Image Processing Reference

In-Depth Information

Fig. 4.5
Gamma-mapping

curves for different gammas

positive
γ
as

f(x,y)
γ

=

g(x,y)

(4.5)

Some gamma-mapping curves are illustrated in Fig.
4.5
.For
γ
=

1 we get the iden-

tity mapping. For 0
<γ <
1 we increase the dynamics in the dark areas by in-

creasing the mid-levels. For
γ>
1 we increase the dynamics in the bright areas by

decreasing the mid-levels. The gamma mapping is defined so that the input and out-

put pixel values are in the range

. It is therefore necessary to first transform the

input pixel values by dividing each pixel value with 255 before the gamma trans-

formation. The output values should also be scaled from

[

0
,
1

]

[

0
,
1

]

to

[

0
,
255

]

after the

gamma transformation.

A concrete example is given. A pixel in a gray-scale image with value
v
in
=

120

is gamma mapped with
γ

=

2
.
22. Initially, the pixel value is transformed into the

interval

[

0
,
1

]

by dividing with 255,
v
1
=

120
/
255

=

0
.
4706. Secondly, the gamma

0
.
4706
2
.
22

mapping is performed
v
2
=

=

0
.
1876. Finally, it is mapped back to the

interval

[

0
,
255

]

giving the result
v
out
=

0
.
1876

·

255

=

47. Examples are illustrated

in Fig.
4.6
.

Fig. 4.6
Gamma mapping to the
left
with
γ
=
0
.
45 and to the
right
with
γ
=
2
.
22. In the
middle

the original image