Image Processing Reference
In-Depth Information
To apply CA to the task of noise reduction, one considers the neighbourhood of
each pixel, and uses an appropriate update rule to replace the value of the current
pixel with some average over the pixel values of the neighbourhood. The following
issues influence the decision of an appropriate update rule, and hence the eventual
practical success of the proposed CA model:
•
the type of noise;
•
the type of image;
•
the noise ratio (how much of the image consists of noisy pixels);
•
the neighbourhood (Von Neumann or Moore);
•
border effects at the edges of the image; and
•
the number of evolutions executed by the CA.
The most basic update rule, as given below, is applicable to impulse noise, and it
replaces the current pixel in a Von Neumann neighbourhood with the mean
2
of all
the neighbourhood pixels:
1
x
i
,
j
(
t
+
1
)=
5
(
x
i
,
j
−
1
(
t
)+
x
i
,
j
+
1
(
t
)+
x
i
,
j
(
t
)+
x
i
−
1
,
j
(
t
)+
x
i
+
1
,
j
(
t
))
.
(8.1)
A better approach for impulse noise is to use the majority update rule [27, 31].
Let all pixel values
k
fall in the range 0 to
n
, and take the value
x
p
,
r
=
k
in the
neighbourhood
N
which occurs the greatest number of times (the majority value) as
the new cell value. If no majority exists, then any random neighbourhood element
may replace the current cell [27].
⊨
k
,
where
||
(
p
,
r
)
|
k
=
x
p
,
r
(
t
)
,
(
p
,
r
)
∈
N
||
=
max
m
=
0
{
x
p
,
r
=
m
}
if
x
i
,
j
(
t
)=
0or
x
i
,
j
(
t
)=
n
x
i
,
j
(
t
+
1
)=
⊩
random
{
x
p
,
r
(
t
)
,
(
p
,
r
)
∈
N
}
otherwise
(8.2)
Figure 8.1 shows the effect of the majority rule applied to a black and white
image and to a colour image with impulse noise [3]. The CA was applied for two
evolutions. Note the degradation of the clarity in the colour image after noise was
removed.
Improvements and/or variants on the majority update rule include the use of a
Moore neighbourhood instead of a Von Neumann neighbourhood, and the use of
reflexive boundaries instead of null boundaries [31] to minimise discrepancies on
the image borders.
To measure the success of any noise reduction technique, the PSNR (peak signal
to noise ratio) is typically used. Consider a clean image
C
without noise, and intro-
duce random noise to get a noisy image
N
. Apply the noise reduction technique to
N
to get a resultant image
R
. The effectiveness of the noise reduction technique can
now be measured by comparing
C
and
R
. Assume the images have size
m
n
.First,
find the mean squared error between the individual pixels
C
i
,
j
of
C
and
R
i
,
j
of
R
:
×
2
The median can also be used to remove impulse noise. Note that the median produces less
blurring than the mean filter [14].
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