Image Processing Reference

In-Depth Information

=

·

g(x,y)

a

f(x,y)

(4.2)

If
a>
1 the contrast is increased and if
a<
1 the contrast is decreased. For exam-

ple when
a

2 the pixels 112 and 114 will get the values 224 and 228, respectively.

The difference between them is increased by a factor 2 and the contrast is therefore

increased. In Fig.
4.4
the effect of changing the contrast can be seen.

If we combine the equations for brightness, Eq.
4.1
, and contrast, Eq.
4.2
,we

have

=

g(x,y)
=
a
·
f(x,y)
+
b

(4.3)

which is the equation of a straight line. Let us look at an example of how to apply

this equation. Say we are interested in a certain part of the input image where the

contrast might not be sufficient. We therefore find the range of the pixels in this part

of the image and map them to the entire range,

in the output image. Say

that the minimum pixel value and maximum pixel values in the input image are 100

and 150, respectively. Changing the contrast then means to say that all pixel value

below 100 are set to zero in the output and all pixel values above 150 are set to 255

in the output image. The pixels in the range

[

0
,
255

]

[

100
,
150

]

are then mapped to

[

0
,
255

]

using Eq.
4.3
where
a
and
b
are defined as follows:

255

f
2
−

a

=

,

b

=−

a

·

f
1

(4.4)

f
1

where
f
1
=

100 and
f
2
=

150.

4.2

Non-linear Gray-Level Mapping

Gray-level mapping is not limited to linear mappings as defined by Eq.
4.3
. In fact

the designer is free to define the gray-level mapping as she pleases as long as there

is one and only one output value for each input value. Often the designer will utilize

a well defined equation/graph as opposed to defining a new one. Below three of the

most common
non-linear mapping
functions are presented.

4.2.1 Gamma Mapping

In many cameras and display devices (flat panel televisions for example) it is use-

ful to be able to increase or decrease the contrast in the dark gray levels and the

light gray levels individually since humans have a non-linear perception of contrast.

A commonly used non-linear mapping is gamma mapping, which is defined for