edge preserving adaptive anisotropic diffusion filter approach for the suppression of impulse noise...

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EUE-51129; No. of Pages 11

Int. J. Electron. Commun. (AEÜ) xxx (2013) xxx– xxx

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International Journal of Electronics andCommunications (AEÜ)

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dge preserving adaptive anisotropic diffusion filter approach for theuppression of impulse noise in images

. Veerakumara,∗, S. Esakkirajanb, Ila Vennilac

Department of Electronics and Communication Engineering, PSG College of Technology, Peelamedu, Coimbatore 641004, IndiaDepartment of Instrumentation and Control Systems Engineering, PSG College of Technology, Peelamedu, Coimbatore 641004, IndiaDepartment of Electrical and Electronics Engineering, PSG College of Technology, Peelamedu, Coimbatore 641004, India

r t i c l e i n f o

rticle history:eceived 27 February 2013ccepted 29 November 2013

a b s t r a c t

This paper proposes a new anisotropic diffusion approach to remove the impulse noise and retain thefine details. The proposed approach contains two stages, the first stage detects the impulse noise, andthe second stage removes the noisy pixel and retains the fine details of the original image. The Laplacian

eywords:mpulse noiseiffusion filteringaplacian operatordge preservation

operator is used to fine-tune the image quality of the restored image in the anisotropic diffusion filter.The proposed approach is tested with PSNR, IEF, correlation factor, and NSER for different test imagesand the results are compared against existing algorithms. The simulation results show that the proposedapproach gives better results than the existing denoising algorithms.

Crown Copyright © 2013 Published by Elsevier GmbH. All rights reserved.

daptive anisotropic diffusion filter

. Introduction

Digital images are corrupted by impulse noise during imagecquisition, transmission and storage. The impulse noises areroadly classified into salt and pepper noise and random valued

mpulse noise (RVIN). Many algorithms have been proposed toemove the salt and pepper noise such as standard median fil-er (SMF), adaptive median filter (AMF), switching scheme, detailreservation algorithm (DPA), decision based algorithm (DBA),odified unsymmetric trimmed median filter (MDBUTMF) andodified switching bilateral filter (MSBF). The main challenges

n noise removal consist of removing the corrupted informationhile retaining the fine details of the original image. Median filter-

ng approach is predominantly adapted for impulse noise removal.he median filter is a function of non-linear operation. Hence, theedian filter has the capability to remove noise without blurring

dges [1,2]. The median filter performs well at low noise density;ut it fails at medium and high noise densities. To overcome thisrawback, the adaptive median filter is introduced; in this algo-ithm the selection of the neighborhood pixels is adaptive in nature.

Please cite this article in press as: Veerakumar T, et al. Edge preserving aimpulse noise in images. Int J Electron Commun (AEÜ) (2013), http://dx.do

ence, the AMF removes the salt and pepper noise at the sameime, introduces the streaking effect due to increase in the sizef the selected window at medium noise density. Many of the

∗ Corresponding author at: Department of Electronics and Communication Engi-eering, PSG College of Technology, Peelamedu, Coimbatore 641004, Tamil Nadu,

ndia. Tel.: +91 9976534050; fax: +91 422 2573833.E-mail address: [email protected] (T. Veerakumar).

434-8411/$ – see front matter. Crown Copyright © 2013 Published by Elsevier GmbH. Attp://dx.doi.org/10.1016/j.aeue.2013.11.008

switching schemes were proposed to overcome the drawback ofthe AMF algorithm; switching schemes first split the image pix-els into noisy and noise free pixels. After that the noisy pixels areprocessed with modified median filter and the noise free pixels areunchanged. Chan and Nikololova proposed a two-phase algorithm[3]. In the first phase, the adaptive median filter is used to classifynoisy and noise free pixels; in second phase, specialized regular-ization method is applied to the noisy pixels to preserve the edgesand noise suppression. The main drawback of this algorithm is thatthe processing time is very huge because it uses a very large win-dow size of 39 × 39 in both phases to obtain restored output. In[4], Srinivasan and Ebenezer proposed a sorting based algorithmin which the noisy pixels are replaced by either median value orthe previous resultant value. At high noise densities this approachdoes not protect edge and fine details adequately. The algorithmreplaces the noisy pixel when all the neighborhood pixels are noisyby the previous result; which introduces the streaking effect in thedenoised image. In [5], Esakkirajan et al. proposed the MDBUTMFalgorithm removes the noisy pixel by the use of unsymmetrictrimmed median filter and mean filter. If all the neighborhood pix-els of the processing pixel are noisy, then the noisy pixel is replacedby the mean value of the selected window. But the entire neighbor-hood pixels are only either ‘0 s’ or ‘255 s’, then the replacement pixelalso noisy (which is either 0 or 255). This algorithm focuses only onto remove the noisy pixel does not concentrate on the detail preser-

daptive anisotropic diffusion filter approach for the suppression ofi.org/10.1016/j.aeue.2013.11.008

vation. This drawback is addressed in modified switching bilateralfilter (MSBF) [6], in which the noisy pixels are processed with themodified bilateral filter. To improve the fine details of the restoredimage, use of adaptive anisotropic diffusion filter is proposed in this

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dx.doi.org/10.1016/j.aeue.2013.11.008

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aper. The anisotropic diffusion filter performs well for the additivend speckle noise removal. Mostly non-linear filters like median fil-er and its variants are commonly employed to minimize the impactf salt and pepper noise in the image. In this work, an attempt isade to minimize the impact of salt and pepper noise in the image

sing adaptive anisotropic diffusion filter. Here an attempt is madeo preserve the edges by using adaptive directional filters. This worklaims the filters to be adaptive because the directionality dependsn the spatial location of the noise free pixels.

The paper organized as follows: Section 2 explains the basic ideabout the impulse noise and anisotropic diffusion filter. The pro-osed algorithm is described in Section 3. The simulation results ofhe proposed algorithm are given in Section 4. Finally, conclusionsre given in Section 5.

. Review of impulse noise and anisotropic diffusion filter

.1. Salt and pepper noise model

a) The salt and pepper impulse noise model is given by

(m, n) =

⎧⎪⎨⎪⎩

Lmin, with probability p

Lmax, with probability q

I(m, n), with probability r

(1)

here I denotes noise free pixels, r = 1 − (p + q). p + q is the noiseevel. Lmin is minimum gray value in an image. Lmax is the maximumray value in an image. y(m,n) is the noisy image.

b) Random valued impulse noise

The impulse noise takes the values between 0 and 255 in a graycale image. Hence, the detection of noise pixel is very difficult.his paper addresses the minimization of implulse noise along withhe preservation of edge details in an image. Noise detection isone using the Rank Ordered Logarithmic Difference (ROLD) [7],he noisy pixels are processed by the adaptive anisotropic diffu-ion filter, which retains the fine details of the images. The ROLD ishe logarithmic function on the absolute difference, which is givenn Eq. (2)

Dst(y(m, n)) = loga|y(m + s, n + t) − y(m, n)| ∀(s, t) ∈ W (2)

here W is the selected neighborhood window. Here a > 1, the num-er LDst is always in (−∞,0]. In order to keep it in the dynamic range0,1], the truncation and a linear transformation is used and the Eq.2) is modified as

D′st(y(m, n)) = 1 + max{loga|y(m + s, n + t) − y(m, n)|, −b}

b, ∀(s, t) ∈ W (3)

here a and b are positive values. The value of a controls the shapef the curves of the logarithmic function and the value of b decideshe truncation. The value of a and b are 2 and 5 respectively [7].

Arrange all LDst′ in an increasing order, and let Rk be the kth

mallest LDst′ for all (s,t) ∈ W. Now the local image statistic as

OLDm(y(m, n)) =m∑

k=1

Rk(y(m, n)) (4)

The noise detection is based on the ROLDm(y(m,n)) and a thresh-ld Th. A current processing pixel y(m,n) is detected as noisy if


OLDm(y(m,n)) > Th otherwise the current processing pixel is noiseree. The selection of threshold is given in [7].

c) Anisotropic diffusion filter

PRESSmun. (AEÜ) xxx (2013) xxx– xxx

Perona and Malik proposed a non-linear diffusion method [8] foravoiding the blurring and localization problems of linear diffusionfiltering. They applied an inhomogeneous process that reduces thediffusivity at those locations which have a larger likelihood to beedges. This likelihood is measured by Eq. (5).

yt = �.∇2y (5)

where yt is the first derivative of the image y in time t, �2 is theLaplacian operator with respect to space variables and � is the con-stant which is independent of space location. Perona and Malikmeasured the anisotropic diffusion equation as

yt = ∂y(m, n, t)∂t

= div(�(m, n, t) · ∇y(m, n, t)) (6)

yt = �(m, n, t)∇2y + ∇� · ∇y (7)

where div is the divergence and � is the gradient operator withspace variables. By taking �(m,n,t) be a constant, (6) reduces to (5),the isotropic diffusion equation. Perona and Malik considered theimage gradient as an estimation of edges and E(�y), in which E(·)has to be a non-negative monotonically decreasing function withE(0) = 1 and tends to zero at infinity. There are some possible choicesfor E(·), the obvious being a binary valued function [9]. Some otherfunctions could be:

E(s) = exp

[−|s|2

k2

]

It can also be given as

E(s) = 1

1 + [|s|/k]2

where k is the threshold value, this threshold value plays animportant role in removing the noise in an image. Eq. (7) can bediscretized using four nearest neighbors (north (N), south (S), east(E), west (W)) [10] and the Laplacian operator [11] and it is givenby

yi+1(m, n)

= yi(m, n) + �[(�N∇N y(m, n) + �S∇Sy(m, n) + �W ∇W y(m, n) + �E∇Ey(m, n))]2

where yi+1(m, n) is the discrete value of y(m,n) in the (i + 1)th iter-ation which is set by i as y is determined by t in continuous space.The expression for different terms in yi+1(m, n) are given below:

�N = U(∣∣∇Ny(m, n)

∣∣)∇Ny(m, n) = y(m − 1, n) − y(m, n)

�S = U(∣∣∇Sy(m, n)

∣∣)∇Sy(m, n) = y(m + 1, n) − y(m, n)

�W = U(∣∣∇W y(m, n)

∣∣)∇W y(m, n) = y(m, n − 1) − y(m, n)

�E = U(∣∣∇Ey(m, n)

∣∣)


∇Ey(m, n) = y(m, n + 1) − y(m, n)

and � is the stability factor. The filtered image is y(m, n)= yi+1(m, n).

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AEUE-51129; No. of Pages 11

T. Veerakumar et al. / Int. J. Electron. Commun. (AEÜ) xxx (2013) xxx– xxx 3

Inpu t noisy image

y(m, n) > 0YES NO

Sele ct 2D 3 x 3 window neig hborhoo d pixels of y(m, n)

All theneig hborhoo d pixels are

‘0’ YES

Incre ase the window size 5 x 5

NO

Remov e 0s in the selected neig hborhoo d pixels

Mean filter

Apply Adaptive Anisotropic Diffusion Filter

Denoised i mage

Apply ROLD approa ch to detect the noisy pixel (‘0 ’), otherwise noise free (‘1 ’)

Binary matrix is multiply with the noisy image

3

rsaiita‘pfpaulth

3

ra

(a) hN (b) hS (c) hE (d) hW

000010010

010010000

000110000

000011000

000010100

100010000

001010000

000010001

M−1m=0

N−1n=0 (I(m, n) − y(m, n))2

Fig. 1. Flowchart of the proposed algorithm.

. Proposed algorithm

The anisotropic diffusion approach cannot be directly used foremoval for impulse noise. The anisotropic diffusion approachhould be modified for the removal of impulse noise in images. Thedaptive anisotropic diffusion filter for the impulse noise removals as follows: the first step of the proposed algorithm identifies thempulse noise in the image. The noisy and noise free pixels are iden-ified by checking the pixel element value against the maximumnd minimum gray value in image. If the processing pixel other than

0’ or ‘255’, then the pixel is noise free. Otherwise the processingixel is noisy, which is processed by the adaptive anisotropic dif-usion filter. In the case of random valued impulse noise the noisyixels are detected by the ROLD approach. The flow chart of thedaptive anisotropic diffusion filter is shown in Fig. 1. From the fig-re, it is obvious that the direction of the gradient depends on the

ocation of the noise free pixels. The diffusion function processeshe output of the gradient operator. Hence, the proposed algorithmas the ability to preserve edges and fine details in the image.

.1. Illustration of adaptive anisotropic diffusion filter


Every pixel in the input image is checked for the occurrence ofandom valued impulse noise and the different cases are illustrateds follows:

(e) hNE (f) hSE (g) hSW (h) hNW

Fig. 2. 2D convolution masks.

Case (i): The processing pixel y(m,n) is a noise free pixel, then theprocessing pixel y(m,n) is retained as it is.Case (ii): The processing pixel y(m,n) is a noisy pixel, and not all thepixels of the neighborhoods are noisy, then the processing pixelis processed by the adaptive anisotropic diffusion filter. The 2Dconvolution mask of the anisotropic diffusion filter is shown inFig. 2, which is edge identification filter.

The process of adaptive anisotropic diffusion filter is shown inFig. 3. The result of the discrete partial differential equation (PDE)replaces the noisy pixel.Case (iii): The processing pixel y(m,n) is a noisy pixel and all theneighborhood pixels are also noisy, then the processing pixel isreplaced by the mean value of the neighborhood pixels with thewindow size 5 × 5.

4. Simulation results and discussion

The proposed algorithm is tested with the different test imageslike Airplane, Bridge, Lena and Barbara images. The test images con-sidered in this work has both low and high frequency content. Ifthe proposed algorithm works well for these set of test images,definitely it will perform well for different set of natural images.The noise density is varied from 10% to 96% for salt and peppernoise and 40% and 60% for random valued impulse noise. The sim-ulation is carried out in MATLAB 7.0.1 environment with PentiumIV-3.0 GHz with 1 GB of RAM. The performance measures of theproposed algorithm are peak signal to noise ratio (PSNR), imageenhancement factor (IEF), correlation factor (CF) and MSSIM. ThePSNR value in dB [12] is calculated as

PSNR = 10 log10

[(2b − 1)

2

(1/MN)∑M−1

m=0

∑N−1n=0 (I(m, n) − y(m, n))2

](5′)

where ‘b’ is the maximum bit rate of the gray scale image, MN is thesize of the input image, I denotes the original image and y representsthe denoised image.

The PSNR value of the proposed algorithm is compared againstthe existing algorithm for different noise densities for Airplaneimage and the obtained results are given in Table 1. From the table,it is evident that the proposed algorithm gives much better PSNRvalue than the state of art denoising algorithms. Number of iter-ations for the diffusion filtering is chosen as 20, the value of ‘k’ isselected as 10 and the value of ‘�’ is 0.1.

The smoothness of the denoised image is obtained from theimage enhancement factor. The IEF value [13] is calculated as

IEF =∑M−1

m=0

∑N−1n=0 (y(m, n) − y(m, n))2∑ ∑ (6′)


The IEF values of the proposed and existing algorithms for Air-plane image are given in Table 2. From the table, the IEF values of

dx.doi.org/10.1016/j.aeue.2013.11.008



4 T. Veerakumar et al. / Int. J. Electron. Commun. (AEÜ) xxx (2013) xxx– xxx

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[][]135130[][]129130128

[][]135130]4.130[[]129130128Noise trimming

filterLocal mean

filter

[][]135130]4.130[[]129130128

000010001

000010010

000010100

000110000

1010000

Edge extraction

),( nmyNW

),( nmyN

),( nmyNE

),( nmyE

),( nmySW

Diffusion

function

Discrete PDE

isotro

ta

atcbroa

R

aimTi

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proposed algorithm, it obvious that the edge preservation of theproposed algorithm much better than the existing algorithms.

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1Correlation Factor Vs Noise Denstiy

Cor

rela

tion

Fact

or

SMFAMFDBAMDBUTMFDPRMSBFAD

Fig. 3. Adaptive an

he proposed algorithm are far better than the existing algorithmst both medium and high noise densities.

The correlation factor gives the similarity between the originalnd denoised image. If the correlation factor is 1, then it indicateshe original and denoised image is 100% perfectly matched. If theorrelation factor is zero; then it indicates that there is no similarityetween the original and denoised images (totally mismatch). Cor-elation factor of −1 indicates the denoised image is the negativef the original image. The correlation factor (R) [14–16] is defineds

=∑M−1

m=0

∑N−1n=0 (y(m, n) − ¯y)(I(m, n) − I)√(∑M−1

m=0

∑N−1n=0 (y(m, n) − ¯y)

2) (∑M−1

m=0

∑N−1n=0 (I(m, n) − I)

2)

(7′)

The correlation factor of the proposed and existing denoisinglgorithms for Airplane image is shown in Fig. 4. From the figure,t obvious that the correlation factor of the proposed algorithm is

uch better than the correlation factor of the existing algorithms.his indicates that the proposed algorithm results in a denoisedmage which closely resembles the original image.

The denoised image obtained using the proposed algorithm andxisting algorithms is given in Fig. 5. The denoised image usinghe proposed algorithm not only removes the noisy pixels, but alsoetains the fine details of the Airplane image.

The non-shift edge based ratio (NSER) [17] can be used to mea-ure the variation of the number of edge points in the referencemage and processed image. The NSER is defined as

N∑


SER(I, y) = −i=1

log10(1 − pi) (8)

here pi = ||EIi ∩ Eyi||/||EIi ||, here EIi and Eyi

are the edge maps ofeference and processed images on scale i [17] respectively.

00

pic diffusion filter.

The proposed algorithm is also tested with Bridge image andthe PSNR value of the different denoising algorithms is shown inFig. 6. From the figure, it is possible to observe that the PSNR valueof the proposed algorithm is than the existing algorithms. The cor-relation factor of the proposed and existing algorithms for Bridgeimage is given in Table 3. It shows that the correlation factor of theproposed algorithm is much better than the correlation factor ofthe existing algorithms. From the higher correlation factor of the


0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

Noise Density in %

Proposed

Fig. 4. Correlation factor plot for airplane image.

dx.doi.org/10.1016/j.aeue.2013.11.008




Table 1PSNR values for airplane image.

Noise density in % PSNR in dB

SMF AMF DBA [4] MDBUTMF [5] MSBF [6] AD [7] DPR [3] Proposed

10 31.8886 24.6759 40.3201 42.0623 42.6394 19.3079 42.2432 42.977620 27.6101 24.5835 36.2623 38.2237 39.2295 16.2546 39.0236 39.728930 22.9402 24.4224 33.3699 35.4408 36.7425 14.2905 36.4578 37.285140 18.5381 23.9319 31.1384 32.8906 34.6171 12.7344 34.0624 35.334950 14.8281 22.1768 28.5660 30.3410 32.2875 11.3588 31.7951 32.861160 12.0385 18.8902 26.3777 28.0427 30.3321 10.2365 30.0214 30.989670 9.7168 15.0005 23.8267 25.4693 27.9407 9.2246 27.6742 28.419580 7.8221 11.2210 21.3910 22.3981 25.2108 8.2818 25.0324 25.972690 6.3553 7.9639 18.4664 18.7879 22.0345 7.4453 21.8621 22.7265

17.7616.8015.88

auia

92 6.1074 7.3565 17.699894 5.8472 6.7923 16.398296 5.5787 6.2315 15.4933

The image details of the denoised image using the proposed


lgorithm and existing algorithms is given in Fig. 7. From the fig-re, it is evident that the image detail preservation of the denoised

mage using the proposed algorithm is far better than the existinglgorithms.

Fig. 5. Visual quality of t

57 20.9410 7.2909 20.6142 21.289572 19.9147 7.1181 19.6843 20.567992 19.0030 6.9534 18.5094 19.4342

The test images like Lena, Bridge and Baboon images are cor-


rupted by random valued impulse noise, which are processed withthe proposed algorithm, and the PSNR results are given in Table 4.From this table, the proposed algorithm gives better PSNR valuethan the existing algorithms.

he airplane image.

dx.doi.org/10.1016/j.aeue.2013.11.008





0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 15

10

15

20

25

30

35

40PSNR Vs Noise Denstiy

Noise Density in %

PSN

R in

dB

SMFAMFDBAMDBUTMFDPRMSBFADProposed

Fig. 6. PSNR plot for bridge image.

Fig. 7. Image details of

Fig. 8. NSER values for baboon image (RVIN).

The NSER result for the Baboon image is shown in Fig. 8. Fromthe figure, it is evident that the proposed algorithm outperforms


the existing algorithms. The image detail of the denoised image isretained by the proposed algorithm with the stability factor (�).

The NSER value of the test images for the different denoisingalgorithms is given in Table 5. From the table, it is evident that

the bridge image.

dx.doi.org/10.1016/j.aeue.2013.11.008




Table 2IEF values for airplane image.

Noise density in % Image enhancement factor


10 46.7837 8.9001 326.0200 486.9358 556.1256 2.5824 510.4273 576.632420 35.1080 17.4790 257.4078 404.3505 509.7321 2.5695 482.5640 532.135230 17.7788 24.9888 196.2765 316.2022 426.7117 2.4262 408.2347 440.532740 8.5638 29.6553 155.8465 233.3009 347.1892 2.2506 334.9821 369.257350 4.6028 24.9836 108.8471 163.8004 256.4296 2.0706 241.3760 281.965760 2.9002 14.0399 78.7684 115.5724 195.7911 1.9153 179.5014 217.223470 1.9795 6.6771 50.9986 74.4408 131.5087 1.7674 126.9104 159.951080 1.4668 3.2062 33.3641 42.0712 80.4012 1.6306 72.5319 102.321790 1.1758 1.7025 19.1183 20.5875 43.4776 1.5113 40.5271 67.477692 1.1339 1.5119 16.3618 16.6119 34.5103 1.4892 29.6549 34.495194 1.0929 1.3580 12.4074 13.6328 27.8823 1.4644 25.3406 30.657296 1.0516 1.2214 10.3111 11.2954 23.1353 1.4432 21.6014 23.8452

Table 3Correlation factor for bridge image.

Noise density in % PSNR in dB


10 0.9778 0.9179 0.9957 0.9973 0.9972 0.8511 0.9969 0.997820 0.9636 0.9156 0.9914 0.9939 0.9940 0.7385 0.9920 0.995130 0.9256 0.9126 0.9857 0.9896 0.9905 0.6149 0.9895 0.992040 0.8471 0.9080 0.9774 0.9834 0.9860 0.5027 0.9840 0.987850 0.7110 0.8895 0.9666 0.9752 0.9806 0.3877 0.9800 0.982560 0.5388 0.8228 0.9493 0.9613 0.9723 0.2841 0.9711 0.974570 0.3908 0.6890 0.9241 0.9408 0.9603 0.2063 0.9658 0.962480 0.2281 0.4664 0.8749 0.8958 0.9370 0.1210 0.9367 0.939290 0.1031 0.2312 0.7756 0.7930 0.8878 0.0554 0.8873 0.890092 0.0913 0.1886 0.7507 0.7540 0.8692 0.0485 0.8689 0.872494 0.0602 0.1344 0.7065 0.6966 0.8420 0.0315 0.8411 0.844096 0.0450 0.0898 0.6264 0.5599 0.8051 0.0227 0.8023 0.8066

Table 4PSNR value for random valued impulse noise removal.

Filters Lena Bridge Baboon

40% 60% 40% 60% 40% 60%

SMF 27.6104 21.5790 22.1016 19.3369 20.5531 19.3243PSMF [18] 28.6782 21.9734 22.5211 19.6440 20.8955 19.4579ACWM [19] 28.6260 21.1255 23.0074 19.1817 21.3980 19.4538PWMAD [20] 31.2745 24.2591 23.6167 20.2752 21.4045 19.8781ROAD [7] 31.9686 28.3658 23.8673 22.3005 20.9819 20.3375

24.3826.20

tvi

Bno

TN

ROLD [7] 32.9271 29.4012

Proposed 34.0125 31.1402

he NSER value of the proposed algorithm is better than the NSERalue of the existing algorithms. The salt and pepper noise densitys chosen as 90%.


The visual quality of the different denoising algorithms forarbara image is shown in Fig. 9. The 85% of salt and pepperoise density image is perfectly denoised and the fine detailsf the image are preserved by the proposed algorithm, which is

able 5SER measure of test images.

Test images Non-shift edge based ratio (NSER)

SMF AMF DBA [4] MDBUTM

Cameraman 0.3897 0.3718 0.3811 0.3793

Lena 0.3877 0.3716 0.3809 0.3725

Barbara 0.3823 0.3513 0.4030 0.3799

Goldhill 0.3808 0.3453 0.3942 0.3680

Livingroom 0.3914 0.3700 0.3987 0.3679

Baboon 0.3999 0.3887 0.4004 0.3675

Boat 0.3972 0.3819 0.3955 0.3644

18 22.5179 21.7162 20.307317 23.9648 22.8963 22.3018

indicated by Fig. 9. The proposed algorithm gives better imagequality measures like PSNR, IEF and correlation factor for the grayand color images. The proposed algorithm performs well even if


the image is corrupted by high density salt and pepper noise.The visual quality of the different denoising algorithms for

Baboon image is shown in Fig. 10. The random valued impulsenoise density is chosen as 40%. Form Fig. 10, it shows that the

F [5] MSBF [6] AD [7] DPR [3] Proposed

0.4065 0.3127 0.4326 0.47690.3845 0.3296 0.4144 0.47180.3982 0.3304 0.4111 0.46600.4002 0.3245 04124 0.46050.3936 0.3521 0.4049 0.46990.4062 0.3216 0.4132 0.47880.3937 0.3354 0.4233 0.4853

dx.doi.org/10.1016/j.aeue.2013.11.008

Please cite this article in press as: Veerakumar T, et al. Edge preserving adaptive anisotropic diffusion filter approach for the suppression ofimpulse noise in images. Int J Electron Commun (AEÜ) (2013), http://dx.doi.org/10.1016/j.aeue.2013.11.008




Table 6PSNR value for different test image at 85% salt and pepper noise density.

Images Stability factor (�)

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Cameraman 21.1154 21.0283 20.9113 20.7628 20.5731 20.4210 20.2301 20.0742 19.8420 19.6866Lena 25.0653 24.6674 24.2595 23.8573 23.4801 23.1176 22.7991 22.4603 22.1438 21.8465Barbara 22.4041 22.2112 22.0041 21.7805 21.5536 21.3359 21.1132 20.9076 20.7027 20.4791Goldhill 25.6611 25.4484 25.1432 24.7753 24.4030 23.9847 23.6267 23.2256 22.8815 22.5168Livingroom 23.4919 23.3139 23.0997 22.8780 22.6343 22.4045 22.1435 21.8772 21.6365 21.3590Baboon 22.5026 22.3672 22.2010 22.0125 21.8284 21.6242 21.4045 21.2006 20.9992 20.7913Boat 23.6525 23.5426 23.3720 23.1681 22.9264 22.6624 22.4191 22.1744 21.8902 21.6493Avg. PSNR 23.4133 23.2256 22.9987 22.7478 22.4856 22.2215 21.9623 21.7028 21.4423 21.1898

Fig. 9. Simulation results of Barbara image.

dx.doi.org/10.1016/j.aeue.2013.11.008




ults o

vt

Ttoa

TC

Fig. 10. Simulation res

isual quality of the proposed algorithm gives better results thanhe visual quality of the existing algorithms.

The image detail of the denoised Lena image is shown in Fig. 11.he random valued impulse noise is considered for the corrup-


ion and the noise density is 60%. The image detail preservationf the proposed algorithm is far better than the existing denoisinglgorithms.

able 7orrelation factor for different test image at 85% salt and pepper noise density.

Images Stability factor (�)

0.1 0.2 0.3 0.4 0.5

Cameraman 0.9339 0.9325 0.9305 0.9279 0.92Lena 0.9566 0.9523 0.9474 0.9422 0.93Barbara 0.9152 0.9112 0.9067 0.9016 0.89Goldhill 0.9625 0.9606 0.9577 0.9539 0.94Livingroom 0.9232 0.9198 0.9156 0.9110 0.90Baboon 0.8779 0.8738 0.8687 0.8626 0.85Boat 0.9472 0.9458 0.9436 0.9408 0.93Avg. CF 0.9309 0.9280 0.9243 0.9200 0.91

f RVIN baboon image.

4.1. Selection of stability factor (�)

The stability factor (�) is chosen as 0.1. The average PSNR val-ues for test images are corrupted by 85% noise density and the


results are given in Table 6. From this table, it is clear that theaverage PSNR value for the proposed algorithm is better at � = 0.1.Hence, in this work, the value of stability factor is chosen as 0.1. The

0.6 0.7 0.8 0.9 1

48 0.9219 0.9182 0.9149 0.9112 0.907261 0.9302 0.9245 0.9181 0.9123 0.905963 0.8908 0.8850 0.8795 0.8736 0.867198 0.9447 0.9400 0.9344 0.9291 0.923057 0.9005 0.8943 0.8876 0.8813 0.873765 0.8494 0.8415 0.8340 0.8263 0.818373 0.9332 0.9293 0.9251 0.9201 0.915552 0.9101 0.9047 0.8991 0.8934 0.8872

dx.doi.org/10.1016/j.aeue.2013.11.008




tails o

citb

5

tihubacsaaaop

Fig. 11. Image de

orrelation factor of the proposed algorithm for different testmages is given in Table 7. From the table, it is possible to observehat the average correlation factor of the proposed algorithm isetter at � = 0.1.

. Conclusion

In this paper, adaptive anisotropic diffusion filter is proposedo remove the impulse noise and retains the fine details of themages. The proposed algorithm performs well at low, medium,igh noise densities because of its edge-preserving nature. The sim-lation results reveal the fact that the proposed algorithm is muchetter than the existing denoising algorithms in both subjectivend objective quality measures. The correlation factor and NSER arehosen as the index for edge preservation. The experimental resultshow that the proposed algorithm gives higher correlation factornd NSER index than the existing denoising algorithms. Hence, this


pproach is suitable for removing impulse noise in the images. Suit-ble optimization technique can be used to get the optimum valuef the stability factor and the number of iterations for better edgereservation and noise removal.

[

[

f the Lena image.

References

[1] Hodgson R, Bailey D, Naylor M, Ng A, McNeil SJ. Properties, implementationsand applications of rank filters. Image and Vision Computing 1985;3:3.

[2] Cree M. Observations on adaptive vector filters for noise reduction in colorimages. IEEE Signal Processing Letters 2004;140(11):2.

[3] Chan RH, Ho CW, Nikolova M. Salt-and-pepper noise removal by median-type noise detectors and detail-preserving regularization. IEEE Transactionson Image Processing 2005;1479(14):10.

[4] Srinivasan KS, Ebenezer D. A new fast and efficient decision based algorithmfor removal of high-density impulse noises. IEEE Signal Processing Letters2007;189:14.

[5] Esakkirajan S, Veerakumar T, Subramanyam AN, PremChand CH. Removal ofhigh density salt and pepper noise through modified decision based unsym-metric trimmed median filter. IEEE Signal Processing Letters 2011;287:18.

[6] Veerakumar T, Esakkirajan S, Ila Vennila. High density impulse noise removalusing modified switching bilateral filter. International Journal of Circuits, Sys-tems and Signal Processing 2012;189:6.

[7] Dong Y, Chan RH, Xu S. A detection statistic for random-valued impulse noise.IEEE Transactions on Image Processing 2007;1112(16):4.

[8] Perona P, Malik J. Scale-space and edge detection using anisotropic dif-fusion. IEEE Transactions on Pattern Analysis and Machine Intelligence1990;629(12):7.

[9] Wang X. Lee filter for multiscale image denoising. In: Proceedings of interna-


tional conference on signal processing, vol. 1. 2006.10] Anil Kumar K [M.Tech thesis] Study of spatial and transform domain filters for

efficient noise reduction. Rourkela: National Institute of Technology; 2011.11] Sapiro G. Geometric partial differential equations and image analysis. New

York: Cambridge University Press; 2001. p. 223.

dx.doi.org/10.1016/j.aeue.2013.11.008

http://refhub.elsevier.com/S1434-8411(13)00293-8/sbref0005

















































































































































































































































ING

A

n. Com

[

[

[

[[

[

[

ARTICLE Model


T. Veerakumar et al. / Int. J. Electro

12] Gonzalez RC, Woods RE, Eddins SL. Digital image processing. Upper SaddleRiver: Prentice Hall; 2008.

13] Janaki SS, Ebenezer D. A blur reducing adaptive filter for the removal of mixednoise in images. In: Proceedings of advances in computer, information, andsystems sciences, and engineering. 2006. p. 25–9.


14] Rodgers JL, Nicewander WA. Thirteen ways to look at the correlation coefficient.American Statistician 1995;59:42.

15] James M. Pattern recognition. New York: John Wiley and Sons; 1988. p. 36–40.16] Press WH, Flannery BP, Teukolsky SA, Vetterling WT. Numerical recipes in

Pascal. New York: Cambridge University Press; 1989. p. 532–4.

[

[

PRESSmun. (AEÜ) xxx (2013) xxx– xxx 11

17] Zhang M, Mou X, Zhang L. Non-shift edge based ratio (NSER): an image qualityassessment metric based on early vision features. IEEE Signal Processing Letters2011;315:18.

18] Wang Z, Zhang D. Progressive switching median filter for the removal ofimpulse noise from highly corrupted images. IEEE Transactions on Circuits and


Systems II 1999;78:46.19] Chen T, Wu HR. Adaptive impulse detection using center-weighted median

filters. IEEE Signal Processing Letters 2001;1:8.20] Crnojevic′ V, Senk V, Trpovski Z. Advanced impulse detection based on pixel-

wise MAD. IEEE Signal Processing Letters 2004;592:11.

dx.doi.org/10.1016/j.aeue.2013.11.008






























































































































































































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