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Image Enhancement 211

f
DN out DN out
f

DN in DN in
(a) (b)

FIGURE 6.7 Nonlinear functions for transforming an input image’s contrast.
(a) Logarithmic function in which the contrast of small DNs is stretched but
larger DNs are suppressed; (b) exponential function in which small DNs are
suppressed but large DNs are stretched.

It is possible to stretch the contrast in one gray level range, and to
reduce the contrast in another gray level range.
There are a number of nonlinear functions for contrast enhance-
ment. Two common examples are logarithmic and exponential func-
tions. The logarithmic function takes the following form:

DN = log DN (6.4)
out 10 in
In the above example, the logarithmic function has a base of 10.
Other common bases are 2 and e. In all logarithmic stretching, the con-
trast is stretched for pixels of a small value, but suppressed for pixels
of a large DN (Fig. 6.7a). The smaller the base, the more stretching at
low values, the more suppression at high values, and vice versa.
In exponential contrast stretching, pixel values in the output
image are adjusted according to the following form:

DN out = e DN in (6.5)

This exponential function has a base of e, but it can be any posi-
tive figure. The exponential function achieves an adjustment effect
just opposite to that of the logarithmic function. Namely, those gray
levels with a smaller value are suppressed, but those with a larger
DN value are stretched (Fig. 6.7b). The larger the base, the more the
stretching. This stretching is effective at suppressing dark-toned fea-
tures (e.g., water) and stretching light-toned features such as urban
residential and industrial.

6.1.6 Histogram Equalization
The histogram of most images rarely has an equal distribution. It is
more likely to be bell shaped. This kind of pixel value distribution
suggests that the large majority of pixels are confined to a small range
that is indicative of a low contrast. On the other hand, few very