Question

How is the expression represented for the normalized histogram?

(a) p(r_k )=n_k

(b) p(r_k )=n_k/n

(c) p(r_k)=nn_k

(d) p(r_k )=n/n_k

The question was posed to me by my school teacher while I was bunking the class.

Question is taken from Histogram Processing in portion Intensity Transformations and Spatial Filtering of Digital Image Processing

Answer 1

Correct option is (b) p(r_k )=n_k/n

To elaborate: It is common practice to normalize a histogram by dividing each of its values by the total number of pixels in the image, denoted by n. Thus, a normalized histogram is given by p(rk )=nk/n, for k=0,1,2…..L-1. Loosely speaking, p(rk ) gives an estimate of the probability of occurrence of gray-level rk. Note that the sum of all components of a normalized histogram is equal to 1.