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Impulse noise features for automatic selection of noise cleaning filter

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Impulse noise features for automatic selection of
noise cleaning filter
Odej Kao
Department of Computer Science
Technical University of Clausthal
Julius-Albert-Strasse 4
38678 Clausthal-Zellerfeld, Germany
Stefan Diener
Imaging GmbH
PO BOX 1166
73442 Oberkochen, Germany
Abstract The noise removal is an important aspect
of image processing, because the human visual
system is very sensitive to the high amplitude of
noise signals, thus noise in an image can result in a
subjective loss of information. There are a lot of
methods for impulse noise removal like the median
or the outlier filter. But there are only few
measuring methods for the quality of a smoothed
image. In most cases the developed filters are tested
on standard images. On the other hand it is difficult
to decide, which filter should be used for a given
image with impulse noise introduced to it.
In this paper two methods for impulse noise
removal are compared in order examine important
features for an automatic detection of adequate
smoothing operators for a given noisy image. The
quality of the smoothed image depends on two
parameters: the quantity of impulse noise and the
structure of the noisy image. These can be
characterised and used for an automatic choice and
for the setting of the appropriate filter options.
Keywords: image processing, impulse noise features,
outlier, ranking
1. Introduction
Impulse noise is a special type of noise
which can have many different causes.
Thus, in the case of satellite or TV images it
can be caused through atmospheric
disturbances. In other applications it can be
caused by strong electromagnetic fields,
transmission errors, etc. Impulse noise is
characterised by short, abrupt alterations of
the colour values in the image. The
concerned points are changed through
overlay of a coincidence value so that they
differ significantly from their local
neighbourhood and disturb the natural
colour run. Thereby the subsequent image
processing, analysis and evaluation can be
affected, regardless whether these actions
are done by a human viewer or in an
automated process. This is the reason why
smoothing operators form the foundation of
each image processing chain. The aim is to
approximately restore the original value of
the noisy point.
A lot of filters for impulse noise
removal [1,2,3,6] have been developed.
Usually they are subdivided into linear and
non linear filters. Another classification is
based on the used image description space,
so the filters fall into two classes: spatial
and frequency domain filter. Frequency
domain operators have usually low-pass
properties. By introduction of a threshold
value, so called cut-off-frequency, the high
image frequencies are eliminated and the
impulse noise level can be decreased. An
essential disadvantage of this method is that
other image components with high
frequency, like edges, are affected resulting
in a blurred image.
Spatial domain filters work directly
on the image matrix. Different methods can
be used in order to identify and eliminate
outliers in an examined image environment.
A standard filter in this class is the median
filter, which was proposed by Tukey [5].
However, there exist plenty of specialised
impulse noise removal filters, which are
adapted to specific image classes. Thus the
achieved smoothing results are better as the
results of the median filter in these special
applications. A general control criterion for
the quality of a noise suppression does not
exist because this depends on the actual
application. The demands on smoothing of
a high-resolution picture, which is the input
for precise measurements, distinguish from
the demand on smoothing of a television
frame. Further an exact mathematical model
of an ideal picture defining image features
like contrast, colour distribution etc. is still
not available, because the set of possible
pictures is not manageable. The operators
are applied and matched to general test
patterns and the smoothing results are
usually evaluated visually. The subjective
opinion of the observer has thereby an
essential meaning.
Therefore, the application of such
operators to general and specific problems
is an iterative process. The picture is added
to a set of available noise removal
operators. Subsequently a visual evaluation
of the smoothed image follows. In the case
of complicated or sensitive processes
essential image components must be
enlarged and properly examined. Beside the
large time effort a certain work experience
with image processing operators is required.
This process can be enhanced and speeded
up by an analysis of the impulse noise and
of the image structure. The results of this
analysis should be image features like e.g.
noise distributions, detail degrees etc. These
can be used for an automatic choice of the
noise removal filter and the corresponding
parameters. Thus the operators can be easily
applied by users without certain image
processing knowledge.
The first step in this direction is a
comparison of the available noise removal
filters in order to determine essential
features, which can be used as a basis for a
problem oriented classification. In this
paper the properties of two standard
methods, the outlier and the rank order
method, are examined and compared.
2. Outlier method
In case of the outlier method an average of
the grey levels in a
nn
filter window, n
odd, around the center pixel is calculated.
This can be performed by using following
mask:
111
101
111
8
1
In the next step an absolute
difference d of the average value and the
grey level of the center pixel is calculated
and compared with a threshold value t. The
analysed pixel is marked as a noise peak, if
d>t. The success of this method for noise
removal depends on the choice of the
threshold value t. Many peaks can not be
recognised, if the value t is too big.
Otherwise too many non noisy points can
be marked as peaks.
Figure 1: Test images Lena, Corvette
0
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60
80
0
20
40
60
80
100
Hit/Miss %
Noise %
Thres-
hold
outlier method, Amplitude 0 (Lena)
0
246
810
20
50
80
0
20
40
60
80
100
Hit/Miss %
Noise %
Thres-
hold
outlier method, Amplitude 255 (Lena)
80-100
60-80
40-60
20-40
0-20
Figure 2: Hit rate in case of the outlier method and the image “Lena”
There are four possibilities for the
marking of an image point:
1) a point is a peak and correctly marked
(hit_peak)
2) a marked point is not a peak
(miss_point)
3) a peak is not marked (miss_peak)
4) a point without noise is not marked
(hit_point)
These values are used for the
calculation of a hit/miss quotient as follows:
In order to examine the
dependencies of the removal quality and the
threshold value practical tests on two
selected images, "Lena" and "Corvette"
(Figure 1), were executed. We used a
33
filter window and examined white and
black impulse noise points in two different
passes. The results of these tests are shown
in figure 2.
With a threshold value t between 60
and 70 a hit/miss rate of approximately 80%
- 90% can be reached. Beyond that
threshold there is no relevant increase in the
removal. Further there exists no significant
difference in the removal of white or black
noisy peaks. The hit/miss rate falls with a
larger noise component in the image. The
amount of miss_point and miss_peak
increases more than the number of the hits,
because of the stronger peak influence in
the averaging.
Precisely test results are as follows:
1939 black and white peaks, corresponding
to a noise component of 3%, were
introduced to the image "Lena". 1818 peaks
are classified correctly by the outlier
method with a 3x3 filter mask and a
threshold value of 60. 181 pixel are
classified wrongly resulting in a 90.93%
hit/miss rate. An application of the same
test and analysis on the "Corvette" image
with 2763 noisy points (3% impulse noise)
is producing following results: with the 3x3
outlier method and threshold of 60 5923
pixel are not recognised or wrongly marked
and 2165 are correctly classified as noise.
Thus the hit / miss rate amounts 26.77%.
Through higher threshold value of 130 the
amount of mismatched points falls onto
1571 points. On the other hand only 1348
peaks can be correctly classified, so a better
46.18% hit rate can be achieved. It becomes
clear that an increase of the threshold value
can essentially enhance the hit / miss rate.
However if the threshold is too high, the
number of the hits falls so considerably that
the opposite effect occurs. All in all
the
 
%100
m_pointm_peakh_peak h_peak
h/m_rate
++
=
0
2
4
6
8
10
50
90
130
0
20
40
60
80
100
Hit/Miss %
Noise %
Thres-
hold
outlier method, Ampli. 255 (Corvette)
0
2
4
6
8
10
50
90
130
0
20
40
60
80
100
Hit/Miss %
Noise %
Thres-
hold
outlier method, Ampli. 0 (Corvette)
80-100
60-80
40-60
20-40
0-20
Figure 3: Smoothing results of the outlier method (Corvette)
high hit rates of the picture "Lena" can not
be reached.
One of the reasons for this
mismatching is the high detail complexity
of the "Corvette" image. These details
affect the averaging and result in blurred
edges. The application of the outlier method
can not be recommended. Figure 3 shows
the results of the test on the image
"Corvette".
Further there is a large difference
between the recognition of black peaks
(60%-70%) and the recognition of white
peaks (about 40%). One of the reasons for
this behaviour can be found in the
histograms of the test images. The image
"Corvette" consists of many bright grey
levels, so it is difficult to identify white
peaks. But if a lower threshold value is
chosen many non noisy points can be
marked as peaks. Thus, the hit/miss rate is
only inessential larger. The grey levels of
the image "Lena" are in the middle of the
histogram, so white and black peaks can be
identified with approximately the same
probability. An increase of the filter
window size e.g. 9x9 amplifies the edge
detecting properties of the outlier filter and
many points are mismatched.
Summarising the outlier method can
reach high hit/miss rate, if following
constraints are fulfilled:
small deviation
the mean grey level of the image is in
the middle of the available grey range.
a low degree of details. This can be
estimated by analysing high frequencies
in the amplitude spectrum.
3. Ranking method
Another possibility for noise removal is the
ranking method. The pixels within the filter
window are sorted and the value of the
pixel being processing is replaced by a
certain element of the sorted sequence. The
best known ranking filter is the median
filter. The center window pixel is replaced
by the median of the sorted sequence [4].
The advantages of the rank order method
are: it is easy to implement, noise is
removed without significantly affecting the
sharpness of edges and of fine image
details. Furthermore no new colour values
are introduced. Disadvantages of the
median filter are the amount of work
required and particular image details and
geometric structuressuch as thin
horizontal or vertical linesare removed
[2]. The right choice of the filter
window size is one deciding factor for the
quality of impulse removal. In case of a
small, inhomogeneous 3x3 environment
without noisy points there is a large
probability, that a pixel is wrongly marked
as peak.
ranking method (Lena)
0
10
20
30
40
50
60
70
80
90
100
0 1 2 3 4 5 6 7 8 9 10
Noise level %
Hit/Miss %
ranking method (Corvette)
0
10
20
30
40
50
60
70
80
90
100
012345678910
Noise level %
Hit/Miss %
Amplitude 0
Amplitude 255
Thus, majority of one specific
colour is usually not available so there is no
identification basis for outliers. Therefore
edge or detail pixel are wrongly marked as
peaks and removed. This pixel majority is
usually given in larger filter windows, e.g.
9x9. Furthermore from certain noise
component on a noisy point can be found in
many neighbourhoods. This guarantees a
correct peak classification. Otherwise the
same problems as in 3x3 case can occur and
the image edges and details can be blurred.
Further research is necessary in order to
determinate thresholds, which could help by
the automatic selection of the filter
attributes. For the following test sequences
a 9x9 filter window is used.
Figure 4 shows the dependency of
the ranking method smoothing results and
the amount of impulse noise in the image.
The hit rate for the „Lena“ image amounts
about 80%, if impulse noise component of
4.5% is introduced to it. A further increase
of the noise component leads to even
higher, up to 90%, hit rates. On the other
hand impulse noise components lower than
4% produce the opposite effect: the
influence of the image structures is essential
for the smoothing process and many edge
and detail points are wrongly marked as
peaks. Thus the hit / miss rate falls clearly.
An application of the ranking
method on the original, noise free „Lena“
image using a 9x9 filter neighbourhood
delivers 1003 wrongly marked points,
which are usually edge points. This
corresponds to 1.53% of all image points. In
order to reduce this amount real peaks in
the processed 9x9 neighbourhood are
necessary. This can be confirmed by
introducing of a 1.5% noise component into
the image. The hit / miss rate amounts 56%.
A further increase of the impulse noise
component (more than 5%) reduces the
influence of the image structures and a
higher hit rate can be achieved.
The disturbing influence of the
image structures on the smoothing process
is even clearer in case of the image
“Corvette”. In the original, noise free image
2931 pixels, corresponding to 3.13% from
all image points, are marked as peaks and
replaced. Figure 4 shows the smoothing
results of the ranking method and variable
noise component in the image “Corvette”. If
4.5% of the pixels are noisy points a hit rate
of approximately 55% (for dark peaks) and
62% (for bright peaks) can be achieved. In
contrast to the image „Lena“ for an
acceptable 80% rate a higher impulse noise
component is needed, because of the large
amount of image details.
Figure 4: Dependency of the ranking method hit rate from the impulse noise component:
for the images “Lena” and “Corvette”
Impulse noise (Lena)
0
10
20
30
40
50
60
70
80
90
100
0 1 2 3 4 5 6 7 8 9 10
Noise level %
Hit/Miss %
Outlier (60)
Ranking
Impulse noise (Corvette)
0
10
20
30
40
50
60
70
80
90
100
0 1 2 3 4 5 6 7 8 9 10
Noise level %
Hit/Miss %
Outlier (120)
Ranking
Figure 5: Comparison of the hit/miss rates of the outlier and of the ranking method on the images
“Lena” and “Corvette”
The maximum reachable hit / miss
rate of the ranking method depends
essentially on the distribution and clearness
of the image details represented by the
amount of high frequencies in the amplitude
spectrum. The hit miss rate is largely
independent from the expectation value of
the image, if this is not near the borders of
the available colour range. The deviation
has no significant influence on the
smoothing process.
4. Comparison of the outlier and
the ranking method
Figure 5 shows the noise removal results of
the outlier and of the ranking method
depending on the impulse noise component
in the image. If the noise component is less
than 7%, the outlier method delivers better
results, in particular for noise percentage
bellow 3%. In this case the ranking method
is more sensitive for small details in the
filter window than the outlier method.
In case of a larger noise component
(>7%) more peaks are found in a
nn
filter
window, so the averaging process of the
outlier method are affected. Noise
components larger than 15% are resulting
into 35% difference between the achieved
hit/miss rates. On the other hand the
influence of the image details is decreasing
and the rank order method reaches hit rates
of more than 90%.
An important problem of the outlier
method is the choice of a suitable threshold
value. Different thresholds must be tested in
order to select the value that delivers the
best compromise between the number of
correctly recognised peaks and the number
of mismatched image points. Many edge
points can be classified as peaks resulting in
a low hit / miss rate.
A fully automatic detection of the
most suitable method for impulse noise
cleaning is not possible with these simple
tools. But these clues can be used as a first
orientation in the noise cleaning process:
For a noise component less than 7% the
application of the outlier method is
suitable. If the noise percentage is larger
than 7% the ranking method should be
applied.
For images containing a lot of details
the noise component threshold value for
the applying of the ranking method
must be decreased. The high detail
degree of an image can be determinated
on the amplitude spectrum of the image.
With the outlier method the
identification of peaks is difficult, if the
average grey level of the image is near
the ends of the grey range. In this case
the ranking method should be used.
5. Applicability of the proposed
methods
This analysis and comparison of standard
noise removal operators is only a first step
for automatic determination of appropriate
smoothing filters. The desired goal of our
research is the creation of a knowledge base
with available noise removal filters, which
are characterised by a set of defined
comparable, common features are proposed,
like percentage of the noise component in
the image, detail degree and colour
distribution in the image histogram. These
features must be extracted from every noisy
image and matched with the patterns in the
knowledge base, so the most suitable filter
for a given noisy image can be chosen.
Efficient and reliable methods for
determination of the noise kind and noise
component of the image as well as
algorithms for analysis of the details must
be developed and tested in practice.
Furthermore, the shown analyses must be
performed for other noise removal
operators.
Another important aspect is the
analysis of white noise in order to find the
most suitable cleaning filter and to
determinate the setting parameters. The
noise distribution curve can be compared
with known probability distributions by an
amount of extracted attributes. In a first
attempt satisfying results by three of ten
noise distributions types were achieved. Six
further types can be recognised, if the noise
parameters are in a certain range. For
recognising of these white noise types new
features must be defined and tested. This is
a part of the future work.
Similar methods can be developed
for other image pre-processing fields like
e.g. edge detection or image segmentation.
6. Conclusions
In this paper two standard methods for
impulse noise removal were compared. In
particular the dependency of the smoothing
results on the noise component in the
image, the detail degree, the mean colour
value, on the deviation and on the colour
distribution were examined. The automatic
determination of a suitable noise cleaning
filter is not yet possible with these simple
tools. But some advice for the choice of an
appropriate smoothing operator can be
given. Future work includes the
comparison of other impulse noise removal
methods and the integration of further noise
attributes like texture etc. The analysis of
white noise and extraction of similar
features is another important aspect of our
research.
References
[1] S. Diener. Noise analysis for medical
images. Master thesis, 1998,
Department of Computer Science, TU
Clausthal.
[2] O. Kao. New Impulse Noise Cleaning
Methods for Monochrome and Colour
Images (Ph. D. Thesis, TU Clausthal)
Papierflieger (Clausthal-Zellerfeld),
1997.
[3] T. Lehmann, W. Oberschelp, E.
Pelikan, R. Repges. Image processing
for medical images. Springer-Verlag
(Berlin, Heidelberg, New York), 1997.
[4] W.K. Pratt. Digital Image Processing.
John Wiley and Sons, Inc, 1991.
[5] J.W. Tukey, Exploratory data analysis,
Addison-Wesley, Reading, MA., 1971
[6] M. Gabbouj, E. Coyle, N.C. Gallagher
Jr. Overview of median and stack
filtering. Circuits Systems Signal
Processing,11(1):7-45,1992
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Article
Full-text available
Within the last two decades a small group of researchers has built a useful, nontrivial theory of nonlinear signal processing around the median-related filters known as rank-order filters, order-statistic filters, weighted median filters, and stack filters. This required significant effort to overcome the bias, both in education and research, toward linear theory, which has been dominant since the days of Fourier, Laplace, and “Convolute.” We trace the development of this theory of nonlinear filtering from its beginnings in the study of noise-removal properties and structural behavior of the median filter to the recently developed theory of optimal stack filtering. The theory of stack filtering provides a point of view which unifies many different filter classes, including morphological filters, so it is discussed in detail. Of particular importance is the way this theory has brought together, in a single analytical framework, both the estimation-based and the structural-based approaches to the design of these filters. Some recent applications of median and stack filters are provided to demonstrate the effectiveness of this approach to nonlinear filtering. They include: the design of an optimal stack filter for image restoration; the use of vector median filters to attenuate impulsive noise in color images and to eliminate cross luminance and cross color in TV images; and the use of median-based filters for image sequence coding, reconstruction, and scan rate conversion in normal TV and HDTV systems.
Noise analysis for medical images
  • S Diener
S. Diener. Noise analysis for medical images. Master thesis, 1998, Department of Computer Science, TU Clausthal.
Image processing for medical images
  • T Lehmann
  • W Oberschelp
  • E Pelikan
  • R Repges
T. Lehmann, W. Oberschelp, E. Pelikan, R. Repges. Image processing for medical images. Springer-Verlag (Berlin, Heidelberg, New York), 1997.