Transcript of "Impulse noise removal in digital images"
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International Journal of Computer Applications (0975 – 8887) Volume 10– No.8, November 2010 Impulse Noise Removal in Digital Images J.Harikiran B.Saichandana B.Divakar Assistant Professor, Assistant Professor, Student , Department of IT, GIT, Department of CSE,GIT, Department of I.T,GIT, GITAM University GITAM University GITAM University distributed over the image. Hence unlike Gaussian noise,ABSTRACT for an impulse noise corrupted image all the image pixelsThis paper introduces the concept of image fusion of are not noisy, a number of image pixels will be noisy andfiltered noisy images for impulse noise reduction. Image the rest of pixels will be noise free. There are differentfusion is the process of combining two or more images into types of impulse noise namely salt and pepper type ofa single image while retaining the important features of noise and random valued impulse noise.each image. Multiple image fusion is an importanttechnique used in military, remote sensing and medical In salt and pepper type of noise the noisy pixels takesapplications. Five different filtering algorithms are used either salt value (gray level -225) or pepper value (greyindividually for filtering the image captured from the level -0) and it appears as black and white spots on thesensor. The filtered images are fused to obtain a high images. If p is the total noise density then salt noise andquality image compared to individually denoised images. pepper noise will have a noise density of p/2.This can beIn-order to better appraise the noise cancellation behavior mathematically represented by (1)of our fusion technique from the point of view of humanperception, an edge detection is performed using canny zero or 255 with probability pfilter for the fused image. Experimental results show that yij=this method is capable of producing better results compared xij with probability 1-p (1)to individually denoised images. where yij represents the noisy image pixel, p is the totalKEYWORDS noise density of impulse noise and xij is the uncorruptedImpulse Noise, Image Enhancement, Image Restoration, image pixel. At times the salt noise and pepper noise mayImage Processing, Image Fusion. have different noise densities p1 and p2 and the total noise density will be p=p1+ p2 .1. INTRODUCTIONOrder statistics filters exhibit better performance as In case of random valued impulse noise, noise can take anycompared to linear filters when restoring images corrupted gray level value from zero to 225. In this case also noise isby impulse noise. Impulse noises are short duration noises randomly distributed over the entire image and probabilitywhich degrade an image. They may occur during image of occurrence of any gray level value as noise will be same.acquisition, due to switching, sensor temperature. They We can mathematically represent random valued impulsemay also occur due to interference in the channel and due noise as in (2).to atmospheric disturbances during image transmission. nij with probability p The goal of the filtering action is to cancel noise while yij=preserving the integrity of edge and detail information. In xij with probability 1-p (2)this paper, we propose a novel technique for impulse noisereduction. In our technique, first an image in captured by a where nij is the gray level value of the noisy pixel.sensor. The image is filtered in parallel with five differentsmoothing filters. The denoised images obtained from fivedifferent filters are fused them to obtain a high quality 3. IMAGE FUSION TECHNIQUEimage free from impulse noise. The process of combining two or more images into a single image while retaining the important features of each image The rest of the paper is organized as follows. Section is called image fusion. In this paper, the filtered imagesII analyzes the impulse noise in images, , Section III from five different smoothing algorithms are fused topresents the image fusion technique with five different obtain a high quality denoised image. The block diagram ofsmoothing filters, Section IV presents the experimental the process is shown in figure 1.results and finally Section V report conclusions. The five different smoothing algorithms used in our technique are described as follows:2. IMPULSE NOISE IN IMAGESImpulse noise [4] corruption is very common in digitalimages. Impulse noise is always independent anduncorrelated to the image pixels and is randomly 39
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International Journal of Computer Applications (0975 – 8887) Volume 10– No.8, November 2010 Median ∆(Xi, Xj) is the distance measure given by the L1 norm or Filter the city block distance which is more suited to non 1 correlated noise. The ordering may be illustrated as R 2 R δ1 ≤ δ2 ≤ δ3 ≤, ...,≤ δ9 (6) VMF and this implies the same ordering to the corresponding Fusion of Noise vector pixels i.e. Noisy Recovere FreeSenso Image BVDF d images Image X(1) ≤ X(2) ≤, ...,≤ X(9) (7)r R where the subscripts are the ranks. Since the vector pixel 3 SMF with the smallest sum of distances is the vector median pixel, it will correspond to rank 1 of the ordered pixels, i.e., 4 R XVMF = X(1) (8) MSMF For Basic Vector Directional Filter (BVDF) [5], Let W be R 5 the processing window of size n, and let xi, i=1,2,…n be the pixels in W. Let also the vector valued image function at Figure 1: Block diagram of image fusion technique pixel xi is denoted as fi. Let αi correspond to fi. n Order-static filters are nonlinear filters whose response is αi = A(fi, fj) based on the ordering (ranking) the pixels contained in the j 1 image area encompassed by the filter, and then replacing where A(fi, fj) denotes the angle between fi and fj. An the value of the center pixel with the value determined by ordering of the αi„s the ranking result. The best known filter in this category is the median filter, which as the name implies, replaces the α(1) ≤ α(2) ≤ …….. ≤ α(m) ≤…… α(n) (9) value of the pixel by the median of the intensity values in the neighborhood of that pixel defined in (3). The pixel implies the same ordering to the corresponding fi‟s with the median magnitude is used to replace the pixel in the signal studied. f(1) ≤ f(2) ≤ …….. ≤ f(m) ≤…… f(n) (10) MEDIANFILTER(x1,x2,……xN) = The first term in (10) constitutes the output of the BVDF MEDIAN(x1,x2,……xN) (3) The median filter is more robust with respect to the BVDF [f1,f2,……fn] = f(1) (11) presence of noise. In the Vector median filter (VMF) [1] for the ordering of The Spatial median filter (SMF) [2] is a uniform the vectors in a particular kernel or mask a suitable distance smoothing algorithm with the purpose of removing noise measure is chosen. The vector pixels in the window are and fine points of image data while maintaining edges ordered on the basis of the sum of the distances between around larger shapes. The SMF is based on the spatial each vector pixel and the other vector pixels in the window. median quantile function which is a L1 norm metric that measures the difference between two vectors. The spatial The sum of the distances is arranged in the ascending order depth between a point and a set of points is defined by and then the same ordering is associated with the vector pixels. The vector pixel with the smallest sum of distances N is the vector median pixel. The vector median filter is 1 X xi Sdepth(X,x1,x2,……xN)=1 - represented as N 1 X - xi i 1 XVMF = vectormedian (window) (4) (12) th Let r1,r2,….rN represent x1,x2,…..xN in rank order such that If δi is the sum of the distances of the i vector pixel with all the other vectors in the kernel, then Sdepth(r1,x1,x2,……xN) N ≥ Sdepth(r2,x1,x2,……xN) δi = ∆(Xi, Xj) (5) ≥ j 1 ≥ Sdepth(rN,x1,x2,……xN) (13) where (1≤ i ≤ N) and Xi and Xj are the vectors, N=9. and let rc represent the center pixel under the mask . Then SMF(x1,x2,……xN )= r1 (14) 40
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International Journal of Computer Applications (0975 – 8887) Volume 10– No.8, November 2010In the Modified Spatial Median Filter (MSMF) [2], first Figure 4 shows the results of filtering the color imagecalculate the spatial depth of every point within the mask parrot which is corrupted by impulse noise.and then sort these spatial depths in descending order. Afterthe spatial depth of each point within the mask iscomputed, an attempt is made to use this information tofirst decide if the mask‟s center point is an uncorruptedpoint. If the determination is made that a point is notcorrupted, then the point will not be changed. If the point iscorrupted, then the point is replaced with the point with thelargest spatial depth.We can prevent some of the smoothing by looking for theposition of the center point in the spatial order statistic. Let (a) (b)us consider a parameter P (where 1≤ P ≤ N, where Nrepresents numbers of points in the mask), which representsthe estimated number of original points under a mask ofpoints. If the position of the center mask point appearswithin the first P ranks of the spatial order statistic, then wecan argue that while the center point is not the bestrepresentative point of the mask, it is likely to be originaldata and should not be replaced. The MSMF is defined by rc c ≤ PMSMF(T,x1,x2,……xN) = (c) (d) r1 c > P (15)We generated five denoised images using the abovesmoothing algorithms. By fusing the best features of thesefive denoised images, a high quality image is obtained. Thefusion of the filtered images is given byF= ζ Ri where i= 1,2,3,4,5 (16) iR1 is the median filtered image, R2 vector median filteredimage, R3 vector directional filtered image, R4 spatialmedian filtered image and R5 modified spatial median (e) (f)filtered image. ζ is the fidelity factor. The fusion criteriondepends on the fidelity factor of the image. For a heavilynoised image the fidelity factor ζ will be smaller comparedto a lightly noised image and hence we fuse the images,each image contributes to the recovered image dependingon its noise density. A lightly noised image contributesmore compared to a heavily noised image. This helps toobtain a high quality fused image. We have taken fidelityfactor ζ=0.2. (g) (h) Figure 4 a) original image, b) impulse noise image4. EXPERIMENTAL RESULTS corrupted by noise density 0.4, c) median filter, d) VMF, e)This section presents the simulation results illustrating the BVDF, f) SMF g) MSMF with P=4 and h) Fused image.performance of the proposed fusion technique. The testimage employed here is the true color image “parrot” with Table (1) shows the results of MSE values of our fusion290×290 pixels. The salt and pepper noise is added into the method, compared with five different smoothing filters. Asimage with noise density 0.4. The noise model was it can be seen, the minimum mean square error (MSE) wascomputer simulated. All filters considered operate using obtained by our proposed approach.3×3 processing window. The performance of filters wasevaluated by computing the mean square error (MSE) Table 1: MSE valuesbetween the original image and filtered image as follow: IMAGES MSE 1 Noise image 40.3457 MSE= ( ) (I(x,y) – I1(x,y))2 (17) Median filter 24.3675 M n F Vector Median Filter 20.2896Where F denotes the set of M processed pixels, I(x,y) BVDF 18.4789denotes the vector pixel value in the original image and Spatial Median Filter 13.1356I1(x,y) denotes the vector pixel value in the filtered image. MSMF 11.6743 Fused Image 10.6356 41
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International Journal of Computer Applications (0975 – 8887) Volume 10– No.8, November 2010Edges define the boundaries between regions in an image, 5. CONCLUSIONwhich helps with segmentation and object recognition. In Image fusion technique for removing impulse noise inorder to better appraise the noise cancellation behavior of digital images is proposed. The image captured by theour filter from the point of view of human perception, an sensor undergoes filtering by different smoothing filtersedge detection is performed for the fused image. Canny and the resultant images are fused to attain high qualityfilter [3] is used for detection of edges in our “parrot” image. This restoration of image data is very likely to findimage. Figure 4 shows that our method significantly potential applications in a number of different areas such asreduces impulse noise and the image details have been electromagnetic imaging of objects, medical diagnostics,satisfactorily preserved. remote sensing, robotics, etc. 6. REFERENCES [1] R. H. Laskar, B. Bhowmick, R. Biswas and S. Kar ,” Removal of impulse noise from color image” , 2009 IEEE. [2] James C. Church, Yixin Chen, and Stephen V. Rice , “A Spatial Median Filter for Noise Removal in Digital Images“, 2008 IEEE. (a) (b) [3] Ehsan Nadernejad, ”Edge Detection Techniques: Evaluations and Comparisions” Applied Mathematical Sciences, Vol. 2, 2008, no. 31, 1507 – 1520. [4] S.Indu , Chaveli Ramesh, “ A noise fading technique for images highly corrupted with impulse noise”, Proceedings of the ICCTA07 , IEEE. [5] Damianos G. Karakos and Panos E. Trahanias, (c) “Generalized Multichannel Image-Filtering Structures Figure 5. Edge detection using canny filter “,IEEE Transactions on image processing” , Vol. 6, a) Original noise free image No. 7, July 1997. b) b) Noise image c) c) Resultant image by our method 42
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