Document5

IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 22, NO. 3, MARCH 2013 1223

Efficient Improvements on the BDNDFiltering Algorithm for the Removal of

High-Density Impulse NoiseIyad F. Jafar, Rami A. AlNamneh, and Khalid A. Darabkh

Abstract Switching median filters are known to outperformstandard median filters in the removal of impulse noise due totheir capability of filtering candidate noisy pixels and leavingother pixels intact. The boundary discriminative noise detection(BDND) is one powerful example in this class of filters. However,there are some issues related to the filtering step in the BDNDalgorithm that may degrade its performance. In this paper, wepropose two modifications to the filtering step of the BDNDalgorithm to address these issues. Experimental evaluation showsthe effectiveness of the proposed modifications in producingsharper images than the BDND algorithm.

Index Terms Impulse noise, median filter, noise detection,switching median filters.

I. INTRODUCTION

CHANNEL transmission errors and faulty switching ofacquisition devices may result in corrupting images withimpulse noise. Pixels contaminated with impulse noise arecharacterized by having relatively low or high intensity valueswhen compared to their neighboring pixels. This could dramat-ically affect images quality and possibly make them unsuitablefor human or machine vision applications. In attempt to restorethe original values of noisy pixels, filtering techniques areusually applied with the objective of suppressing the noisewhile minimizing the distortion introduced to the sharpness ofedges and details in the original image. The standard medianfilter [1], which is a nonlinear order-statistic filter, is one ofthe most popular filters that is used in the removal of impulse.This fact triggered the development of several algorithms thatbuild on the standard median filter to improve its performance.Examples include, but not limited to, weighted median filters[2], [3], center weighted median filters [4], recursive medianfilters [5], [6], and adaptive length median filters [7].

Despite the simplicity and effectiveness of these median-based filters, they still result in unnecessary degradation in

Manuscript received February 8, 2012; revised October 30, 2012; acceptedNovember 7, 2012. Date of publication November 20, 2012; date of currentversion January 30, 2013. The associate editor coordinating the review of thismanuscript and approving it for publication was Dr. Farhan A Baqai.

I. F. Jafar is with the Computer Engineering Department, University ofJordan, Amman 1192, Jordan (e-mail: [email protected]).

R. A. AlNamneh is with Department of Software Engineering at Jor-dan, University of Science and Technology, Irbid 22110, Jordan (e-mail:[email protected]).

K. A. Darabkh is with the Computer Engineering Department at theUniversity of Jordan, Amman 1192, Jordan (e-mail: [email protected]).

Color versions of one or more of the figures in this paper are availableonline at http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TIP.2012.2228496

image quality [8][10]. This is related to the fact that filteringin such algorithms is applied to all pixels in the image andignoring the fact that not all pixels are noisy. A simplesolution to this problem is to apply these filters selectivelysuch that only noisy pixels undergo the filtering operation.This requires using a detection mechanism to reliably identifycandidate noisy pixels in the image. These filters are usuallyreferred to as switching median filters [11][19]. The key issuein switching median filters is the detection of noisy pixels.Thresholding filtering [20] utilizes efficient noise detectors toreduce the misclassification of noise-free pixels. A trilateralfilter [21] combined with an impulse detector that detectsimpulse noise according to the local image statistics wasalso proposed. In [22], noise detection incorporates edge-directed approach to preserve the details and edges. A fuzzytechnique that is capable of detecting and removing impulsenoise was proposed in [23]. The technique relies on long-range correlation within different parts of the image. The noiseadaptive soft-switching median filter [24] applies an approachthat utilizes the fuzzy-set concept to classify pixels into noise-free pixels, isolated noisy pixels, non-isolated noisy pixels,and edge pixels. The filter applies the identity filter, standardmedian filter, or a new class of fuzzy filter to filter the pixeldepending on the class it belongs to. Reference [25] presentsan adaptive hierarchal filter that can remove impulse noisewhile preserving the details of the image by inferring theglobal structure of the image from a set of pyramid imagesthat are used as prior information in order to apply differentfilters adaptively.

Generally, the proposed algorithms produce satisfactoryresults; however, they still tend to remove fine details of theimage and fail to detect some of the noisy pixels, especiallywhen the noise density is high. In fact, most of the presentedalgorithms are tested under moderate noise densities (< 50%).A quite interesting switching median filter is the boundarydiscriminative noise detection (BDND) filter that is proposedin [26]. The BDND filter is proven to operate efficiently whencompared to other filters, even under high noise densities (upto 90%). Being a switching-based median filter, the BDNDalgorithm filters the noisy image in two steps. The first step isessentially a noise detection step which is based on clusteringthe pixels in the image in a localized window into three groups,namely; lower intensity impulse noise, uncorrupted pixels, andhigher intensity impulse noise. The clustering is based ondefining two boundaries using the intensity differences in the

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1224 IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 22, NO. 3, MARCH 2013

ordered set of the pixels in the window. The pixel is classifiedas uncorrupted if it belongs to the middle cluster. Otherwiseit is a noisy pixel. This noise detection mechanism showedimpressive detection accuracy under different impulse noisemodels [26].

Once the noise map is determined, the second step is thefiltering step, which is supposed to replace the noisy pixelwith an estimate of its original value. This step is applied onthe identified noisy pixels only. The filtering is essentially amedian filtering operation that is applied on the uncorruptedpixels found in the filtering window. The critical parameterthat is required to be defined in the filtering step of the BDNDalgorithm is the size of the filtering window. The size of thiswindow is determined as follows. A window of size 3 3 isused as initial size for the filtering window. If the number ofuncorrupted pixels in the window is less than half the windowsize, then the window is expanded outward by one pixel in alldirections. This is repeated until the number of uncorruptedpixels in the window is greater than or equal half the numberof pixels in the window or the current window size is less thanor equal a maximum window size. The maximum window sizeof the condition is ignored and the window is expanded if nouncorrupted pixels are found. In this case, window expansionis repeated until one uncorrupted pixel is found. Basically,this step is an adaptation from the filtering process proposedin [24] and is reported to perform well even under high noisedensities.

The BDND filter is proven to operate effectively underdifferent impulse noise models. However, two main observa-tions can be made about its filtering step. First, expanding thewindow until the number of uncorrupted pixels is at least halfthe number of pixels in the window may impose additionalblurring in the output image. The impact of this is clearlynoticeable under high noise densities. Second, the filteringstep relies on computing the median value of the uncorruptedpixels found in the window without any regard to the spatialrelationship of these pixels to the noisy pixel, and the deviationof the pixels intensities from the median value. This alsoaffects the quality and the sharpness of the edges in the filteredimage.

In this paper, we propose two modifications to the filteringstep in the BDND algorithm in order to improve its perfor-mance. The rest of the paper is organized as follows. Theproposed modifications are explained in Section II. Compre-hensive evaluation of the proposed modifications is presentedin Section III. Finally, the paper is concluded in Section IV.

II. PROPOSED MODIFICATIONS

In this section, we discuss the modifications introduced tothe filtering step of the BDND algorithm. These modificationsare based on some observations related to the BDND and themedian filter itself as outlined earlier. The first modificationis based on loosening the condition imposed on expandingthe filtering window. The second modification is proposed toincorporate the spatial information of uncorrupted pixels inthe filtering window and the deviation of their intensities fromthe median when computing the estimated value of the noisy

20 20 23 22 2122 21 18 19 152 21 22 20 151 152 21 20 152 150 153 22 150 151 149 153

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* 20 * * *22 * 18 * 152 * * * 151 152 21 20 * * ** * 151 * 153

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* 20 23 * * 22 * * * 15221 * * * 15221 * * * 153* * * 149 153

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Fig. 1. (a) Hypothetical image and two noisy versions. (b) Noisy image I.(c) Noisy image II. Noisy pixels are indicated by .

pixel. These are explained through examples in the followingsubsections.

A. Expansion of Filtering WindowThe first observation is related to the way filtering is

performed in the BDND algorithm which starts by using a3 3 filtering window that is centered on the noisy pixel.However, the size of this window is considered insufficient forfiltering under two conditions: i) the number of uncorruptedpixels Nu is less than half of the number of pixels in thewindow Nh, where Nh = 1/2 (WF WF) and WF is thewindow width, ii) if the number of uncorrupted pixels is zero.In case any of these conditions is violated for the currentwindow, the window is expanded outward by one pixel in alldirections. For the first condition, expansion is allowed as longas the size of the window is less than or equal to a maximumwindow size of Wmax Wmax.

Such approach in expanding the filtering window could beuseful in providing a better estimate for the value of the noisypixel. However, the strict condition of requiring the numberof uncorrupted pixels to be greater than half the numberof pixels in the window is easily violated under high noisedensities. Thus, with high noise densities the filtering windowis expected to be expanded and most likely it will reach themaximum size. The direct impact on increasing the windowsize is the possible loss of correlation between the pixel valuesinside the filtering window. This may directly affect the valuethat replaces the noisy pixel, which may lead to blurring andunnecessary distortion in the filtered image.

To demonstrate the idea, consider the 5 5 image shownin Fig. 1(a), which contains an edge along the 45 diagonalthat separates between two smooth regions. Suppose that thisimage is corrupted with 60% impulse noise as shown inFig. 1(b), with the noisy pixels indicated by (*). These noisypixels are assumed to be detected reliably by the detection stepof the BDND algorithm. When the filtering step of the BDND

JAFAR et al.: EFFICIENT IMPROVEMENTS ON THE BDND FILTERING ALGORITHM 1225

algorithm is applied on the central pixel with a 3 3 window,then the set of uncorrupted pixels Vu in the window is simply{18, 20, 151}. This implies that Nu is 3, which is less than halfthe number of pixels in the window (Nh = 4.5). This violatesthe first condition that is imposed on the size of the filteringwindow, since Nu is less than Nh. If Wmax is set to 3, thenthe filtering window is expanded to 5 5 since WF equalsWmax. Given this new window, the set of uncorrupted pixelsVu is {18, 20, 20, 21, 22, 151, 151, 152, 152, 153}. This meansthat the number of uncorrupted pixels Nu is 10, which still lessthan half the window size (Nh = 12.5). Thus, the conditionis violated again. However, the current window size is greaterthan Wmax, so window expansion stops. Of course, the secondcondition for window expansion is false since the number ofuncorrupted pixels is not zero. Consequently, the filtered valueof the pixel under consideration Xij is replaced by a new valueYij, which is simply the median of the uncorrupted pixelsfound in the filtering window using

Yi j = median{Xis, jt |(s, t) W Xis, jt Vu} (1)where

W = {(s, t)|(WF 1)/2 s, t (WF 1)/2}. (2)For the example image given in Fig. 1(b), this implies that

the output value for the center pixel after filtering is 86, whichis far away from the original pixel value. Additionally, thisimplies that the edge position between the two regions isdisplaced by one pixel.

The main reason for such a problem in the BDND algorithmresults from the condition imposed on expanding the filteringwindow which requires the number of uncorrupted pixels tobe at least half the window size. However, such requirement ishard to satisfy under high noise densities. Actually, expandingthe window in such circumstance may not solve the problemsince the number of required uncorrupted pixels increasesnonlinearly when the window is expanded. As a result, themaximum window size is usually reached with high noisedensities, which in turn results in additional blurring and edgedisplacement in the filtered image.

In order to address this problem, we propose the followingmodification to the window expansion process in the BDNDalgorithm. Basically, the condition is modified to take intoconsideration the estimated noise density P that is determinedfrom the detection step of the algorithm and the total numberof pixels NT in the filtering window, such that while thenumber of uncorrupted pixels Nu is less than 1/2(1P)NT andWF is less than or equal to Wmax, then the filtering windowis expanded by one pixel outward in all directions. The term(1-P) basically is the percentage of uncorrupted pixels that areexpected to be found in the filtering window. Including thisterm in the condition makes it adaptive to the noise density. Inother words, when the noise density increases, the conditionis loosened since the expected number of uncorrupted pixelsdecreases. This in turn reduces the occasions of windowexpansion. This is unlike the BDND algorithm that uses a fixedthreshold of 1/2(WF WF) regardless of the noise density.As a matter of fact, this is hard to achieve with high noisedensities and small windows.

The use of the total number of pixels instead of1/2(WF WF ) makes it explicit that windows centered atboundary pixels in the image utilize pixels available in thewindow instead of replicating boundary pixels to match thesize of the window. This issue was not explicitly discussedin the BDND algorithm. In fact, the way boundary pixelsare treated is crucial and significantly affects the process ofexpanding the filtering window.

In general, the modification outlined earlier is expected toreduce the cases where the window is expanded unnecessarily,which in turn results in filtering windows containing valuesthat are likely to be more correlated to the original value ofthe noisy pixel. This is based on the fact that there is a strongcorrelation between pixels values and their spatial locations insmall neighborhoods in images [1]. In other words, if a set ofuncorrupted pixels is found in the filtering window, even withsmall count, then it is more logical to use their values in thefiltering operation since they are spatially closer to the centralpixel (the noisy pixel) than those uncorrupted pixels found inthe expanded filtering window. This would imply a strongercorrelation between the pixel values in the small window andthe original value of the noisy pixel than the case for the pixelvalues in the larger window.

Once the filtering window is determined based on thecondition discussed previously, filtering is performed using(1). However, since expanding the filtering window is nowadaptive to the noise density, the occasions of over expandingthe window in the modified condition are less likely to occur.In case the filtering window size reaches the maximum allowedvalue and no uncorrupted pixels are found in the window, then,and similar to BDND, the second condition is invoked and thewindow is expanded until at least one pixel is found.

In the example presented earlier, when the window size is3 3, the set of uncorrupted pixels Vu is {18, 20, 151} and thenoise density is 60%. This implies that Nu is 3, NT is 9, andthe percentage of uncorrupted pixels is 40%. Based on thesevalues, the proposed modification on the window expansioncondition is false since Nu is greater than 1/2(1P)NT ,(3 > 1.8), thus the window is not expanded. Accordingly, thenew pixel value Yij is basically the median of Vu, which is 20.Comparing this value with that obtained using BDND, 86, wecan see that this case is more consistent with original pixelsvalue. This in turn implies that the edge location in the filteredand the original images is located at the same place.

B. Incorporating Spatial and Intensity InformationActually, there is another observation that can be made

about the performance of the BDND filtering step and othermedian-based filters which rely on replacing the noisy pixelswith the median of uncorrupted pixels in the filtering win-dow. Consider the noisy image shown in Fig. 1(c), whichis basically a different noisy version of the image shown inFigure 1(a) with the noise density being 60%. In this example,if the central pixel is to be replaced, then a 3 3 filteringwindow would be insufficient for both the BDND algorithmand the modification proposed in the previous subsection sinceNu is zero. Thus, in both cases, the window size is expanded


(a) (b) (c) (d)

Fig. 2. Experimental results for different images. (a) Original images. (b) Original images corrupted by 80% impulse noise. (c) Proposed approach. (d) BDND.

to 5 5. In this window, Vu is {20, 21, 21, 22, 23, 149, 152,152, 153, 153}. This makes the number of uncorrupted pixels10. For the BDND algorithm, if Wmax is assumed to be 3,then window expansion stops. Similarly, window expansionis stopped using the modified condition discussed previously

since Nu is greater than 1/2(1P)NT , (10 > 5). Now, for bothcases, the output value Yij is 86, which is the median of Vu.Note how this value is not consistent with the original pixelvalue. The reason behind this large deviation of the outputvalue from the expected value is that the median filter is based


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Fig. 3. PSNR values for different test images. (a) Lena. (b) Boat. (c) Peppers. (d) Cameraman. (e) Baboon. (f) Toys.

on ranking the values of the uncorrupted pixels found in thefiltering window without any regard to the deviation of thepixels values from the median value and the spatial relationof the uncorrupted pixels to the noisy pixel.

In order to address this issue, the output value Yij, whichis essentially the value that is in the middle of sorted versionof Vu, has to be either decreased or increased by consideringthe relative difference between the pixel values and the medianvalue, and by exploiting the spatial relationship between pixelsin the filtering window. Actually, this problem might be seriousin case the number of uncorrupted pixels is even as illustratedin the previous example.

To deal with this issue, we propose the following modifi-cation to the computation of the estimated pixel value in thefiltering window. As outlined previously, the values of pixels insmall regions in images tend to be correlated to some degree.In other words, pixels that are close to each other tend to haveclose values, especially in smooth regions. Accordingly, theproposed adjustment of Yij incorporates the spatial relationbetween the noisy pixel and the uncorrupted pixels in thewindow and the relation between the values in Vu and theYij. Basically, the adjustment corresponds to adding a termto Yij, which is sum of deviations of the values in Vu fromYij weighted by a factor that is inversely proportional to thedistance of the uncorrupted pixels to the noisy pixel underconsideration, i.e. the center of the window. In other words,the adjusted output value Zij is given by

Zi j = Yi j + 1DNu

k=1

Vu(k) Yi jd(k)

(3)

where d(k) is the spatial distance between the pixels of the kthvalue in Vu and the noisy pixel at location (i,j)

d(k) = |S(k) i | + |T (k) j| (4)with S(k) and T(k) are the row and column indices of thepixel, and

D =Nu

m=1

1d(m)

. (5)

Note how the adjustment term could be positive or negative.Let Vu1 be the set of values in Vu that are less than Yij whileVu2 be the set of values that are greater than Yij. In case thetotal difference of values in Vu2 from Yij is greater than thetotal difference of the values in Vu1 from Yij and they arespatially closer to the noisy pixel, then the adjustment termwill be positive. This implies that Yij is increased to be morecoherent with the values in Vu2 since they are spatially closerto the noisy pixel. On the other hand, if the difference of thevalues in Vu1 from Yij is greater than that of the values inVu2 and their spatial coordinates are closer to the noisy pixel,then the adjustment term will be negative. This implies thatYijis decreased to be more coherent with the values in Vu1.So, the median value Yij is adjusted based on the intensitydifferences as well as the spatial relationship between pixelsin the filtering window.

For the noisy image given in Fig. 1(c), the median setof uncorrupted pixels Vu is {20, 21, 21, 22, 23, 149, 152,152, 153, 153} with a median value of 86. Accordingly, thesets Vu1 and Vu2 are {20, 21, 21, 22, 23} and {149, 152,152, 153, 153}, respectively. The corresponding distances for


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the pixels in these two sets from the center pixel are {3, 2,3, 3, 2} and {3, 3, 4, 2, 3}, while the deviation from themedian value are {66, 65, 65, 64, 63} and {63, 66,66, 67, 67}, respectively. Note the closer distances and lowerdeviations of pixels values in Vu1 when compared to those inVu2. This implies that the adjusted median Zij value would bepulled toward the intensities of the upper region in the imageaccording to (3). Actually, the adjusted median value using (3)is 81 while it is 86 for the case of the BDND algorithm. Suchadjustment is expected to reduce the distortion introduced intothe filtered image as discussed in Section III.

III. EXPERIMENTAL RESULTSIn this section, we present some of the results obtained by

the proposed modifications and compare them with those ofthe original filtering step of the BDND algorithm [26]. Theresults discuss the effectiveness of the proposed modificationsover the BDND algorithm for both monochrome and colorimages. The comparison and discussions are based on visualevaluation and different objective measures. Also, we investi-gate and discuss the effect of the new modification on thesize of filtering window under different noise densities. Inall experiments, it is assumed that noisy pixels are identifiedideally by the detection step of the BDND algorithm. This isessential in order to put aside any issues related to the detectionsince our focus is on the performance improvements achievedby the modifications introduced to the filtering step. In otherwords, the input to the original and proposed filtering stepsis basically the noise map that is obtained when the noiseis randomly generated. This completely neutralizes any effect

TABLE ISUGGESTED FILTERING WINDOW SIZE BASED ON NOISE DENSITY P

Noise Density WmaxWmax0% < P 20% 3 3

20% < P 40% 5 5P > 40% 7 7

of the detection step, such as its dependence on the noisemodel [26], on the evaluation of the filtering step. However,when noisy images are displayed, the salt-and-pepper noisemodel is assumed. Regarding the maximum size of the filteringwindow, we use the suggested values in [26] which are shownin Table I.

A. Performance MetricsTo aid the subjective evaluation of the results, we utilize

different performance metrics that are commonly used inthis regard. The first metric is the Peak-Signal-to-Noise-Ratio(PSNR) which is defined by

PSNR = 10 log10

2552

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(Zi j Xij )2

(6)

where M and N are the number of rows and columns inthe image, respectively. PSNR values are usually used tomeasure the similarity between two images with higher valuesindicating higher similarity or lower distortion. To evaluate


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Fig. 5. FOM values for different test images. (a) Lena. (b) Boat. (c) Peppers. (d) Cameraman. (e) Baboon. (f) Toys.

the distortion in color images, we use the CIELAB colorspace as it provides more accurate quantitative measurementsof perceptual error between two color images [27]. Thus, theoriginal and processed color images are converted to CIELABcolor space and then the difference of colors is computed using

Eab =

(L)2 + (a)2 + (b)2. (7)The remaining metrics are related to the edge quality. The

Tenegrad (TEN) measure [28] is used to evaluate the strengthof the edges in the filtered image. The Tenegrad is a well-known benchmark image sharpness measure which is basedon gradient magnitude maximization and is considered oneof the most robust and functionality accurate image qualitymeasures. It is computed from the gradient at each pixel inthe image where the partial derivatives are obtained by a high-pass filter such as the Sobel operator. For the whole image,the TEN is computed using

TEN =

i

j i j , i j > (8)

where ij is the gradient magnitude and is a threshold that isused to eliminate low edge responses which usually correspondto low levels of noise in the image. In our experiments, ischosen to be the mean value of the gradient magnitude. Thefigure of merit (FOM) metric proposed by Pratt [29] is alsoused to quantify the distortion introduced into edges in termsof edge localization. The FOM is defined by

FOM = 1max{nd , nt }

nd

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TABLE IICOUNTS OF THE FILTERING WINDOW SIZE FOR DIFFERENT

NOISE DENSITY P

P = 10% P = 50% P = 90%WF WF Proposed BDND Proposed BDND Proposed BDND

3 3 25 994 25 994 112 164 47 784 134 075 1575 5 108 108 17 655 22 642 49 237 07 7 0 0 1109 12 973 31 909 09 9 0 0 36 47 565 20 493 235 557

11 11 0 0 0 0 68 6813 13 0 0 0 0 1 1

where nd and nt are the number of edge pixels detectedin the original and output images, respectively, dk is thedistance from the kth edge pixel in the output image to theclosest possible edge pixel in the original image. The termalpha is usually set to 1/9. FOM value is unity for idealedge match and it decreases as the miss-localization of edgesincreases.

B. Size of Filtering WindowOne of the proposed modifications introduced in this paper

is related to the condition used to define the size of the filteringwindow. Unlike the condition defined in the BDND algorithm,the modified condition is made adaptive to the noise density.This has the effect of reducing the occasions in which thewindow is expanded unnecessarily.

Table II lists the counts of the filtering window size usedin the BDND and proposed modification for the image Lena


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Fig. 6. Filtering results for color images. (a) Original. (b) Original corrupted with 80% impulse noise. (c) Proposed. (d) BDND.

(shown in Fig. 2) when it is corrupted by 10%, 50%, and90% impulse noise. Note that with 10% noise density thecounts for both filtering schemes are the same. However, asthe noise density increases, the proposed condition has lowercounts for larger windows. This is clear under 90% noisedensity, where the average window size over the entire imageis 3.74 for the proposed modification and 5.99 for the BDNDalgorithm. As mentioned before, this is because the BDNDcondition is easily violated with high noise densities, whichin turn forces the window to expand. For windows greaterthan (Wmax + 1 Wmax + 1), these are used in the twoapproaches when the number of uncorrupted pixels in thewindow is zero. This would happen in high noise densitiessince noise blotches could present due to the irregularity inthe noise distribution in the image. In this case, the behaviorof BDND and the proposed condition is the same. Rememberhere that the condition for expansion is applied as long as thewindow size is less than or equal to Wmax.

C. Monochrome ImagesFor the purpose of evaluating the proposed modifications

on monochrome images, several tests were conducted. Inthis section we present six examples, which are: Lena,Boat, Peppers, Cameraman, Baboon, and Toys. Fig. 2 shows

the original test images and the noisy version of eachthat is corrupted by 80% impulse noise (more results forother noise densities are available on the following web-site http://driyad.ucoz.net/index/ieee_results/0-39). The filter-ing results are also shown in Fig. 2. Inspecting these resultsreveals the power of the two approaches in restoring theoriginal images efficiently. However, careful investigation ofthe results proves the capability of the proposed approach inproducing higher quality images when compared to the BDNDalgorithm. This is supported by the PSNR values that areshown in Fig. 3 under noise densities ranging from 10% to90%. From these values, we can see how the performance ofthe two approaches is close to each other under low noisedensities. This is due to the fact that the size of the filteringwindow in both approaches is almost the same in this caseas discussed in the previous subsection. As a matter of fact,higher PSNR values for the proposed modifications under lowdensities are strongly associated with the second modificationexplained in Section II.

Regarding the strength and localization of edges, it isevident in Fig. 3 how the images produced by the proposedmodifications are visually sharper and more distinctive thanthose obtained using the BDND algorithm. Fig. 4 showsthe TEN values for the original and processed images. Theproposed modifications produced higher values which imply


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8 x 105

Noise Density %

E

* ab

ProposedBDND

10 20 30 40 50 60 70 80 900

1

2

3

4

5

6

7 x 105

Noise Density %

E

* ab

ProposedBDND

(a) (b) (c)

Fig. 7. Eab values under different noise densities for color images. (a) Family. (b) House. (c) Plane.

stronger edges. This is consistent with the perceived sharpnessfor the filtered images in Fig. 3. Note how the TEN values forthe proposed modifications are closer to the TEN values ofthe original images and while the TEN values of the BDNDalgorithm drops dramatically as the noise density increases.

Moreover, Fig. 5 shows that the proposed modificationsresulted in higher FOM values compared to the BDNDalgorithm. This reflects their capability of preserving edgelocations better than the original BDND filtering algorithm.

D. Color Images

For the purpose of evaluating the performance of the pro-posed modifications on color images, P% of pixels in eachcolor channel are assumed to be contaminated with noise. Asmentioned at the beginning of this section, the ideal noisemap of each channel is used to identify noisy pixels, however,when the images are displayed, salt-and-pepper noise model isused. This is essential to study the performance of the filteringstep only. Filtering of color images is done using the scalarapproach instead of the vector approach. That is, each RGBchannel is filtered separately. It was shown in [26] that scalarapproach is more efficient that the vector approach since thewindow size in the vector approach will result in excessivewindow expansion since uncorrupted pixels are searched inthe three color channels for any filtering window.

The results for three color images that are corrupted by80% impulse noise are presented here, namely: Family, House,and Plane. The original and noisy images as well as thefiltering results for the BDND and the proposed modificationsare shown in Fig. 6 (color results are available on the fol-lowing website http://driyad.ucoz.net/index/ieee_results/0-39).Comparing the filtering results of the two approached revealsthe effectiveness of the proposed approach in producing higherquality and sharper images. For further investigation, Fig. 7illustrates the values of Eab for the two approaches and whenthe original images are corrupted by noise densities rangingfrom 10% to 90%. From these numbers, it is clear how theproposed modifications result in lower distortion in the colorswhen compared to the BDND numbers.

IV. CONCLUSION

Switching median filters are effective in removing impulsenoise as they are applied to candidate noisy pixel only. TheBDND filter is one of the popular switching median filtersas it is proven to overtake other filters especially at highnoise densities. However, the filtering step imposes a strictcondition on the size of the filtering window that does nottake into account the noise density. Additionally, it does notconsider the spatial relationship and deviation of the pixelsintensities in the filtering window from the central pixel andthe median value of the window. In this paper, we proposedtwo modifications to the BDND filtering step to alleviate theeffect of these problems on the quality of the filtered image.The modifications basically loosen the condition imposed onexpanding the filtering window and incorporate the spatialinformation of the pixels in the filtering process. Experimentalevaluation showed the effectiveness of these modifications onimproving the performance of the BDND algorithm.

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Iyad F. Jafar received the B.Sc. degree in electricalengineering from the University of Jordan, Amman,Jordan, in 2001, the M.Sc. degree in electrical engi-neering from the Illinois Institute of Technology,Illinoise, in 2004, and the Ph.D. degree in computerengineering from Wayne State University, Michigan,in 2008.

He is currently an Assistant Professor with theDepartment of Computer Engineering, Universityof Jordan. His current research interests includesignal and image processing, pattern recognition,

and multimedia and computer networks.

Rami A. AlNamneh received the B.S. degree incomputer engineering from the Jordan University ofScience and Technology, Amman, Jordan, in 2000,the M.S. and Ph.D. of Philosophy degrees from theUniversity of Alabama in Huntsville, Huntsville, in2003 and 2006, respectively.

He is an Assistant Professor with the Departmentof Software Engineering, Jordan University of Sci-ence and Technology. His current research interestsinclude parallel programming, signal processing, andwireless communications.

Khalid A. Darabkh received the Ph.D. degreein computer engineering from the University ofAlabama, Huntsville, Alabama, in 2007.

He is currently an Associate Professor with theComputer Engineering Department, University ofJordan, Amman, Jordan. His current research inter-ests include wireless and mobile communications,queuing theory, traffic management, multimedia sys-tems and networking, congestion control architec-tures and resource allocation, parallel computing,and pattern recognition.

Dr. Darabkh is a member of many honor societies, such as Phi Kappa Phi,Tau Beta Pi, Eta Kappa Nu, and Sigma Xi.

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