Image Processing Reference
In-Depth Information
Its performance can be very convincing since it is well mapped to the properties of
human vision. If a linear brightness transformation is applied to the original image then the
equalised histogram will be the same. If we replace pixel values with ones computed
according to Equation 3.1 then the result of histogram equalisation will not change. An
alternative interpretation is that if we equalise images (prior to further processing) then we
need not worry about any brightness transformation in the original image. This is to be
expected, since the linear operation of the brightness change in Equation 3.2 does not
change the overall shape of the histogram, only its size and position. However, noise in the
image acquisition process will affect the shape of the original histogram, and hence the
equalised version. So the equalised histogram of a picture will not be the same as the
equalised histogram of a picture with some noise added to it. You cannot avoid noise in
electrical systems, however well you design a system to reduce its effect. Accordingly,
histogram equalisation finds little use in generic image processing systems, though it can
be potent in
specialised
applications. For these reasons, intensity normalisation is often
preferred when a picture's histogram requires manipulation.
In implementation, the function
equalise
in Code
3.3
, we shall use an output range
where
N
min
= 0 and
N
max
= 255. The implementation first determines the cumulative
histogram for each level of the brightness histogram. This is then used as a look-up table
for the new output brightness at that level. The look-up table is used to speed implementation
of Equation 3.9, since it can be precomputed from the image to be equalised.
range
←
255
number
←
rows(pic)·cols(pic)
for bright
∈
0..255
pixels
-
at
-
level
bright
←
0
for x
∈
0..rows(pic)-1
for y
∈
0..rows(pic)-1
pixels at level
equalise(pic) :=
pixels at level
+1
--
pic
y,x
--
pic
y,x
sum
←
0
for level
∈
0..255
sum
←
sum+pixels
-
at
-
level
level
range
number
⋅
hist
floor
sum+0.00001
level
for x
∈
0..cols(pic)-1
for y
∈
0..rows(pic)-1
newpic
hist
y,x
pic
y,x
newpic
Code 3.3
Histogram equalisation
An alternative argument against use of histogram equalisation is that it is a non-linear
process and is irreversible. We cannot return to the original picture after equalisation, and
we cannot separate the histogram of an unwanted picture. On the other hand, intensity
