Image Processing Reference

In-Depth Information

4.2.2 Logarithmic Mapping

An alternative non-linear mapping is based on the logarithm operator. Each pixel is

replaced by the logarithm of the pixel value. This has the effect that low intensity

pixel values are enhanced. It is often used in cases where the dynamic range of the

image is too great to be displayed or in images where there are a few very bright

spots on a darker background. Since the logarithm is not defined for 0, the mapping

is defined as

log
1

+
f(x,y)

g(x,y)
=
c
·

(4.6)

where
c
is a scaling constant that ensures that the maximum output value is 255. It

is calculated as

255

log
(
1

c

=

(4.7)

+

v
max
)

where
v
max
is the maximum pixel value in the input image.

The behavior of the logarithmic mapping can be controlled by changing the pixel

values of the input image using a linear mapping before the logarithmic mapping.

The logarithmic mapping from the interval

is seen in Fig.
4.7
.

This mapping will clearly stretch the low intensity pixels while suppressing the

contrast in high intensity pixels. An example is illustrated in Fig.
4.7
.

[

0
,
255

]

to

[

0
,
255

]

4.2.3 Exponential Mapping

The exponential mapping uses a part of the exponential curve. It can be expressed

as

g(x,y)
=
c
·
k
f (x,y)

1

−

(4.8)

where
k
is a parameter that can be used to change of shape of the transformation

curve and
c
is a scaling constant that ensures that the maximum output value is 255.

It is calculated as

255

k
v
max

c

=

(4.9)

−

1

where
v
max
is the maximum pixel value in the input image.
k
is normally chosen as

a number just above 1. This will enhance details in the bright areas while decreasing

detail in the dark areas. An example is illustrated in Fig.
4.7
.

Please note that both linear and non-linear gray-level mapping can also be applied

to color images. This is simply done by performing gray-level mapping on each of

the three color channels.