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Comparative study of Salt & Pepper filters and Gaussian filters
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Comparative study of Salt & Pepper filters and Gaussian filters

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  • 1. [February 2012] Comparative study of Salt & Pepper filters and Gaussian filters By Ankush Srivastava [Email: anksrizzz@gmail.com, anksri000@gmail.com]Abstract: This article attempts to integers, called pixels, representing aundertake the study of two types of physical quantity such as scenenoise such as Salt & Pepper Noise and radiance, stored in a digital memory,Gaussian Noise. Different noise have and processed by computer or otherbeen removed by using various type digital hardware [25]. The importanceof filters as Minimum Filter, Maximum of image sequence processing isFilter, Mean Filter, Rank Order Filter, constantly growing with the everMedian Filter, Blur Method, Gaussian increasing use of digital television andFilter and Weight Median Filter. The video systems in consumer,comparative study is conducted with commercial, medical, andthe help of Peak Signal to Noise Ratio communicational applications. Digital(PSNR). image processing has many advantages over analog imageIntroduction: Digital image processing; it allows a much widerprocessing is a rapidly evolving field range of algorithms to be applied towith growing application in science the input data and can avoid problemsand engineering [1]. Various such as build-up of noise and signaltechniques have been developed in distortion during processing. So noiseImage Processing during the last four cancellation/filtering are anto five decades. Image processing important task in image processing.holds the possibility of developing theultimate machine that could perform Image Noise: Noise representsthe visual functions of all living being. unwanted information whichThe primary purpose of image deteriorates image quality. It isprocessing is to convert image into defined as a process which affects thevaluable information [7]. The term acquired image and is not part of thedigital image processing generally sense. Noise is introduced into imagesrefers to processing of a two- usually while transferring anddimensional picture by the digital acquiring them.computer [1]. Digital imageprocessing is a subset of the electronic Types of Noise: The main type ofdomain wherein the image is noise added while image acquisitionconverted to an array of small is called Gaussian noise while
  • 2. Impulsive noise is generally ideally should smooth the distinctintroduced while transmitting image parts of the image. A universal noisedata over an unsecure communication removing scheme is implementedchannel, while it can also be added by which weighs each pixel with respectacquiring. to its neighborhood and deals with Gaussian noise. Such noise is usuallySalt & Pepper Noise: The salt and introduced during image acquisition.pepper noise is caused by sharp,sudden disturbances in the image Filters: Various techniques aresignal; its appearance is randomly employed for the removal of thesescattered white or black (or both) types of noise based on the propertiespixels over the image [25]. Salt & of their respective noise models.Pepper Noise or impulse noise Image filtering is not only used togenerally is digitized as extreme (pure improve image quality but also is usedwhite or black) values in an image. An as a preprocessing stage in manyimage containing salt-and-pepper applications including imagenoise will have dark pixels in bright encoding, pattern recognition, imageregions and bright pixels in dark compression and target tracking, toregions. This type of noise can be name a few. General-purpose imagecaused by dead pixels, analog-to- filters lack the flexibility anddigital converter errors, and bit errors adaptability of un-modeled noisein transmission. In the case of types.impulsive noise removal, the aim of Noise reduction is a two-step process:optimal filtering is to design noise 1) Noise detection andreduction algorithms that would 2) Noise replacement.affect only corrupted image pixels, In first step location of noise iswhereas the undistorted image pixels identified and in second step detectedshould be invariant under the filtering noisy pixels are replaced by estimatedoperation. Thus, an impulse detector value. Efficiency of noise reductioncan be employed to classify each pixel algorithm depends on both noisein the noisy images as noise or not detection and noise replacement.prior to filtering. Salt & Pepper Noise RemovalGaussian Noise: Gaussian noise is aset of values taken from a zero mean Noise detection: if the intensity valueGaussian distribution which are of pixel is less than or equal to 0 thenadded to each pixel value. Impulsive there is Pepper noise and if thenoise involves changing a part of the intensity value of pixel is greater thanpixel values with random ones. or equal to 255 then there is Salt noiseGaussian Noise removal algorithms
  • 3. [17]. These pixels are beingprocessed.Intensity value of pixel at position (x,y) ={ Histogram of corrupted image Minimum Filtering: Minimum filter removes the white (salt) dots because any single white pixel within the selected filter region is replaced by one of its surrounding pixels with aOriginal Image smaller value [2], [5]. I’ (u, v) ← min {I (u+i, v+j) | (i, j) ∈ R} Steps: 1. Put pixel value of surrounding (of noisy pixel) pixels in a single dim array. 2. Sort this array in ascending order. 3. The noisy pixel value is replays by first element of the sorted array.Histogram of Original Image Applying Minimum AlgorithmImage corrupted by Salt & Pepper Noise
  • 4. HistogramHistogram Mean Filtering: In mean filtering, weMaximum Filtering: Minimum filter replace the desired pixel intensityremoves the black (pepper) dots with the arithmetic mean of itsbecause any single black pixel within surrounding pixel’s intensity valuethe selected filter region is replaced [5].by one of its surrounding pixels with a Steps:greatest value [2], [5]. 1. Take the arithmetic mean ofI’ (u, v) ← max {I (u+i, v+j) | (i, j) ∈ R} surrounding (of noisy pixel) pixelSteps: values.1. Put pixel values of surrounding (of 2. The noisy pixel value is replays by noisy pixel) pixels in a single dim the resulted arithmetic mean of its array surrounding pixels.2. Sort this array in ascending order.3. The noisy pixel value is replays by last element of the sorted array. Applying Mean AlgorithmApplying Maximum Algorithm
  • 5. Histogram HistogramRank Order Filtering: In rank order Median Filtering: In median filtering,filtering, first we sort the surrounding first we sort the surrounding pixels ofpixels of desired pixel behalf of its desired pixel behalf of its intensityintensity value then desired pixel will value then desired pixel will bebe replaced by as per user define replaced by middle element of sortedorder [23]. pixel values [2], [5].Steps: I’ (u, v) ← mid {I (u+i, v+j) | (i, j) ∈ R}1. Put pixel values of surrounding (of Steps: noisy pixel) pixels in a single dim 1. Put pixel values of surrounding (of array noisy pixel) pixels in a single dim2. Sort this array in ascending order. array3. Take the order ‘r’ of element from 2. Sort this array in ascending order. the user. 3. The noisy pixel value is replays by middle element of the sorted array.The noisy pixel value is replays by rthelement of the sorted array. Applying Median AlgorithmApplying Rank Order Algorithm with order 2
  • 6. Applying Proposed Method 1Histogram HistogramProposed Method 1: In proposedmethod 1, first we sort the Proposed Method 2: In proposedsurrounding pixels of desired pixel method 2, first we sort thebehalf of its intensity value then we surrounding pixels of desired pixeltake the arithmetic mean of middle-1, behalf of its intensity value then wemiddle, middle+1 of sorted pixel take the arithmetic mean of minimumvalues and this will replays the and maximum element of sorted pixeldesired pixel value. values and this will replays theSteps: desired pixel value.1. Put pixel values of surrounding (of Steps: noisy pixel) pixels in a single dim 1. Put pixel values of surrounding (of array noisy pixel) pixels in a single dim2. Sort this array in ascending order. array3. Now take arithmetic mean of 2. Sort this array in ascending order. (middle-1), (middle) and 3. Now take arithmetic mean of first (middle+1) element of the sorted and last element of the sorted array. array.The noisy pixel value is replays by The noisy pixel value is replays byresulted arithmetic mean value. resulted arithmetic mean value.
  • 7. Applying Proposed Method 2 Proposed Method 1 37.3239 Proposed Method 2 34.7473 Gaussian Noise Removal Noise detection: We compare and take absolute difference of each pixel from original image and corrupted image. If there is any difference then that pixel is noisy pixel and being process for the noise removal.HistogramExperimental Results: Theperformance evaluation of thefiltering operation is quantified by thePSNR (Peak Signal to Noise Ratio) andMSE (Mean Square Error) calculatedusing formula:PSNR = ⁄ √Where MSE is stands for Mean SquareError and calculated by the followingformula, ∑ ∑MSE = Original ImageWhere M is with of the image, N isheight of the image, i and j are thepixel positioning coordinates. o PSNR value of noisy image is 31.4395 dB. Filter Type PSNR value of image (in dB) Minimum 32.8731 Maximum 30.7662 Histogram Mean 37.1102 Rank Order with 34.4930 order is 2 Median 37.3239
  • 8. Image corrupted by Gaussian Noise Applying BlurHistogram HistogramBlur Method: In blur method, we Gaussian Filter:replace the noisy pixel intensity with In Gaussian Filter, the noisy pixel isthe arithmetic mean of its replays by the resulted value ofsurrounding pixel’s intensity value. multiplication of kernel matrix andSteps: selected region from the image. [2][3]1. Take the arithmetic mean of Steps: surrounding (of noisy pixel) pixel 1. First we create the kernel matrix values. by using he following formula:2. The noisy pixel value is replays by K[x, y] = the resulted arithmetic mean of its 2. Take addition of all the elements of surrounding pixels. kernel matrix. 3. Multiply the kernel matrix and selected region of the image and
  • 9. take the addition of these values in Steps: another variable. 1. Put pixel values of surrounding (of4. And divide this value with the noisy pixel) pixels in a single dim addition of kernel matrix. array5. Now the noisy pixel is replays by 2. Sort this array in ascending order. resulted value comes from step 4. 3. The noisy pixel value is replays by middle element of the sorted array.Applying Gaussian Algorithm Applying Median AlgorithmHistogram HistogramMedian Filter: In median filtering,first we sort the surrounding pixels of Weight Median Filter:desired pixel behalf of its intensity In weight median filter, the noisy pixelvalue then desired pixel will be is replays by the middle element ofreplaced by middle element of sorted the sorted array which full of pixelpixel values. [2][5] values [5].I’ (u, v) ← mid {I (u + i, v + j) | (i, j) ∈ Steps:R}
  • 10. 1. First we create weight matrix with Experimental Results: The following values: performance evaluation of the filtering operation is quantified by the PSNR (Peak Signal to Noise Ratio) and MSE (Mean Square Error) calculated2. Put the values of surrounding using formula: (noisy pixel) pixels in single dim array with the repetitive values PSNR = ⁄ √ according to the values of weight matrix. Where MSE is stands for Mean Square4. Sort this array in ascending order. Error and calculated by the following5. The noisy pixel value is replays by formula, middle element of the sorted array. ∑ ∑ MSE = Where M is with of the image, N is height of the image, i and j are the pixel positioning coordinates. o PSNR value of noisy image is 32.4583 dB. Filtering Type PSNR value of image(in dB) Blur Method 33.6072 Gaussian 33.1504 Median 33.5380 Weight Median 33.4232Applying Weight Median Algorithm Conclusion: This paper highlighted the noise removal algorithms for gray scale images as well as color images corrupted by Salt & Pepper and Gaussian noise. This work primarily focuses on comparing the efficiency of noise removal algorithms. The comparative study is explained by with the help of Peak Signal to Noise Ratio (PSNR). For removing the salt &Histogram Pepper noise we applied various noise filtering algorithms such as Minimum, Maximum, Mean, Rank Order and
  • 11. Median Filters. The Median Filter Noise from Remote Sensingproduces the correct image as Image”.compare to all other filtering 11. Paul Murry and Stephen Marshall,algorithms. In other side for removing “A Fast Method for compute theGaussian noise we applied Blur output of rank order filters withinmethod, Gaussian, Median and Weight arbitrarily shaped windows”.Median filtering algorithms and 12. Gajanand Gupta, “Algorithm forcompare these algorithms with help Image Processing Using Improvedof Peak Signal to Noise Ratio (PSNR) Median Filter and Comparison ofvalue. Mean, Median and Improved Median Filter”.References: 13. Shitong Wang, Yueyang Li, Fu-lai1. Anil K. Jain, “Fundamentals of Chung and Min Xu, “An Iterative Digital Image Processing”. Self-adaptive Algorithm to2. Rafael C. Gonzalez, Richard E. Impulse Noise Filtering for Color Woods, “Digital Image Images”. Processing”. 14. Krisana Chinnasarn, “Removing3. Alasdair McAndrew, “An Salt-and-Pepper Noise in Introduction to Digital Image Text/Graphics Images”. Processing with MATLAB”. 15. Minakshi Kumar, “Digital Image4. Bernd Jahne, “Digital Image Processing”. Processing”. 16. Dr. K. Sri Rama Krishna, A. Guruva5. Wilhelm Burger, Mark J. Burge, Reddy, Dr. M.N. Giri Prasad, Dr. K. “Principles of Digital Image Chandrabushan Rao, M. Madhavi, Processing”. “Genetic Algorithm Processor for6. Nick Efford, “Digital Image Image Noise Filtering Using Processing”. Evolvable Hardware”.7. Dr. Puneet Misra, “A Primary 17. Manohar Annappa Koli, “Robust Study on Digital Image Algorithm for Impulse Noise Processing”. Detection”.8. Mark Nixon and Alberto Aguado, 18. K.M.M. Rao, “Overview of Image “Feature Extraction & Image Processing”. Processing”. 19. John Eakins, Margaret Graham,9. Gerhard X. Ritter and Joseph N. “Content-based Image Retrieval”. Wilson, “Computer Vision 20. Ziv Yaniv, “Median Filtering”. Algorithms in Image Algebra”. 21. Mahmoud Saeidi, Khadijeh Saeidi,10. Mr. Salem Saleh Al-amri, Dr. N.V. Mahmoud Khaleghi, “Noise Kalyankar and Dr. Khamitkar S.D, Reduction in Image Sequences “A Comparative Study of Removal
  • 12. using an Effective Fuzzy Corrupted by Additive Gaussian Algorithm”. Noise”.22. Ce Liu, William T. Freeman, 30. L. Nataraj, A. Sarkar and B. S. Richard Szeliski, Sing Bing Kang, Manjunath, “Adding Gaussian “Noise Estimation from a Single Noise to Denoise JPEG for Image”. Detecting Image Resizing”.23. Anthony Edward Nelson, “Implementation of Image Processing Algorithms on FPGA Hardware”.A. Gasteratos, I. Andreadis and Ph. Tsalides, “Realization of Rank Order Filters based on Majority Gate”.24. Er. Harish Kundra, Er. Monika Verma, Er. Aashima, “Filter for Removal of Impulse Noise by Using Fuzzy Logic”.25. Yiqiu Dong, Raymond H. Chan, and Shufang Xu, “A Detection Statistic for Random-Valued Impulse Noise”.26. Umesh Ghanekar, “A Novel Impulse Detector for filtering of Highly Corrupted images”.27. Jian-Feng Cai, Raymond H. Chan, and Mila Nikolova, “Two-Pahse approach for Deblurring Images Corrupted by Impulse Plus Gaussian Noise”.28. Naga Sravanthi Kota, G. Umamaheswara Reddy “Fusion Based Gaussian noise Removal in the Image using Curvelets and Wavelets with Gaussian Filter”.29. Shyam Lal, Mahesh Chandra and Gopal Krishna Upadhyay, “Noise Removal Algorithm for Images