This document discusses contrast adjustment using histogram equalization. Histogram equalization is useful for images with both bright and dark backgrounds/foregrounds. It can improve the visibility of bone structures in x-rays and over/under-exposed photos by increasing contrast. The technique redistributes pixel intensities according to the original frequency distribution to make pixel levels more evenly distributed. It linearizes the cumulative frequency distribution rather than flattening the histogram. An example shows the original histogram, cumulative distribution function, scaled cumulative distribution, and equalized values for an 8x8 pixel image.

2. € Contrast adjustment method by using the image's
histogram.
€ Useful for images with backgrounds and foregrounds
that are both bright or both dark.
€ It can be used for viewing the bone structure in x-ray
images, and photographs that are over or under-exposed
in order to get better detail .
€€ Advantage=> If the histogram equalization function
is known, then the original histogram can be
recovered.
€€ Disadvantage=>It may increase the contrast of
background noise, while decreasing the usable
signal.

3. € Rather than saying that equalization flattens a
histogram, it is more accurate to say that it
linearizes the cumulative frequency distribution.
€ Histogram equalization redistributes pixel
intensities according to the origin ratio of pixel
distribution to make the number of pixel
redistribute into each allowed discrete intensity
levels.
€ Histogram equalization doesn’t force the
distribution “flat” which means the number of
pixel in each intensity levels distributed equally
or closely.

5. Row(M)=8
Column(N)=8
MxN= 64
Total number of pixel in this image is 64.
P(r)= no of pixel in each intensity value/ Total no of pixel
P(52)=1/64

7. 60
70
No of Pixel
40
50
20
30
No of Pixel
0
10
0
52
58
60
62
64
66
68
70
72
75
77
79
85
88
94
106
113
126
154

8. Value No of
pixel P(r)
52 1 1/64
55 3 4/64
Value cdf cdf,
scaled
71 39 154/64
Value cdf cdf,
scaled
106 58 231/64
109 59 235/64
58 6 6/64
59 9 9/64
60 10 10/64
72 40 158/64
73 42 166/64
75 43 170/64
76 44 174/64
113 60 239/64
122 61 243/64
126 62 247/64
61 14 53/64
62 15 57/64
63 17 65/64
64 9 3/77 45 178/64
78 46 182/64
79 48 190/64
144 63 251/64
19 73/64
65 22 85/64
66 24 93/64
67 25 97/64
83 49 194/64
85 51 202/64
87 52 206/64
88 53 210/64
68 30 117/64
69 33 130/64
70 37 146/64
90 54 215/64
94 55 219/64
104 57 227/64
154 64 255/64

9. 1.2
Equalized Value
0.8
1
0.4
0.6
Equalized Value
0
0.2
52
58
60
62
64
66
68
70
72
75
77
79
85
88
94
106
113
126
154