IJACT2452PPL

A New Denoising Method and Its Application in Face Recognition
1
Shengnan Wu, 2
Yongxin Ge
1,
School of Software Engineering, Chongqing University, Chongqing, China,
wsn1023@163.com
*2,
School of Software Engineering, Chongqing University, Chongqing, China,
yongxinge@cqu.edu.cn
Abstract
Based on analyzing the main principles and characteristics of switching median filter and
switching mean filter respectively, and aiming at the restriction of simplex improved median and mean
filters, a new algorithm named “switching mean-median filter” is proposed in this paper. This
algorithm combines effectively the traits of both median and mean without numerous calculations, and
makes the judgment and process of noises diversified. At the same time, this algorithm is expandable,
as it could be combined with other improved median filters to achieve better performances. The results
of experiments in this paper show that in face recognition this algorithm is more effective than
switching median filter and switching mean filter.
Keywords: Denoise, Filter, Face Recognition
1. Introduction
The idea of median filter was first proposed in early 1974 and it was initially supposed to solve the
problem of one dimension signals which need to be smoothed. Because the performance of this method
is great, it was introduced to two dimensions later. Median filter is better than linear methods not only
in the performance of denoising but also of reserving details, so this algorithm attracted numerous
experts of image processing, which accelerated strongly the development of non-linear methods.
Although median filter has a lot of advantages, it also contains some defects. Firstly, it is aimless in
denoising. Secondly, the performance of denosing becomes worse while the density of noise is
increasing. Furthermore, the process may damage the geometrical structure of images. To make the
performance better, some improved methods based on standard median filter have been proposed from
various aspects [1-5]. Some of them are famous, such as, progressive median filter[1], multistage
median filter[2], median filter with adaptive length [3], switching median filter[4], and so on.
Progressive median filter based on mean filter was proposed in 1982 and its improvement relative to
mean filter was theoretically analyzed in detail [1]. The main idea of progressive median filter is to
include in the filtering window the denoised pixels, with which it will predict the medians. The
improvement makes better denoising performance, but can not protect properly the details and contours,
because the results are based on the gray scales of denoised pixels but not those of original pixels.
Multistage median filter was proposed by Nieminen et. al. in 1987 [2], whose main idea is to
consider the original filtering window as four small congruent windows. Firstly, the medians of these
four small windows are calculated, and then the largest and smallest medians are integrated in the
median calculation of the original filtering window. This algorithm can reduce noises better than
median filter and preserve details, but it can not restrain some special noises, and as it involves a large
amount of calculation, its computing time is fairly long.
In 1988, Lin and Wilson proposed median filter with adaptive length [3]. In standard median filter
the size of filtering window would directly affect the performance of denoising and the ability of
protecting the details, and there is a contradiction between them: when the size of filtering window
becomes smaller, the ability of protecting details turns stronger while the performance of denoising
becomes worse; when the size of filtering window becomes larger, the ability of protecting details turns
weaker while the performance of denoising becomes better. Median filter with adaptive length was
improved against this contradiction. The main idea of this algorithm is to revise the size of filtering
window by detection of feature value of gray scales of pixels’ neighborhoods to achieve the optimality
of both denoising and protection of details. However, when the noise density was high, the
performance would be reduced by the increasing detection error rate of, and the method needs
Shengnan Wu, Yongxin Ge
International Journal of Advancements in Computing Technology(IJACT)
Volume5,Number5,March 2013
doi:10.4156/ijact.vol5.issue5.134
1122

detection to adjust the size of filtering window, which requires a lot of calculation and prolongs the
runtime.
In 1994, Sun and Neuvo proposed switching median filter [4]. The main idea of switching median
filter is to set a threshold first, and if the distance between the original gray scale of the pixel and its
median of neighborhood is larger than the threshold, the pixel will replace with its median; if the
distance is smaller, the pixel will be considered as it was not noise and would not be changed. This
algorithm introduces the judgment of noise and protects better the details. But when the density of
noise is high enough, the advantages become less obvious, because the simple judgment and the
replacement of medians have their limits. Wang and Zhang proposed progressive switching median
filter [5] in 1999. Although this algorithm ameliorates the performance of denoising against the noise
with high density, it involves complicated noise detections and requires lots of circulation, which
lengthens the execution time. In 2000, Xing and her partners proposed a new filtering algorithm based
on extremum and median value [6]. The main idea of this method is that if the gray scale of pixel
equals the largest or smallest one of its neighborhood, it would be replaced with the median; otherwise
it would not be changed. This method runs faster, but its defect is that it would damage the details and
delete some information of borderline in images.
Besides what had been introduced before, researchers proposed other improved median filters, such
as: the max median filter [7], center weighted median filer [8] and so on [9-14]. In addition, other
researchers also combined median filter with other advanced denoising methods, such as wavelet
domain [15, 16], neural network [17, 18] and fuzzy reasoning [19, 20], and proposed more improved
median filters. Numerous denoising methods which contain high quality in both denoising and details
protection were generated, while the application of median filter was extending. These achievements
are cardinal to the development of image denoising, even to the whole field of image processing. On
the whole, the technique of image denoising developed rapidly in recent years and better algorithms
were proposed by researchers. This is why Priyam Chatterjee and Peyman Milanfar wrote “Is
Denoising Dead?” to describe whether denoising has been to the end, in another word, whether there is
still room for denoising to improve [21].
The switching mean-median filter proposed in this paper is designed for recognition while
considering the calculation time. When the thresholds are appropriate, this method could reduce well
noise in images and raise the recognition rate in a short time. The experiments in this paper have
proved that for various densities of noise, the new method could improve essentially recognition rate
compared with switching median filter.
2. Switching median filter
The “gray biased value” is defined in this section, which means the distance between the gray
value of one pixel and the median gray value of its neighborhood pixels.
Suppose ( , )x y is gray biased value of a pixel, whose coordinate is x and y; ( , )f x y is gray
scale of a pixel, whose coordinate is x and y; ( , )median x y is the median gray value of
neighborhood pixels of a pixel, whose coordinate is x and y. The ( , )x y is defined as:
( , ) ( , ) ( , )x y f x y median x y (1)
The principle of switching median filter is as follows: set a threshold, and then if gray biased value
of the pixel is larger than the threshold, consider this pixel as noise and replace its value with the
median of its neighborhood; if it is smaller than the threshold, do not consider this pixel as noise and
do not change its gray value.
Suppose is the threshold; ( , )x y is gray biased value of a pixel, whose coordinate is x and y;
( , )f x y is the gray value of a pixel, whose coordinate is x and y; ( , )median x y is the median gray
value of neighborhood pixels of a pixel, whose coordinate is x and y; ( , )g x y is the denoised pixel
value, whose coordinate is x and y. The ( , )g x y is defined as:
( , ), ( , )
( , )
( , ), ( , )
f x y x y
g x y
median x y x y
(2)
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3. Switching mean filter
The “gray difference value” is defined in this section, which means the distance between the gray value
of one pixel and the average gray value of its neighborhood pixels.
Suppose ( , )x y is gray difference value of a pixel, whose coordinate is x and y; ( , )f x y is gray
value of a pixel, whose coordinate is x and y; ( , )mean x y is the average gray value of neighborhood
pixels of a pixel, whose coordinate is x and y. The ( , )x y is defined as:
( , ) ( , ) ( , )x y f x y mean x y (3)
The principle of switching mean filter is as follows: set a threshold, and if gray difference value of
the pixel is larger than the threshold, consider this pixel as noise and replace its gray value with the
average of its neighborhood; if it is smaller than the threshold, do not consider this pixel as noise and
do not change its gray value.
Suppose is the threshold; ( , )x y is gray difference value of a pixel whose coordinate is x and
y; ( , )f x y is gray value of a pixel, whose coordinate is x and y; ( , )mean x y is the average gray value
of neighborhood pixels of a pixel whose coordinate is x and y; ( , )g x y is the denoised pixel value,
whose coordinate is x and y. The ( , )g x y is defined as:
( , ), ( , )
( , )
( , ), ( , )
f x y x y
g x y
m ean x y x y
(4)
4. Switching mean-median filter
Every kind of improved median filters replaces the noise with the median of gray value in the
filtering window, which limits inevitably the algorithm. In switching mean-median filter, the judgment
and replacement are various. First of all, theoretically, two kinds of feature values could describe the
characteristics of one group of data more comprehensively and accurately than only one of them. So in
this paper it believes that theoretically the switching mean-median filter is more effective than simple
switching median filter. Second, the results of experiments in this paper prove that the method
proposed is better than switching median filter in improving recognition rate. The defect of switching
median filer is when the density of noise increases, the performance of denoising becomes worse. This
is the limit lying in simple improved median filters. While the density of noise is increasing, it becomes
harder for the simple median to represent the characteristics of the pixel. The method proposed in this
paper introduces the conception of mean value to restrain this limit. The results of experiments show
that the recognition rate improved by new method is increasing while the density of noise is also rising,
and higher than that of switching median filter, essentially when the density of noise is very high.
While making the performance better, the new method does not involve complicated calculation like
other improved median filters, which would prolong the run time. At last, the new method proposed in
this paper is very expandable. It can be combined with progressive median filter, multistage median
filter and other improved filters to achieve better performance of denoising.
The principle of switching mean-median filter is based on both switching median filter and
switching mean filter. The new method improves the rules of judgment and replacement of noise by the
special relations of thresholds of those two methods. According to the judgment of the gray value of a
pixel, the method would process the pixel in different ways. The gray biased value and gray difference
value were defined in this paper, so they will not be repeated here.
The principle of switching mean-median filter is to set two thresholds, the first of which is the
threshold of gray biased value and the second is threshold of gray difference value. There are four
situations among the gray value of the pixel and the two thresholds:
Gray biased value is smaller than the first threshold, and gray difference value is also smaller than
the second threshold.
Gray biased value is larger than or equal to the first threshold, but gray difference value is smaller
than the second threshold.
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Gray biased value is smaller than the first threshold, but gray difference value is larger than or
equal to the second threshold.
Gray biased value is larger than or equal to the first threshold, and gray difference value is also
larger than or equal to the second threshold.
In the first situation, both switching median and switching mean filter will not regard the pixel as
noise, neither does the new method, so the value of this pixel will not be changed.
In the second situation, switching mean filter will not consider the pixel as noise, but switching
median filter does, so the new method will consider it as noise and replace its value with the median
value.
In the third situation, switching mean filter consider the pixel as noise, but switching median filter
does not, so the new method will consider it as noise and replace its value with the mean value.
In the fourth situation, both switching median and switching mean filters consider the pixel as noise,
so the new method will consider it as noise too. If this happened, the gray value in the filtering window
is supposed to be much different from one to the others, if replaced by mean value, it will be more
inaccurate. So the new method will replaces this with the median value.
Suppose is the first threshold; is the second threshold; ( , )x y is gray biased value of a pixel,
whose coordinate is x and y; ( , )x y is gray difference value of a pixel, whose coordinate is x and y;
( , )f x y is gray of a pixel, whose coordinate is x and y; ( , )median x y is the median scale value of
neighborhood pixels of a pixel, whose coordinate is x and y; ( , )mean x y is the average gray value of
neighborhood pixels of a pixel, whose coordinate is x and y; ( , )g x y is the denoised pixel, whose
coordinate is x and y. The definition of ( , )g x y is updated as:
( , ), ( , ) & ( , )
( , ), ( , ) & ( , )
( , )
( , ), ( , ) & ( , )
( , ), ( , ) & ( , )
f x y x y x y
median x y x y x y
g x y
mean x y x y x y
median x y x y x y
(5)
In switching mean-median filter, if threshold and are set to the maximum, ( , )g x y will
congruent to ( , )f x y , which means there is no process to the image; if threshold and are set to
zero or is set to the maximum and is set to zero, ( , )g x y will congruent to ( , )median x y , which
means the image is filtered by the median filter; if is set to the maximum and equals to zero,
( , )g x y will congruent to ( , )mean x y , which means the image is filtered by the mean filter. So the two
thresholds are critical to the performance and different thresholds will lead various results.
5. Results and analysis of experiments
In the experiments, filtering window is distance template which contains pixels whose distance is less
than or equal to two pixels to central pixel, and 2DPCA is applied for face recognition.
We report our results on experiments on the public face database, ORL face database, which
contains ten different images of each of 40 distinct subjects. For some subjects, the images were taken
at different times, varying facial expressions and the lighting. All the images were taken against a dark
homogeneous background with the subjects in an upright, frontal position. The images in the database
are all gray images with size of 92 * 112.
In the experiments, the first 9 eigenvectors are chosen. The number of training samples is from 1 to 9.
Ten kinds of combinations would be chosen in training samples with the same amount of images. At
last the average recognition rate of different combinations is calculated as a result of training samples
with the same amount. The final results have 9 average values for different amount of training samples.
Also we conducted the experiment on the images of various densities, and then do the same
experiments on the same denoised images processed by three different denoising methods. At last, we
compare these results, and analyze the influence of the rates by different methods.
Because the results only show the different recognition rates of different methods and can not reveal
the essential relations among them, U-detection method is adopted to analyze the results.
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Suppose X is the average value of different training samples with the same amount of images in one
group of results; 0 is the average value of different training samples with the same amount of images
in another group of results; S is the variance of the data with respected to 0 ; n is the number of
images in one group, as ORL face database is adopted, it is constant 10 here; U is the result of this
detection method, and it could indicate whether the data of X group is significant to the data of 0
group, which is formulated as:
0
/
X
U
S n
(6)
In the experiment, two significant levels are involved, 0.01 and 0.05 , and their rejection
region are 1 1 0.01 2.32u u and 1 1 0.05 1.46u u respectively.
Table 1 shows that, all the recognition rates become higher except when the number of training
samples is 4, but the decrement is so subtle that can be ignored, and some increasing amount are
obvious, which proves our method is effective for face recognition of 2DPCA.
Table 2 shows that all the recognition rates become higher except when the number of training
samples is 3, but the decrement is only 0.003, which makes no sense, and the increasing amount are
more obvious than Table 1, which means in Table 2 the recognition rate is better improved.
Table 1.Face recognition rates of ORL images with 0.1 density of noise before and after process
Amount of
training samples
ORL images with 0.1
density of noise
before process
After process of switching mean-median filter
with thresholds 30 and 100
1 0.414167 0.441389
2 0.510625 0.52625
3 0.557857 0.578571
4 0.626667 0.623333
5 0.6495 0.663
6 0.7 0.72125
7 0.7675 0.77
8 0.78125 0.81
9 0.7975 0.8275
Amount of
training samples
ORL images with 0.2
density of noise
before process
1 0.412778 0.439445
2 0.493438 0.51625
3 0.546429 0.546072
4 0.594167 0.616667
5 0.6095 0.664
6 0.7025 0.73
7 0.736667 0.774167
8 0.8 0.82375
9 0.8 0.84
Amount of
training samples
ORL images with 0.3
density of noise
before process
1 0.390556 0.443333
2 0.471563 0.527188
3 0.499286 0.571071
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4 0.592917 0.634583
5 0.616 0.6455
6 0.673125 0.706875
7 0.706667 0.7775
8 0.755 0.785
9 0.81 0.8075
Amount of
training samples
ORL images with 0.4
density of noise
before process
1 0.341945 0.441111
2 0.444688 0.515938
3 0.477143 0.589643
4 0.51 0.605
5 0.5625 0.6485
6 0.645 0.71875
7 0.668333 0.77
8 0.71375 0.8075
9 0.775 0.8225
Amount of
training samples
ORL images with 0.5
density of noise
before process
1 0.333333 0.416111
2 0.404375 0.5175
3 0.441786 0.581786
4 0.49875 0.60625
5 0.5365 0.6385
6 0.534375 0.71875
7 0.648334 0.761667
8 0.62125 0.80875
9 0.735 0.825
Table 3 shows that all the recognition rates become higher except when the number of training
samples is 9, but the decrement is just 0.025, which could be ignored. And the increasing amount are
more obvious than Table 2.
Table 4 shows that all the recognition rates after denoising are much higher than that before, and
nearly half of them increase around 10%.
Table 5 is similar to Table 4, but the increasing amount in Table 5 is more significant than that in
Table 4. In most of the cases, the recognition rate increases about 10%, even 20% in one or two cases.
These five tables show that switching mean-median filter can increase the face recognition rates of
images which contain various noises. The increasing amounts of rates become higher while the density
of noise is increasing. Especially when the density of noise is high, the improved recognition rate is
considerable.
Table 6.Results of U-detection method of ORL images with various densities of noise before and after
denoising process of switching mean-median filter with thresholds 30 and 100
0.1 density of
noise
0.2 density of
noise
0.3 density of
noise
0.4 density of
noise
0.5 density of
noise
#1.831447 1.265357 *2.652883 *4.221962 *4.110598
1.338206 1.317972 #1.872251 *3.817688 *5.4695
#1.721509 -0.02504 *4.112766 *6.230625 *8.951049
-0.18754 1.305264 *2.462564 *5.921285 *6.857045
0.600923 *3.407559 #1.986863 *4.563478 *3.285349
1.217384 #2.211102 #2.208432 *3.36364 *13.91515
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0.153694 #1.781257 *4.194401 *3.816649 *4.574165
#2.221189 #1.718629 1.264136 *3.123496 *8.85759
1.281641 #2.065599 -0.23426 #1.839659 *3.408443
Notice: # means that it has passed the significant level of 05.0 ; * means that it has
passed the significant level of 01.0
In Table 6, 7 and, 8, numbers with # show these numbers are larger than 1.46 (meet 05.0 )
after the U-detection, which means there are significant differences between these two groups of data.
In this experiment, it also represents that the method can fundamentally increase the recognition rates;
numbers with * show these numbers are larger than 2.32 (meet 01.0 ) after the U-detection,
which means there are significant differences between these two groups of data. In the experiment, it
also implies that the increases of the rate by the method are very essential.
Table 6 contains several or many # or * indicates that the method can essentially increase the rates.
Although there are several negative values, their absolute values are so small that can be ignored.
While the density of noise is increasing, there are more * in the columns, which shows that the
performance is better. When the density is larger than 0.4, all numbers are with *, which means the
method is extremely effective in the situation of high density.
Table 7.Results of U-detection method of ORL images with various densities of noise after process of
switching mean-median filter with thresholds 30 and 100 versus switching mean filter with threshold
50
0.1 density of
noise
0.2 density of
noise
0.3 density of
noise
0.4 density of
noise
0.5 density of
noise
-1.52601 -0.43087 *2.724672 *5.889384 *11.78595
0.089091 0.428212 #1.493557 *6.445691 *6.233621
0.285143 -5.09845 *3.251088 *7.373122 *7.373399
0.425106 #2.041215 *3.704019 *5.967337 *7.23529
1.021727 0.232733 *2.65688 *5.054704 *6.831667
1.022313 *4.121445 #2.236715 *5.143938 *9.954514
1.327063 *2.351342 *3.801621 *7.047448 *5.367123
*2.5083 #2.006192 *3.199295 *5.451897 *8.367439
*3.123484 *4.882426 #2.235576 *3.041064 *6.89955
Notice: # means has passed the significant level of 0.05 ; * means has passed the
significant level of 0.01
In Table 7, the data compared with the new method are gotten with switching mean method. In the
whole table, most numbers are with # or *, which proves that the new method is much better than
switching mean filter in improving recognition rates of 2DPCA. While the density of noise is
increasing, there are more * which indicates that the advantage is extending with the density. When the
density of noise is larger than 0.3, the numbers are almost with # or * and most of them are much larger
than 2.32. The conclusion is that the new method is generally much better than switching mean filter in
improving recognition rates, and while the density of noise is increasing, the advantages of new
method become more and more significant.
Table 8.Results of U-detection method of ORL images with various densities of noise after process of
switching mean-median filter with thresholds 30 and 100 versus switching median filter with threshold
30
0.1 density of
noise
0.2 density of
noise
0.3 density of
noise
0.4 density of
noise
0.5 density of noise
-1.46782 0.793323 *3.426252 #1.978542 0.755732
0.612944 -3.37878 0.888154 0.106481 #1.646343
-0.66075 -1.04481 0.108312 *2.462475 1.180937
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-0.90352 -0.9551 0.131136 -1.53945 1.107152
0.43337 -0.6957 -0.63843 0.474296 0.615658
-0.68996 0.267259 -0.65611 1.019029 #2.086277
0.602006 0.843017 -0.81213 -0.25324 #1.743174
0.240192 1.307793 0.054946 1.280393 #1.653957
0.208387 -0.65218 -0.40089 -1.35664 -0.95752
Notice: # means has passed the significant level of 0.05 ; * means has passed the significant
level of 0.01
In Table 8, the data compared with the new method are gotten with switching median method.
When the density of noise is between 0.1 and 0.4, the absolute values of numbers are on the small side,
and there are still several # and *. This shows that the new method is a little better than switching
median filter, but the effect is not essential. When the density of noise is 0.5, there is only one negative
value and almost half numbers are with #. This means when the noise density is 0.5, the new method
can be fundamentally better than switching median filter in recognition rate. This also indicates that
while the density of noise is increasing, the performance of the method turns better. In a word, the new
method is generally better than switching median filter in improving recognition rate, and while the
density of noise is increasing, the advantages of new method become more obvious, especially in high
density situation.
6. Conclusion
This paper mainly studies median and mean filters and proposes switching mean-median filter. It also
calculates the face recognition rates are calculated in ORL face database with various densities and
rates after denosing these images by three different denoising methods respectively. At last, we
compare these results and analyze the influence of the rates by different methods. The results of
experiments prove the validity of the new method. Besides, the thresholds chosen in the paper may not
be the best combination, and the combinations of switching mean-median filter in various
circumstances should be studied further. Also, this new method could combine with other improved
filters to achieve better performance, and it is can be used in other applications, such as image
segmentation and image semantics recognition.
7. Acknowledgement
Project No. CDJZR12090002 supported by the Fundamental Research Funds for the Central
Universities.
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