Histogram Equalization (continued)

For digital image processing the concepts developed must be formulated in discrete form. For gray levels which assume discrete values, we deal with probabilities given by the relation

L is number of levels

is the probability of k th gray level

is the number of times this level appears in image

is the total number of pixels in an image

A plot of vs. is usually called a histogram and the technique used for obtaining a uniform histogram is known as histogram equalization or histogram linearization.

Discrete form of relation is

Inverse transformation

where both and satisfy conditions (a) and (b) stated earlier. Note can be found directly from the image in question using

Examples:

Suppose that a (64 ´ 64), 8 level image has the gray level distribution as given below:

	790	0.19
	1023	0.25
	850	0.21
	656	0.16
	329	0.08
	245	0.06
	122	0.03
	81	0.02

The histogram of the gray levels is:

(continued in the next slide)