Modified Directional Weighted Median Filter

Modified Directional Weighted Median Filter Ayyaz Hussain 1, Muhammad Asim Khan 2, Zia Ul-Qayyum 2 1 Faculty of Basic and Applied Sciences, Department of Computer Science, Islamic International University Islamabad, Pakistan 2 University Institute of Information Technology Pir Mehar Ali Shah Arid Agriculture University Rawalpindi Rawalpind Pakistan ayyaz.hussain@iiu.edu.pk, m.asimkhattak@gmail.com, ziaqayum@uaar.edu.pk ABSTRACT Removal of random value impulse noise is essential to help successive process like image segmentation, analysis, pattern recognition etc. To remove uniform/randomvalued impulse noise without compromising the image detail information such as sharp edges, Modified Directional Weighted Median Filter (MDWMF) is proposed. The proposed filter utilizes the second order difference (SOD) along with a threshold to identify the set of noisy pixels. Detected noisy pixel are then replaced by using the direction based weighted median value. Detailed experimentation is performed which show that the proposed approach provides better results of suppressing uniform/random-value impulse noise from gray scale images. Keywords. Image restoration, random valued impulse noise, directional weighted median 1. Introduction Noise removing is very essential area for research. Because it is considered to be backbone process in image segmentation, analyses, pattern recognition etc. Generally Impulse noise is generated during image acquisition and transmission. There are two types of Impulse noise which includes. Salt and paper (SPN). Random value impulse noise (RIVN). SPN (0) {0,255} (255) RVIN (0) [0,255] (255) Figure 1: SPN Njє{Imin, Imax}, (b) RVIN Njє[Imin, Imax] The difference between SPN and RVIN is that, in case of SPN noise pixels either belong to 0 or 255 gray values for 8 bit images. However, noisy pixels can have any value in the range 0~255 in case of RVIN. Therefore, removal of RVIN is difficult as compare to SPN. Different techniques have been proposed previously to deal with noise in which most of the schemes fail for RIVN removal while these techniques work better for SPN removal. Experimental results show that the performance of noise removal technique can be improved by detecting noisy pixels more accurately. Filters are presented by some researchers to remove random value impulse noise includes [1] [6] which perform well for RVIN removal. The main negative aspect of these algorithms is that they don t use noise detector to preserve edges and fine details present in the non-noisy pixels of the corrupted image and hence looses the vital information. The problem is to remove RVIN, which is more difficult as compare to SPN while preserving the essential information present in the non-noisy pixels of the degraded image. Therefore, an efficient noise detector based on directional statistics along with threshold values proposed to efficiently detect the corrupted pixels. Major contributions of this manuscript include. Improved and efficient detectors are proposed for the classification of corrupted pixels. An improvement has been made in directional weighted median filter for better removal of RIVN. The proposed work is divided into two major phases which includes noise detection and noise removal. In detection phase, direction based Second Order derivative (SOD) along with threshold values are used to detect noisy pixels. In second phase, modified directional weighted median filter is used to estimate value for corrupted pixels and replace them with estimated value. This paper comprises of the following sections. In section 2, we present literature review. Proposed work is elaborated in section 3. In section 4, simulation results are presented along with some discussion. 2. Literature Review: Noise removal from corrupt image is one of the rising fields of image processing. Large numbers of algorithms have been presented by researchers and we have compared their results with latest techniques. The main objective of all those algorithms is to preserve detail and remove noise. Mostly noise is removed from images in two stages. In first stage, noisy pixels are detected whereas in second stage those pixels are replaced with the estimated ones. Order statistics based filter is used for removal of impulse noise by most of the researchers. However there are many other variants of order statistics filter which are proposed by researchers in

subsequent years. T. Chen et al. [7] proposed a filter which uses new adaptive operator to compute the outputs of center-weighted median (CWM) [8] filtered with diverse center weights. Based on the impulse detection technique it uses switching scheme in which noisy pixels are detected first and then noise is removed from the noisy pixels only. The final output of standard median and the central pixel itself are swapped. Furthermore, T. Chen et al. [9] proposed Multi State Median Filter (MSM) that is a comprehensive structure of median based switching schemes. Both MSM filter and adaptive CWM filter are corresponding, with a space changeable middle weight which is limited signal information dependent. K.-K. Ma et al. [10] proposed Tri-State Median Filter (TSM). Major contribution of the proposed filter is to suppress impulse noise and preserve image detail. Prior to applying filtering completely, Tri-state median filter uses standard order statistic filter and the CWM filter to determine whether a pixel is noisy or not. In case of noisy pixel(s), it uses switching mechanism, which is controlled by threshold. Major advantage of TSM filter is its adaptive decision support to discover local noise using outputs of the above mentioned filters. V. Senk et al. [11] proposed a robust detector which utilizes modified pixel wise MAD (median of the absolute deviation from the median) is used for separation of noisy pixel in order to retain image detail efficiently. This algorithm successfully removes all types of noises while keeping the computational complexity very low. For estimating details in image median-mad are used that provide efficient separation noise-free pixels from noisy pixels. Removal of impulse noise which is arbitrarily distributed is reliable through iterative execution of pixel wise modification. S. K. Mitra et al. [12] proposed a filter for removal of impulse noise in which the filtering process is trained on a condition variable that is defined by using a classifier. The algorithm produces an excellent switching between noise suppression and retaining detail while keeping the computational complexity low. Moreover, the technique can successfully remove noise from images degraded with Gaussian noise, impulse noise and mixture of these two as well. T. Chen et al. [13] proposed another method for removal of RVIN which uses directional statistics to compute median value. The impulse detector is introduced in that paper is based on the directional order statistics to identify and remove noise. Both detection and removal process works iteratively and gives better results. Aloke Datta [14] proposed a RVIN removal scheme which is based on second-order-derivative and uses four main directions for computing the directional statistics. In propose scheme, we have used more than four directional statistical estimators to detect noise present in the images. The technique uses the second-order difference to identify the set of noisy pixels which are then used by directional biased median filter for estimation of the new non-noisy value. 3. Proposed Methodology In this paper, a new solution for the removal of RVIN has been proposed. This approach can be divided into two different stages, explicitly detection of corrupted pixels followed by the noise removal of only those pixels which are detected degraded while keeping the other non-degraded pixels intact. The noise discovery scheme employ second order difference of pixels in considered test mask of size 5x5 and the filtering scheme is a weighted median filter which considers edge information along all possible directions to estimate the value of the degraded pixel. 3.1 Second Order Difference In digital image processing the derivative refers to difference between pixels. Both derivative and differences have same meaning in digital function. The definition of difference can be represented in different ways. However, the term difference is defined in digital image as, 1 st difference must be zero at same gray level (flat region of image). At the onset of a gray level or ramp 1 st difference must be non zero. Along ramps must be nonzero. I / x = I ( x + 1) I ( x) (1) Similarly second derivative will be defined as, Same as 1 st derivative at flat area (same gray level) must be zero. At the onset of a gray level or ramp 2 nd difference also must be non zero. The main difference in 1 st and 2 nd derivative is 2 nd difference must be zero along ramps of constant slope. 2I / x2 = I ( x + 1) + I ( x 1) 2I ( x) (2) Normally first order derivative produce thicker edges whereas thin line or fine details are produced by second order derivative. However, at stair changes in gray level, second order derivative gives double response. The second difference is used in proposed noise filtering technique to estimate impure pixels present in the source image. 3.2 Noise Detection In proposed detection algorithm second order derivative (SOD) is used between the pixels in a test mask to find out the impurity present in the current pixel under consideration. The SODs give a strong response to finer details such as edges and texture

(a) (b) (c) Figure 2: filter image Lena image degraded with 40% of RVIN (a) True image, (b) Noisy image, and (c) Proposed. (a) (b) (c) Figure 3: Filter image of Bridge image corrupted with 40% of RVIN (a) True image, (b) Noisy image, and (c) Proposed. Table 1: Comparison of PSNR for Lena Image Method 10% 20% 30% 40% 50% 60% SD- 35.89 32.48 29.86 27.32 24.96 22.35 ROM ACWM 34.47 32.44 30.40 27.86 25.66 22.51 PWMAD 34.86 30.58 25.94 22.41 19.42 17.08 DWM 35.15 33.81 32.43 30.64 29.14 26.57 Propose 38.89 36.35 34.53 32.90 29.22 25.84 Table 2: Comparison of PSNR for Bridge Image Method 10% 20% 30% 40% 50% 60% D-ROM 26.62 26.35 24.89 23.03 21.18 19.21 ACWM 25.89 25.14 23.99 22.61 20.88 19.09 PWMAD 25.89 25.14 23.99 22.61 20.88 19.09 DWM 26.02 26.50 24.87 24.09 23.08 21.41 Propose 29.80 29.20 25.91 24.73 22.14 20.02 knowledge present in the image. Therefore, it gives better noise detection accuracy than other existing techniques. In order to detect impurity present in the pixel, consider mask M of size 5 5 to test impurity present in the center pixel I(x,. M = { I( x+ / 2 j 2} (3) Dn= I( x+ + I( x y 2 I( x, (4) Edges associated with all possible directions are considered by calculating the SODs using equation (4). Where ( n, = {( 1,2,2),(21,,2),(3, 2,2)...(, n 2,0)} and (5) 0 n 20 For the detection of impulse noise, all possible directions present in the mask M of size 5x5 are considered and the detections having minimum SOD has been computed as show in equation (5). D min = min( Dn :1 n max directions) (5) Following decision are made by looking at the values of Dmin. If the Dmin value is smaller than some predefined threshold, then it means the considered pixel is non noisy one and belongs to a smooth slow varying region and all the differences are small. When a current pixel lies on an edge, it will give a smaller SOD along the edge will result in a smaller value of Dmin. So, the examined pixel is noise-free. The test pixel will be noisy if Dmin have large value. In the result it is observed that the

impulse noise can be identified by Dmin based on suitable threshold T. 3.3 Proposed Noise Filter Once impurity has been detected in a certain pixel then that pixel will be a candidate of the proposed filtering process. The substitution value of the impure pixel is estimated using the improved version of directional weighted median filter. Let D n (x, indicate the absolute difference between the two adjacent pixels having gray level value of I(x, in the n th direction (1 n maxdirections). Dn= I( x+ + I( x y 4 I( x, Where ( n, = {( 1,2,2),(21,,2),(3, 2,2)......(, n 2,0)} and 0 n max Directions The Closeness of the nearest pixels is indicated by the values calculated in all directions given in D n. Let D min be the direction of minimum D n (1 n maxdirections). It means the pixels associated with D min are nearest to one another and the central value should be close to them. While replacing the noise value these pixels are allocated with extra weight and will be considered twice while computing the median of that particular window. If noise is found in examined pixel I(x,, then the new value of the noisy pixel can be estimated as L( x, = median{ W, w IDn} (7) Where, w is the mask, and ID n represents the four nearest pixels of I(x, beside the direction D n. Operator " " is use for repetition operator which shows that the four pixel values in the direction having minimum difference will be repeated in that window. Due to iterative operation the filtered pixels take part in noise detection. In order to ensure better restoration accuracy, the proposed scheme is applied recursively on the corrupted image. Compared to previous iteration, current iteration uses smaller threshold to detect and remove more noise. It is examined that the following threshold values produce better result. T T T 33 23 16 (8) [ ] [ ] 1 2 3 = 4. Simulation Results and Discussions Comprehensive experimentation has been performed to test the performance of this newly proposed algorithm. Standard images like Lena, Boat and Bridge are used for to calculate the results in various simulations. The performance measures in terms of peak signal to noise ratio (PSNR) for Lena and Bridge images are shown in Table 1 and 2 respectively. Table 1 and 2 shows the comparison between proposed and other noise removal schemes. However the (6) proposed scheme performs better than other in same environment and under same amount of noise. 5. Conclusion and Future Work In this paper we have proposed an improved weighted median filter which uses second order difference (SOD) to detect edges along all possible directions and then detected corrupted pixel value are replace by newly estimated value computed through modified directional weighted median. Experiments and Simulations show that the proposed approach can provide excellent performance of suppressing random value impulse noise in all situations and preserve detail. In future we are planning to introduce some variant of directional weighted median filter to restore color images. REFERENCES [1] B Chandra and D Dutta Majumder. Digital Image Processing and Analysis Prentice-Hall, India, first edition, 2007. [2] K. S. Srinivasan and D. Ebenezer. A new fast and efficient decision based algorithm for removal of high-density impulse noises. IEEE Signal Process. Lett., 14(3):189 192, March 2007. [3] Pankaj Kumar Sa. On the development of impulsive noise removal schemes. M.Tech thesis NIT Rourkela, 2006. [4] T. Chen and H. R. Wu. Adaptive impulse detection using center-weighted median filters. IEEE Signal Process. Lett., 8(1):1 3, January 2001. [5] S. Ko and Y. Lee. Center weighted median filters and their applications to image enhancement. IEEE Trans. Circuits Syst, 38(9):984 993, September 1991. [6] Zong Chen and Li Zhang. Multi-stage Directional Median Filter, International Journal of Signal Processing 5:4 2009 [7] T. Chen and H. R. Wu. Adaptive impulse detection using center-weighted median filters. IEEE Signal Process. Lett., 8(1):1 3, January 2001. [8] S. Ko and Y. Lee. Center weighted median filters and their applications to image enhancement. IEEE Trans. Circuits Syst, 38(9):984 993, September 1991. [9] T. Chen and H. R.Wu. Space variant median filters for the restoration of impulse noise corrupted images. IEEE Trans. Circuits Syst. II, 48(8):784 789, August 2001. [10] K.-K. Ma T. Chen and L.-H. Chen. Tri-state median filter for image denoising. IEEE Signal Process. Lett, 8(12):1834 1838, December 1999. [11] V. Senk V. Crnojevic and Trpovski. Advanced impulse detection based on pixelwise mad. IEEE Signal Process. Lett, 11 (7):589 592, July 2004. [12] S. K. Mitra E. Abreu, M. Lightstone and K. Arakawa. A new efficient approach for the removal

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