4. Assume continuous intensity values, and suppose that the intensity values of an image have the PDF

pr(r) = 2r/(L-1)² for 0 ≤ r ≤ L-1 and pr(r) = 0 for other values of r.

(a). Find the transformation function that will map the input intensity values, r, into values, s, of a

histogram-equalized image.

(b). Find the transformation function that (when applied to the histogram-equalized intensities, s) will

produce an image whose intensity PDF is p₂(z) = 3z²/(L-1)³ for 0 ≤ z ≤ L-1 and for other values

of z.