impulse noise removal by k-means clustering identified fuzzy … · before filtering, a detection...

Turk J Elec Eng & Comp Sci(2020) 28: 2838 – 2862© TÜBİTAKdoi:10.3906/elk-1910-34

Turkish Journal of Electrical Engineering & Computer Sciences

http :// journa l s . tub i tak .gov . t r/e lektr ik/

Research Article

Impulse noise removal by k-means clustering identified fuzzy filter: a newapproach

Aritra BANDYOPADHYAY1,∗, Kaustuv DEB1, Atanu DAS2, Rajib BAG11Department of Computer Science and Engineering, Supreme Knowledge Foundation Group of Institutions,

Mankundu, India2Department of Computer Science and Engineering, Netaji Subhash Engineering College, Kolkata, India

Received: 05.10.2019 • Accepted/Published Online: 19.05.2020 • Final Version: 25.09.2020

Abstract: Removal of impulse noise from corrupted digital images has been a hitch in the field of image processing.Random nature of impulse noise makes the task of noise removal more critical. Different filters have been designedfor noise removal purpose and have shown formidable results mostly for low and medium level noise densities. In thispaper, a new two-stage technique called k-means clustering identified fuzzy filter (KMCIFF) is proposed for de-noisinggray-scale images. KMCIFF consists of a k-Means clustering-based high density impulse noise detection, followed by afuzzy logic-oriented noise removal mechanism. In the detection process, a 5 × 5 window centering upon each pixel of theimage is considered. K-Means clustering is applied on each 5 × 5 window to group the pixels into different clusters todetect whether the central pixel of each window is noisy or not. In the noise removal process, a 7 × 7 window centeringupon each noisy pixel of the image, as detected by the clustering is considered. Fuzzy logic is used to find the nonnoisypixel in each 7 × 7 window having the highest influence on the central noisy pixel of the window. Finally, that pixelis replaced by the approximated pixel intensity value calculated from the highest influencing non-noisy pixel. KMCIFFis evaluated upon seven different standard test images using peak signal to noise ratio (PSNR), structural similarityindex measurement (SSIM), Percentage of actual nonnoisy pixels detected as erroneous out of the total number of pixels(PDAE) and average run time (ART). It has been observed that KMCIFF shows significantly more competitive visualand quantitative performances vis-a-vis most of the extant traditional filters at high noise densities of up to 90% .

Key words: Impulse noise, random valued impulse noise, k-means clustering, fuzzy filter

1. IntroductionImage noise removal is the single most essential and challenging aspect of image processing. Numerous typesof noises can corrupt images. The foundation of these noises can be attributed to transmission faults, cameramovements, and atmospheric turbulence. Salt and pepper noise (SPN) [1] and random valued impulse noise(RVIN) [2] are the results of these faults. Salt and pepper noise is a constant category of impulse noise thataffects images with black (0) and white (255) dots. The other category of impulse noise is random valuedimpulse noise. The detection and removal of this category of noise is a tough task due to its unpredictablenature. This type of noise can take on any value between 0 and 255 for a gray-scale image.

Various noise filtering techniques [3–5] had been used to remove such instances in the past. Only a fewfiltering techniques [6] had been successfully tested at higher noise contamination. Traditional nonlinear filters∗Correspondence: [email protected]

This work is licensed under a Creative Commons Attribution 4.0 International License.2838

https://orcid.org/0000-0002-2302-6284

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https://orcid.org/0000-0003-1573-4253

https://orcid.org/0000-0001-5195-6588

BANDYOPADHYAY et al./Turk J Elec Eng & Comp Sci

[7–20] worked fairly well at low noise densities, but had failed at higher ones. The median filters [7–10] were themost accepted conventional filters designed to suppress impulse noises. The conventional standard median filter(SMF) [11] of the early 1980s was the most fundamental median filter designed as of then. It had removed thespots in images, but could not preserve the details even at low noise densities. A weighted median filter, adaptivecentre weighted median filter (ACWMF) [12] removed this deficiency by focusing on the weights of some pixelsin the images and preserved more details than SMF. But it could not work efficiently at higher noise densities.To bypass this downside, adaptive median filter (AMF) [13] was proposed, where nonnoisy pixels were keptaside and only the noisy pixels were approximated. This showed a remarkably improved result at lower noisedensities. Subsequently, switching median filters were proposed where multiphase approaches were taken. Justbefore filtering, a detection option was introduced which made it a two phase approach. Different switchingmedian filters like multistate median filter (MSM) [14], progressive switching median filter (PSM) [15] wereintroduced which followed an iterative approach that worked at higher density noises. Simultaneously, somedecision based filters like decision based approach (DBA) [16], decision based unsymmetric trimmed medianfilter (DBUTMF) [17], modified decision based unsymmetric trimmed median filter (MDBUTMF) [18] wereproposed. They approximated the noisy pixels based on certain decisions but they were unable to preserve theedges of the images. To preserve the edges, some directional weighted filters like directional weighted medianfilter (DWM) [19], modified directional weighted median filter (MDWM) [20] were developed.

Meanwhile, fuzzy filters [21–24] got a platform as it was better at removing impulse noises from images.Such filters used fuzzy membership functions to find the fuzzy relationship between the pixels in the images andshowed tremendous progress in impulse noise filtering [25–27] problems. A fuzzy approach brought flexibility infiltering methods which worked well in noise filtering problems. A two-staged fuzzy approach [22] was proposedwhich was able to improve image detail preservation. After a few years, a fuzzy inference ruled by else-action(FIRE) [23] operator based approach was proposed with the incorporation of genetic algorithm. It could detectthe image edges smoothly and rapidly. Around this time, a new neuro-fuzzy-based filter [28] was proposed.This filter was capable of removing high density impulse noises. Another two stage fuzzy filter, fuzzy impulsenoise detection and reduction method (FIDRM) [29] was proposed with fuzzy gradient value-based detectionmechanism and fuzzy set representation-based filtering method. A switching fuzzy filter [30] overtook theprevious ones. This filter incorporated iterative fuzzy approach. An improvised version of the previous filter,noise adaptive fuzzy switching median filter (NAFSM) [31], was proposed, again with a two-step noise adaptiveapproach. It handled the ambiguity in the mined noise information. At the same time, a fuzzy switchingmedian filter, called, fuzzy based decision algorithm (FBDA) [32] was introduced. Based on the membership ofdifference between the central pixel and all the other pixels in the image window, the decision of identifying apixel as noisy or nonnoisy was taken. Also, median approach was used in this filter as a removal mechanism.It showed remarkably better results than the previous fuzzy switching filters. FBDA was followed by a dualthreshold fuzzy switching median filter (FSMF) [33]. This filter used fuzzy membership to identify and separatenoise levels. A decade after FSMF, some recent fuzzy filters have shown significant improvements in terms ofquantitative and qualitative results. An assessment based fuzzy switching median filter [34] was proposed andshowed improved performance in all aspects. Most recently, a region-discriminating iterative fuzzy filter [35]had been proposed. The latest version demonstrated a markedly better performance over all preceding filtersbased on all metrics. A few other recent filters had also shown impressive results in removing impulse noisesfrom images.

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Among these recent filters, an ANN-based approach [36] was designed to detect and regularise edgepreservation. Besides, a nonlinear adaptive median [37] and an adaptive mean [38] filter were designed tooperate on colour images and exhibited improved results when compared to some of the more recent fuzzyfilters. After a while, a new rank deficient Hankel matrix based aloha approach [39] was designed for impulsenoise removal. Its effectiveness was boosted by its ability to preserve image details at high impulse noise densities.Most recently, a two-stage filter [40] was designed with the use of empirical mode decomposition to detect thenoisy pixels and a bilateral filter for removal. This filter preserved finer image details using the juxtapositionof these filters, one for detection and the other for removal. The automated threshold scheme provided greateraccuracy. All of the aforementioned methods highlighted the flood of image filters while showcasing a lackof filters capable of operating at high density impulse noise detection and noise filtering. This presented aninteresting challenge for researchers in the field of image processing.

This paper introduces a new high density impulse noise detection technique using k-means clusteringmethod and a new noise filtering technique with the blend of fuzzy logic. We propose the use of k-meansclustering which helps to detect high density impulse noise through cohesive cluster formation of image pixels.Fuzzy logic is incorporated in noise filtering to use not only its flexibility but also its tested and realisticvagueness-blended characteristics.

This concludes Section 1 of the paper. The rest is arranged as follows: Section 2 demonstrates the modelfor impulse noises. Section 3 presents the proposed method, KMCIFF. Section 4 presents quantitative andqualitative results and discussions. The paper ends with a conclusion and the proposed future use of our newtechnique.

2. Impulse noise modelImpulse noise can be categorized by two types: random valued impulse noise and fixed valued impulse noise.

Random valued impulse noise is universally defined as a varied noise, distributed throughout the imagewith any possible value. For an 8-bit image, the noise can assume any value between 0 and 255 including thetwo. H(i,j) denotes the random value distributed when R(i,j) is the grey value of any pixel in the uncorruptedoriginal image and F(i,j) is the grey value of the corrupted image at a position (i,j). Then, the noise model ofan image affected by random valued impulse noise with probability ’p’ can be represented as:

F (i, j) = H(i, j) with probability p

F (i, j) = R(i, j) with probability (1− p)(1)

Bi-sided fixed valued impulse noise is known as salt and pepper noise. Salt and pepper noise creates suddenwhite and black dots in an image. In gray-scale images, a pixel can take any value between 0 to 255. The’255’ intensity is denoted as the white ’salt’ noise and ’0’ intensity is reflected by the black ’pepper’ noise. If p1signifies the probability of ’salt’ noise and p2 signifies the probability of ’pepper’ noise and if O(i,j) is the pixelat a position (i,j) in the uncorrupted image and the ’salt’ noise is symbolized by Ns and ’pepper’ by Np . Thenthe noise model of the salt and pepper noise can be represented as:

CP (i, j) = Ns with probability p1

CP (i, j) = Np with probability p2

CP (i, j) = O(i, j) with probability 1− (p1 + p2)

(2)

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where CP(i,j) is the central pixel. Between these two impulse noises, it is easy to detect salt and pepper noise,as it takes a fixed 0 and 255 pixel value but its tougher to detect random valued impulse noise as it can takeany value in the distributed range of 0 to 255.

3. Proposed method KMCIFF

A Random valued noisy image denoted as IMN is taken with dimensions 512 × 512. The image matrix of IMNis denoted by MIMN (512 × 512). In the following text, the proposed stages of high density impulse noisedetection and removal are briefly discussed.

3.1. Detection of impulse noise

A new k-means clustering-based noise detection algorithm has been successfully designed, which detects thenoisy pixels. To carry out the noise detection process, MIMN is segregated into a number of 5 × 5 matricessuch that each of these matrices contains a pixel ‘X’ at the junction of the two diagonals of that matrix. Incase of choosing the patch or window size, conventional window sizes of 3 × 3 and 7 × 7 shows inferior resultsexperimentally. Hence, 5 × 5 window size have been considered for the proposed algorithm. Let the positionof X in IMN be (p,q) and the pixel intensity value of X be denoted as PIVX . The proposed noise detectionalgorithm is applied on each of these 5 × 5 matrices. The algorithm has generated a flag image, denoted by,IMF of dimensions which are the same as those of IMN. The image matrix of IMF is denoted by MIMF (512× 512) containing binary (0 or 1) cell values. When the proposed noise detection algorithm detects the (i,j)thpixel of IMN as an uncorrupted pixel, i = 1,2,...512 and j = 1,2,...512, then assigns MIMF[i][j] = 0. Whereas,when the (i,j)th pixel of IMN is detected as a noisy pixel, the detection algorithm assigns MIMF[i][j] = 1, i =1,2,...512 and j = 1,2,...512. The following subsection proposes the novel noise detection algorithm.

3.1.1. Proposed noise detection algorithm with explanation

i Formation of an array, denoted as ARR, by sorting the corresponding 5 × 5 matrix elements in ascendingorder:In this first step, the locally considered 5 × 5 matrix elements are scanned and sorted in an ascendingorder. These sorted sequences of elements are stored in an ARR array.

ii Application of k-means clustering on the corresponding 5 × 5 matrix elements to form four clusters: C1 ,C2 , C3 , C4 :K-means clustering technique has been applied on the elements of the corresponding 5 × 5 matrix andfour separate clusters C1 , C2 , C3 , C4 - which are formed by properly placing those matrix elementsin such a way that elements having cohesive values are placed in the same cluster. The noise detectionprocess has dealt with images which are corrupted by impulse noise of random nature. So, the noisypixels of a corrupted image contain random pixel intensity values whereas, the nonnoisy pixels containnonrandom original pixel intensity values. Now, if the corrupted image is segregated into a number of 5x 5 windows and K-means clustering is applied on each 5 × 5 window, then as the nonnoisy pixels arehaving original pixel intensity values which are not random in nature, there is a more possible chancefor these nonnoisy pixels to form clusters showing cohesiveness. On the other hand, in compare to thenonnoisy pixels, the noisy pixels, having random pixel intensity values, are less cohesive. Thus, it is lesspossible for the noisy pixels to form clusters containing more number of member elements compare to

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the clusters formed by nonnoisy pixels. So, the cluster having highest number of member elements willindicate the cluster formed by nonnoisy pixels and will contain the nonnoisy pixel intensity values. Thesenonnoisy pixel intensity values present in the highest membership cluster can be very much useful forfurther noise detection purpose. By experiment we have seen that, considering the number of clusters 4has given better result compared to the number of clusters being 2, 3, 5 or 6. As the result deterioratescontinuously for cluster number 5 and 6, values greater than 6 are not tried. Initial clusters are selectedrandomly by considering the inherent nature of the k-means clustering method without making any furtherrefinements.

iii Finding the most effective cluster (MEC), where MEC=Ck such that k ϵ 1,2,3,4:The MEC is being chosen by comparing clusters on the basis of their number of member elements. Thecluster with highest membership is treated as the MEC. If more than one cluster has the same number ofmember elements, then the coefficient of variance i.e. the ratio of standard deviation and mean of clustermembers is used to identify the MEC. The cluster having minimum co-efficient of variance is identified asthe MEC.

iv Calculation of the mean value, denoted as MMEC, of MEC members:MEC helps us to find effective pixel intensity values for further detection procedures. In order to take asingle value from these most effective pixel values, MMEC is calculated. MMEC synoptically representsa most effective pixel intensity value. Here ’mean’ operation is prioritized over ’median’ or ’mode’. Amedian value of the nonnoisy pixels present in MEC is the value of one of the nonnoisy pixels presentin MEC. Hence, the median cannot provide the combined effect of all the nonnoisy pixels present in theMEC. Thus, the median cannot be very much useful for the further noise detection purpose. Again, asour work deals with high density noises, the chance of getting a good number of nonnoisy pixels is low inmost of the cases. So, the frequencies of nonnoisy pixels present in MEC are low. Thus, the mode cannotbe very much useful for the further noise detection purpose. But as the mean value of the nonnoisy pixelspresent in MEC provides a combined impact of all of the nonnoisy pixels in the MEC, it can be very muchuseful for the further noise detection purpose. Thus, the mean value is given priority over median andmode for the further noise detection purpose.

v Identifying an element, therein denoted as EARR, of ARR closest to MMEC:Elements of ARR are the sorted pixel intensity values of considered 5 × 5 matrices. Each element ofARR is compared with MMEC and the element EARR closest to MMEC is found. MMEC is a calculatedvalue that may not exist in the considered 5 × 5 matrix. Thus, to find the most effective pixel intensityvalue present in the 5 × 5 matrix, EARR is identified.

vi Formation of a set, denoted as EARRS, containing EARR, left adjacent element of EARR, denoted asLEARR, and right adjacent element of EARR, or REARR, in ARR:EARR can be influenced by its neighbouring immediate left and right pixels present in the 5 × 5 matrix.Thus, better accuracy can be achieved when the left and right pixel intensity values, along with the EARR,are considered to find the effective pixel. Therefore, EARRS is formed with left and right adjacent valuesof EARR and the EARR itself.

vii Calculation of the mean value, denoted as MEARRS, of the elements of EARRS:The combined effect of EARR and its immediate neighbouring pixel intensity values can be perfectly

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reflected by their mean value, denoted as the MEARRS. MEARRS adds the desired accuracy in thedetection procedure.

viii Comparison of |PIVX -MEARRS| with standard deviation, identified as SD, of the 5 × 5 matrix todetect whether X is corrupted or uncorrupted:If |PIVX -MEARRS| ≤ SD then X, or the (p, q)th pixel of IMN, is detected as an uncorrupted pixel; orelse, as a corrupted pixel. If X is detected as uncorrupted, then the entry of the corresponding binary flagimage matrix MIMF is replaced with ’0’ i.e. MIMF[p][q] = 0, else replaced with ’1’ i.e. MIMF[p][q] = 1.As the ”SD” parameter is generally used to measure the variability, hence following convention, standarddeviation has been considered here for detection purpose, instead of using a particular threshold.

3.2. Flow diagram of the detection procedureThe whole detection procedure is portrayed by a flow diagram, shown in Figure 1.

3.3. Removal of the impulse noiseThe proposed noise removal process is blended with fuzzy logic to use its flexibility and its ability to deal withrealistic vagueness and uncertainty. The noise removal stage is carried out by applying a fuzzy logic-orientednoise removal algorithm which has successfully cleansed the noisy pixels of IMN, as detected by the proposednoise detection algorithm, with a great deal of accuracy. To perform the noise removal process, MIMF issegregated into some 7 × 7 matrices such that each of these matrices contains a noisy pixel denoted as ‘N’at the junction of the two diagonals of that matrix. Let us consider that, NNPS denotes a set of uncorruptedpixels of a particular 7 × 7 matrix and NPS denotes a set of noisy pixels of the same matrix. The proposednoise removal algorithm is applied on each of these segregated 7 × 7 matrices.

The proposed noise removal process aimed to predict the pixel intensity values of noisy pixels as close aspossible to their original pixel intensity values. For the purpose of predicting the pixel intensity value of a noisypixel, two reference pixels such as the noisy pixel’s nearest neighbouring nonnoisy pixel and the median pixel ofthe noisy pixel’s neighbouring nonnoisy pixels are considered. The pixel intensity values of the reference pixelsare considered as reference pixel intensity values. In case of having more than one nearest nonnoisy pixels, themean of the pixel intensity values of those nearest neighbouring nonnoisy pixels is considered as a reference pixelintensity value. The predicted pixel intensity value of the noisy pixel is assumed to lay between the two referencepixel intensity values. The reason behind choosing the nearest neighbouring nonnoisy pixel as a reference pixelis that, this pixel being the nearest nonnoisy neighbouring pixel of the noisy pixel, has an influence on the noisypixel and can be very useful in the prediction process with its uncorrupted pixel intensity value. Again, thereason behind choosing the median pixel of the noisy pixel’s neighbouring nonnoisy pixels as another referencepixel is that, this median pixel is synoptically indicative of noisy pixel’s neighbouring nonnoisy pixels and caninfluence the realistic prediction with its uncorrupted pixel intensity value. The degree of influences of thetwo above mentioned reference pixels on the noisy pixel are essentially needed to be calculated to be used tocalculate the predicted pixel intensity value. Let us call the degree of influence of a reference pixel on the noisypixel as the induction factor of that reference pixel on the noisy pixel. Both the reference pixels have inductionfactors on the noisy pixel and we have to find out which the induction factor of reference pixel is higher. Butat the same time, we cannot totally ignore the induction factor of the other reference pixel. Thus, the problemof properly predicting the pixel intensity value of the noisy pixel, by calculating the induction factors of boththe reference pixels, involves inherent vagueness and uncertainties.

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Figure 1. Flow diagram of the detection procedure.

Fuzzy logic is used to deal with this vagueness and uncertainties and has successfully enlightened us byproperly calculating the induction factors of two reference pixels on the noisy pixel with its realistic vaguenessand uncertainty dealing capability. A fuzzy set “Near” is formed with a fuzzy membership function µNear . TheManhattan distance between the coordinate position of the noisy pixel in the corrupted image and the coordinateposition of a reference pixel in the corrupted image is taken as an input by µNear and the membership valueof that Manhattan distance in fuzzy set ”Near” is produced as an output. The characteristic of the triangularmembership function µNear is such that, high membership value is produced for small Manhattan distance andvice-versa. The highest membership value of 1 is produced for the Manhattan distance being 1. membership

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values of 0.5 and 0 are obtained for Manhattan distance being 3 and 6 respectively. In this regards it is to benoticed that the minimum and maximum Manhattan distances between a noisy pixel, positioned at the junctionpoint of the two diagonals of a 7 × 7 matrix, and any other pixel in the matrix are 1 and 6 respectively.

The produced membership value of a Manhattan distance between the noisy pixel and a reference pixelin the fuzzy set ”Near” indicates the induction factor of that reference pixel on the noisy pixel. Manhattandistance is used to calculate the induction factor due to the fact that a pixel in an image in most of the cases,holds a pixel intensity value similar to its nearest neighbouring nonnoisy pixel. The induction factor can havea value from 0 to 1, where, 0 indicates no induction and 1 indicates the highest induction. If a reference pixelhas an highest induction factor of 1 on the noisy pixel and the other reference pixel does not have an inductionfactor of 1 on the noisy pixel, then the reference pixel intensity value corresponding to the reference pixel withhighest induction factor is assigned as the predicted pixel intensity value. If both the reference pixels havesame induction factors on the noisy pixel, then the mean value of the two reference pixel intensity values isassigned as the predicted pixel intensity value. This situation is called as neutral situation. The predicted pixelintensity value is assigned closer to a reference pixel intensity value if the corresponding reference pixel hasnonone and higher induction factor on the noisy pixel compare to the other reference pixel. This situation iscalled as nonneutral/biased situation. In a biased situation, the predicted pixel intensity value deviates from itsneutral situation value towards the reference pixel intensity value corresponding to the reference pixel havinghigher induction factor on noisy pixel.

The amount of deviation is calculated as the multiplication of the half of the absolute difference of tworeference pixel intensity values and the absolute difference of the induction factors of two reference pixels onthe noisy pixel. In order to understand why the deviation is calculated as per the aforesaid manner, we needto consider some of the following facts. Clearly, two reference pixel intensity values are apart from each otherby an amount of their absolute difference. Again, the predicted pixel intensity value, in the neutral situation,is apart from each reference pixel intensity value by an amount of half of the absolute difference of the tworeference pixel intensity values. Now, it is assumed that the predicted pixel intensity value deviates following aroutine deviation pattern with the uniform variation of the absolute difference of the induction factors of the tworeference pixels on the noisy pixel. Thus, by considering the above assumption, the multiplication of the half ofthe absolute difference of two reference pixel intensity values and the absolute difference of the induction factorsof two reference pixels on the noisy pixel will give us the amount of deviation. The predicted pixel intensityvalue of the noisy pixel, in a biased situation, is obtained by taking the floor or ceiling value of the result ofaddition or subtraction of the calculated amount of deviation with the neutral situation pixel intensity value ofthe noisy pixel. Taking the floor or ceiling value is useful for better and accurate approximation. Decisions likewhether to perform addition or subtraction and whether to take the floor or ceiling value are taken dependingon the condition that which reference pixel intensity value is greater. The following subsection proposes thenovel noise removal algorithm.

3.3.1. Proposed noise removal algorithm with explanation

i Finding the median pixel, denoted as M, of uncorrupted pixels of the 7 × 7 matrix :In the first step of our algorithm, all the uncorrupted pixels are sorted in an ascending order of theirrespective pixel intensity values to determine the median pixel M. M has a pixel intensity value denotedas PIVM such that PIVM is the median value of the sorted uncorrupted pixel intensities.

ii Calculation of Manhattan distance, denoted as DNM , of M from N:

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In the next step, Manhattan distance DNM of M from N is calculated using the equation (3)

DNM =| a− c | + | b− d | (3)

(a,b) and (c,d) in equation (3) are the co-ordinate positions of N and M in IMN respectively.

iii Calculation of Manhattan distances of each uncorrupted pixel, denoted as NNPϵ NNPS – {M}, from N :The Manhattan distance of a uncorrupted pixel NNPϵ NNPS – {M} from N is denoted by DNNNP andis calculated using equation (4) -

DNNNP =| a− e | + | b− f | (4)

(a,b) and (e,f) in equation (4) are the coordinate positions of N and NNP in IMN, respectively. Accordingly,Manhattan distances of each NNPϵ NNPS – {M} from N are calculated.

iv Finding the shortest Manhattan distance, denoted as DNSNNP , and the nearest uncorrupted pixel,denoted as SNNP from N :DNNNP values are sorted in ascending order to find the shortest Manhattan distance DNSNNP , andthe corresponding nearest uncorrupted pixel SNNP from N. SNNP values are kept in a set of the nearestuncorrupted pixels denoted as SNNPS. SNNPS is formed to deal with such cases where more than oneSNNP values are obtained.

v Finding the membership values, denoted as µNear(DNM ) and µNear(DNSNNP ) , of DNM and DNSNNP

respectively, in the fuzzy set “Near”:We have defined a fuzzy set Near with a triangular membership function denoted as µNear in the followingway-Near = µNear(DNM )/DNM + µNear(DNSNNP )/DNSNNP

Figure 2 shows the characteristics of µNear over D values such that, D ϵ {DNM } ∪ {DNSNNP }.

1

1 2 3 4 5 6

D

µNear (D)

0.5

Figure 2. Characteristics of µNear over D values.

It can be easily seen from Figure 2 that, µNear(D)α( 1D ) . Obviously, the highest value of µNear(D) is 1

and it is obtained when D = 1. Subsequently, µNear(D) achieves values of 0.5 and 0 corresponding to Dvalues 3 and 6 respectively.

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µNear is applied on D to find the membership value of D in the fuzzy set “Near”.

vi Finding the ‘induction factor’ of a pixel on N:Induction factor of a pixel denoted as P, P ϵ SNNPS ∪ {M}, on N reflects the degree of influence of P onN. If DNP is the Manhattan distance of P from N then µNear(DNP ) indicates the induction factor of Pon N. Clearly, higher µNear(DNP ) values indicate higher induction factors. The Manhattan distance ischosen as a parameter to calculate the induction factor given that a pixel in an image mostly carry pixelintensity value similar to its nearest neighbouring pixels. So, the nearest neighbouring pixels of N leave ahigh degree of influence on N.

vii Calculation of predicted pixel intensity value denoted as PPIVN of N:Obviously, the most important task of the noise removal algorithm is to replace the noisy pixel intensityvalue of N with a predicted suitable value. The prediction has to be done in such a way that the estimatedvalue is very close to the original pixel intensity value of N. The better the prediction, the finer is thequality of the noise removed image. A SNNP having high induction factor on N depicts a strong influenceon N. Also, M being the median pixel, it is synoptically indicative of uncorrupted pixel intensity valuesand can be realistically useful for calculating PPIVN . Thus, pixel intensity value denoted as PIVSNNP

of SNNP and pixel intensity value denoted as PIVM of M can certainly be used to predict the pixelintensity value of N closest to its original value. As | SNNPS | ≥ 1, so we have used the mean pixelintensity value denoted as MPIVSNNP while predicting. MPIVSNNP is calculated using equation (5)below:

MPIVSNNP =∑

SNNPϵSNNPS

(PIVSNNP )/ | SNNPS | (5)

We have defined the following rules to calculate PPIVN :Rule 1: If µNear(DNM )=1 and µNear(DNSNNP ) ̸= 1, then PPIVN = PIVM

Rule 2: If µNear(DNSNNP )=1 and µNear(DNM ) ̸= 1, then PPIVN = MPIVSNNP

Rule 3: If µNear(DNM )=µNear(DNSNNP ), then PPIVN =(PIVM +MPIVSNNP )/2

Rule 4: If µNear(DNM ) > µNear(DNSNNP ) and µNear(DNM ) ̸= 1, then −Sub-rule 4.1: If PIVM < MPIVSNNP , then PPIVN =⌈((PIVM +MPIVSNNP )/2–(A/2)*B)⌉Sub-rule 4.2: If PIVM > MPIVSNNP , then PPIVN =⌊((PIVM +MPIVSNNP )/2+(A/2)*B)⌋Where A = ( | PIVM − MPIVSNNP |) and B = | µNear(DNM ) -µNear(DNSNNP ) |Rule 5: If µNear(DNSNNP ) > µNear(DNM ) and µNear(DNSNNP ) ̸= 1, then−Subrule 5.1: If PIVM < MPIVSNNP , then PPIVN =⌊((PIVM +MPIVSNNP )/2+(A/2)*B)⌋Subrule 5.2: If PIVM > MPIVSNNP , then PPIVN =⌈((PIVM +MPIVSNNP )/2 -(A/2)*B)⌉Where A = ( | PIVM − MPIVSNNP |) and B = | µNear(DNM ) -µNear(DNSNNP ) |

The aforementioned rules are described below:Rule 1 is applicable in the situation when M has the highest induction factor of 1 on N and SNNP doesnot have an induction factor of 1 on N. Thus, it is obvious that M is the most influencing pixel for N, andthereby, PPIVN is approximated with PIVM .

Rule 2 is applicable in the situation when SNNP has the highest induction factor of 1 on N and M doesnot have induction factor of 1 on N. Thus, it is apparent that SNNP is the most influencing pixel for N,and thereby, PPIVN is approximated with MPIVSNNP .

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Rule 3 is applicable in a neutral situation when both M and SNNP have the same induction factor on N.Thus, PPIVN is approximated with the mean value of PIVM and MPIVSNNP .Rules 4 and 5 are applicable in the nonneutral situations when M has higher induction factor on N thanSNNP and vice-versa respectively. Clearly in these situations PPIVN should tend towards the higherinfluencing intensity value of pixel. Based on this, we have defined variable B in Rules 4 and 5 to denotethe possible tendency of PPIVN . In this context, it is very useful to take note of Rule 3 that describes aneutral situation when PPIVN has same possible tendency towards PIVM and MPIVSNNP , and thusPPIVN is calculated as a mean of PIVM and MPIVSNNP . Thus it is obvious that in biased situations ofRules 4 and 5, PPIVN will deviate from its neutral value denoted as NV = (PIVM + MPIVSNNP )/2towards PIVM and MPIVSNNP respectively with some deviation value denoted as DV. In order tocalculate DV, we have defined variable ’A’ in Rules 4 and 5 which denotes the absolute difference ofthe pixel intensity values of M and SNNP. So it can be safely said that PIVM and MPIVSNNP are’A’ amount apart. It is obvious that NV is ’A/2’ amount apart from each of PIVM and MPIVSNNP .Clearly, it can be reiterated that PPIVN will have to deviate from NV to positive or negative ’A/2’amounts to reach PIVM and MPIVSNNP . Positive or negative deviation will depend on which valueamong PIVM and MPIVSNNP is higher. Again it can be found that 0≤B≤1. B=0 indicates a neutralsituation whereas B=1 indicates the situation when either M or SNNP has the highest induction factor of1 on N. Obviously, if B=1, PPIVN reaches from NV to either PIVM or MPIVSNNP . From the abovediscussion one can say that if B=0, then DV=0, and if B=1, then DV=A/2. This observation leads to afinding that if 0<B<1, then PPIVN is either between NV and PIVM or between NV and MPIVSNNP .Now, one can calculate the value of DV using DV=(A/2)*B by assuming that DV changes routinely withuniform change in B. DV can be added or subtracted to or from NV to calculate PPIVN . The Subrulesof 4 and 5 describe the use of addition and subtraction. Floor and ceiling values are taken in subrules togain a more accurate approximated value of PPIVN .

3.4. Flow diagram of the removal procedureThe whole removal procedure is portrayed by a flow diagram, shown in Figure 3.

4. Experimental resultsUpon the application of the algorithm to highly noisy imagery, interesting experimental yields had been noted.KMCIFF was executed in Matlab R2018a, installed on a Windows PC running an Intel Core i5 processorand with 8 GB RAM. The algorithm was assessed with different test images each having a size of 512 ×512. Primarily we had concentrated on random valued impulse noise, but in order to find the performanceof our filter on other type of noise, we had applied KMCIFF on salt and pepper noise also. KMCIFF wascompared against several other existing methods: Standard median filter (SMF), progressive switching medianfilter (PSMF), adaptive centre weighted median filter (ACWMF), multistate median filter (MSM), modifieddecision based unsymmetric trimmed median filter (MDBUTMF), multiclass support vector machine basedadaptive filter (MSVMAF), DAWOOD, GUPTA, TURKMEN, combination of adaptive vector median filterand weighted mean filter(CAVMFWMF), adaptive noise-exclusive and assessment based fuzzy switching medianfilter (ANEA-FSMF), region adaptive fuzzy filter (RAFF), LUO, fuzzy impulse noise detection and reductionmethod (FIDRM), JIN, and empirical mode decomposition and adaptive bilateral filter (EMDABF). Noisedensity had been abbreviated as ”ND” in required tables.

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Figure 3. Flow diagram of the removal procedure.

The performance of detection procedure was shown in Figure 4. Three different images Lena, Barbaraand Fingerprint had been considered in this case. Figure 4 showed an arbitrarily chosen 5 × 5 window of theoriginal image, 80% noisy image and the corresponding flag image depicting corrupted and uncorrupted pixelsof the original image. Flag value ’1’ denoted corrupted pixels and ’0’ denoted uncorrupted pixels. The minimumerror spotted through the detection procedure had been circled for proper understanding. It was evident fromthe figure that, minimum percentage error was identified even at a high noise density of 80%. The error ratethus obtained was significantly low yet yielded effective results through the proposed KMCIFF at high noisedensities.

The visual performance of the proposed filter was assessed with various test images, such as Lena, Goldhill,Baboon, Barbara, Boat, Cameraman, and Fingerprint. From these images, only two had been shown in thispaper. Figure 5 showed a visual output of Goldhill image for JIN, RAFF, EMDABF and KMCIFF at 70%

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Figure 4. Proposed detection example for three images at 80% noise density.

noise density. From a visual perspective, it must be noted that KMCIFF produced better results even at highernoise density of 70% . Figure 6 showed a visual output of Lena image at various noise densities for KMCIFF.It produced exceptional results, especially at high noise densities. KMCIFF was also compared quantitativelywith four parameters: peak signal to noise ratio (PSNR), structural similarity index measurement (SSIM) andnumber of actual uncorrupted pixels detected as erroneous out of total number of pixels (PDAE) and averagerun time (ART). These parameters were defined as follows:

Peak signal to noise ratio (PSNR) in db, was defined as follows:

PSNR = 10log102552

MSE. (6)

The resemblance between the original image and the restored image was measured by SSIM. The SSIM wasdefined by the following equation:

SSIM(x, y) =(2µxµy + C1)(2σxy + C2)

(µ2x + µ2

y + C1)(σ2x + σ2

y + C2), (7)

where µx and µy was the mean of image x and image y respectively. The standard deviation of image x andimage y was represented by σx and σy respectively. C1 , C2 were the constants. σxy was the covariance of xand y. An error percentage was calculated to show the error rates for the detection algorithm in this two-phaseapproach, termed as PDAE. The error percentage had been calculated as follows:

PDAE =

(ENP

TNP

)× 100, (8)

where ENP was the total number of actual nonnoisy pixels detected as erroneous and TNP was the total numberof pixels in the whole image. Average run time of the procedure were measured by simulation in MATLAB

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2018a. The time was calculated in minutes. It covered the total simulation time of both the phases i.e. detectionand filtering of proposed KMCIFF.

Figure 5. Visual output of Goldhill image at 70% noise for random valued impulse noise (a) original image (b) 70%noisy image (c) JIN (d) RAFF (e) EMDABF (f) KMCIFF.

In Table 1, Table 2 and Table 3, different existing filters such as SMF, PSMF, ACWMF, MSM, MD-BUTMF, LUO, FIDRM, DAWOOD, GUPTA, ANEA-FSMF, MSVMAF, TURKMEN, CAVMFWMF, JIN,RAFF, EMDABF gone up against with KMCIFF with respect to PSNR for random valued impulse noise. Testimages Lena, Goldhill and Baboon were used in respective Table 1, Table 2 and Table 3 for performance com-parison against the existing filters discussed above. In these three tables, the traditional filters SMF, PSMF,ACWMF, MSM, MDBUTMF were outperformed by the proposed KMCIFF, by a margin of 6–8 db with respectto PSNR. The filters, LUO, FIDRM, DAWOOD, GUPTA, ANEA-FSMF were beaten by a margin of 0.8–3 dbPSNR values in average. The success margin was greater for the Lena image and lesser for the Goldhill andBaboon image as the later images carried more details than the previous ones. The most recent filters, CAVM-FWMF, JIN, RAFF, EMDABF had a close margin as the tables showed. But, from 60% noise density andabove, KMCIFF had shown healthier PSNR result than all the traditional and recent filters for all three testimages.

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Figure 6. Visual output of KMCIFF on Lena image for random valued impulse noise (a) KMCIFF output (40% ND)(b) KMCIFF output (60% ND) (c) KMCIFF output (80% ND).

The proposed KMCIFF was also evaluated with salt and pepper noise. Table 4 compared some of thetraditional and recent filters up against KMCIFF for Lena image at a varied noise density for salt and peppernoise type. KMCIFF depicted a PSNR value 0.7–3 db greater than the mentioned filters at noise density ashigh as 70%. From the table it was very much evident that KMCIFF had shown better outcome than all othercompared filters.

The proposed method had been executed three times for each of the test image and noise density, forboth random valued impulse noise and salt and pepper noise. It had been observed that, the variation of PSNRvalues obtained, was within the range of 0.05–0.2 db. For example, at 60% noise density, Lena image resultedin PSNR values of 31.82 db, 31.78 db, and 31.69 db and Baboon image portrayed 30.62 db, 30.55 db, and 30.46db PSNR values while executing our proposed method subsequently. Hence, it was clear that the deviation ofresult was within a negligible limit.

Table 5 showed the performance of KMCIFF, up against existing filters with respect to SSIM at variousnoise densities. Particularly at noise densities, higher than 60% to 90%, KMCIFF produced 1%–5% higherresult than other state of art filters. At a high noise density of 90%, the proposed method held a 80% abovestructural similarity which was unparalleled. It was apparent from the face-off that KMCIFF showed betterstructural symmetry than the compared filters, particularly at higher noise densities.

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Table 1. Comparison of PSNR (dB) values of various filters up against KMCIFF for Lena image at diverse noisedensities in terms of random valued impulse noise.

Image Filters Noise density40% 50% 60% 70% 80% 90%

Lena

SMF [11] 27.61 23.32 21.77 17.19 14.54 11.56PSMF [15] 28.74 25.61 22.24 19.78 16.09 13.65ACWMF [12] 28.88 26.54 21.33 19.89 17.05 14.12MSM [14] 31.36 26.75 22.09 20.59 18.09 15.87MDBUTMF [18] 29.18 27.69 25.81 23.48 20.88 18.13LUO [26] 28.27 26.23 24.21 22.51 20.71 18.65FIDRM [29] 31.16 29.08 26.13 24.17 21.22 19.67DAWOOD [2] 34.92 30.06 27.90 25.45 22.14 19.92GUPTA [25] 31.45 29.15 27.02 24.78 23.62 21.23ANEA-FSMF [34] 30.16 28.32 24.27 21.85 19.43 18.06MSVMAF [27] 32.34 28.14 24.22 21.67 19.11 16.26TURKMEN [36] 31.79 29.96 28.80 27.62 24.94 22.48CAVMFWMF [38] 35.69 31.84 29.15 26.33 24.31 22.33JIN [39] 30.60 27.14 24.32 19.42 16.02 14.36RAFF [35] 35.14 31.43 27.29 24.41 21.32 18.07EMDABF [40] 35.26 32.52 30.55 27.96 24.98 22.76KMCIFF 35.02 32.47 31.82 28.47 25.07 23.12

Table 2. Comparison of PSNR (dB) values of various filters up against KMCIFF for Goldhill image at diverse noisedensities in terms of random valued impulse noise.


Goldhill


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Table 3. Comparison of PSNR (dB) values of various filters up against KMCIFF for Baboon image at diverse noisedensities in terms of random valued impulse noise.


Baboon


Table 4. Comparison of PSNR (dB) values of various filters against KMCIFF for Lena image at diverse noise densitiesin terms of salt and pepper noise.

Filters Noise density40% 50% 60% 70% 80% 90%

SMF [11] 18.82 15.22 12.31 10.04 8.13 6.60MDBUTMF [18] 33.50 31.46 29.35 27.19 24.30 19.99MSVMAF [27] 34.10 30.69 25.25 22.59 20.02 17.97CAVMFWMF [38] 37.44 34.63 31.92 27.56 24.92 21.73EMDABF [40] 36.00 34.21 31.25 29.35 27.01 25.60KMCIFF 36.23 33.89 32.37 30.06 28.81 25.62

Comparison between the existing filters up against KMCIFF with respect to ART (in minutes) wasshown in the Table 6. It had been observed that the proposed filter took a time of 1–1.5 min to execute thewhole algorithm which was better when compared to recent filters like MSVMAF, CAVMFWMF. The primaryconcern of the proposed filter was to enhance the quality of the restored image. In this process, two highlyaccurate and sophisticated techniques such as k-means clustering and fuzzy logic were applied. But, as thesetwo techniques demanded high amount of time for their computation, the ART of the proposed filter was foundto be comparatively higher than few other existing filters. KMCIFF had produced first-rated PSNR and SSIMresults for all test images which validated the inherent background theory of the proposed filter.

The proposed method was evaluated for both salt and pepper noise and random valued impulse noise forseven different images such as, Lena, Goldhill, Baboon, Barbara, Boat, Cameraman and Fingerprint at variousnoise densities with respect to PSNR, SSIM, PDAE and ART. The results were portrayed in Table 7.

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Table 5. Comparison of SSIM values of KMCIFF up against various filters at diverse noise densities for Lena image.

Filters SSIM40%ND 60%ND 80%ND 90%ND

SMF [11] 0.5292 0.4065 0.3334 0.3052PSMF [15] 0.8209 0.6637 0.5450 0.4873ACWMF [12] 0.8281 0.5464 0.5583 0.4959MSM [14] 0.9222 0.6538 0.5836 0.5203MDBUTMF [18] 0.8822 0.7306 0.6890 0.5828LUO [26] 0.8560 0.7048 0.6792 0.6088FIDRM [29] 0.5862 0.1917 0.7190 0.6240DAWOOD [2] 0.9233 0.7910 0.7043 0.6382GUPTA [25] 0.9191 0.7675 0.7431 0.6646ANEA-FSMF [34] 0.8948 0.6976 0.6317 0.5836MSVMAF [27] 0.9205 0.6948 0.6210 0.5450TURKMEN [36] 0.9234 0.8321 0.7822 0.7190CAVMFWMF [38] 0.9231 0.8104 0.7653 0.7043JIN [39] 0.9081 0.6160 0.5160 0.5034RAFF [35] 0.9121 0.7691 0.6646 0.5836EMDABF [40] 0.9199 0.8194 0.7934 0.7068KMCIFF 0.9192 0.8775 0.8407 0.8193

Table 6. Comparison of average run time of different filters up against KMCIFF for Lena image at diverse noise densitiesin terms of random valued impulse noise.

Filters ART40%ND 50%ND 60%ND 70%ND 80%ND 90%ND

SMF [11] 0.0030 0.0030 0.0031 0.0032 0.0033 0.0034MSVMAF [27] 2.35 2.61 2.76 3.23 3.47 3.73CAVMFWMF [38] 2.59 2.74 2.98 3.37 3.68 4.02RAFF [35] 0.79 0.97 1.08 1.18 1.27 1.39KMCIFF 1.28 1.29 1.33 1.38 1.41 1.43

Lena, Baboon and Cameraman images provided better outcome than the other images for random valuedimpulse noise. These three images resulted greater than 30 db PSNR value at 60% noise density which wascredible. Rest four images, Boat, Goldhill, Barbara and Fingerprint showed lower result than the other imagesdue to their image detail intricacy. For salt and pepper noise, Lena, Baboon, and Cameraman along withGoldhill demonstrated above 30 db PSNR. Other images showed comparatively good yet lower result thanLena, Baboon, Goldhill, and Cameraman images due to the same grounds of image complexity.

From results based on SSIM perspective illustrated in Table 7, it was apparent that our proposed filterupheld 80% similarity for Lena and Baboon images at very high noise density of 90% for random valued impulsenoise. For salt and pepper noise, Lena, Baboon and Goldhill images also touched the mark of 80% similarityat the high noise density of 90%. Moreover, all the images at a lower noise density of 40% showed remarkableresults of 83% and 84% resemblance for both random valued impulse noise and salt and pepper noise respectively.From this result it was quite evident that our proposed filter preserved the structural resemblance at both lower

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Table 7. PSNR, SSIM, PDAE, and ART values of KMCIFF for various images at diverse noise densities for impulsenoise.

Noise Approach Lena Goldhill Baboon Barbara Boat Cameraman Fingerprint

RVIN

PSNR

40%ND 35.02 31.96 33.86 30.78 31.34 33.72 29.1260%ND 31.82 28.87 30.62 27.21 28.93 30.18 26.3480%ND 25.07 24.54 25.57 23.98 24.89 25.12 21.6390%ND 23.12 22.16 23.03 21.23 22.76 22.94 18.12

SSIM

40%ND 0.9192 0.8745 0.8927 0.8489 0.8519 0.8667 0.831860%ND 0.8775 0.8442 0.8569 0.8201 0.8304 0.8311 0.814380%ND 0.8407 0.8164 0.8203 0.7997 0.8067 0.8089 0.787990%ND 0.8193 0.7957 0.8004 0.7643 0.7869 0.7874 0.7527

PDAE

40%ND 1.97 2.32 10.50 6.93 2.83 3.72 7.2360%ND 2.17 2.57 8.28 5.60 2.97 2.96 7.4980%ND 4.12 4.55 6.88 5.59 4.62 6.02 7.0390%ND 4.11 4.33 4.89 4.43 4.25 6.08 6.12

ART

40%ND 1.28 1.30 1.33 1.32 1.31 1.29 1.3860%ND 1.33 1.34 1.39 1.37 1.35 1.33 1.4780%ND 1.41 1.43 1.45 1.46 1.42 1.42 1.5890%ND 1.43 1.47 1.48 1.49 1.44 1.43 1.65

SPN

PSNR

40%ND 36.23 33.12 35.36 32.78 33.26 34.92 30.5660%ND 32.37 30.21 32.16 28.43 29.97 31.07 28.0480%ND 28.81 26.97 27.89 25.02 26.29 26.79 24.2390%ND 25.62 25.24 24.98 22.93 24.56 24.34 21.06

SSIM

40%ND 0.9234 0.8821 0.8998 0.8559 0.8608 0.8724 0.840260%ND 0.8867 0.8516 0.8624 0.8293 0.8452 0.8466 0.819880%ND 0.8534 0.8227 0.8309 0.8069 0.8144 0.8126 0.795690%ND 0.8268 0.8006 0.8094 0.7706 0.7969 0.7938 0.7635

PDAE

40%ND 1.88 2.28 10.44 6.87 2.78 3.67 7.1760%ND 2.14 2.54 8.26 5.54 2.91 2.91 7.4180%ND 4.10 4.50 6.84 5.56 4.59 5.97 6.9490%ND 4.09 4.31 4.87 4.39 4.22 6.05 6.08

ART

40%ND 1.24 1.24 1.29 1.26 1.27 1.23 1.3460%ND 1.29 1.29 1.34 1.32 1.29 1.28 1.3980%ND 1.32 1.38 1.39 1.42 1.38 1.39 1.5290%ND 1.36 1.43 1.45 1.44 1.41 1.41 1.59

and higher noise densities. Thus, these results of PSNR and SSIM had validated the background theory of theproposed noise filtering process discussed in section 3.2.

PDAE results showed minimal percentage of error for all the seven test images for KMCIFF, againespecially at high noise densities. Table 7 showed maximum error value of 10.50% and 10.44% for Baboonimage and a minimum error value of 1.97% and 1.88% for Lena image at a lower noise density of 40% forrandom valued impulse noise and salt and pepper noise respectively. At higher noise densities of 90%, KMCIFFdepicted a maximum error value of 6.12% and 6.08% for Fingerprint image and a minimum error value of 4.11%and 4.09% for Lena image for random valued impulse noise and salt and peppers noise respectively. These

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error values yielded are significantly low considering higher noise densities. The analysis hence depicted thatthe proposed algorithm generated minimized errors. Thus, these results had validated the background theoryof the proposed noise detection process discussed in section 3.1.1.

From ART viewpoint mentioned in Table 7, it had been noticed that our proposed filter maintained1.5–1.65 min and 1.24–1.59 min average run time at the noise density span of 40% to 90%, for random valuedimpulse noise and salt and pepper noise respectively. Minor time variations had been observed for the differenttest images considering different noise densities.

Based on all the results mentioned in Table 7, it was inherent that salt and pepper noise fared betterthan random valued impulse noise due to its fixed nature.

The strength and weakness of different filters up against proposed KMCIFF was compared in Table 8.From the comparison, it was found that no compared filter had performed clustering for noise detectionoperation. Although fuzzy was applied in different compared filters for noise removal operation, but herewe had used its flexibility and its ability to deal with realistic vagueness and uncertainty.

From the above visual and quantitative results, it was transparent that KMCIFF outperformed all theother compared filters, particularly at high noise density levels.

Table 8. Comparison of strength and weakness of different filters up against KMCIFF.Filters Strength WeaknessSMF [11] A two dimensional nonrecursive and

recursive median filtering was pro-posed. Proposal of performing filteringprospect in both recursive and nonre-cursive way, is the strength of this pa-per.

Could not preserve image details ateven low noise densities for even fixedvalued impulse noise.

ACWMF [12] The method detected impulse noisewith the difference between the currentpixel with the diverse weighted outputof the center weighted median filter.Taking diverse weighted median for de-tection aspect, was the strength of pa-per.

Could not detect impulse noise at highnoise densities.

MSM [14] A multistate space varying switchingadaptive center weighted median filterwas proposed. Space variation alongwith threshold scheme was its strength.

Could not remove impulse noises athigh noise densities.

PSMF [15] An iterative switching median filter wasproposed which used numerous itera-tions of detection and filtering schemeto detect and filter high density fixedvalued impulse noise.

Could not remove random valued im-pulse noise from images and several it-erations increased the complexity andrun time of the whole procedure.

MDBUTMF [18] A decision based trimmed median fil-ter was proposed, which replaced onlythe uncorrupted pixels by trimmed me-dian of a windowed portion of the colorimages. Decision making and trimmedmedian concept was the main strengthof the paper.

Could not remove random valued im-pulse noise from images.

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Table 8. (Continued).Filters Strength WeaknessLUO [26] A filter, for removing impulse noise was

proposed which preserved the image de-tails up to an extent. At lower noisedensity the method showed good resultvia PSNR.

Could not remove even medium densityimpulse noise from images.

FIDRM [29] A fuzzy filter was proposed which usedfuzzy gradient value for detection andfuzzy averaging of the local pixels forcorrection approach. Using Fuzzy tech-nique for removing impulse noise andalso establishing edge preservation werethe strength of the filter. Moreover thefilter could also work on mixed noisepatterns.

The method did not worked at highdensity noises.

DAWOOD [2] The method had used a related neigh-boring statistics based detection and aremoval with minimal diverged similarvalue. Using similar neighboring in-formation for detection was the mainstrength of the method.

Multiple iterations built high complex-ity in the procedure. Run-time was afactor also. Moreover, the method didnot worked at very high density impulsenoises.

GUPTA [25] The method used an averaged dualthreshold for detection purpose andsimple median filter for removal. Thestrong dual threshold based detectionmethodology had improved the simplemedian filter by a lot of margin whichwas the main strength of the paper.

Simple median filter was used in thisapproach. But simple median filter hadinherent problem in approximation asthe filter used only the median of thewindow for noise approximation. Themedian was a value present in the samewindow. So, the approximation accu-racy was reduced.

ANEA_FSMF [34] The method had proposed a adap-tive, varying window size based, fuzzyswitching median filter for high densityimpulsive noise removal. Using adap-tive, varying window size for differentnoise densities, was the strength of themethodology.

The method was unable to maintainthe removal performance at high den-sity noises, which was reflected by thePSNR metric.

MSVMAF [27] The method proposed a support vec-tor machine (SVM) based adaptive me-dian filter for removing impulse noise.The main strength of method was usingSVM for filtering operation. Moreoverthe filter worked well on the color im-ages.

The method produced promising resultfor high density noises but failed at lowdensities. Also, other machine learningfeatures could be incorporated to en-hance the methodology.

TURKMEN [36] The method proposed a artificial neu-ral network based detection followed bya edge preserving regularized removalprocedure. Both these operations werethe main strength of the methodology.

The method’s edge-preserving regular-ization (EPR) procedure for removaloperation took a lot of computationaltime.

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Table 8. (Continued).Filters Strength WeaknessCAVMFWMF [38] In this method, amalgamation of adap-

tive vector median filter and weightedmean filter were used for noise removal.The filter worked at high noise densi-ties and also applicable for color imageswhich were its strength factors.

As nonnoisy pixels were also substi-tuted by weighted mean of uncorruptedpixels in the surrounding window, theactual nonnoisy values were lost.

JIN [39] An annihilating filter-based low-rank Hankel matrix (ALOHA) basedmethod was proposed. Reconstructingtexture images and color images werethe main strength of this method.

The method had good result at low andmedium density noises but was unsuc-cessful at very high density noises.

RAFF [35] A region adaptive fuzzy filter was pro-posed. Minimum mean value detec-tion and region discriminating fuzzybased removal was used in this method.Its region discriminating approach pro-vided edge preservation of images athigh noise densities.

Detection performance could be fur-ther improved. Enhanced mapping rulecould be used during filtering method.

EMDABF [40] An empirical mode decompositionbased detection and adaptive bilateralfiltering based removal mechanism wasproposed in this paper. Detection wasthe main strength of this paper.

Impulse noise affected blurred region inthe images could not be recovered withthis methodology.

KMCIFF A two stage filter, KMCIFF was pro-posed. K-means clustering was used inthe detection stage and a fuzzy filteringwas used in the removal. The strengthof our approach was the detection ac-curacy which was showed for seven dif-ferent images by PDAE. At a huge 80%noise density it produced at most 7.03% error for Fingerprint texture imageand a minimum result of 4.12 % errorfor Lena image for random valued im-pulse noise. This showed the detectionprecision of our method. The proposednoise removal process was blended withfuzzy logic to use its flexibility andits ability to deal with realistic vague-ness and uncertainty. The strength ofthe method is validated by appreciablePSNR, SSIM, PDAE and ART values.

It was evident in the proposed algo-rithm, that the k-means clustering hadbeen used for noise detection and fuzzylogic had been used for noise removal.As the main priority of the proposedfilter had been to enhance the qualityof the restored image through k-meansclustering and fuzzy logic based highcomputational time prone approach,the execution time might be longerthan few other existing filters in thisdomain. The aforesaid techniques hadworked rigorously, by taking some moretime which was validated by the excel-lent PSNR and SSIM results for all thetest images.

5. ConclusionA combination of clustering-based noise detection and fuzzy logic-based noise removal techniques has beenproposed in this paper. K-Means clustering, along with coefficient of variance, is used for unimpeachable clusteridentification in the detection phase. K-means clustering approach is used to find the most effective cluster which

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contains the maximum number of similar groups of pixels depending on their cohesiveness. A similar approachleads to the intrinsic analogous pattern in the original reference image which shows the path to noise detection.In the removal phase, a fuzzy membership set “Near” is used to measure the induction factor of the pixels whichare nearest to the noisy one and a predictive pixel intensity value measured from the highest influenced pixelis used to approximate the noisy pixel of interest. KMCIFF highlights demonstrable performances for randomvalued impulse noise. The performance of KMCIFF is tested visually and quantitatively at diverse noise densitiesranging between 10% to 90% using PSNR, SSIM, PDAE and ART. As the results show, KMCIFF demonstratessuperior performances than most of the recent filters, particularly at high noise densities, i.e. above 60% . Also,at 90% noise density, KMCIFF provides adequate PSNR value. The SSIM also indicates high-value structuralhomogeneity across various noise densities. KMCIFF promises affordable results for filtering high-density noisyimages. Going a step ahead, other related clustering methods like k-medoids and fuzzy c-means can be usedto detect corrupted pixels in the near future. Moreover, we would like to investigate the impact of KMCIFFon other noise patterns for empirical and commercial purposes, including, but not restricted to, Gaussian andPoisson noises.

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[3] Civicioglu P. Removal of random-valued impulsive noise from corrupted images. IEEE Transactions on ConsumerElectronics 2009; 55 (4): 2097-2104. doi: 10.1109/TCE.2009.5373774

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