Comparative study of Salt & Pepper filters and Gaussian filters
7 likes7,037 views
The document compares Salt & Pepper noise and Gaussian noise removal methods. It discusses various filtering techniques like minimum, maximum, mean, median, and rank order filters. For Salt & Pepper noise, minimum and maximum filters remove white and black pixels respectively, while mean, median, and rank order filters replace pixel values with local statistics. The document proposes two additional methods that calculate the mean of middle pixel values after sorting. It analyzes noise removal using these filters and concludes median filtering best reduces Salt & Pepper noise.
![[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 a
undertake the study of two types of physical quantity such as scene
noise such as Salt & Pepper Noise and radiance, stored in a digital memory,
Gaussian Noise. Different noise have and processed by computer or other
been removed by using various type digital hardware [25]. The importance
of filters as Minimum Filter, Maximum of image sequence processing is
Filter, Mean Filter, Rank Order Filter, constantly growing with the ever
Median Filter, Blur Method, Gaussian increasing use of digital television and
Filter and Weight Median Filter. The video systems in consumer,
comparative study is conducted with commercial, medical, and
the help of Peak Signal to Noise Ratio communicational applications. Digital
(PSNR). image processing has many
advantages over analog image
Introduction: Digital image processing; it allows a much wider
processing is a rapidly evolving field range of algorithms to be applied to
with growing application in science the input data and can avoid problems
and engineering [1]. Various such as build-up of noise and signal
techniques have been developed in distortion during processing. So noise
Image Processing during the last four cancellation/filtering are an
to five decades. Image processing important task in image processing.
holds the possibility of developing the
ultimate machine that could perform Image Noise: Noise represents
the visual functions of all living being. unwanted information which
The primary purpose of image deteriorates image quality. It is
processing is to convert image into defined as a process which affects the
valuable information [7]. The term acquired image and is not part of the
digital image processing generally sense. Noise is introduced into images
refers to processing of a two- usually while transferring and
dimensional picture by the digital acquiring them.
computer [1]. Digital image
processing is a subset of the electronic Types of Noise: The main type of
domain wherein the image is noise added while image acquisition
converted to an array of small is called Gaussian noise while](https://image.slidesharecdn.com/imageprocessingalgorithms-121102110347-phpapp02/85/Comparative-study-of-Salt-Pepper-filters-and-Gaussian-filters-1-320.jpg)
![Impulsive noise is generally ideally should smooth the distinct
introduced while transmitting image parts of the image. A universal noise
data over an unsecure communication removing scheme is implemented
channel, while it can also be added by which weighs each pixel with respect
acquiring. to its neighborhood and deals with
Gaussian noise. Such noise is usually
Salt & Pepper Noise: The salt and introduced during image acquisition.
pepper noise is caused by sharp,
sudden disturbances in the image Filters: Various techniques are
signal; its appearance is randomly employed for the removal of these
scattered white or black (or both) types of noise based on the properties
pixels over the image [25]. Salt & of their respective noise models.
Pepper Noise or impulse noise Image filtering is not only used to
generally is digitized as extreme (pure improve image quality but also is used
white or black) values in an image. An as a preprocessing stage in many
image containing salt-and-pepper applications including image
noise will have dark pixels in bright encoding, pattern recognition, image
regions and bright pixels in dark compression and target tracking, to
regions. This type of noise can be name a few. General-purpose image
caused by dead pixels, analog-to- filters lack the flexibility and
digital converter errors, and bit errors adaptability of un-modeled noise
in 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 and
reduction algorithms that would 2) Noise replacement.
affect only corrupted image pixels, In first step location of noise is
whereas the undistorted image pixels identified and in second step detected
should be invariant under the filtering noisy pixels are replaced by estimated
operation. Thus, an impulse detector value. Efficiency of noise reduction
can be employed to classify each pixel algorithm depends on both noise
in the noisy images as noise or not detection and noise replacement.
prior to filtering.
Salt & Pepper Noise Removal
Gaussian Noise: Gaussian noise is a
set of values taken from a zero mean Noise detection: if the intensity value
Gaussian distribution which are of pixel is less than or equal to 0 then
added to each pixel value. Impulsive there is Pepper noise and if the
noise involves changing a part of the intensity value of pixel is greater than
pixel values with random ones. or equal to 255 then there is Salt noise
Gaussian Noise removal algorithms](https://image.slidesharecdn.com/imageprocessingalgorithms-121102110347-phpapp02/85/Comparative-study-of-Salt-Pepper-filters-and-Gaussian-filters-2-320.jpg)
![[17]. These pixels are being
processed.
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 a
Original 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 Algorithm
Image corrupted by Salt & Pepper Noise](https://image.slidesharecdn.com/imageprocessingalgorithms-121102110347-phpapp02/85/Comparative-study-of-Salt-Pepper-filters-and-Gaussian-filters-3-320.jpg)
![Histogram
Histogram
Mean Filtering: In mean filtering, we
Maximum Filtering: Minimum filter replace the desired pixel intensity
removes the black (pepper) dots with the arithmetic mean of its
because any single black pixel within surrounding pixel’s intensity value
the selected filter region is replaced [5].
by one of its surrounding pixels with a Steps:
greatest value [2], [5]. 1. Take the arithmetic mean of
I’ (u, v) ← max {I (u+i, v+j) | (i, j) ∈ R} surrounding (of noisy pixel) pixel
Steps: 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 Algorithm
Applying Maximum Algorithm](https://image.slidesharecdn.com/imageprocessingalgorithms-121102110347-phpapp02/85/Comparative-study-of-Salt-Pepper-filters-and-Gaussian-filters-4-320.jpg)
![Histogram Histogram
Rank Order Filtering: In rank order Median Filtering: In median filtering,
filtering, first we sort the surrounding first we sort the surrounding pixels of
pixels of desired pixel behalf of its desired pixel behalf of its intensity
intensity value then desired pixel will value then desired pixel will be
be replaced by as per user define replaced by middle element of sorted
order [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 dim
2. Sort this array in ascending order. array
3. 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 rth
element of the sorted array.
Applying Median Algorithm
Applying Rank Order Algorithm with order 2](https://image.slidesharecdn.com/imageprocessingalgorithms-121102110347-phpapp02/85/Comparative-study-of-Salt-Pepper-filters-and-Gaussian-filters-5-320.jpg)
![Image corrupted by Gaussian Noise Applying Blur
Histogram Histogram
Blur Method: In blur method, we Gaussian Filter:
replace the noisy pixel intensity with In Gaussian Filter, the noisy pixel is
the arithmetic mean of its replays by the resulted value of
surrounding pixel’s intensity value. multiplication of kernel matrix and
Steps: 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](https://image.slidesharecdn.com/imageprocessingalgorithms-121102110347-phpapp02/85/Comparative-study-of-Salt-Pepper-filters-and-Gaussian-filters-8-320.jpg)
![take the addition of these values in Steps:
another variable. 1. Put pixel values of surrounding (of
4. And divide this value with the noisy pixel) pixels in a single dim
addition of kernel matrix. array
5. 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 Algorithm
Histogram
Histogram
Median 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 pixel
value then desired pixel will be is replays by the middle element of
replaced by middle element of sorted the sorted array which full of pixel
pixel values. [2][5] values [5].
I’ (u, v) ← mid {I (u + i, v + j) | (i, j) ∈ Steps:
R}](https://image.slidesharecdn.com/imageprocessingalgorithms-121102110347-phpapp02/85/Comparative-study-of-Salt-Pepper-filters-and-Gaussian-filters-9-320.jpg)
Comparative study of Salt & Pepper filters and Gaussian filters
- 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 a undertake the study of two types of physical quantity such as scene noise such as Salt & Pepper Noise and radiance, stored in a digital memory, Gaussian Noise. Different noise have and processed by computer or other been removed by using various type digital hardware [25]. The importance of filters as Minimum Filter, Maximum of image sequence processing is Filter, Mean Filter, Rank Order Filter, constantly growing with the ever Median Filter, Blur Method, Gaussian increasing use of digital television and Filter and Weight Median Filter. The video systems in consumer, comparative study is conducted with commercial, medical, and the help of Peak Signal to Noise Ratio communicational applications. Digital (PSNR). image processing has many advantages over analog image Introduction: Digital image processing; it allows a much wider processing is a rapidly evolving field range of algorithms to be applied to with growing application in science the input data and can avoid problems and engineering [1]. Various such as build-up of noise and signal techniques have been developed in distortion during processing. So noise Image Processing during the last four cancellation/filtering are an to five decades. Image processing important task in image processing. holds the possibility of developing the ultimate machine that could perform Image Noise: Noise represents the visual functions of all living being. unwanted information which The primary purpose of image deteriorates image quality. It is processing is to convert image into defined as a process which affects the valuable information [7]. The term acquired image and is not part of the digital image processing generally sense. Noise is introduced into images refers to processing of a two- usually while transferring and dimensional picture by the digital acquiring them. computer [1]. Digital image processing is a subset of the electronic Types of Noise: The main type of domain wherein the image is noise added while image acquisition converted to an array of small is called Gaussian noise while
- 2. Impulsive noise is generally ideally should smooth the distinct introduced while transmitting image parts of the image. A universal noise data over an unsecure communication removing scheme is implemented channel, while it can also be added by which weighs each pixel with respect acquiring. to its neighborhood and deals with Gaussian noise. Such noise is usually Salt & Pepper Noise: The salt and introduced during image acquisition. pepper noise is caused by sharp, sudden disturbances in the image Filters: Various techniques are signal; its appearance is randomly employed for the removal of these scattered white or black (or both) types of noise based on the properties pixels over the image [25]. Salt & of their respective noise models. Pepper Noise or impulse noise Image filtering is not only used to generally is digitized as extreme (pure improve image quality but also is used white or black) values in an image. An as a preprocessing stage in many image containing salt-and-pepper applications including image noise will have dark pixels in bright encoding, pattern recognition, image regions and bright pixels in dark compression and target tracking, to regions. This type of noise can be name a few. General-purpose image caused by dead pixels, analog-to- filters lack the flexibility and digital converter errors, and bit errors adaptability of un-modeled noise in 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 and reduction algorithms that would 2) Noise replacement. affect only corrupted image pixels, In first step location of noise is whereas the undistorted image pixels identified and in second step detected should be invariant under the filtering noisy pixels are replaced by estimated operation. Thus, an impulse detector value. Efficiency of noise reduction can be employed to classify each pixel algorithm depends on both noise in the noisy images as noise or not detection and noise replacement. prior to filtering. Salt & Pepper Noise Removal Gaussian Noise: Gaussian noise is a set of values taken from a zero mean Noise detection: if the intensity value Gaussian distribution which are of pixel is less than or equal to 0 then added to each pixel value. Impulsive there is Pepper noise and if the noise involves changing a part of the intensity value of pixel is greater than pixel values with random ones. or equal to 255 then there is Salt noise Gaussian Noise removal algorithms
- 3. [17]. These pixels are being processed. 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 a Original 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 Algorithm Image corrupted by Salt & Pepper Noise
- 4. Histogram Histogram Mean Filtering: In mean filtering, we Maximum Filtering: Minimum filter replace the desired pixel intensity removes the black (pepper) dots with the arithmetic mean of its because any single black pixel within surrounding pixel’s intensity value the selected filter region is replaced [5]. by one of its surrounding pixels with a Steps: greatest value [2], [5]. 1. Take the arithmetic mean of I’ (u, v) ← max {I (u+i, v+j) | (i, j) ∈ R} surrounding (of noisy pixel) pixel Steps: 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 Algorithm Applying Maximum Algorithm
- 5. Histogram Histogram Rank Order Filtering: In rank order Median Filtering: In median filtering, filtering, first we sort the surrounding first we sort the surrounding pixels of pixels of desired pixel behalf of its desired pixel behalf of its intensity intensity value then desired pixel will value then desired pixel will be be replaced by as per user define replaced by middle element of sorted order [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 dim 2. Sort this array in ascending order. array 3. 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 rth element of the sorted array. Applying Median Algorithm Applying Rank Order Algorithm with order 2
- 6. Applying Proposed Method 1 Histogram Histogram Proposed Method 1: In proposed method 1, first we sort the Proposed Method 2: In proposed surrounding pixels of desired pixel method 2, first we sort the behalf of its intensity value then we surrounding pixels of desired pixel take the arithmetic mean of middle-1, behalf of its intensity value then we middle, middle+1 of sorted pixel take the arithmetic mean of minimum values and this will replays the and maximum element of sorted pixel desired pixel value. values and this will replays the Steps: 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 dim 2. Sort this array in ascending order. array 3. 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 by resulted 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. Histogram Experimental Results: The performance evaluation of the filtering operation is quantified by the PSNR (Peak Signal to Noise Ratio) and MSE (Mean Square Error) calculated using formula: PSNR = ⁄ √ Where MSE is stands for Mean Square Error and calculated by the following formula, ∑ ∑ MSE = Original Image 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 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 Blur Histogram Histogram Blur Method: In blur method, we Gaussian Filter: replace the noisy pixel intensity with In Gaussian Filter, the noisy pixel is the arithmetic mean of its replays by the resulted value of surrounding pixel’s intensity value. multiplication of kernel matrix and Steps: 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 (of 4. And divide this value with the noisy pixel) pixels in a single dim addition of kernel matrix. array 5. 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 Algorithm Histogram Histogram Median 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 pixel value then desired pixel will be is replays by the middle element of replaced by middle element of sorted the sorted array which full of pixel pixel 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) calculated 2. 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 Square 4. Sort this array in ascending order. Error and calculated by the following 5. 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 33.4232 Applying 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 Sensing produces 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 the Gaussian noise we applied Blur output of rank order filters within method, Gaussian, Median and Weight arbitrarily shaped windows”. Median filtering algorithms and 12. Gajanand Gupta, “Algorithm for compare these algorithms with help Image Processing Using Improved of Peak Signal to Noise Ratio (PSNR) Median Filter and Comparison of value. Mean, Median and Improved Median Filter”. References: 13. Shitong Wang, Yueyang Li, Fu-lai 1. Anil K. Jain, “Fundamentals of Chung and Min Xu, “An Iterative Digital Image Processing”. Self-adaptive Algorithm to 2. Rafael C. Gonzalez, Richard E. Impulse Noise Filtering for Color Woods, “Digital Image Images”. Processing”. 14. Krisana Chinnasarn, “Removing 3. Alasdair McAndrew, “An Salt-and-Pepper Noise in Introduction to Digital Image Text/Graphics Images”. Processing with MATLAB”. 15. Minakshi Kumar, “Digital Image 4. Bernd Jahne, “Digital Image Processing”. Processing”. 16. Dr. K. Sri Rama Krishna, A. Guruva 5. 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 for 6. 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