Problem$-1$: A $3-$bit gray$-$scale $55$ image given on the right side

Perform histogram matching $($specification$)$ so that the histogram of the output image

becomes the following histogram

In your solution

a$-)$ Fill up the following table

b$-)$ give the matching table between $r_k$ and $z_q$

c$-)$ give the transformed$($output$)$ image

d$-)$ plot the actual histogram $($pdf$)$ of the transformed$($output$)$ image