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CHAPTER 8
SWITCHING BASED ADAPTIVE MEAN FILTER
TO REMOVE MIXED NOISE WITH
EDGE PRESERVATION
8.1 INTRODUCTION
Noise cancellation is an important step in image processing and
many algorithms have been proposed to solve this problem. The algorithms
used for noise cancellation mainly depend on the types of noise in images. For
example, in image acquisition step, the photoelectric sensor introduces the
white Gaussian noise due to the thermal motion of electrons. With the
unstable network transfer, impulse noise is added into the image.
In many applications, these two types of noise are present in the
image together named as mixed noise. Mixed noise could occur when sending
an already corrupted image over a noisy communication channel. Neither
mean filter nor median filter alone can efficiently reduce the mixed noise.
There are many mixed noise removal methods presented in recent literatures.
A hybrid filter (Peng and Lucke 1995) that consists of a nonlinear filter and a
weighted linear filter is proposed to reduce the mixed noise. A combination of
mean and median filter (Khriji and Gabbouj 1998, and Rabie 2004) has been
reported to suppress the mixed noise. A histogram based fuzzy filter
(Wang et al 2002) has been proposed to remove the heavy tailed and Gaussian
noise. Three filters (Chio and Krishnapuram 1997) were introduced for
removing impulse noise, smoothing out non-impulse noise and enhancing
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edges. A novel fuzzy filter (Taguchi 1998) has been reported in the literature
to suppress mixed Gaussian and impulse noise. A Signal Dependent Rank
Ordered Mean (SD-ROM) filter (Abreu et al 1996) has been proposed to
remove low density mixed noise effectively. Srinivasan and Ebenezer (2007)
has proposed two new filters to remove Gaussian and mixed noise. These
filters suppress mixed noise of lower densities.
A hybrid filter, introduced by, (Rui Li and Yu-Jin Zhang 2003)
which combines the advantage of the improved adaptive Wiener filter and
bilinear interpolation filter can efficiently reduce both white Gaussian noise
and impulse noise has been introduced. A Trilateral Filter (Garnett 2005) that
is based on a Rank Ordered Absolute Difference (ROAD) statistic to detect
impulse noise pixels in an image is reported. Instead of applying the “detect
and replace” methodology of most impulse noise removal techniques, the
trilateral filter integrates such a statistic into a filter designed to remove
Gaussian noise. The behavior of the filter can be adaptively changed to
remove impulses while retaining the ability to smooth Gaussian noise.
Additionally, the filter can be easily adopted to remove mixed noise.
Although these existing filters have impressive quantitative results, when
applied to images with mixed noise, it often produces visually disappointing
output similar to that of other median-based filters. In addition, the circuit
complexity and computation time are high for Trilateral Filter.
In this chapter, a new simple two stage algorithm called as
switching based adaptive mean filter (SBAMF), which can effectively remove
Gaussian, impulse and mix of Gaussian and impulse noise in images is
proposed. To begin with, mixed noise model is defined. Next, the proposed
algorithm is described. The performance of the proposed filter is tested and
compared with existing filters for different noise corrupted test images. The
visual and quantitative results show that the proposed filter is particularly
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effective in suppressing high density mixed Gaussian and impulse noise. In
addition, the proposed filter is shown to exhibit good edge and detail
preserving characteristics.
8.2 MIXED NOISE MODEL
The images contaminated by Gaussian noise can be modeled by the
following equations:
GG(i,j) = O(i,j) + N (i,j) (8.1)
where O(i,j) and G(i,j) are the gray scale value of original image and
Gaussian noise corrupted image located at the pixel (i,j), NG(i,j) is the
Gaussian noise positioned at the pixel (i,j).The corresponding pixel of the
mixed noise image will be X(i,j), then the probability density function of Xi,j
is ,
p for x=02(x) 1 p for x=Gi,j
p for x=2552
(8.2)
8.3 SWITCHING BASED ADAPTIVE MEAN FILTER (SBAMF)
The noise variance is calculated using the flat region of the noisy image.
A sliding window size of 3x3 is taken with only those pixels that are less than the
maximum value in the sliding window (i.e salt noise of value 255) and greater than
the minimum value in the sliding window (i.e, pepper noise of value 0). Pixels are
taken along the boundary of the current window (Refer Figure 8.1) and their mean
values are calculated.
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8.4 RESULTS AND DISCUSSIONS
In this section, noise removal capability of the proposed SBAM
filter is tested separately for Gaussian noise, impulse noise and mix of
Gaussian and impulse noise. The results are compared with existing methods
such as standard median filter, and alpha trimmed mean filter. The SBAM
filter is tested using different test images such as Elaine, Pepper, Lena and
Parrot (colour) of size 512x512, 8 bits/pixel.
Figures 8.3 and 8.4 show the restoration results of various filters for
the Elaine image and Pepper image corrupted by Gaussian noises of standard
deviation 20 and 40 respectively. Figure 8.5 show that the performance of
various filters for the Lena image corrupted by Salt and Pepper noise of
density 70%.
Figures 8.6, 8.7 and 8.8 shows the filtered outputs of the proposed
algorithm for Elaine, Pepper and Parrot (colour) images corrupted by mixed
Gaussian and impulse noise .The restoration results of SMF, Alpha trimmed
mean filter, Trilateral filter and the proposed filter for the pepper image
corrupted by Gaussian noise of Standard deviation 20 and salt and pepper
noise of density 40% is shown in Figure 8.9.
The visual quality clearly shows that the proposed filter
outperforms the other methods in terms of noise removal and edge
preservation. Figures 8.2 (e) and 8.3 (e) show that the proposed method has
better noise suppression than the existing methods. Comparing Figures 8.5 (e)
and 8.5 (f) the streaks present in the Srini-Ebenezer method is not present in
the proposed method. Figure 8.9 (f) shows that the SBAMF has better noise
suppression and detail preservation compared to the recently proposed
Trilateral filter and well known Alpha trimmed mean filter outputs as shown
in Figures 8.9 (e) and 8.9(d) respectively.
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A quantitative comparison is performed between the conventional
and the proposed filter on the basis of three objective quality measures,
namely, PSNR, MAE and MSE as defined in equations (2.3), (2.4) and (2.5)
respectively. Tables 8.1, 8.2, and 8.3 show the comparison of PSNR, MAE
and MSE of various filters for the Pepper image corrupted by Gaussian noise
of different standard deviations for an impulse noise density of 40%.
Tables 8.4, 8.5, and 8.6 show the comparison of PSNR, MAE and MSE of
various filters for the Pepper image corrupted by impulse noise densities at
Gaussian noise of standard deviation 20. Figure 8.10 shows the comparison
graph of PSNR of various filters for the Pepper image at different Gaussian
noise standard deviations with a salt and pepper noise density of 40%.
Figure 8.11 shows the comparison graph of PSNR of various filters for
Pepper image at different salt and pepper noise densities with a Gaussian
noise of standard deviation 20. The simulations are performed in a PC (2.4
GHz CPU and 256 MB of RAM) equipped with MATLAB 7.1.
(a) (b) (c)
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(d) (e)
Figure 8.3 (a) Original Elaine image (b) Noisy image (SD = 20).
Restoration results of (c) Alpha-Trimmed Mean Filter (d)
K-means Filter (e) Proposed method – SBAMF
(a) (b) (c)
(d) (e)
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Figure 8.4 (a) Original Pepper Image (b) Noisy Image (SD = 40).
Restoration Results of (c) Alpha-Trimmed Mean Filter (d)
K-Means Filter (e) Proposed Method – SBAMF
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(a) (b) (c)
(d) (e) (f)
Figure 8.5 (a) Original Lena Image (b) Noisy Image (SP = 70%).
Restoration Results of (c) PSMF (d) AMF (e) Srini-Ebenezer
Method (f) Proposed Method – SBAMF
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(a) (b) (c)
(d) (e) (f)
(g) (h) (i)
Figure 8.6 (a,d,g)Original Elaine Image (b) Noisy Image (SD=20,
SP=10%). (e) Noisy Image (SD=20, SP=30%) (h) Noisy
Image (SD=20, SP=50%) (c,f,i) Restoration Results of
Proposed Method – SBAMF
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(a) (b) (c)
(d) (e) (f)
(g) (h) (i)
Figure 8.7 (a,d,g)Original Pepper Image (b) Noisy image (SD=10,
SP=30%). (e) Noisy Image (SD=20, SP=30%) (h) Noisy
Image (SD=30, SP=30%) (c,f,i) Restoration Results of
Proposed Method – SBAMF
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(a) (b) (c)
(d) (e) (f)
(g) (h) (i)
Figure 8.8 (a,d,g)Original Parrot Image (b) Noisy image (SD=20,
SP=10%). (e) Noisy Image (SD=20, SP=30%) (h) Noisy
Image (SD=20, SP=50%) (c,f,i) Restoration Results of
Proposed Method – SBAMF
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(a) (b) (c)
(d) (e) (f)
Figure 8.9 (a) Original Pepper Image (b) Noisy Image (SD=20,
SP= 40%). Restoration Results of (c) SMF (d) Alpha
Trimmed Mean Filter (e) Trilateral Filter (f) Proposed
Method – SBAMF
Table 8.1 PSNR of Various Filters for Pepper Image at Different Noise
Standard Deviations for Salt and Pepper Noise Density of
40% (in dB)
SD SMF Alpha Trimmed Trilateral Filter SBAMF 10 18.44 19.35 20.63 30.16 15 18.09 18.34 19.52 29.86 20 17.75 17.93 18.65 29.11 25 17.26 16.25 17.45 27.01 30 16.94 15.92 16.71 26.89 35 15.42 14.64 15.88 26.01
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Table 8.2 MAE of Various Filters for Pepper Image at Different Noise
Standard Deviations for Salt and Pepper Noise density of
40%
SD SMF Alpha Trimmed Trilateral Filter SBAMF 10 12.336 21.361 6.45 4.91 15 14.81 21.422 8.74 5.57 20 17.34 21.583 10.79 6.17 25 19.933 21.43 13.13 8.26 30 22.16 21.567 16.59 8.35 35 24.752 21.736 18.23 9.38
Table 8.3 MSE of Various Filters for Pepper Image at Different Noise
Standard Deviations for Salt and Pepper Noise Density of
40%
SD SMF Alpha Trimmed Trilateral filter SBAMF 10 929.62 753.93 155.97 53.055 15 1007.5 900.66 254.02 67.016 20 1090.4 958.59 410.73 79.701 25 1220.8 1077.9 512.51 129.2 30 1315.4 1107.6 629.23 133.03 35 1479.8 1277 712.34 163.1
Table 8.4 PSNR of Various Filters for Pepper Image at Different
Noise Densities for Noise Standard Deviation of 20
Noise Density SMF Alpha Trimmed Trilateral filter SBAMF 10 26.8 25.01 27.74 29.55 20 24.63 22.83 26.31 29.31 30 21.18 20.97 22.85 29.12 40 17.81 19.31 21.79 28.96 50 14.64 17.97 19.35 27.82
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Table 8.5 MAE of Various Filters for Pepper Image at Different Noise
Densities for a Noise Standard Deviation of 20
Noise Density SMF Alpha Trimmed Trilateral Filter SBAMF 10 8.5404 10.109 7.28 6.1993 20 9.9882 13.772 1.4852 6.3442 30 2.6688 17.451 3.89 6.4925 40 7.2598 21.583 10.95 6.5321 50 25.205 25.523 26.47 6.1729
Table 8.6 MSE of Various Filters for Pepper Image at Different Noise
Densities for a Noise Standard Deviation of 20
Noise Density SMF Alpha Trimmed Trilateral Filter SBAMF 10 135.55 204.86 109.17 19.679 20 223.78 338.78 151.82 25.109 30 494.86 519.19 337.15 26.024 40 1079.4 761.59 1053.3 25.403 50 2231.4 1036.8 2.8973 29.212
Standard Deviation vs PSNR
05
101520253035
10 15 20 25 30 35Noise Standard Deviation
Peak
Sig
nal t
o N
oise
R
atio
SMF
AlphaTrimmed
Trilateralfilter
SBAMF
Figure 8.10 PSNR Plot of Various Filters for Pepper Image at Different
Gaussian Noise Standard Deviations with Salt and Pepper
Noise Density of 40%
Peak
sign
al to
noi
se ra
tio
(dB
)
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Noise Density vs PSNR
0
5
10
15
20
25
30
10 20 30 40 50Noise Density
Peak
Sig
nal t
o N
oise
R
atio
SMF
AlphaTrimmed
Trilateralfilter
SBAMF
Figure 8.11 PSNR Plot of Various Filters for Pepper Image at Different
(SP) Noise Densities with a Gaussian Noise of SD=20
Figure 8.12 shows the original Pepper image, restored image and
error image corrupted by a Gaussian noise standard deviation of 20 and salt
and pepper noise of 40% to emphasize the noise removal capability of the
proposed SBAM filter.
Peak
sign
al to
noi
se ra
tio
(dB
)
150
(a)
(b)
(c)
Figure 8.12 (a) Original Pepper Image (b) Restored Image using the
proposed SBAM filter corrupted by SD = 20 and SP = 40%
(c) Error Image
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8.4.1 Computational Complexity
Table 8.7 shows the computation time required to restore a Pepper
image corrupted at 60% random valued impulse noise. The computational
time is calculated for all seven filtering techniques in a PC (Pentium CPU 2.4
GHz and 256-MB RAM) equipped with MATLAB 7.1. Even though the
proposed SBAM filter takes slightly higher time to restore the original image,
it produces superior results in terms of subjective and objective measures.
Table 8.7 Comparison of Computation Time for Pepper image
Corrupted at SD = 20 and SP = 40%
Methods Time in seconds
SMF 3.3
Alpha-Trimmed Mean Filter 40.23
Trilateral Filter 60.68
SBAM Filter 171.23
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8.5 SUMMARY
In this chapter, a new Switching Based Adaptive Mean filter
(SBAMF) is proposed to remove mixed Gaussian and impulse noises in
images, in a single filtering pass. The proposed SBAM filter has been tested
for different test images and the results have been compared with the existing
methods for Gaussian noise, impulse noise and mixed Gaussian and impulse
noise. The better performance of the proposed filter over the existing methods
is due to the computation of correct threshold, based on noise variance and
smoothing factor. The visual and quantitative results show the superior
performance of the proposed filter over the existing filters in terms of noise
removal and detail preservation.
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