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    Volume 1, No. 9, November 2012 ISSN 2278-1080The International Journal of Computer Science &

    Applications (TIJCSA)RESEARCH PAPER

    Available Online athttp://www.journalofcomputerscience.com/

    2012,http://www.journalofcomputerscience.com-TIJCSAAllRightsReserved 9

    Adaptive Fuzzy Approach to Gaussian Noise Removal

    in Gray Scale Images

    Deepinder Kaur1

    Department of Computer Science & Engineering,

    B.B.S.B.E.C,

    Fatehgarh Sahib(Punjab), India

    [email protected]

    Baljit Singh2

    Department of Computer Science & Engineering,

    B.B.S.B.E.C,

    Fatehgarh Sahib(Punjab), India

    [email protected]

    Abstract

    Visual information transmitted in the form of digital images is becoming a major method of

    communication in the modern age, but the image obtained after transmission is often corrupted

    with noise. The received image needs processing before it can be used in applications. A New

    Fuzzy Filter that adopts Fuzzy Logic is proposed in this paper which removes Gaussian Noise

    from the Corrupted Gray scale Images. The main concern of the present filter is to distinguish

    between local variations due to noise and due to image structure. It uses 14 fuzzy rule based

    convolution mask on every pixel of the image. Objective performance of the proposed algorithm

    is compared with conventional methods based on Mean Square Error (MSE), Root Mean Square

    Error (RMSE), Signal to Noise Ratio (SNR) and Peak Signal to Noise Ratio(PSNR). The results

    illustrate that the proposed method can be used as an effective Noise removal method for

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    Gaussian noise. Results show that by using the proposed method improved SNR and PSNR and

    minimized MSE and RMSE are achieved. Hence proposed algorithm leads to better image

    enhancement.

    Keywords: Fuzzy logic; Gray scale; Median Filter; Mean Filter; Gaussian noise; Impulse

    noise; Multiplicative Noise; Correction term.

    1. IntroductionDigital images are used in various applications in todays life. Digital images are corrupted by

    noise during image acquisition or transmission process. There are different types of noises indigital images. For example, Additive white Gaussian noise (AWGN) is due to image sensors

    operating at low light levels, poor image acquisition or by transferring the image data in noisycommunication channels. Gaussian noise is statistical noise that has its probability density

    function equal to that of the normal distribution, which is also known as the Gaussiandistribution. In other words, the values that the noise can take on are Gaussian-distributed.

    Gaussian noise is properly defined as the noise with a Gaussian amplitude distribution. This saysnothing of the correlation of the noise in time or of the spectral density of the noise. Labeling

    Gaussian noise as 'white' describes the correlation of the noise. It is necessary to use the term"white Gaussian noise" to be precise. Gaussian noise is sometimes misunderstood to be white

    Gaussian noise, but this is not the case.

    Noise is modeled as additive white Gaussian noise (AWGN), where all the image pixelsdeviate from their original values following the Gaussian curve. That is, for each image pixel

    with intensity value fij

    (1 i m, 1 j n for an m x n image), the corresponding pixel of the

    noisy image gij

    is given by,

    (1)

    where, each noise value n is drawn from a zero -mean Gaussian distribution as shown in fig 1.

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    Fig 1. Gaussian Distribution Curve

    Denoising is the pre-processing step in the Image Enhancement process. Denoising isnecessary and first step to be taken before the image data is analyzed for further use. Because

    after introducing the noise in image, the important details and features of image are destroyed. Itis necessary to apply efficient denoising technique to compensate for such data corruption. Image

    denoising is used to remove the noise while retaining as much as possible the important signalfeatures. The purpose of image denoising is to estimate the original image from the noisy data.

    2. Existing Methods

    Generally, the Gaussian noise can easily be removed by locally averaging the pixels inside thewindow and replace the current pixel with this average value. Conventional linear filters such as

    arithmetic mean filter and Gaussian filter smooth noises effectively but blur edges. Statisticalcharacteristics of images are of fundamental importance in removing Gaussian noise. The well

    known wiener filter assumes the images are second order stationary. But for most natural imagesthe stationary assumption is not valid. The Wiener filter [2] experiences uniform filtering

    throughout the image, with an unacceptable blurring of fine detail across edges and inadequatefiltering of noise in relatively flat areas. To overcome the problem of linear filtering, non-linear

    filtering techniques become popular as an alternative to preserve signal structure. Median filter[3][4]is quite popular non linear denoising filter because it provide excellent noise reduction

    capabilities with considerably less blurring than linear smoothening filters of same size. Forimpulsive noise, the median filter is one of the best. But for Gaussian noise, it is less successful.

    A compromise between the mean and median is trimmed mean filters. The idea behind atrimmed mean is to reject the most probable outliers-some of the very smallest and very largest

    values and average the rest. Alpha trimmed mean filter [5] is a one which performs the operationof both mean and median filter based on the value of. It gives better noise reduction with some

    smoothening capabilities. The K-nearest neighbour filter [6] also a trimmed mean filter. Ithandles only the values closest to the value of the center sample. The value K decides the

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    smoothening capability. In [7] Perona and Malik have proposed an anisotropic diffusion method

    for Gaussian noise removal. In [8] Tomasi and Manducci have proposed a bilateral filter toremove Gaussian noise with edge preservation. Recently Tamer Rabie [9] proposed a robust

    estimation based algorithm to remove gaussian noise. It effectively removes low to mediumdensity Gaussian noise with edges are better preserved. In [10] R.Garnett and T.Huegerich have

    proposed a universal noise removal algorithm to remove Gaussian noise and other types ofnoises. In all these methods complexity of the algorithm is high. In this paper we proposed a

    Fuzzy rule based method to remove low to high density Gaussian noise with detailspreservation.

    3. Proposed Method

    Fuzzy set theory [11,12,13] has been successfully applied to pattern recognition fields. It is

    suitable for dealing with problems containing high levels of uncertainty, to which class patternrecognition or image processing problems usually belong. Obviously, the recovery of heavilynoise-corrupted images is a task with high uncertainty levels. The general idea behind the filter is

    to average a pixel using other pixel values from its neighborhood, but simultaneously to take careof important image structures such as edges. The main concern of the present filter is to

    distinguish between local variations due to noise and due to image structure. It uses 14 fuzzy rulebased convolution mask on every pixel of the image. Fuzzy membership functions used in this

    algorithm are not static instead it uses an adaptive approach based on the neighborhood pixels.The 3*3 mask selected for image scanning passes on pixel values to the fuzzy system input. In

    this mask each pixel is considered as an input image processing values between 0-255. Valuesof the mask are obtained by hit and trial method. Rules are determined based on pixel vicinity

    status. These rules have been written studying different states and special edge conditions. Theconsidered 3*3 mask scans all image gray surfaces and pixels are examined according to

    predefined rules[19,20,21].

    Algorithm:

    Step-1: Take Noisy Image as Input image.

    Step2: Repeat the steps 3 to 8 for each pixel present in the input image.

    Step3: Consider current pixel as Center Pixel (Centre_pixel).

    Steps4: Clear the values Linear arrays Fuzzy[] and Possible_outcomes[].

    Step5: Apply 14 Fuzzy rule based filter masks on the Centre_pixel and initialize the linear arrayFuzzy[] by Fourteen different responses Ri.

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    X X X

    X X

    X

    X X

    X

    X

    X

    X

    X XX

    X

    X X

    X

    X

    X

    XX X

    X

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    Fig 2: The collection of fuzzy masks

    Step6. Update Linear array Possible_outcomes[] with the values of linear array Fuzzy[]according to the following rules:

    a) Add The values of linear array Fuzzy[] to Possible_outcomes[] if the values lies betweenthe range of Value(Left_pixel) and Value(Centre_pixel). Do not repeat the contents ifalready exists in linear array possible_outcomes[].

    b) Add The values of linear array Fuzzy[] to Possible_outcomes[] if the values lies betweenthe range of Value(Right_pixel) and Value(Centre_pixel). Do not repeat the contents if

    already exists in linear array possible_outcomes[].c) Add The values of linear array Fuzzy[] to Possible_outcomes[] if the values lies between

    the range of Value(Up_pixel) and Value(Centre_pixel). Do not repeat the contents if

    already exists in linear array possible_outcomes[].d) Add The values of linear array Fuzzy[] to Possible_outcomes[] if the values lies betweenthe range of Value(Down_pixel) and Value(Centre_pixel). Do not repeat the contents if

    already exists in linear array possible_outcomes[].

    Step7: Sort the contents of linear array Possible_outcomes[] in ascending order.

    Step8: Find the median M from the contents of Linear array Possible_outcomes[] .

    Step 9: Set Value[Center_pixel]=M in output image.

    Step 10: Exit.

    X

    X X

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    Output Image

    Fig 3. Flowchart for proposed algorithm

    4. Results And Conclusions

    The proposed algorithm has been implemented on a set of different digital images. Fuzzy Logic

    has been used to get the denoised image of any digital image. All the simulations are done using

    VB.Net.

    NOISY IMAGE

    APPLY 3*3 CONVOLUTION

    MASK IN ALL POSSIBLE WAYS

    APPLY FUZZY RULES TO SELECT

    THE REQUIRED POSSIBLE

    OUTCOMES

    FIND MEDIAN OF ALL POSSIBLE

    OUTCOMES

    KNOWELDGE BASE

    CORRECTION

    TERM

    REPLACE THE CURRENT PIXEL

    WITH MEDIAN

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    Noisy Image Mean Filter

    Median Filter Proposed Algorithm

    Fig4. Comparison of Filters for Figure 1.tif with noise variance 2.6

    Table 1. Comparison of MSE of existing filters with proposed algorithm for 1.tif

    Variance( ) 1 1.4 1.8 2.2 2.6

    Mean Filter 0.0077 0.0043 0.0026 0.0020 0.0016

    Median Filter 0.0011 0.0005 0.0003 0.0002 0.0002

    Proposed

    Algorithm

    0.0006 0.0002 0.0001 0.0001 0.0001

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    Table 2. Comparison of RMSE of existing filters with proposed algorithm for 1.tif

    Variance( ) 1 1.4 1.8 2.2 2.6

    Mean Filter 0.0880 0.0657 0.0517 0.0448 0.0408

    Median Filter 0.0341 0.0238 0.0182 0.0156 0.0142

    Proposed

    Algorithm

    0.0246 0.0170 0.0130 0.0113 0.0103

    Table 3. Comparison of SNR of existing filters with proposed algorithm for 1.tif

    Variance( ) 1 1.4 1.8 2.2 2.6

    Mean Filter 0.5260 0.3483 0.2558 0.2123 0.1863

    Median Filter 0.7862 0.5359 0.3984 0.3322 0.2930

    Proposed

    Algorithm

    2.2095 1.6426 1.2675 1.0701 0.9427

    Table 4. Comparison of PSNR of existing filters with proposed algorithm for 1.tifVariance( ) 1 1.4 1.8 2.2 2.6

    Mean Filter 69.231 71.773 73.854 75.093 75.897

    Median Filter 77.456 80.587 82.900 84.227 85.032

    Proposed

    Algorithm

    80.279 83.519 85.801 87.064 87.829

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    0

    0.001

    0.002

    0.003

    0.004

    0.005

    0.006

    0.007

    0.008

    0.009

    1 1.4 1.8 2.2 2.6

    MSE

    VARIANCE

    MeanFilter

    MedianFilter

    FuzzyFiltering

    Fig 6. Comparison of MSE of existing filters with proposed algorithm for 1.tif

    0

    0.01

    0.02

    0.03

    0.04

    0.05

    0.06

    0.07

    0.08

    0.09

    0.1

    1 1.4 1.8 2.2

    RMSE

    VARIANCE

    MeanFilter

    MedianFilter

    FuzzyFiltering

    Fig 7. Comparison of RMSE of existing filters with proposed algorithm for 1.tif

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    0

    0.5

    1

    1.5

    2

    2.5

    1 1.4 1.8 2.2 2.6

    SNR

    VARIANCE

    MeanFilter

    MedianFilter

    FuzzyFiltering

    Fig 8. Comparison of SNR of existing filters with proposed algorithm for 1.tif

    0

    1020

    30

    40

    50

    60

    70

    80

    90

    100

    1 1.4 1.8 2.2 2.6

    PSNR

    VARIANCE

    MeanFilter

    MedianFilter

    FuzzyFiltering

    Fig 9. Comparison of PSNR of existing filters with proposed algorithm for 1.tif

    This thesis has briefly overviewed the methods for Gaussian Noise Removal so many methodshave been proposed till now but the proposed algorithm has shown better results. The work

    presented in this thesis concludes that Fuzzy Based Approach is best method for yieldingdenoised images provided appropriate Fuzzy rules are chosen. Improved value of SNR, PSNR

    and minimized value of MSE and RMSE of proposed algorithm shows that objectiveperformance improvement is achieved. In the proposed method all the techniques and operations

    provide an efficient working and the output image is enhanced according to the usersrequirements. Proposed Filter can clean an image completely of noise without making it blurry.

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    [19] A.Taguchi, H.Takahima, and F.Russo," Data Dependent Filtering using The Fuzzy

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