The 19th Korea -Japan Joint Workshop on Frontiers of Computer Vision

High Density Impulse Noise Removal based onLinear Mean-Median Filter

Fitri Utaminingrum, Keiichi Uchimura and Gou KoutakiComputer Science and Electrical Engineering

Graduate School of Science and Technology, Kumamoto University2-39-1 Kurokami Kumamoto, 860-8555 JapanEmail: f3-ningrum@navi.cs.kumamoto-u.ac.jp

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Abstract-This paper presents Linear Mean-Median (LMM)filter that used to reduce impulse noise. LMM filter is a combi­nation between Mean and Median filter. Wherein, linear valueis acquired from the linearity between mean and median value.Mean and Median filter are only applied for free-noise pixel onthe 3x3 windows that has been sorted from the smallest to thelargest value. The mean value is obtained from the average valueof all free-noise pixels without including the median pixel position.Meanwhile, median pixel is the middle position of the pixel thathas been sorted. LMM uses nine sample pixels to determine apixel for replacement a corrupted pixel. Our filter also providesthe impulse noise prediction systems that serve as a facilitator togive information about noise content. If the noise is greater than30%, the performance of LMM filter needs to be improved byan adaptive rank order mean filters. The filtering results haveshown satisfactory results in terms of the quality result and thecomputation time process. A good image quality can be evidencedby PSNR (Peak Signal to Noise Ratio). Our methods always havehigher PSNR value than the comparison methods. In addition,the speed computation time of our method is faster than thecomparison method.

I. INTRODUCTION

Original image data can also corrupted by noise on theimage. Many different types of noise causes the damage in thedigital image, one of them is impulse noise. Impulse noise alsoknown as salt-and-pepper noise, which appears in the imageas a dark and bright spots spread on the image that can disturbthe quality of digital images. Important information must bemaintained in the image.

The main purpose of our research is to get a good quality ofimpulsive noise filter. Many cases need to be attention includeas follows:

1) The visual of filtering result must be smooth.2) The filtering process is conducted especially on the

noisy pixel, without engaging the important pixel thatis indicated as original pixel.

3) The filtering process to obtain fast computation time.

Noise removal especially to reduce impulse noise is oftenrequired in the digital image processing. In previous research,the linear and non-linear filtering methods have been proposedto remove impulse noise, however the performance filter oftenobtains the blurred image and disappearance the importantinformation details.

The classical method to reduce impulse noise removal is aStandard Median Filter (SMF) [1], [2]. SMF is also often used

978-1 -4673 -5621 -3/13/$31.00 02013 IEEE

in the filtering process, however it has infirmity on the highimpulse noise content, this caused it doesn't have the capabilityto remove high noise content. Wherein, its only optimal toreduce small noise content. K. S. Srinivasan et al [3] proposeA new decision-based algorithm, unlike other nonlinear filters,it removes only corrupted pixel by the median value or byits neighboring pixel value. His method shows significantlybetter image quality than a Standard Median Filter. The nextstudies were also developed Median Filter theories conductedby Fabijanska [4]. His research introduces a switching filterwhich identifies the noisy pixels and then corrects them byusing Median Filter. Hybrid model combination from fourthorder PDE and relaxed median filter is proposed by Jeny Rajanet al [5].

A detail preserving filter for impulse noise removal basedon the soft-switching median filter is proposed by Dagao Duanet al [6] where impulse noise candidates are detected by arrang­ing the pixels in order in the sliding window. TVL1 methodfor impulse noise removal is proposed by Junfeng Yang etal [7] which minimize the sum of a multichannel extensionof total variation (TV), either isotropic or anisotropic, anda data fidelity term measured in the L1-norm. Krishna KantSingh [8], his research is focused on an edge preserving filterfor removal of impulse noise. The noisy pixel is replacedwith a pixel from its neighborhood which is nearest to theadaptive median of the noisy pixel. FMLAWK (Fuzzy MeanLinear Aliasing Window Kernel) Filter is a spatial filter, whichcombines fuzzy method and Linear Aliasing Filter (LAF) [9].The weakness on FMLAWK, it has many filtering steps thatinfluence on the length of computation time. To overcomethe previous drawbacks, we propose a new method not onlypay attention on the quality of filtering result, but also on thecomputation time problem. Our new method is Linear Mean­Median (LMM) Filter that obtained from the linearity betweenMean and Median value.

The structure of our paper is organized as follows: In sec­tion 2 presents the basic theory of impulse noise. The filteringmethod of LMM filter is discussed in Section 3. In Section 4,we present simulation result and analysis, that are contains ofseveral experimental results. Some final conclusions are writtenin Section 5.

II. IMPULSE NOISE

The common problem often interferes with the image pro­cessing is impulse noise [10]. Impulse noise is an interferenceinformation pixel which result the black and white dots are

The 19th Korea -Japan Joint Workshop on Frontiers of Computer Vision

Fig. 1. Diagram block filtering system

spread evenly distributed on the image. This type of noise canbe caused by analog-to-digital converter errors, bit errors intransmission, etc [11], [12].

Salt-and-pepper impulse noise model, if data pixel corrup­tion has two fixed extreme values, 0 and 255 (for gray levelimage 8 bits). The probability density function for salt-and­pepper impulse noise models can be written as (1) [13].

{

P/ 2 for x=Of(x) == 1 - P for x=Sxy

p/2 for x=255

Denoted:f(x) is the probability density functionp is noise densitySxy is intensity value of image pixels at coordinate (x, y)x is noisy pixel.

III. PROPOSED METHOD

(1)

Figure 1 shows Diagram block filtering system consist ofImpulse noise prediction, noise detector, Pre-filtering usingLMM, two Rank Order Mean Filter and pixel reconstruction.The detail Information in every block is explained on thefollowing subsections.

Fig. 2. Six possibilities position of free-noise pixel.

A. Impulse Noise Density Prediction

Density Impulse Noise Prediction (p) is amount of noisewhich mixes on the original image (f (x, y)), that expressed inpercent (%).The p data is used to determine the options. Theoutput options of the pre-filtering should be forwarded to thepixel reconstruction or the output of the pre-filtering should beplaced into ROM-lor ROM-2. If P value is equal less than30% (fJ ::; 30%), the output of pre-filtering is forwarded tothe pixel reconstruction. If p value is higher than 70 (p 2:70%) then the output pre-filtering is entered on the ROM-I.Meanwhile, If p on the density range (30% < p < 70%) sothe output pre-filtering is entered on the ROM-2. We predictthe density of impulse noise by:

1) We make 2D index matrix fd(x, y) with elementvalue 0 or 1. The reference of f d(x, y) matrix isthe corrupted image fn(x, y). Determining the valueof index 0 or 1 in each element matrix f d(x, y) isspecified by:

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• If the f n(x, y) matrix element is the origi­nal pixel element, then f d(x, y) element isreplaced by O.

• If the f n(x, y) element matrix is impulsenoise, then f d(x, y) elements matrix is re­placed by 1.

The mathematical formulation can be written as (2).

fd(x, y) == {Ol if fn(x, y) = 0 or 255 (2)if other

Denoted:f n(x, y) is the corrupted image at coordinate (x, y)f d(x, y) is index matrix 2D at the coordinate (x, y)

2) The percentage of the impulse noise prediction isobtained by calculating percentage of the average

The 19th Korea-Japan Joint Workshop on Frontiers of Computer Vision

No Impulse Noise Impulse Noise Absolute ErrorDensity (p in %) Prediction (f> in %) (AE) in %

I 10 10.0796 0.79602 20 19.9852 0.07403 30 30.0350 0.11674 40 39.9986 0.00355 50 49.9374 0.12526 60 59.9686 0.05237 70 69.8959 0.14878 80 80.0278 0.03479 90 90.0162 0.0180

value of fd(x,y) uses (3):

1 N M

i > NMLLfd(x,y) x 100% (3)x=ly=l

Denoted:p is the percentage of impulse noise predictionfd(X, y) is index matrix 2D at coordinate (x, y)N is the total of rowM is the total of column

TABLE I. TESTING RESULT OF NOISE PREDICTION

B. Noise Detector

Noise detector serves to detect the matrix elements offn(x, y) is the noisy pixel or not. Indications elements matrixof fn(x, y) containing of noise if fn(x, y) '" [0,255]. If thematrix element fn(x, y) is the noise, its data filtered by pre­filtering. Meanwhile, if the element of fn(x, y) is free-noise,then the pixel is forwarded on the reconstruction part.

with the median value of free-noise pixels. Meanwhile, themathematical formulation to get the average free-noise valuewithout Crelement is obtained as (5)

(5)

C. Pre-filtering (6)

Denoted:C f is median value from free-noise pixelst is rounding upN f is the number of free-noise pixelW f is the sample element data of free-noise pixels that hasbeen sorted

The mathematical formulation to calculate pre-filteringprocess Pf(x, y) uses (5) and (6). Pre-filtering value in (6)is obtained by calculating the linearity value between the av­erage free-noise values without Cf-element on its calculation,

(7)if noise pixelif free noise pixel

D. Rank Ordered Mean (ROM) Filter

Rank Order Mean (ROM) filter serves to improve thequality of Pre-filtering process especially on the high corruptednoise. ROM is applied in the noise density (p) greater than30%. The filtering system in Fig. I provides two ROM. Both ofROM uses the 3x3 window size. ROM-I took the average valuefrom seven pixels data on the median position. MeanwhileROM-2, the averaging value is taken from three data pixels onthe median position. As shown on the Block Diagram in Fig.l,ROM-I only works on (fj> 70%)). Whilst, ROM-2 work onnoise density in the range (30% < P~ 70%).

The last stage of the filtering process in this system isthe pixel reconstruction. Pixel reconstruction is the placementprocess of free-noise pixel and the pixel that has been filteredon each coordinate. The output of this stage is fo(x, y). TheMathematical formulation to illustrate this process is writtenas (7).

Denoted:fo(x, y) is the final output filterio(x, y) is the noise pixel that has been filteredfn(x, y) is the pixel is indicated as the free-noise pixel

E. Pixel Reconstruction

Denoted:mf is the average value of free-noise on the wf withoutincluding of C f elementCf is median value from free-noise pixelwf is sample element data of free-noise pixels that has beensortedn is the number of W f elements reduced by an amount of CfelementsPf(x, y) is pre-filtering

(4)if Nf is oddif Nf is even

Before the filtering process is conducted, we set the valueof each element noise, where "salt or 255" on be replacedby "0". So that, fn(x, y) only has one noise model, that is"pepper or 0". This is very useful in the filtering process,especially for our filter design. We design pre-filter by LinearFilter (LF). Linear Filter (LF) is designed from the blendbetween of the median and the average values on the free­noise pixels. Furthermore, we call this filter by Linear Mean­Median (LMM) filter. In LMM is using 3x3 windows. Wedecided to use the 3x3 window size in our research paper,because based on our experiment, the 3x3 window size is themost ideal window size. Selection of the 3x3 window size isintended for obtaining a better computation time. In here, ifthe window size is greater than 3x3, it will give impact in themathematical calculations also be getting longer. In other hand,it will effect in the resulting of the computational time whichneeds a long time process. Matrix element of the 3x3 windowshould be sorted which starting from the smallest value to thelargest value. Figure 2 shows six possibilities position of noisepixel, free-noise pixel and the median value.

Observation on Fig.2, the median value of the free-noisehas two possibilities (one pixel data or between two pixels). Ifthe median value of the free-noise is between two pixels, thentake the average value of both its pixels. The mathematicalformulation of the median value of the free-noise (Cf) can bewritten as (4):

{Wf (t Nf )

C = N 2 Nf Wf(-f) +wf(-f +1)

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The 19th Korea -Japan Joint Workshop on Frontiers of Computer Vision

Fig. 3. Lena image filtering result for impulse noise density (p= 50%)

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The 19th Korea -Japan Joint Workshop on Frontiers of Computer Vision

Fig. 4. Barbara image filtering result for impulse noise density (p= 80%)

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The 19th Korea -Japan Joint Workshop on Frontiers of Computer Vision

TABLE II. COMPARISON RESULT OF PSNR VALUE (DECIBEL) IN THE LENA AND BARBARA IMAGES GRAY COLOR

Methods Noise density (P) in % for Lena Image Noise density (P) in % for Barbara Image10 20 30 40 50 60 70 80 90 10 20 30 40 50 60 70 80 90

Hybrid 22.29 20.78 19.76 18.96 18.36 17.65 16.86 15.54 14.34 20.36 19.23 18.50 17.91 17.39 16.71 15.95 14.86 13.54TVL1 28.64 28.57 28.61 28.48 28.34 27.63 26.16 24.89 21.38 23.15 23.14 23.15 23.13 23.08 22.92 22.40 21.67 19.44DPF 36.24 34.17 32.05 29.05 24.42 19.37 15.17 11.45 8.97 28.75 25.94 24.37 23.32 22.62 22.08 21.56 20.96 19.97

ASMBF 38.05 35.56 32.18 30.33 27.35 22.44 17.27 11.81 8.02 26.28 25.24 24.36 23.17 21.09 17.80 14.21 11.14 8.70DBA 41.48 37.27 34.47 31.87 29.80 27.64 25.30 22.84 19.42 32.13 28.67 26.48 25.65 23.88 20.66 16.07 11.64 7.84NEPF 34.01 31.08 29.58 28.73 28.04 27.62 27.04 26.15 23.73 32.83 29.44 27.26 25.63 24.19 22.85 21.37 19.81 17.21

FMLAWK 41.72 38.08 36.34 34.51 32.94 31.10 29.30 26.67 23.34 33.56 30.45 28.62 27.20 26.02 24.92 23.85 22.57 20.48Our Method 42.93 39.38 37.11 34.97 33.34 31.37 29.41 26.77 23.75 33.81 30.52 28.62 27.21 26.02 24.94 23.88 22.83 20.88

TABLE III. COMPARISON OF COMPUTATION TIME (SECONDS) IN THE LENA AND BARBARA IMAGES GRAY COLOR

Methods Noise density (P) in % for Lena Image Noise density (P) in % for Barbara Image10 20 30 40 50 60 70 80 90 10 20 30 40 50 60 70 80 90

Hybrid 8.33 16.44 24.56 32.86 41.23 49.51 57.89 65.94 74.06 8.33 16.64 25.02 33.20 41.95 50.44 58.39 66.69 75.64TVL1 33.78 33.14 30.83 30.16 30.20 28.81 31.20 40.38 62.53 35.83 35.09 32.06 31.55 31.59 30.28 33.30 42.22 69.58NEPF 2.73 3.89 5.02 6.16 7.33 8.58 9.61 10.91 12.39 3.11 3.06 3.08 3.17 3.14 3.14 3.11 3.20 3.13DPF 2.875 3.28 3.75 4.27 4.75 5.14 5.44 5.63 5.73 2.83 4.00 5.06 6.23 7.41 8.58 9.70 11.00 12.52

ASMBF 2.28 3.69 5.08 7.12 8.69 10.11 11.67 13.19 14.70 3.08 3.44 3.91 4.36 4.86 5.25 5.58 5.73 5.80DBA 3.19 3.05 3.09 3.02 3.05 3.13 3.08 3.08 3.11 2.33 3.75 5.22 7.17 8.70 10.30 11.80 13.38 14.89

FMLAWK 3.11 5.88 8.86 11.67 14.5 17.53 20.25 23.39 26.39 3.08 6.00 8.91 11.81 14.73 17.67 20.56 23.50 26.41Our Method 1.12 1.14 1.17 1.23 1.30 1.36 1.41 1.45 1.50 1.11 1.19 1.20 1.31 1.34 1.41 1.47 1.52 1.53

IV. SIMULATION RESULT AND ANALYSIS

Denoted:p is impulse noise prediction(%) p is the actual value of impulse noise (%)AEp is Absolute error of pAEp is average of absolute error of pn is total data sample.

Different noise contents and different image sample areconducted to evaluate performance of our proposed method.Performance filter is analysed by qualitative and quantitativeparameters. Qualitative parameter is conducted by visual ob­servation. Meanwhile, quantitative parameter is conducted by

We use Lena and Barbara images gray color (8 bits) withthe size (512x512) to test the simulation result. Specificationscomputer are CPU 1.86 GHz and RAM 2 GB that have beenused for testing the performance of our filtering result.

In this section illustrates the result of our filter method.Initial testing has been conducted by measuring the noiseprediction as shown in Table I. Table I shows the calculationof noise prediction which contained in the f n(x, y). The testresults indicate the noise prediction has been working well.Wherein, the value of impulse noise prediction (jJ in %) wasapproaching the actual value of impulse noise (p in %). Thiscase means our prediction noise relatively has high accuracy,that proven it has small error value as shown in Table I. Basedon the Table I, we got the average value of percentage errorfrom nine data samples is 0.152%.

Furthermore, to measure percentage of error in the noiseprediction can be calculated by using (8). Meanwhile theaverage of percentage error can be calculated as (9).

AEj! = Ip - pi x 100%p

__ 1 nAEp == - 2:: AEp(i )

ni=l

(8)

(9)

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PSNR (Peak Signal to Noise Ratio) calculation and com­putation time. Both of them commonly used to measurequantitative performance of digital filter.

2552NM

PSNR==10log10 M N 2 (10)~y=l ~x=l (f(x, y) - fo(x, y))

Denoted:PSNR is Peak Signal to Noise RatioN is the total of rowM is the total of columnf (x, y) is the original image dataf o(x, y) is the final output image filtering data

The PSNR often used as a measurement of the reconstruc­tion quality. The high PSNR value, the filtering reconstructionquality has good performance and vice versa. In our researchpaper to calculate PSNR value uses (10). Table II shows thecomparison PSNR result in many filtering methods which areour proposed method, Decision-based Algorithm (DBA) [3],Adaptive Switching Median Based Filter (ASMBF) [4], Hybridfilter [5], Detail Preserving Filter (DPF) [6], TVL-l [7], ANovel Edge Preserving Filter (NEPF) [8] and Fuzzy MeanLinear Aliasing Window Kernel (FMLAWK) [9].

Performance filter is tested in the several impulse noisedensities on the corrupted image, starting from noise densityp = 10% to p = 90%. The testing result shows our proposedmethod always has a consistency PSNR value greater thanthe several comparison methods. It is applicable in the allvariations of impulse noise density that ranging from p = 10%up to p = 90%. After we observe carefully PSNR results byusing Lena and Barbara images on the Table II. PSNR valuesalmost equal on FMLAWK [9] and our proposed methods.However our method is a little bit higher than FMLAWK [9].

The quantitative parameter in our research not only usesPSNR measurement but also measure the computation timeprocess. The fast computation time indicates that filtering pro­cess optimal in the time. Table III shows the numerical data ofcomputation time process on the different methods. The detailspecifications of our computer are CPU 1.86 GHz and RAM

The 19th Korea -Japan Joint Workshop on Frontiers of Computer Vision

2 GB. Moreover, the size of the digital image in the Barbaraand Lena images that has been used in this filtering process is512x512 data pixels. It can be concluded that our proposedmethod has a computation time faster than all comparisonmethods. The longest computation time process especially forsmall impulse nose density in the range(lO% ::; p ::; 30%) ison TVL1 methods. Meanwhile, for impulse noise density in therange (40% ::; p ::; 90%), the longest computation time is onHybrid methods. This applies in the both types of images (Lenaand Barbara). Our method in many variation of impulse noisedensities have faster computation time than the all comparisonmethod.

We also consider using the Qualitative parameter to mea­sure our performance filters. Qualitative testing is performedby visual observation. However, it is not an easy thing espe­cially for images that have almost the same visually results.

Figure 3 presents visual simulation result impulse noisedensity (p=50%) by using Lena image. In here, Hybrid filteringresult has very rough texture. That causes difficult to knowthe important information on the image. While, on DPF andASMBF still have spread impulse noise on the filtering image.The texture was too expressly and a little bit roughly is shownon TVL1. Meanwhile, the quality filtering of DBA and NEPFare almost the same. If we look carefully, both of them havea little bit rough texture especially on edge region. FMLAWKand our proposed methods have smooth qualities. However,our method has superiority in terms of computation time.

Moreover, the image filtering result for impulse noisedensity (p=80%) by using Barbara image sample is presentedon Fig.4. In here Hybrid, DPF and ASMBF methods havea very rough texture, so the original image is difficult todetect. The recovery image is good enough on TVL1 method,however the filtering quality result is too blurry. Meanwhilein DBA method, Barbara image have visible, however thequality filtering result has very rough texture especially inedge location. Image details in DBA method are lost afterthe filtering process. Moreover NEPF, FMLAWK and ourproposed method have the quality of filtering result almostsimilar. However, if considered more carefully, our proposedmethod has a better quality result than NEPF and FMLAWKmethods. By visual observation, our method is smoother thanall the comparison method.

The qualitative and quantitative on our proposed methodin the overall analysis has a good quality filters compared tothe all comparison methods.

V. CONCLUSION

Our research paper presents impulse noise removal basedon the Linear Mean-Median filter. The linear value is measuredbetween mean and median values of the free-noise pixel thathave been able to reduce impulse noise in the several variationsof impulse noise density. Our methods attest that new filteringmethod has the capability to reduce impulse noise across invarying ranges of noise 10% up to 90% in generally well. Thesuccess of our method to reduce impulse noise is measured byQualitative and Quantitative parameters.

Qualitative parameter is conducted by visual observation.Meanwhile, quantitative parameter is conducted by calculation

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of PSNR (Peak Signal to Noise Ratio) and computation timemeasurement. Our method has higher value than all compar­ison method that indicates the filtering result almost closeto the original image quality. Moreover, our method has thecomputation time faster than the comparison methods. Overall,the qualitative or quantitative testing of our new method showssignificantly better image quality than DBA, Hybrid, TVL-1,DPF, ASMBF, NEPF and FMLAWK.

For next research, we will to apply and develop in the thesequence image filters to reduce impulse noise densities.

ACKNOWLEDGMENT

The authors would like to thank the Directorate General ofHigher Education Ministry of National Education (DGHE)ofIndonesia which providing scholarship.

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