$($a$)$ Write a computer program in MATLAB for computing the histogram of an image.

$($b$)$ Implement the histogram equalization technique discussed in Section $3\mathrm{.}3\mathrm{.}1.$

$($c$)$ Download Fig. $3\mathrm{.}8($a$)$ from the book web site and perform histogram equalization on it$.$ Include the original image, a plot of its histogram, a plot of the histogram$-$equalization transformation function, the enhanced image, and a plot of its histogram. Use this information to explain why the resulting image was enhanced as it was.