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ICGST-GVIP Journal, Volume 7, Issue 3, November 2007 A Detail Preserving Filter for Impulse Noise Detection and Removal S. Md. Mansoor Roomi , T. Pandy Maheswari , V. Abhai Kumar Dept of ECE, Thiagarajar College of Engineering. Madurai, TN, India smmroomi@tce.edu, pandimaheswari@tce.edu, vakece@tce.edu Abstract schemes, by applying “no filtering” to preserve true It is imperative to remove impulse noise corrupted pixels pixels and Simple Median filter to remove impulse noise. in images, in order to facilitate the subsequent processing In [23], Manglem singh et al. have proposed adaptive such as image analysis, segmentation, pattern recognition rank ordered median filter(AROM) that employs two etc. Many linear and non linear filtering techniques have stage switching schemes utilizing rank-conditioned been proposed earlier to remove impulse noise, however median filter(RCM)[10] and center-weighted the removal of impulse noise is often accomplished at the median(CWM) filter[6]. The shortcoming of impulse expense of blurred and distorted features of edges; detection and switching scheme is that they employ therefore it is necessary to preserve the edges and fine different optimizing parameters: four thresholds in SD- details during filtering. In this paper a no reference blur ROM in [12], a set of fuzzy rules and membership metric based iterative edge preserving filtering technique functions, etc. Additionally, methods such as fuzzy filters has been proposed, that is selective on noisy and edge [13-15], and the neural network method [15], were also pixels. Experimental results show that the proposed filter developed but their performances depend on previous is superior over the state of art filters in maintaining training. In this context, a detail preserving, least higher peak signal to noise ratio (PSNR), near ideal blurring, noise removal technique becomes essential. structural similarity index measurement (SSIM) and This paper proposes an iterative, selective, filtering lower blur. technique the uses blur metric (BM) [19] in its frame work to remove impulse noise. The outline of the paper is Keywords: as follows. Section 2, reviews impulse noise model, Impulse noise, SSIM, PSNR, Perceptual blur metric Section 3, presents the novel iterative, adaptive filtering scheme. Section 4, provides the experimental results and 1. Introduction discussion. A robust image enhancement technique has to suppress the noise while preserving natural information in the 2. Impulse noise model images. A large number of linear and non linear filtering Consider an image I and an observation image X of same algorithms [1] have been proposed to remove impulse size noise from corrupted image to enhance image quality. Most of the linear filters generally have a neighborhood ⎧ N i , j with probabilty p ⎪ ⎫ ⎪ X ij = ⎨ ⎬ averaging mechanism to remove impulse noise and tend ⎪ I i, j with probabilit y 1 - ⎩ p⎪ ⎭ (1) to destroy all high frequency details like edges, lines and other fine image details. This led to the development of Where i=1,2,…..s1 and i=1,2,…..s2 and 0<p<1. nonlinear median-type filters such as stack filters [3], Iij and Nij denotes the pixel values at location (i,j) of the multistage median [5], weighted median [6,7], rank original image and the noisy image, respectively and Nij a conditioned median [10], and relaxed median [11]. noise value independent from Iij.For gray level images However, most of these filters are implemented with 8 bits per pixel ,when the images are contaminated uniformly across the image and thus tend to modify both by fixed value impulse noise, Nij the corrupted pixel is noisy and noise-free pixels. Consequently, the removal of equal to 0 or 255 each with equal probability (p/2). impulse noise is often accomplished at the expense of blurred and distorted features, thus removing fine details in the image. Therefore, a noise-detection process to 3. Proposed work discriminate the uncorrupted pixels from the corrupted In an impulse detection based noise filtering technique, pixels prior to applying nonlinear filtering is highly the first step is to find the position of impulse from the desirable. Raymond H.Chan and Nikolova [16] and corrupted image to apply filtering on the noisy pixels Florencio and Schafer [17] have proposed switching alone, while preserving other noise free pixels. There is a 51 ICGST-GVIP Journal, Volume 7, Issue 3, November 2007 tendency for any impulse detection scheme to misclassify edge(local minima and local maxima) the edge pixels in the corrupted image as noise and vice • Calculate edge width (local blur) versa, since the nature of the noise and edge in an image • Blur measure=sum of all edge width (2) appear to be similar due to their sudden transition in the No of edges gray level value. It becomes imperative to differentiate between noisy and edge pixels. Extracting the edges from the corrupted image is also a difficult task without having Corrupted Image f’(x,y) prior knowledge about the edge information. The issue of identifying noise free, noisy and edge pixels still looms large, which has a direct implication on preserving details Noise detection N(i,j) in an image during filtering. The proposed iterative, selective detail preserving filter (DPF) takes these issues into account and tends to isolate pixels belonging to Edge detection e(i,j) edge, noise, and noise free even at higher noise levels as discussed below. Noise filtering along edge direction 3.1 Selective Filtering One of the main properties of the classical filters [1] is that all input samples X are unconditionally affected by Yes If the filtering process. In the presence of impulse noise BM(i+1)<BM (i) model stated above, this approach is not optimal in contrast to continuous noise distributions, only certain samples of the original Image I are corrupted and others No remain unchanged. The concept of selective filtering is accomplished by, 1. Deciding whether the input sample considered (centre Stop pixel in the processing window) is corrupted by an impulse. Figure 2.Framework for Detail Preserving Filter 2. If so, replace it by a value estimated from its neighbors in the window; otherwise pass it to the output 3.2.1 Impulse noise Detection unprocessed. as shown in figure 1 As a first step in DPF, Adaptive Median Filter based impulse detector [16] is applied for finding the position of impulses. Consider a (2m+1) x (2m+1) window W around Noisy Image a pixel Xp, q given by, ⎧ X i, j | p − m ≤ i ≤ p + m , ⎫ ⎪ ⎪ (3) W p ,q (X ) = ⎨ ⎬ ⎪ ⎩ q − m ≤ j ≤ q + m⎪ ⎭ Is pixel Noisy Where p,q denotes the index of the current pixel. It could be observed that the corrupted pixels belong to the set {Wmin ,Wmax}, where Wmin is the minimal pixel value in Yes the defined window and Wmax is the maximum pixel value. A pixel may be corrupted and assigned to a flag Detail preserving filter matrix ‘N’ as, (DPF) ⎧1 if {( Χ i , j ≠ M i , j ) & Χ i , j ∈ { min,Wmax }} W (4) N (i, j ) = ⎨ ⎩0 else Where X and M are the corrupted and filtered images respectively. This impulse detection scheme detects Figure 1 Selective filtering scheme impulse noise even at higher corruption levels setting the flag matrix N(i.j) values as 1 wherever noise exists. 3.2 Detail Preserving Filter (DPF) It is necessary to extract noise and edge information from 3.2.2 Edge detection the corrupted image before filtering. Locations of noisy In order to isolate the noisy pixels present on the edge, pixels are obtained by applying adaptive impulse noise edge information from the noisy image is necessary. detection. The knowledge of the rough estimate of edge Extracting edges from the corrupted image is a difficult positions from the corrupted image is obtained by task, since the noisy edges will also be detected. So filtering and detecting edges. Such a DPF framework is median filtering is applied on the corrupted image f’(x,y), given in figure 2, where the final filtering is oriented Canny edge detector is applied on the median filtered towards the edge direction which ultimately tends to output m(i,j) since Canny detects true edges at higher reduce the blur metric (BM) given by the algorithm[19], level corruption also. In Canny, location of edges are identified using non maximal suppression (eqn 5) • Find strong vertical edges in the filtered image ∂ (5) • For each corresponding edge in the processed (G * I ) = 0 ∂n image: Find the start and end positions of the 52 ICGST-GVIP Journal, Volume 7, Issue 3, November 2007 e(i, j ) = ∇(G * I ) (6) In the above figure, an example noisy edge flag, Ne(i,j) of size 7x7is shown ,where Z is a noisy edge pixel . Shaded Where G is a Gaussian function of standard deviation regions indicate the direction of edge, Here noisy edge and I(i,j) is obtained from the median filtered output pixels indicated by the 1’s and 0’s represent either noise m(i,j). Edge matrix e(i,j), will have the value 1 if there is free or non- edge pixels. The proposed method tends to an edge pixel and value 0 for pixels not on edge. Initially replace ‘Z’ by median of nearest non noisy pixels edge is detected from the median filtered output, and then contained in the vector ‘Y’ along the direction of the edge. edge is detected from the iterative filtered result. ⎧ m (i , j ) I (i, j ) = ⎨ when k = 1 when k > 1 (7) { S1 i , j = med ( Y ) i , j = s , t ∀ Ne i, j = 1 (11) ⎩ s k −1 (i, j ) Where k is the order of iteration Here the corrupted pixel position x(i,j) indicated by the flag matrix of noisy edge Ne(i,j) and S1(i,j) is filtered m (i , j ) = adaptive median filtered output output of the noise other than on edge. If the population sk (i , j ) = proposed filtered output at kth iteration of non noisy pixel along the edge is less, then a greater I(i, j) = input image for canny edge detection window of size [s,t] along the direction of edge is selected. 3.2.3 Categorization of noisy pixels In second filtering scheme, the noisy pixels Categorization of a noise pixel as “Noise on Edge” or indicated by flag Ne’(i,j) are filtered by applying median “Noise but not on Edge” is accomplished by comparing filter on the non noisy neighborhood as given below. the noise(Ne) and edge(Ne’ ) flag, obtained from section 3.2.1 and section 3.2.2 respectively and given by,. S2 i, j = {med (V ) i , j = s , t ∀ Ne ' i , j = 1 (12) ⎧1 if e(i, j) = 1 & N(i, j) = 1 ⎫ (8) N e (i, j ) = ⎨ ⎬ where S2(i,j) is filtered output of the noisy edge pixels. ⎩0 otherwise ⎭ And ‘V’ is vector containing non noisy pixels present in its neighborhood. Here again the window size varies ⎧1 if e(i, j) = 0 & N(i, j) = 1 ⎫ (9) N ' (i, j ) = ⎨ ⎬ depending on the population of non noisy pixels in ‘V’. A e ⎩0 otherwise ⎭ filtered pixel at location (i, j) is included in the estimation where next noisy pixel thus making the method Recursive. The N(i,j)=noise matrix final filtered image S(i,j) is obtained as, e(i,j)=edge matrix S ( i , j ) = S 1i, j ∪ S 2 i, j (13) Ne(i,j)=Noise on Edge The entire filtering scheme functions with median filtered Ne’ (i,j)=noise other than edge image as its input which is not completely reliable to Thus Ne(i,j) gives the location of noisy pixels present obtain all the edge details of the original image. In order only on edge is and Ne’ (i,j) gives the remaining noisy to compensate this, an iterative procedure is adopted pixels . which improves the quality of image by minimizing the blur. In all iterations, the output filtered image is given as 3.2.4 Filtering schemes an input to the next iteration for edge detection. This Two filtering schemes are presented here, one for noise process depends on the blur metric (eqn 1) and repeats indicated on edge pixels by Ne(i,j)and other for noisy until there is no further significant improvement as given pixels not on edge indicated by Ne’(i,j). During the in eqn 14. filtering of the noisy edges, each noisy edge pixel is ⎧k = k + 1 if blur metric( sk +1 (i, j ) < sk (i, j )) replaced by taking the median of closest non noisy edge sk (i, j ) = ⎨ ⎩sk (i, j) if blur metric( sk +1 (i, j ) ≥ sk (i, j )) pixel present along the direction of the edge which is described in Figure 3. The direction of edge is found by using the connectivity of the edge pixels. (14) Where‘k’ is the number of iteration k=1,2 ,3 ,4---------N, N8 ( P) = N4 ∪ {(i + 1, j + 1), (i + 1, j − 1), (i − 1, j + 1), (i − 1, j − 1)} (10) ‘N’ is the last iteration ,the iteration stops when blur Where N8(P) and N4(P) is 8 connected and 4 connected metric of ‘N-1’ iteration is less than the Nth iteration. Thus neighbors for the pixel N’(i,j). filtering is done efficiently on the corrupted image preserving the sharpness of edges. 0 1 0 1 0 0 1 1 0 1 0 1 0 0 4. Experimental Results 0 0 1 0 0 0 0 In this section, extensive experimental results with 0 0 0 Z 1 0 0 commonly used gray-scale test images of size 256 x 256 are presented to assess the performance of the 1 0 0 0 0 0 0 proposed impulse noise removal technique. These images 0 1 0 1 0 1 1 including Lena, boat have distinctly different features in 1 0 0 0 0 0 0 terms of details as shown in figure 4d. These images are corrupted by various levels of salt and pepper noise. The Figure 3 .Edge direction performance of the proposed method is compared with that of many other well-known algorithms. such as 53 ICGST-GVIP Journal, Volume 7, Issue 3, November 2007 adaptive median filter, progressive switching median 5(b).The above results clearly depicts that (figure 5(d) is filter, Central weighted median filter. The performance of sharper when compared to figure 5(b) and figure 5(c) each filter is validated in terms of quality metrics respectively, hence sharper the image, lower the blur PSNR,SSIM and BM metric. M N MSE = ∑ ∑ ( S (i, j ) − I (i , j )) 2 (15) ii = 1 j = 1 ⎛ ⎞ ⎜ 255 2 ⎟ PSNR = 10 log 10 ⎜ ⎟ (16) ⎜ ⎟ ⎜ MSE ⎟ ⎝ ⎠ I--- Original input image S --- Output filtered image (a) 40% corrupted image (b) 1st Iteration output The Structural Similarity (SSIM)[20] index is a method for measuring the similarity between two images. Blur metric= 3.2632 SSIM (x, y ) = [l (x, y )]α .[c(x, y )]β .[s(x, y )] γ (17) l(x,y)=luminance c(x,y)=contrast s(x,y)=structure where α , β , γ are positive values used to adjust the relative importance of the three components. Amount of blur can be measured by applying blur metric (eqn 2) ( c) 2nd Iteration output (d) 3rd Iteration output algorithm [19]. Blur metric=2.8140 Blur metric= 2.5485 Results & Discussions Figure5. Comparison of Iterative Results Table1. Blur Metric Analysis Noise 10% 20% 30% 40% 50% 60% 70% level Iteration 1 2.13 2.03 2.74 3.26 3.17 3.68 2.95 Iteration 2 2.08 2.09 2.42 2.81 2.17 2.81* 2.74* Iteration 3 2.10 2.21 2.42 2.54 2.44* 2.94 3.22 (a) Original image (b) 50% corrupted Image Iteration 4 2.10* 2.17* 2.21 2.16* 2.47 2.35 4.62 Iteration 5 2.08 2.18 2.15* 3.02 2.56 2.41 4.28 3.5 3 2.5 2 1.5 (c) Adaptive Median filtered d)Detail preserving filtered output 1 Blur Metric= 2.5166, Blur Metric= 2.4269 0.5 SSIM=0.8691 SSIM=0.8923, 0 1 2 3 4 5 Figure 4 Comparison of filtered output i t e r a t i on The figure (4a) shows the original Image figure (4b) shows the 50% (salt & pepper) noise corrupted boat image of size (256x256) and the adaptive median filtered image is shown in (4c) has the blur metric value of Figure 6 Blur metric Vs Number of Iteration 2.5166 and proposed Detail preserved filtered image is shown in the figure (4d) and has the blur metric value of 2.4269 which is lesser than adaptive median filtered The above table shows the blur metric analysis of various image figure (4c). iterative output of the filtered image for different levels of corruption. It can be seen from figure 6 that blur reduces Similarly other results are shown for Lena image for all gradually till it reaches the minimum value. iterations considered. From the above results the proposed filter blur metric value for the 2nd iteration output shown in figure 5(c) is 2.8140 which is less than the 1st iteration output blur metric 3.2632 shown in figure 54 ICGST-GVIP Journal, Volume 7, Issue 3, November 2007 Table 3 SSIM Comparisons For different filters 1.2 Filter 10% 20% 30% 40% 50% 60% 70% 1 SD[12] SD[12] 0.96 0.88 0.70 0.44 0.23 0.11 0.05 SM[2] SM[2] 0.83 0.78 0.65 0.44 0.24 0.12 0.06 0.8 SSIM Values PSM[8] PSM[8] 0.95 0.91 0.87 0.81 0.70 0.49 0.25 CWM[6] 0.6 CWM[6] 0.89 0.77 0.52 0.30 0.15 0.08 0.04 PWMAD[9] PWMAD[9] 0.94 0.83 0.57 0.32 0.16 0.09 0.04 0.4 MF[2] MF[2] 0.98 0.95 0.92 0.88 0.83 0.77 0.68 AM[4] 0.2 DPF AM[4] 0.98 0.96 0.93 0.90 0.86 0.80 0.74 0 DPF 0.98 0.96 0.94 0.91 0.89 0.85 0.79 10 20 30 40 50 70 Noise level in % Table 2 PSNR Comparisons For Iterative Results Noise Figure8. SSIM Vs Noise level in % With Different 10% 20% 30% 40% 50% 60% 70% Level -> Filters Median 30.42 27.49 22.99 18.74 15.15 12.31 9.96 output Iterative Table 2 shows the PSNR comparison for the Iterative Results 37.81 34.53 32.09 30.24 28.13 26.10 24.17 filter results.* indicates the highest PSNR value. It can be 1 seen that the PSNR value increases after each iteration. 2 37.96 34.68 32.57 30.82 29.15 27.29 25.36 Table 3 Shows the Structural similarity based image quality assessment [20], For an Ideal Image Quality 3 38.03 34.83 32.83 31.05 29.16 27.43 25.44 index of the SSIM value=1, the above Table 3 depicts * * * * clearly that proposed filters values are approaching 4 38.14 34.65 32.69 30.87 29.22 27.30 25.62 towards quality index of an ideal image. In Figure 8, the * * * varying noise level in percentage Vs. SSIM values are 5 37.98 34.84 32.84 30.98 29.28 27.51 25.60 plotted for different filtered results, we can see that for the proposed filter Q approaches nearly to 1 and the value is high when compared to other filters. Conclusion The proposed Filtering technique applies Iterative, selective and directional filtering on the corrupted image to reduce the blur. The results shows that this method removes impulse noise, also simultaneously preserves edges at higher levels of noise as is evident from comparison with existing filters. (a) 70% noise filtered (b) 70% noise filtered References boat image Barbara image [1] Rafael Gonzalez Richard Woods , Digital Image Processing, Pearson Publications. [2] M. Gabbouj, E.J. Coyle and N.C. Gallagher, “An overview of median filtering",Circuits, Systems and Signal Processing, Vol.11, no.1, pp.7-45, Jan. 1992. [3] P. D. Wendt, E. J. Coyle, and N. C. Gallagher, “Stack filters,” IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-34, pp. 898–919,Aug. 1986. [4] Xiaoyin Xu and Eric Miller “Adaptive two pass (c) 70% noise filtered (d) 70% noise filtered median filter to remove impulsive noise”, IEEE, Baboon image Lena image 2002. [5] G. R. Arce and R. E. Foster, “Detail preserving Figure 7 Comparison of 70% Noise Corrupted Image ranked-order based filters for image processing,” Filtered Image with Different Quality Metrics IEEE Trans. Acoust., Speech, Signal Processing, ol. 37, pp. 83–98, Jan. 1989. In above figure (7), 70% noise corrupted boat, Barbara [6] S. J. Ko and Y. H. Lee, “Center weighted median and baboon images of size 256x256 are filtered using filters and their applications to image enhancement” proposed edge preserving filtering algorithm. It can be IEEE Trans. Circuits Syst., vol. 38, no.9, pp. 984– seen that proposed filter works well for higher level 993, Sep. 1991. corruption, thus preserving sharp edges. [7] R. Yang, L. Yin, M. Gabbouj, J. Astola, and Y. Neuvo, “Optimal weighted median filters under 55 ICGST-GVIP Journal, Volume 7, Issue 3, November 2007 structural constraints,” IEEE Trans.Signal S.Mohamed Mansoor Roomi Processing, vol. 43, pp. 591–604, Mar. 1995. received his BE in electronics , ME [8] Wang and D. Zhang, “Progressive switching degrees in Power system median filter for the re-moval of impulse noise Engineering and in Communication from highly corrupted images,” IEEE Trans. Cir- Engineering from Madurai Kamaraj cuits Syst., vol. 46, pp. 78–80, Jan. 1999. University in 1990 , 1992 and 1997 [9] Vladimir Crnojevic´,Vojin Senk, and Željen respectively and is pursuing PhD Trpovski, “Advanced Impulse Detection Based on from Madurai Kamaraj Pixel-Wise MAD” , IEEE Signal Processing letters, University,Madurai, ,India. Currently, he is an Assistant July 2004. Professor of Electronics and Communication Engineering [10] R. C. Hardie and K. E. Barner, “Rank conditioned at Thiagarajar College of Engineering,Madurai, India. He rank selection filters for signal restoration,” IEEE is a Member of IEEE, IUPRAI and published more than Trans.Image Processing, vol. 3, pp.192–206, Mar. 25 papers in both International and National 1994. Conferences. His Research interests include Image [11] A. Ben Hamza, P. Luque, J. Martinez, and R. Enhancement and Image Analysis. Roman, “Removing noise and preserving details with relaxed median filters,” J. Math. Imag. Vision, Abhaikumar Varadhan received his vol. 11, no. 2, pp. 161–177, Oct. 1999. BE and M.E. degree from PSG [12] E. Abreu and S.K. Mztra,” A Signal-Dependent college of Technology in 1977 and Rank Ordered Mean (SD-ROM) Filter – A 1979 respectively. He received his NewApproach for Removal of Impulses, from PhD degree from Indian Institute of Highly Corrupted Images”, 1995 IEEE. Technology, Madras, India in 1987. [13] H.K.Kwan “ Fuzzy filters for noisy image Currently, he is the Principal of filtering” ,” IEEE Trans Image Processing. Thiagarajar College of [14] F. Russo and G. Ramponi, “A fuzzy filter for Engineering, Madurai, India. He is a senior Member of images corrupted by impulse noise," IEEE Signal IEEE. He is the recipient of two awards for research, Process. Lett., vol. 3, no. 6, pp. 168-170,1996. teaching and advising excellence. He has co-authored 70 [15] C.-S. Lee, C.-Y. Hsu, and Y.-H. Kuo, “Intelligent technical papers in reputed journals, International and fuzzy image filter for impulse noise removal,” in National Conferences. Proc. IEEE Int. Conf. Fuzzy Syst., vol. 1, May 2002, pp. 431–436. [16] Raymont H. Chan, “An Iterative procedure for T.Pandy Maheswari is currently removing random- valued impulse noise," IEEE doing her masters in Communica- Signal Process. Lett., vol. no. 11, pp. Dec 2004. ion system at Thiagaraar College of [17] D. A. Florencio and R. W. Schafer, “Decision- Engineering, Madurai, India. Her based median filter using local signal statistics,” in research interests are in the areas of Proc. SPIE Symp. Visual Comm. Image Processing, Image processing, Multimedia vol. 2038, pp. 268-275, Sep. 1994. compression and Artificial [18] S Md. Mansoor roomi, IM.Lakshmi,.V.Abhai Intelligence. Kumar, “A Recursive Modified Gaussian Filter For Impulse Noise Removal”, Proc of International Conference on Visual Information Engineering VIE), September 2006. [19] P. Marziliano, F. Dufaux, S. Winkler, T. Ebrahimi, “A no-reference perceptual Blur metric”, in: Proceedings of the International Conference on ImageProcessing, Vol. 3, Rochester, NY, 2002, pp. 57–60. [20] Zhou Wang, Alan Conard Bovik, Hamid Rahim Sheik and Erno P Simoncelli, “Image Quality Assessment: From Error Visibility to Structural Similarity”, IEEE Trans. Image Processing, and Vol. 13, (2004). [21] R.ferzli,and Lina J.karam ,”No-Reference Objective Wavelet Based Noise Immune Image Sharpness Metric” ,in IEEE trans 2005. [22] “Local Scale Control for Edge Detection and Blur Estimation”.IEEE Trans on pattern analysis and machine intelligence, vol. 20, no. 7, July 1998. [23] Kh. Manglem Singh and Prabin K. Bora, “Rank Threshold Median Filter for Removal of Impulse Noise from Images “ 56

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