Problem $5.$ Image Quantization and Dithering

$(20$ points$)$

Consider the barbara.png image. Convert it to Grayscale using library function.

Perform n$-$bit uniform quantization. Accept n as a user input. Compute the

decision boundaries and the corresponding N$=2^($n$)$ representation levels. Display

the quantized image I$\_($Q$).$ Compute the quantization error E$=||$I$-$I$\_($Q$)||^(2)$ for each n

and display a plot of E versus n$.$

Perform dithering. Scale the input image pixels to $0,1$ and add a zero$-$mean Gaus$-$

sian noise matrix with standard$-$deviation in $0\mathrm{.}05,0\mathrm{.}5.$ Perform n$-$bit quantiza$-$

tion on the resulting image and display the output. Report for different values of

standard$-$deviation.