Image Processing Reference
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
g(x,y) = c ·
where c is a scaling constant that ensures that the maximum output value is 255. It
is calculated as
log ( 1
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
0 , 255
4.2.3 Exponential Mapping
The exponential mapping uses a part of the exponential curve. It can be expressed
g(x,y) = c · k f (x,y)
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
k v max
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.