Adaptive Bi-Stage Median Filter for Images Corrupted by High Density Fixed- Value Impulse Noise

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1 Adaptive Bi-Stage Median Filter for Images Corrupted by High Density Fixed- Value Impulse Noise Eliahim Jeevaraj P S 1, Shanmugavadivu P 2 1 Department of Computer Science, Bishop Heber College, Tiruchirappalli 2 Department of Computer Science & Applications, Gandhigram Rural Institute (Deemed to be University), Gandhigram 1 eliahimps@gmail.com, 2 psvadivu@yahoo.com Abstract: This paper proposes Adaptive Bi-Stage Median Filter (ABSMF) to eliminate fixed-value impulse noises in the corrupted images. The denoising rate of the proposed filter as measured in terms of Peak Signal - to - Noise Ratio and human visual perception is proved to be efficient even on highly corrupted images with 90% of noise. Keywords: Image Restoration, Standard Median Filter, Highly Corrupted Image, Fixed - Value Impulse Noise. I. INTRODUCTION Image restoration is a vital pre-processing technique of eliminating noise from corrupted images whereas noise is an irrelevant/ unwanted information in the image that degrades the quality of an image. This technique especially focuses on restoring images, corrupted by noise/blur. The distribution of noises such as impulse noise, gaussian noise, poisson noise, thermal noise, speckle noise, exponential noise, uniform noise over an image can be modeled as a mathematical or statistical function [1]. Review of literature reveals the fact that non-linear noise filters are more efficient than linear filters with respect to noise elimination as well as edge/detail preservation. Linear filters like mean filter, by principle processes, each pixel in the corrupted image and invariably approximate both corrupted and uncorrupted pixels, despite their noise reduction potential, whereas non-linear filters like median filters promise better detail and edge preservation in the restored images [1], [2]. In this paper, a new adaptive median-based denoising filter, ABSMF is presented that performs noise suppression using the medians of the adjacent pixels and diagonal pixels and mean of those medians. The mathematical model of fixed-value impulse noise is given in section II and the principle of standard median filter is explained in section III. The quality metric, Peak Signal - to - Noise Ratio (PSNR) is described in section IV. The algorithmic description of ABSMF is detailed in section V. The results and discussion is presented in section VI and the conclusions in section VII. II. NOISE MODEL Impulse noise creeps into images during acquisition and transmission respectively due to the imperfections and/or limitations in capturing devices and transmission channels. Among the types of the impulse noises namely, fixed-value and random-value impulse noise, the former is often referred to as salt-and-pepper noise or binary noise. Fixed value impulse noise assumes either minimum or maximum intensity value of images and the percentage of noise distribution is evenly divided by those intensity values. Random value impulse noise arbitrarily assumes any value between the minimum and maximum intensity of the image [3] [4]. The probability density function of the impulsive noise is given as: p x p p 0 a b for for x a x b otherwise (1) If b>a, gray level b appears as white dot and conversely level a appears as black dot [5]. The probability distribution of fixed-value impulse noise is: 0 with probabilty (r/2)% I 255with probabilty (r/2)% (2) U i, j with probabilty (1 r)% where I is the noisy image and U i,j is the probability the uncorrupted pixels [6,7]. III. STANDARD MEDIAN FILTER (SM) Any given digital gray scale image is represented as an array of size M N pixels. Generally, the input image and the output image is represented as X and Y respectively. As per the mechanism of the median filter, the input image is first divided into subimages, using a overlapping sliding window (W), computes the median of pixels in each window W and the central pixel of the W is replaced by the computed median. Y ij = median {X i-s, j-t (s,t) W} (3) where, X ij refers to the input pixel at the i th row and j th column and Y ij refers to the pixels of the output image. The size of the window W is defined as: W = {(s,t) -k s k, -k t k}, (4) 106

2 where k = (n-1)/2. For instance, if the window size is 3x3, then, W = {(s,t) -1 s 1, -1 t 1}. (5) This process of computing median and replacing the central pixel of the sliding window is repeated for all pixels of the input image. The technique of selectively treating the corrupted pixels alone is referred to as apdative median filter [8]-[10]. 107 IV. METRICS Peak To Signal Noise Ratio (PSNR) It is important to assess the performance of any devised filter in comparison with the existing high performing filters can be evaluated quantitatively and qualitatively. The PSNR and Mean Square Error (MSE) are widely used to quantitatively measure the degree of denoising of corrupted images. The Peak Signal to Noise Ratio is computed as PSNR 10 log10 db (6) MSE Where as mean square error(mse) is as M N 1 MSE I r, c I r, c M N r1 c1 (7) where I r,c and I r,c denote the original image and restored image respectively while M and N are the rows and columns of the image[13]. V. PROPOSED TECHNIQUE The proposed filter, Adaptive Bi-Stage Median Filter (ABSMF), first divides noisy image using a overlapping sliding square window (W) of size n n. For each window W, if the central pixel M ij is corrupted, then its intensity is estimated using the principle of ABSMF. This technique, in the first level computes the median of adjacent pixels (A) and diagonal pixels (D) as shown in Fig. 1 as MED A and MED D. Secondly, mean of MED A and MED D is computed as AVG that replaces the corrupted pixel M ij. D A D A M ij A D A D Fig. 1. Illustration of 3 3 Window For instance, in a 3 3 window, the central pixel is represented as M ij and the adjacent and diagonal pixels of the M ij are represented as A and D respectively (Fig..1). In fig. 1, a 3 3 window is illustrated, in which A and D represents adjacent and diagonal pixels, whereas M ij is the central pixel, which can either be corrupted or uncorrupted. A. Algorithm for Proposed Technique: The algorithmic description of the ABSMF is given below Step 1: Read the noisy image, I Step 2: Divide the image into subimages using overlapping sliding window (W) of size n n Step 3: For each window, check the central pixel (M ij ) of W Step 4: If M ij is uncorrupted, go to Step 3 Step 5: If M ij is corrupted,then 1. Read the Adjacent pixels (A) of M ij in W and find the median (MED A ) 2. Read the Diagonal pixels (D) of M ij in W and find the median (MED D ) 3. Compute the median of those medians. AVG mean (MED A,MED D ) Step 6: Replace the central pixel M ij with AVG Step 7: Repeat the procedure for entire image. Step 8: Stop B. FLOWCHART: No Start Read the noisy image I Divide I as subimages using overlapping sliding window (W)of size n n Repeat for each window W in image Is centre pixel M i,j corrupted? YES Read the Diagonal pixels of M ij in W and compute the median (MED D )

3 108 Read the Adjacent pixels of M ij in W and compute the median (MED A ) Compute: AVG mean (MED DMED A) Replace M ij by AVG Stop Fig. 2. Flowchart of ABSMF VI. RESULTS AND DISCUSSION The proposed filter was developed in Matlab 6.5. The performance of ABSMF was tested on many real images and standard images like lena, mandrill and cameraman which were subjected to noise densities between 10% and 90% and the window size was varied from 33 to The performance of the proposed filters is compared with various filters. The filters such as Standard Median Filter (SM), Centered Weighted Median Filter (CWM), Progressive Switching Median Filter (PSM), Table I. Comparison of PSNR Values for Lena Image Iterative Median Filter (IMF), Signal Dependent Rank Order Median Filter (SDROMR), Non-Recursive Adaptive Center Weighted Median Filter (ACWM), Recursive Adaptive - Center Weighted Filter (ACWMR), Russo s fuzzy Filter (RUSSO), Zhang s Filter (ZHANG), Sun and Nauvo s Switching Based Filter (SUN), Impulsive Rejecting Filter (IRF) and Tri- State Median Filter (TSM) [12],[13]. The enlisted PSNR values for lena and mandrill (Table I and II) and a few restored images are given in Fig. 3 depict the quantitative and qualitative measure of ABSMF respectively. It is apparent from Table I for lena image, the Adaptive Bi-Stage Median Filter produces comparable PSNR values with respect to ZHANG, ACWMR, PSM and IMF and higher PSNR values than the other filters for 10% - 50%. For the remaining noise densities, the ABSMF produces the highest PSNR values. In Table II, for mandrill Image, it is evident that ABSMF produces the highest PSNR values for noise densities for 10% and 50% - 90% whereas for 20% - 40% of noise, the PSNR values are higher than all those filters and has given comparable results with respect to equal to RUSSO, PSM and IMF. The merit of ABSMF is further elucidated by the filtered images shown in fig. 3, for 50%, 60% and 70% of noise, for the optimal window size of 33. Noise Density (%) Method Corrupted SM CWM PSM IMF SDROM SDROMR ACWM ACWMR RUSSO ZHANG SUN IRF TSM ABSMF (Proposed Filter) Table II. Comparison of PSNR Values for Mandrill Image Noise Density (%) Method Corrupted SM CWM

4 PSM IMF SDROM SDROMR ACWM ACWMR RUSSO ZHANG SUN IRF TSM ABSMF (Proposed Filter) (a) (b) (c) (d) (e) (f) (g) (h) (i) (j) Fig 3. (a) Original Lena Image (b) Lena Image with 50% Noise; (c) Filtered Image of (b); (d) Lena Image with 60% Noise; (e) Filtered Image of (d); (f) Lena Image with 70% Noise; (g) Filtered Image of (f); (h) Original Image of Mandrill (i) Mandrill Image with 50% Noise; (j) Filtered Image of (i); (k) Mandrill Image with 60 % Noise; (l) Filtered Image of (k); (m) Mandrill Image with 70% Noise; (n) Filtered Image of (m); 109 (k) (l) (m) (n) VII. CONCLUSIONS The proposed ABSMF guarantees restoration of digital images degraded by fixed-value impulsive noise of densities up to 90%. Hence, it is proved to be very efficient especially in denoising the highly corrupted images. Further, ABSMF also ensures better preservation of the details and edges which is confirmed quantitatively in terms of PSNR values and qualitatively by visual perception.

5 ACKNOWLEDGEMENT One of the authors Dr. P.Shanmugavadivu thanks the University Grants Commission, New Delhi for the financial support in the form of project grant and the Authorities of Gandhigram Rural Institute, Gandhigram for their support and encouragement. VIII. REFERENCES [1] Gonzalez.R.C, Wood.R.E, Digital Image Processing, 3rd edition, Pearson Prentice Hall, [2] Berveglieri L, Piuri V., Digital median Filters, Journal VLSI Signal Process System. Signal Image Video Technology, Vol.31, No.2,pp ,2002. [3] Besdok E. and Emin Yuksel M., Impulsive Noise suppression for images with Jarque-Bera test based median filter, International Journal of Electronics and Communications, Vol.59, pp , [4] Bovik A.C, Huang Y. and Munson D.C, A Generalization of Median Filtering using Linear Combination of Order Statistics, IEEE Trans. Acoustics Speech, Signal Processing, Vol. ASSP 31, No.6, pp ,1983. [5] How-Lung Eng. and Kai-Kuang Ma, Noise Adaptive Soft-Switching Median Filter, IEEE Transactions on Image Processing, Vol.10, No.2, pp , [6] Mohammed Mansor Roomi. S, Impulse Noise Detection and Removal, ICGST-GVIP,Journal Vol. 7, No.2, pp.51-56, [7] Ben Hamza.A and Krim.H,Image Denoising: A Nonlinear Robust Statistical Approach,IEEE trans. Signal Processing, vol.49, ,2001. [8] Windyga P.S., Fast Impulsive Noise Removal, IEEE Trtans. on Image Processing, Vol.10, No.1,pp ,2001. [9] Somasundaram K and Shanmugavadivu P, Adaptive Iterative Order Statistics Filters, ICGST- GVIP, Journal Vol.09,pp.23-32,2009. [10] Somasundaram K and Shanmugavadivu P, Impulsive Noise Detection by Second Order Differential Image and Noise Removal using Nearest Nieghbourhood Filter, International Journal of Electronics and Communications, (Elsevier), pp ,2007. [11] Satpathy S.K, Panda S, Nagwanshi K.K and Ardil C, Image Restoration in Non-linearing Domain using MDB Approach, IJICE, Journal Vol. 6, No.1,2010. [12] Shanmugavadivu P and Eliahim Jeevaraj P S, Fixed Value Impulse Noise Suppression for Images using PDE based Adaptive Two -Stage Median Filter, ICCCET-11 (IEEE Explore), pp , [13] Shanmugavadivu P and Eliahim Jeevaraj P S, Selective 8-Neighbourhood based Medan Filter for Images Corrupted with High Density Fixed Value Impulse Noise, 3rd IIST,