by Power law transform, s=$(r)^2$

By Power law transform we get input image as,

$\begin{bmatrix} 0.04 & 0.09 & 0.25 & 1 \ 0.16 & 0.36 & 0.16 & 1 \ 0.49 & 0.01 & 0.09 & 0.09 \ \end{bmatrix}$

Step 3: Find output pixel value

Output Pixel Value = Normalized Output Value X Maximum Pixel Value(10)

$\begin{bmatrix} 0.4 & 0.9 & 2.5 & 10 \ 1.6 & 3.6 & 1.6 & 10 \ 4.9 & 0.1 & 0.9 & 0.9 \ \end{bmatrix}$

By Rounding we get Output image as,

$\begin{bmatrix} 0 & 1 & 3 & 10 \ 2 & 4 & 2 & 10 \ 5 & 0 & 1 & 1 \ \end{bmatrix}$