(a) Show that the discrete transformation function given in Eq. (3.3-8) for histogram equa...

(a) Show that the discrete transformation function given in Eq. (3.3-8) for histogram equalization satisfies conditions (a) and (b) in Section 3.3.1.

(3.3-8)

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(b) Show that the inverse discrete transformation in Eq. (3.3-9) satisfies conditions (a′) and (b) in Section 3.3.1 only if none of the intensity levels rk, k = 0, 1,..., L − 1, are missing.

(3.3-9)