Suppression of Impulse Noise in Medical Images with ... - Springer Link
J Med Syst (2006) 30:465–471 DOI 10.1007/s10916-006-9031-2
ORIGINAL PAPER
Suppression of Impulse Noise in Medical Images with the Use of Fuzzy Adaptive Median Filter ˙ ¨ Abdullah Toprak · Inan Guler
Received: 18 May 2006 / Accepted: 25 May 2006 / Published online: 3 November 2006 C Springer Science+Business Media, Inc. 2006
Abstract A new rule based fuzzy filter for removal of highly impulse noise, called Rule Based Fuzzy Adaptive Median (RBFAM) Filter, is aimed to be discussed in this paper. The RBFAM filter is an improved version of Adaptive Median Filter (AMF) and is presented in the aim of noise reduction of images corrupted with additive impulse noise. The filter has three stages. Two of those stages are fuzzy rule based and last stage is based on standard median and adaptive median filter. The proposed filter can preserve image details better then AMF while suppressing additive salt&pepper or impulse type noise. In this paper, we placed our preference on bell-shaped membership function instead of triangular membership function in order to observe better results. Experimental results indicates that the proposed filter is improvable with increased fuzzy rules to reduce more noise corrupted images and to remove salt and pepper noise in a more effective way than what AMF filter does. Keywords Fuzzy adaptive median filter . Adaptive median filter . Impulse response A. Toprak · ˙I. G¨uler Dicle University, Meslek Y¨uksek Okulu, Elektrik-Elektronik Bolumu, 21280 Diyarbakır, Turkey A. Toprak e-mail: [email protected] ˙I. G¨uler () Gazi University, Teknik Egitim Fakultesi, Elektronik-Bilgisayar Bolumu, 06500 Teknikokullar, Ankara, Turkey e-mail: [email protected]
Introduction Median filter is an image filter that is more effective in situations where the impulse noise is less than 0.2. If this ratio exceeds 0.2, adaptive median filter is used. As is the case in other filters, a Sxy window is selected for the adaptive median filter. However a feature that differentiates the adaptive median filter from the other filters is the fact that the size of this window can be changed. Unfortunately, while adaptive median filter removes the impulse noise, it also deteriorates the details in the image it accompanies. In order to prevent this, the pixel values of the image are determined by the fuzzy adaptive median filter, and as such Rule based fuzzy adaptive median filter (RBFAMF) is defined in this study. RBFAMF filter is made up of three basic sections. These are decision units that decide on whether or not there are median filter, fuzzy logic rules and noise. The basic purpose of using this filter is while destroying the noise on the image, it prevents the details of the image from disappearing. It is for this reason that RBFAMF is an effective filter in destroying the impulse noise. Image processing with fuzzy logic, starts with the fuzzy digital topology of Rosenfeld and continues with the studies of Abreu et al. on suppression of noise or improvement of image by using fuzzy logic rules [1, 2]. Wang et al. have realized histogram based noise suppression by using fuzzy logic [3]. Kong and Guan have deteriorated the impulse noise in the images by using adaptive filter technique [4]. Russo and Peng and Lucke have performed studies on purifying the noise from an image by using fuzzy rule base [5, 6]. Arakawa has worked on purifying high amounts of impulse noise contaminated images from the noises by using fuzzy logic [7]. Lee et al. have performed an image improvement study by using weighted median filter [8]. One of the most
Springer
466
effective methods in suppressing impulse noise in images is the median filter (MF). Although MF is a method used in suppressing noises with low density (20%), it can even be said it may even be insufficient in destroying these types of noises. While the MF suppresses the noise, some of the details in the display are also lost. This situation is especially a major drawback in medical imaging and diagnosis. When the Median filter screening window is downsized although it suppresses more noise, the most of the details in the picture are lost when the window is enlarged. When median filter is used, due to the fact that even the pixel value is switched with the median value, nearly all pixels shall be switched with an erroneous value. Consequently, adaptive median filter (AMF) that is more successful compared to MF, is used especially in destroying high density noises. As is the case in other filters, an Sxy window is selected for AMF as well. However, a feature of AMF that differentiates it from other filters is the fact that window size can be changed. Unfortunately, although AMF is successful in destroying impulse noise, it also destroys the details of images it is together with. In order not to lose the details in this study while removing the noise to a big extent, pixel values are determined by fuzzy logic rules and fast fuzzy adaptive median filter is defined. RBFAMF filter is made up of three basic sections. These are, median filter, fuzzy logic rules, and the decision unit that decides whether there is noise. The main purpose of using this filter is to avoid losing details in the image while destroying the noise in the image. It is for this reason that RBFAMF is en effective filter in destroying impulse noise. The impulse that mixes digitally with the MR images, causes the magnetic resonance (MR) image to become unusable for diagnoses, moreover it results in the image becoming unrecognizable or even an image that may contain misleading information depending on the quantity of the noise amount. These images may be formed in the reconstruction phase or may be originating from external RF waves. Furthermore, during the MR, there could be noise originating from many errors. Under these circumstances, it becomes necessary to clear MR from such noises. The model proposed for this purpose carries out a good filtering job even in images with high rates of mixed noise and it will especially help in making the MR images more understandable. Median filter is one of the most effective methods used in suppressing impulse noise seen in images. The mixed noises that are mixed with the image can be suppressed by using the median filter, however there are some negative sides to this filter. If we are to summarize them as items, these are:
r Median filter is a method effective in suppressing noise amounts up to 20%. However, it does not show sufficient success in this rate as well.
Springer
J Med Syst (2006) 30:465–471
r When the noise is suppressed by using median filter, some of the important details in the image may also be lost, and this causes the user to miss or not take into consideration a very important piece of information. r While the median filter’s screening window is downsized it suppresses less noise, when the window size is enlarged, details in the picture disaapear to a great extent. r While the median filter determines the value of new pixel it is to replace with noise pixel, because it only takes into consideration the mid value, it sometimes ends by using values that may have serious error levels. r When median filter is used since even real pixel value is replaced by the median value, nearly all pixels are replaced with pixels containing errors. Besides the significance of losing some of the details in the images used in daily life, if we think that these images are used in medicine to be able to make diagnosis we can easily understand how important such details are. The fact that sometimes even a minute noise signal can cause a very important error in the judgement of the diagnosis must be taken into consideration as a parameter as the point of no return can be reached as such. With the model filters that we will develop the noise determination will be carried out with fuzzy logic and the pixel value of this noise will be changed with another value by using a median. However in this operation where switch mode will be used, the image where no noise is available will not be touched upon and the filters will only be activated when noise is present. In a case as such the pixels without any noise will be maintained in their original states, the noise pixels will be changed with the most appropriate median values. However in some situations the median values of the pixels chosen in the image screen can be the noise value and in a case as such the noise in the image will continue to prevail. This situation especially is valid and clearly resurfaces when the noise element exceeds 40%. In cases where the median value represents noise, by increasing the size of the image screen one unit, a new median value can be obtained. The determination whether the median value is noise or not will be made by using fuzzy logic again.
Method and model General definitions If we define X[( i,j )] image matrix p(k, l) to be made up of pixel values (Fig. 1), a matrix of 3 × 3 will be in the form of W[(k, l)] ∈ X[( i,j )] . This window matrix will scan the whole X[( i,j )] matrix from top to bottom and left to right. In every 3 × 3 scan it will calssify 9 pixels according to grey intensity. P(k, l) ∈ Ximp , if p(k, l) = Min{W[k, l]} or Max{W[k, l]}
J Med Syst (2006) 30:465–471
467
p (k-1,l-1)
p (k -1,l)
p(k -1,l+1)
p (k,l-1)
p (k,l)
(k ,l+1)
p(k+1, l -1)
p (k+1, l-1)
p(k+1,l+1)
Fig. 1 Pixels intensity and Coordinates of a 3 × 3 window
The window W[(k, l)], that we will scan over the entire image to clarify the noise from is a 3 × 3 matrix and this matrix is shown below. On the other hand Ximp matrix is a noise matrix that is mixed up with X[( i,j )] image matrix. In a case as such ⎡ ⎢ ⎢ X =⎢ ⎢ ⎣
x11 x21 · xH1
x12 x22 · · xH2
. . . xi j . . . x2 j · · . . . xH j
⎤ . . . x1W . . . x2W ⎥ ⎥ ⎥ = [xi j ] H x W · ⎥ ⎦ · . . . xHW
Here H and W are height and width and xij ∈ {0, 1, 2, . . ., 255} shows the grey intensity of pixel in i, j coordinate of X matrix. x1 = p(k −1, l −1), x2 = p(k −1, l), x3 = p(k −1, l +1), x4 = p(k, l −1), x5 = p(k, l), x6 = (k, l +1), x7 = p(k +1, l −1), x8 = p(k +1, l −1), x9 = p(k +1, l +1). In this case,
is of two dimensions, the median filter for images would be developed. m(k) = MED w(k) = MED{x−n (k), . . . , x−1 (k), x0 (k), x1 (k), . . . , xn (k)} The filter that suppresses the noise in the images as explained is called “Median Filter.” In the figure below it can be seen that the 20% median filter is an effective method. The images obtained by using median filter are shown under Fig. 2. Adaptive median filter Median filter is an image filter that can be more effective under conditions where the noise rate is less than 0.2. However under conditions when the rate of noise exceeds 0.2 the adaptive median filter must be considered. One other advantage of adaptive median filter is that, it makes sure that the details on the screen are not lost while the noise is suppressed. As with the other filter, for adaptive median filter a Sxy window will be chosen. However in adaptive median filter the size of this window can be changed and even if the size of the window is changed the result of the operation conducted will be one and single, and this value can be changed with the central pixel value of the window. If we take into consideration the notations below:
W [(k, l)] = [ p(k − 1, l − 1), p(k − 1, l), p(k − 1, l + 1), p(k, l − 1), p(k, l), (k, l + 1), p(k + 1, l − 1), p(k + 1, l − 1), p(k + 1, l + 1)]
Zmin = Sxy Is the lowest grey level value inside. Zmax = Sxy Is the highest grey level value inside. Zxy = (x, y) grey level at the subject matter coordinates Zmed = is the maximum possible Sxy window size.
Each component is defined as a fuzzy variable and the membership function is the intensity value of each input pixel.
We should analyze the flow diagram of adaptive median filter at two levels. Let’s name these as level A and Level B.
Median filter This is a filter that makes possible for the elimination of a divergent value by changing the divergent value in a finite series with the medium value in the same series [9]. When it
Level A: A1 = Zmed − Zmin A2 = Zmed − Zmax If A1 > 0 and A2 0 and B2
ORIGINAL PAPER
Suppression of Impulse Noise in Medical Images with the Use of Fuzzy Adaptive Median Filter ˙ ¨ Abdullah Toprak · Inan Guler
Received: 18 May 2006 / Accepted: 25 May 2006 / Published online: 3 November 2006 C Springer Science+Business Media, Inc. 2006
Abstract A new rule based fuzzy filter for removal of highly impulse noise, called Rule Based Fuzzy Adaptive Median (RBFAM) Filter, is aimed to be discussed in this paper. The RBFAM filter is an improved version of Adaptive Median Filter (AMF) and is presented in the aim of noise reduction of images corrupted with additive impulse noise. The filter has three stages. Two of those stages are fuzzy rule based and last stage is based on standard median and adaptive median filter. The proposed filter can preserve image details better then AMF while suppressing additive salt&pepper or impulse type noise. In this paper, we placed our preference on bell-shaped membership function instead of triangular membership function in order to observe better results. Experimental results indicates that the proposed filter is improvable with increased fuzzy rules to reduce more noise corrupted images and to remove salt and pepper noise in a more effective way than what AMF filter does. Keywords Fuzzy adaptive median filter . Adaptive median filter . Impulse response A. Toprak · ˙I. G¨uler Dicle University, Meslek Y¨uksek Okulu, Elektrik-Elektronik Bolumu, 21280 Diyarbakır, Turkey A. Toprak e-mail: [email protected] ˙I. G¨uler () Gazi University, Teknik Egitim Fakultesi, Elektronik-Bilgisayar Bolumu, 06500 Teknikokullar, Ankara, Turkey e-mail: [email protected]
Introduction Median filter is an image filter that is more effective in situations where the impulse noise is less than 0.2. If this ratio exceeds 0.2, adaptive median filter is used. As is the case in other filters, a Sxy window is selected for the adaptive median filter. However a feature that differentiates the adaptive median filter from the other filters is the fact that the size of this window can be changed. Unfortunately, while adaptive median filter removes the impulse noise, it also deteriorates the details in the image it accompanies. In order to prevent this, the pixel values of the image are determined by the fuzzy adaptive median filter, and as such Rule based fuzzy adaptive median filter (RBFAMF) is defined in this study. RBFAMF filter is made up of three basic sections. These are decision units that decide on whether or not there are median filter, fuzzy logic rules and noise. The basic purpose of using this filter is while destroying the noise on the image, it prevents the details of the image from disappearing. It is for this reason that RBFAMF is an effective filter in destroying the impulse noise. Image processing with fuzzy logic, starts with the fuzzy digital topology of Rosenfeld and continues with the studies of Abreu et al. on suppression of noise or improvement of image by using fuzzy logic rules [1, 2]. Wang et al. have realized histogram based noise suppression by using fuzzy logic [3]. Kong and Guan have deteriorated the impulse noise in the images by using adaptive filter technique [4]. Russo and Peng and Lucke have performed studies on purifying the noise from an image by using fuzzy rule base [5, 6]. Arakawa has worked on purifying high amounts of impulse noise contaminated images from the noises by using fuzzy logic [7]. Lee et al. have performed an image improvement study by using weighted median filter [8]. One of the most
Springer
466
effective methods in suppressing impulse noise in images is the median filter (MF). Although MF is a method used in suppressing noises with low density (20%), it can even be said it may even be insufficient in destroying these types of noises. While the MF suppresses the noise, some of the details in the display are also lost. This situation is especially a major drawback in medical imaging and diagnosis. When the Median filter screening window is downsized although it suppresses more noise, the most of the details in the picture are lost when the window is enlarged. When median filter is used, due to the fact that even the pixel value is switched with the median value, nearly all pixels shall be switched with an erroneous value. Consequently, adaptive median filter (AMF) that is more successful compared to MF, is used especially in destroying high density noises. As is the case in other filters, an Sxy window is selected for AMF as well. However, a feature of AMF that differentiates it from other filters is the fact that window size can be changed. Unfortunately, although AMF is successful in destroying impulse noise, it also destroys the details of images it is together with. In order not to lose the details in this study while removing the noise to a big extent, pixel values are determined by fuzzy logic rules and fast fuzzy adaptive median filter is defined. RBFAMF filter is made up of three basic sections. These are, median filter, fuzzy logic rules, and the decision unit that decides whether there is noise. The main purpose of using this filter is to avoid losing details in the image while destroying the noise in the image. It is for this reason that RBFAMF is en effective filter in destroying impulse noise. The impulse that mixes digitally with the MR images, causes the magnetic resonance (MR) image to become unusable for diagnoses, moreover it results in the image becoming unrecognizable or even an image that may contain misleading information depending on the quantity of the noise amount. These images may be formed in the reconstruction phase or may be originating from external RF waves. Furthermore, during the MR, there could be noise originating from many errors. Under these circumstances, it becomes necessary to clear MR from such noises. The model proposed for this purpose carries out a good filtering job even in images with high rates of mixed noise and it will especially help in making the MR images more understandable. Median filter is one of the most effective methods used in suppressing impulse noise seen in images. The mixed noises that are mixed with the image can be suppressed by using the median filter, however there are some negative sides to this filter. If we are to summarize them as items, these are:
r Median filter is a method effective in suppressing noise amounts up to 20%. However, it does not show sufficient success in this rate as well.
Springer
J Med Syst (2006) 30:465–471
r When the noise is suppressed by using median filter, some of the important details in the image may also be lost, and this causes the user to miss or not take into consideration a very important piece of information. r While the median filter’s screening window is downsized it suppresses less noise, when the window size is enlarged, details in the picture disaapear to a great extent. r While the median filter determines the value of new pixel it is to replace with noise pixel, because it only takes into consideration the mid value, it sometimes ends by using values that may have serious error levels. r When median filter is used since even real pixel value is replaced by the median value, nearly all pixels are replaced with pixels containing errors. Besides the significance of losing some of the details in the images used in daily life, if we think that these images are used in medicine to be able to make diagnosis we can easily understand how important such details are. The fact that sometimes even a minute noise signal can cause a very important error in the judgement of the diagnosis must be taken into consideration as a parameter as the point of no return can be reached as such. With the model filters that we will develop the noise determination will be carried out with fuzzy logic and the pixel value of this noise will be changed with another value by using a median. However in this operation where switch mode will be used, the image where no noise is available will not be touched upon and the filters will only be activated when noise is present. In a case as such the pixels without any noise will be maintained in their original states, the noise pixels will be changed with the most appropriate median values. However in some situations the median values of the pixels chosen in the image screen can be the noise value and in a case as such the noise in the image will continue to prevail. This situation especially is valid and clearly resurfaces when the noise element exceeds 40%. In cases where the median value represents noise, by increasing the size of the image screen one unit, a new median value can be obtained. The determination whether the median value is noise or not will be made by using fuzzy logic again.
Method and model General definitions If we define X[( i,j )] image matrix p(k, l) to be made up of pixel values (Fig. 1), a matrix of 3 × 3 will be in the form of W[(k, l)] ∈ X[( i,j )] . This window matrix will scan the whole X[( i,j )] matrix from top to bottom and left to right. In every 3 × 3 scan it will calssify 9 pixels according to grey intensity. P(k, l) ∈ Ximp , if p(k, l) = Min{W[k, l]} or Max{W[k, l]}
J Med Syst (2006) 30:465–471
467
p (k-1,l-1)
p (k -1,l)
p(k -1,l+1)
p (k,l-1)
p (k,l)
(k ,l+1)
p(k+1, l -1)
p (k+1, l-1)
p(k+1,l+1)
Fig. 1 Pixels intensity and Coordinates of a 3 × 3 window
The window W[(k, l)], that we will scan over the entire image to clarify the noise from is a 3 × 3 matrix and this matrix is shown below. On the other hand Ximp matrix is a noise matrix that is mixed up with X[( i,j )] image matrix. In a case as such ⎡ ⎢ ⎢ X =⎢ ⎢ ⎣
x11 x21 · xH1
x12 x22 · · xH2
. . . xi j . . . x2 j · · . . . xH j
⎤ . . . x1W . . . x2W ⎥ ⎥ ⎥ = [xi j ] H x W · ⎥ ⎦ · . . . xHW
Here H and W are height and width and xij ∈ {0, 1, 2, . . ., 255} shows the grey intensity of pixel in i, j coordinate of X matrix. x1 = p(k −1, l −1), x2 = p(k −1, l), x3 = p(k −1, l +1), x4 = p(k, l −1), x5 = p(k, l), x6 = (k, l +1), x7 = p(k +1, l −1), x8 = p(k +1, l −1), x9 = p(k +1, l +1). In this case,
is of two dimensions, the median filter for images would be developed. m(k) = MED w(k) = MED{x−n (k), . . . , x−1 (k), x0 (k), x1 (k), . . . , xn (k)} The filter that suppresses the noise in the images as explained is called “Median Filter.” In the figure below it can be seen that the 20% median filter is an effective method. The images obtained by using median filter are shown under Fig. 2. Adaptive median filter Median filter is an image filter that can be more effective under conditions where the noise rate is less than 0.2. However under conditions when the rate of noise exceeds 0.2 the adaptive median filter must be considered. One other advantage of adaptive median filter is that, it makes sure that the details on the screen are not lost while the noise is suppressed. As with the other filter, for adaptive median filter a Sxy window will be chosen. However in adaptive median filter the size of this window can be changed and even if the size of the window is changed the result of the operation conducted will be one and single, and this value can be changed with the central pixel value of the window. If we take into consideration the notations below:
W [(k, l)] = [ p(k − 1, l − 1), p(k − 1, l), p(k − 1, l + 1), p(k, l − 1), p(k, l), (k, l + 1), p(k + 1, l − 1), p(k + 1, l − 1), p(k + 1, l + 1)]
Zmin = Sxy Is the lowest grey level value inside. Zmax = Sxy Is the highest grey level value inside. Zxy = (x, y) grey level at the subject matter coordinates Zmed = is the maximum possible Sxy window size.
Each component is defined as a fuzzy variable and the membership function is the intensity value of each input pixel.
We should analyze the flow diagram of adaptive median filter at two levels. Let’s name these as level A and Level B.
Median filter This is a filter that makes possible for the elimination of a divergent value by changing the divergent value in a finite series with the medium value in the same series [9]. When it
Level A: A1 = Zmed − Zmin A2 = Zmed − Zmax If A1 > 0 and A2 0 and B2
