2010 yılında Doç. Dr. Refik Samet hocamla birlikte Ankara Üniversitesi Bilgisayar Mühendisliği 1. dönem bitirme tezimle ilgili bir makale yazmıştık.

Median filtresinin daha hızlandırılmış ve daha etkili bir algoritma haline getirdiğimiz filtreye geliştirilmiş median filtresi adını koymuştuk.

buradan yayınlandığı dergiden indirebilirsiniz

ya da buradan buradan indirebilirsiniz.

İndirmeden göz atmak isteyenler için :)

ADVANCED ADAPTIVE MEDIAN FILTER FOR IMPULSIVE NOISES

Refik Samet1, Muhammed Tanriverdi2

Ankara University, Ankara, Turkey

1samet@eng.ankara.edu.tr, 2muhammedtanriverdi@gmail.com

One of the most important stages of signal and image processing is noise elimination.

Noise is an unwanted perturbation to a wanted analog or digital signal or image [1]. A noise can

be categorized depending on its source, frequency spectrum and time characteristics. Depending

on a source, the noises are categorized into six types: acoustic noise; thermal and shot noise;

electromagnetic noise; electrostatic noise; channel distortions, echo and fading; processing

noise. On the other hand, depending on the frequency spectrum or time characteristics, the

noises are also categorized into six types: white noise; band-limited white noise; narrowband

noise; coloured noise; impulsive noise; transient noise pulses [2].

A lot of methods have been improved to eliminate noises. Filters are one of the most

common tools which are used to eliminate noises. Many filters have been designed so far

because of over plus of the noise varieties and differences between the properties of these

noises. Generally, filters are divided into two groups as linear and non-linear. Linear filters have

simple design and encoding and they are intended for general aim. These filters can be used to

smooth the images or enhance the edges but they have weak capacity for noise elimination.

Non-linear filters have been designed for specific aim and they produce better results. Nonlinear

filters are divided in many categories. Order statistic filter is one of the categories of nonlinear

filters. It is the most popular filter for noise elimination [3].

The subject of this study is to investigate and improve the noise eliminating methods

related to digital images. Noise is unwanted pixels to be corrupted into digital images. The

principal sources of noises in digital images arise during image acquisition (digitization) and/or

transmission. The performance of imaging sensors is affected by a variety of factors such as bad

focusing; motion and non-linearity of the sensors, etc. [1]. Type of noises has to be known for

elimination of noises in digital image. If the noise type is unknown, the filter which will be

applied to image can’t be known. In such a case all filters are applied to images and each image

is examined and then the filter which will produce the best result can be determined. The first

problem occurs if it is unknown that there is noise in images or if the type of noises is unknown.

This problem has not been solved yet. The second problem is the lack of values that will be used

to compare the images which are filtered, without original image. The images, to which filters

are applied, are being compared by using the relationships between original images.

Impulsive Noise (IN) is the most widespread and important noise in digital images [3]. IN

is caused by malfunctioning pixels in camera sensors, faulty memory locations in hardware, or

transmission through noisy channels. IN is categorized into two types: 1) SPN (Salt & Pepper

Noise or Fixed Valued Impulsive Noise) and 2) RVIN (Random Valued Impulsive Noise). An

aim of this study is to investigate and improve the techniques to deal with IN.

Many filters are used and investigated for elimination of SPN [3]. The most common

ones are median filter (MF) and adaptive median filter (AMF). These filters produce good

results in IN elimination because of being order statistics filters. AMF is suitable when ratio of

noise is high. Because of adaptive property, it has decision mechanism for determining if the

pixel is noisy or not. But this mechanism reduces time performance. Despite of producing better

results on images, that have low noise, than other filters, they are not preferred on images when

time performance is significant.

The noise properties of RVIN are different from the noise properties of SPN. Filters are

used to eliminate this noise type and performances are compared. AMF may not eliminate well

because of different noise types.

Because IN elimination in digital images is aimed, the filters which are used on spatial

domain and the filters that are in order statistic category will be investigated, improved and

analyzed. More specifically, enhancement of time performance of AMF and the elimination of

RVIN type noises by AMF are aimed.

IN is corrupted to image by two different ways. One of them is SPN. In this noise types,

there are 2 pixels which are corrupted in digital image. These 2 pixels are usually the minimum

and the maximum values of the gray-level. Thus for 256 gray-level digital image, the minimum

value is 0 and the maximum value is 255. The other one is RVIN. In this noise type, the noise

pixels may be any value of the gray-level of digital image.

There are many works on the restoration of image corrupted by IN [4]. The median filter

was one the most popular nonlinear filter for eliminating impulsive noises because of its good

denoising power and computational efficiency [5]. However, when the noise level is over 50%,

some details and edges of the original image are smeared by the filter. Different remedies of the

median filter have been proposed, e.g., the adaptive median filter [6], the multistage median

filter [7], and the median filter based on homogeneity information [8], [9]. These so-called

“decision-based” or “switching” filters, firstly, identify possible noise pixels and then replace

them by using the median filter or its variants, while leaving all other pixels unchanged. These

filters are good at detection noise even at a high noise level. Their main drawback is that the

noise pixels are replaced by some median value in their vicinity, details and edges are not

recovered satisfactorily when the noise level is very high. A noise removal method by mediantype

noise detectors and detail-preserving regularization is proposed in [10]. In that method,

SPN with noise ratio 90% can be cleaned quite efficiently, however its computation is huge.

AMF does not work well for RVIN when noisy pixels are not the minimum and

maximum pixel value in the image. There are some works for RVIN [3].

As mentioned above, this paper aims to propose the advanced adaptive median filter

which improves the time performance of AMF and eliminates the RVIN by AMF.

First, the existing AMF, and then, the model of proposed advanced AMF will be

described.

Adaptive Median Filter. AMF is an updated version of median filter. It successfully

removes fixed valued impulsive noise types (salt & pepper noise) from image. AMF increases

size of the window xy S during filtering depending on certain conditions. This is the most

difference of adaptive median filter from other median type filters. AMF usage has 3 main

purposes:

1.To remove the salt & pepper noise;

2.To smooth other noises;

3.To reduce the distortions such as excessive thickening or thinning of object boundaries.

Notation:

min Z is minimum gray level value in window xy S ;

max Z is maximum gray level value in xy S ;

med Z is median of gray levels in xy S ;

xy Z is gray level value at (x, y) ;

max S is maximum allowed size of xy S .

AMF algorithm is divided into two levels:

Level A:

min A1 Z Z med = - ;

max A2 Z Z med = - ;

if A1 > 0 and A2 < 0

Go to Level B;

else

Increase the window size by 2;

end

if window_ size £ Smax

Repeat Level A;

else

Output xy Z ;

end

Level B:

min B1 Z Z xy = - ;

max B2 Z Z xy = - ;

if B1 > 0 and B2 < 0

Output xy Z ;

else

Output med Z ;

end

Advanced Adaptive Median Filter. The noise corrupted pixels in the image are found.

To do this, the noise gray-level value must be known. For SPN noise, the gray-level values are 0

and 255. However, for RVIN noise, the gray-level values are random values between 0 and 255.

1) Find the noise gray-level values.

min N is a small gray-level value of noise;

max N is a big gray-level value of noise.

2) Change the gray-level values of noise pixels.

if min X N ij =

= 0 ij X

if max X N ij =

= 255 ij X

3) Apply AMF only to 0 and 255 gray-level value pixels.

As conclusion, in this study, advanced adaptive median filter has been proposed.

Proposed filter improves the performance of known AMF for IN and gives the best results for

eliminating RVIN. Simulation results showed that proposed filter increase the time efficiency

50% and works better for RVIN.

Literature

1. R. C. Gonzalez and R. E. Woods. “Digital Image Processing.” Addison Wesley,

2nd edition, 1992.

2. Saeed V. Vaseghi. “Advanced Digital Signal Processing and Noise Reduction.” John Wiley

& Sons, Ltd. 3td edition, 2006.

3. Subrajeet Mohapatra. Development of Impulsive Noise Detection Schemes for Selective

Filtering in Images. Department of Computer Science and Engineering National Institute of

Technology Rourkela, Rourkela–769 008, Orissa, India, September 2008.

4. J. Astola and P. Kuosmanen, Fundamentals of Nonlinear Digital Filtering. Boca Raton,

FL:CRC, 1997.

5. T.A. Nodes and N.C. Gallagher, Jr., “The output distribution of median type filters,” IEEE

Trans. Commun., vol. COM-32, no.5, pp. 532-541, May 1984.

6. H. Hwang and R. A. Haddad, “Adaptive median filters: New algorithms and results,” IEEE

Trans. Image Process., vol. 4, no. 4, pp. 499-502, Apr. 1995.

7. T. Chen and H.R.Wu, “Space variant median filters for the restoration of impulsive noise

corrupted images,” IEEE Trans. Circuits Syst. II. Analog Digit. Signal Process., vol. 48, no.

8, pp. 784-789, Aug. 2001.

8. H.-L. Eng and K.-K. Ma, “Noise adaptive softswitching median filter,” IEEE Trans. Image

Process., vol. 10, no.2, pp. 242-251, Feb. 2001.

9. G. Pok, J.-C. Liu, and A. S. Nair, “Selective removal of impulsive noise based on

homogeneity level information”, IEEE Trans. Image Process., vol.12, no.1, pp. 85-92, 2003.

10. Raymond H. Chan, Chung-Wa Ho, and Mila Nikolova, “Salt-and-Pepper Noise Removal by

Median-Type Noise Detectors and Detail-Preserving Regularization”, IEEE Trans. Image

Process., vol. 14, no. 10, Oct. 2005.

Median filtresinin daha hızlandırılmış ve daha etkili bir algoritma haline getirdiğimiz filtreye geliştirilmiş median filtresi adını koymuştuk.

buradan yayınlandığı dergiden indirebilirsiniz

ya da buradan buradan indirebilirsiniz.

İndirmeden göz atmak isteyenler için :)

ADVANCED ADAPTIVE MEDIAN FILTER FOR IMPULSIVE NOISES

Refik Samet1, Muhammed Tanriverdi2

Ankara University, Ankara, Turkey

1samet@eng.ankara.edu.tr, 2muhammedtanriverdi@gmail.com

One of the most important stages of signal and image processing is noise elimination.

Noise is an unwanted perturbation to a wanted analog or digital signal or image [1]. A noise can

be categorized depending on its source, frequency spectrum and time characteristics. Depending

on a source, the noises are categorized into six types: acoustic noise; thermal and shot noise;

electromagnetic noise; electrostatic noise; channel distortions, echo and fading; processing

noise. On the other hand, depending on the frequency spectrum or time characteristics, the

noises are also categorized into six types: white noise; band-limited white noise; narrowband

noise; coloured noise; impulsive noise; transient noise pulses [2].

A lot of methods have been improved to eliminate noises. Filters are one of the most

common tools which are used to eliminate noises. Many filters have been designed so far

because of over plus of the noise varieties and differences between the properties of these

noises. Generally, filters are divided into two groups as linear and non-linear. Linear filters have

simple design and encoding and they are intended for general aim. These filters can be used to

smooth the images or enhance the edges but they have weak capacity for noise elimination.

Non-linear filters have been designed for specific aim and they produce better results. Nonlinear

filters are divided in many categories. Order statistic filter is one of the categories of nonlinear

filters. It is the most popular filter for noise elimination [3].

The subject of this study is to investigate and improve the noise eliminating methods

related to digital images. Noise is unwanted pixels to be corrupted into digital images. The

principal sources of noises in digital images arise during image acquisition (digitization) and/or

transmission. The performance of imaging sensors is affected by a variety of factors such as bad

focusing; motion and non-linearity of the sensors, etc. [1]. Type of noises has to be known for

elimination of noises in digital image. If the noise type is unknown, the filter which will be

applied to image can’t be known. In such a case all filters are applied to images and each image

is examined and then the filter which will produce the best result can be determined. The first

problem occurs if it is unknown that there is noise in images or if the type of noises is unknown.

This problem has not been solved yet. The second problem is the lack of values that will be used

to compare the images which are filtered, without original image. The images, to which filters

are applied, are being compared by using the relationships between original images.

Impulsive Noise (IN) is the most widespread and important noise in digital images [3]. IN

is caused by malfunctioning pixels in camera sensors, faulty memory locations in hardware, or

transmission through noisy channels. IN is categorized into two types: 1) SPN (Salt & Pepper

Noise or Fixed Valued Impulsive Noise) and 2) RVIN (Random Valued Impulsive Noise). An

aim of this study is to investigate and improve the techniques to deal with IN.

Many filters are used and investigated for elimination of SPN [3]. The most common

ones are median filter (MF) and adaptive median filter (AMF). These filters produce good

results in IN elimination because of being order statistics filters. AMF is suitable when ratio of

noise is high. Because of adaptive property, it has decision mechanism for determining if the

pixel is noisy or not. But this mechanism reduces time performance. Despite of producing better

results on images, that have low noise, than other filters, they are not preferred on images when

time performance is significant.

The noise properties of RVIN are different from the noise properties of SPN. Filters are

used to eliminate this noise type and performances are compared. AMF may not eliminate well

because of different noise types.

Because IN elimination in digital images is aimed, the filters which are used on spatial

domain and the filters that are in order statistic category will be investigated, improved and

analyzed. More specifically, enhancement of time performance of AMF and the elimination of

RVIN type noises by AMF are aimed.

IN is corrupted to image by two different ways. One of them is SPN. In this noise types,

there are 2 pixels which are corrupted in digital image. These 2 pixels are usually the minimum

and the maximum values of the gray-level. Thus for 256 gray-level digital image, the minimum

value is 0 and the maximum value is 255. The other one is RVIN. In this noise type, the noise

pixels may be any value of the gray-level of digital image.

There are many works on the restoration of image corrupted by IN [4]. The median filter

was one the most popular nonlinear filter for eliminating impulsive noises because of its good

denoising power and computational efficiency [5]. However, when the noise level is over 50%,

some details and edges of the original image are smeared by the filter. Different remedies of the

median filter have been proposed, e.g., the adaptive median filter [6], the multistage median

filter [7], and the median filter based on homogeneity information [8], [9]. These so-called

“decision-based” or “switching” filters, firstly, identify possible noise pixels and then replace

them by using the median filter or its variants, while leaving all other pixels unchanged. These

filters are good at detection noise even at a high noise level. Their main drawback is that the

noise pixels are replaced by some median value in their vicinity, details and edges are not

recovered satisfactorily when the noise level is very high. A noise removal method by mediantype

noise detectors and detail-preserving regularization is proposed in [10]. In that method,

SPN with noise ratio 90% can be cleaned quite efficiently, however its computation is huge.

AMF does not work well for RVIN when noisy pixels are not the minimum and

maximum pixel value in the image. There are some works for RVIN [3].

As mentioned above, this paper aims to propose the advanced adaptive median filter

which improves the time performance of AMF and eliminates the RVIN by AMF.

First, the existing AMF, and then, the model of proposed advanced AMF will be

described.

Adaptive Median Filter. AMF is an updated version of median filter. It successfully

removes fixed valued impulsive noise types (salt & pepper noise) from image. AMF increases

size of the window xy S during filtering depending on certain conditions. This is the most

difference of adaptive median filter from other median type filters. AMF usage has 3 main

purposes:

1.To remove the salt & pepper noise;

2.To smooth other noises;

3.To reduce the distortions such as excessive thickening or thinning of object boundaries.

Notation:

min Z is minimum gray level value in window xy S ;

max Z is maximum gray level value in xy S ;

med Z is median of gray levels in xy S ;

xy Z is gray level value at (x, y) ;

max S is maximum allowed size of xy S .

AMF algorithm is divided into two levels:

Level A:

min A1 Z Z med = - ;

max A2 Z Z med = - ;

if A1 > 0 and A2 < 0

Go to Level B;

else

Increase the window size by 2;

end

if window_ size £ Smax

Repeat Level A;

else

Output xy Z ;

end

Level B:

min B1 Z Z xy = - ;

max B2 Z Z xy = - ;

if B1 > 0 and B2 < 0

Output xy Z ;

else

Output med Z ;

end

Advanced Adaptive Median Filter. The noise corrupted pixels in the image are found.

To do this, the noise gray-level value must be known. For SPN noise, the gray-level values are 0

and 255. However, for RVIN noise, the gray-level values are random values between 0 and 255.

1) Find the noise gray-level values.

min N is a small gray-level value of noise;

max N is a big gray-level value of noise.

2) Change the gray-level values of noise pixels.

if min X N ij =

= 0 ij X

if max X N ij =

= 255 ij X

3) Apply AMF only to 0 and 255 gray-level value pixels.

As conclusion, in this study, advanced adaptive median filter has been proposed.

Proposed filter improves the performance of known AMF for IN and gives the best results for

eliminating RVIN. Simulation results showed that proposed filter increase the time efficiency

50% and works better for RVIN.

Literature

1. R. C. Gonzalez and R. E. Woods. “Digital Image Processing.” Addison Wesley,

2nd edition, 1992.

2. Saeed V. Vaseghi. “Advanced Digital Signal Processing and Noise Reduction.” John Wiley

& Sons, Ltd. 3td edition, 2006.

3. Subrajeet Mohapatra. Development of Impulsive Noise Detection Schemes for Selective

Filtering in Images. Department of Computer Science and Engineering National Institute of

Technology Rourkela, Rourkela–769 008, Orissa, India, September 2008.

4. J. Astola and P. Kuosmanen, Fundamentals of Nonlinear Digital Filtering. Boca Raton,

FL:CRC, 1997.

5. T.A. Nodes and N.C. Gallagher, Jr., “The output distribution of median type filters,” IEEE

Trans. Commun., vol. COM-32, no.5, pp. 532-541, May 1984.

6. H. Hwang and R. A. Haddad, “Adaptive median filters: New algorithms and results,” IEEE

Trans. Image Process., vol. 4, no. 4, pp. 499-502, Apr. 1995.

7. T. Chen and H.R.Wu, “Space variant median filters for the restoration of impulsive noise

corrupted images,” IEEE Trans. Circuits Syst. II. Analog Digit. Signal Process., vol. 48, no.

8, pp. 784-789, Aug. 2001.

8. H.-L. Eng and K.-K. Ma, “Noise adaptive softswitching median filter,” IEEE Trans. Image

Process., vol. 10, no.2, pp. 242-251, Feb. 2001.

9. G. Pok, J.-C. Liu, and A. S. Nair, “Selective removal of impulsive noise based on

homogeneity level information”, IEEE Trans. Image Process., vol.12, no.1, pp. 85-92, 2003.

10. Raymond H. Chan, Chung-Wa Ho, and Mila Nikolova, “Salt-and-Pepper Noise Removal by

Median-Type Noise Detectors and Detail-Preserving Regularization”, IEEE Trans. Image

Process., vol. 14, no. 10, Oct. 2005.