DENOISING COLOR IMAGES USING WAVELET BASED FUZZY FILTERING Dr.R.Dineshkumar, Dr.M.Kalimuthu, Dr.C.Sridhathan

INTERNATIONAL JOURNAL OF SCIENTIFIC & TECHNOLOGY RESEARCH VOLUME 9, ISSUE 03, MARCH 2020 ISSN 2277-8616 DENOISING COLOR IMAGES USING WAVELET BASED FUZZY FILTERING Dr.R.Dineshkumar, Dr.M.Kalimuthu, Dr.C.Sridhathan

Abstract— Image processing involves various steps to be carried on selected images. The first process includes, noise removal, the process to remove irrelevant information present in the images. Mostly the images are affected with noise (blur, cracks etc,).Preprocessing steps applied on the image gains the original quality of the image in terms of color, shape, size etc.Denoising gives the good quality image by applying either linear or non linear filtering. The various traditional linear and non linear filtering techniques applied to remove noise present in the images. In this paper, the wavelet based fuzzy filtering is applied on different images and the performance analysis is made with other different filtering techniques. The implementation is processed in MATLAB with four different images with good accuracy and quality of images. Index Terms— Linear Filtering, Non linear filtering, Noise removal, Mean Square Error, PSNR, Fuzzy filtering, Median filtering

1 INTRODUCTION Denoising is the procedure to remove the noise from the image without affecting the quality of the image. The images 2 RELATED WORKS are normally carried out with additive, Gaussian and random 2.1 Hann Window (Mean filtering) noise. The noise image reduces the quality of the image and Hann window is defined as smooth function given in Equation also the low contrast images are not visible to the human 2. eyes. Noise removal is the important process to enhance the quality and also to identify the hidden data in the images. Two H(t)=1+COS(t), -π ≤ t ≤ π types of filtering are used to remove the noise such as linear (2) and non linear filters [1].Linear filters are used to remove the The Hann window works with the complex exponent which Gaussian noise. The linear filters are implemented by increases the accuracy without affecting the quality of the convolution mark and weighted sum of pixels in successive image. [3] windows [2]. The linear filter is shown below in Equation (1) 2.2 Gaussian Filtering ∞ y (t) = In horizontal direction the mask is used to smooth an image. ∫∞ (h (r). x (t – r) dr) (1) Horizontal and vertical directions are the two dimensional Gaussians. The mask weight is obtained from the discrete Image Filtering Gaussian distributions to ensure the intensity is not affected [4]. 10 5 3 F * n 1 1 2 2 2 1 1 1 2 2 4 2 2 1 4 5 1 7 2 2 4 8 4 2 2 1 1 7 2 4 8 16 8 4 2

2 2 4 8 4 2 2 Linear filtering 7 1 2 2 4 2 2 1 1 1 2 2 2 1 1

10 5 3 0 0 0 Fig 2. 7 X 7 Gaussian mask 2.3 Median filtering 4 5 1 0 0.5 0 The steps included in median filtering are: 1 1 7 0 1.0 0.5 Step 1: In a given image consider all the pixels in to account Fig 1.Image and linear filtering Step 2: With their intensities sort the neighboring pixels in order Step 3: The median value is replaced on the original value of the pixel Non linear filter doesn’t match the property of output with its In median filtering the output pixel is obtained by median of the input. This filtering technique uses the neighboring pixel values neighboring pixel. The median filtering is suitable than the instead of convolution or Fourier multiplication. mean filtering in terms of sharpness of the image [5]. 3 PROPOSED WORK 3.1 Wavelet based Fuzzy Filter  Dr.R.Dinesh Kumar Professor, Siddhartha Institute of Tech.& Sciences, Wavelet based fuzzy filter provides the better performance and Hyderabad, India E-mail: [email protected]  Dr.M.Kalimuthu, Professor, Malla Reddy Institute of Technology, accuracy on the quality of the image when compared to other Hyderabad, India. filtering techniques. It recovers more noise affected images  Dr.C.Sridhathan, ,Technical Head, TechGarage ,Chennai ,India also.

The results of different and proposed filtering techniques is Wavelet Filter Fuzzy Filter shown in the fig

Magnitude Weighted Local Correction Noisy and function Derivative Terms Noiseless image Spatial image Similarity Fig 4.Sample Input Images Fig 3.Wavelet based Fuzzy Filter

This filtering technique is used to remove additive noise. It consists of two phases namely, wavelets, which differentiate between local variations and fuzzy filter remove the noise without affecting the quality of the image by considering the Red, Green, Blue local differences. Fig 5. Hann window 3.2 Gaussian Noise Removal RGB model is constructed in 3D vector.Color image is denoted as 2D vector.The Gaussian coefficients is expressed in terms of the Equation (1) N (I,j,1)N (I,j,2)N (I,j,3)=[(C (I,j,1)+η1)(C (I,j,2))+ s,d s,d s,d s,d s,d η2)(Cs,d(I,j,3) )+η3)] (3) Fig 6. Gaussian filtering Ns,d --> wavelet coefficient s and d with noise free

Cs,d --> wavelet coefficient s and d with noisy

3.3 Wavelet filter The steps for the wavelet filters are as follows: Step 1: Consider Image pixel at position (i,j) create window size of (2K+1)*(2K+1) Fig 7. Median filtering Step 2: In each single channel obtain the feature from non linear averaging filter Step 3: Calculate large weights and assign to neighboring coefficients. The weights for the red, green and blue at position (i+k,j+l) are w(i+k,j+l,1), w(i+k,j+l,2) and w(i+k,j+l,3) respectively. Step 4: Next, for the red, green and blue component calculate the magnitude and spatial similarity fuzzy function. and Fig 8. Wavelet based fuzzy filtering is shown in Equation (4)(5)(6)

4 PERFORMANCE ANALYSIS w(i+k,j+l,1)= m(i+k,j+l,1) * s(i+k,j+l,1) (4) The proposed method is used to remove the additive noise w(i+k,j+l,2)= m(i+k,j+l,2) * s(i+k,j+l,2) (5) from the colored image. This wavelet based fuzzy filtering technique applied to different images and the performance is w(i+k,j+l,3)= m(i+k,j+l,3) * s(i+k,j+l,3) (6) obtained by comparing the output of each filtering technique with the proposed work. The two metrics have been Step 5: The red, green and blue component, output image considered, Mean Square Error and Peak Signal to Noise wavelet filter is calculated Ratio, to obtain the good quality of the image.

3.4 Fuzzy filter 4.1 Mean Square Error The working of fuzzy filter is provided below The minimum MSE reflects the high quality image from the noisy image. The Equation (7) is used to calculate MSE Step 1: For the red (LDR) ,green (LDG) and blue (LDB) the

gradient and derivatives are calculated ∑ ∑ ( ( . ) ( . )) Step 2: Correction terms is calculated for 3X3 window

Step 3: Obtain the fuzzy filter output for RGB. (7)

Where I1 Denoised image I2  Image with noise M Input image row M Input image column

4.2 Peak Signal to Noise Ratio

The measurement of the quality of the image depends on the peak signal to noise ratio. The higher PSNR denotes the good quality image. The Equation (8) is used to calculate PSNR values.

2 PSNR = 10 log10 (R / MSE) (8)

Table 1 MSE values for different filtering technique Fig 8.Chart representation of average MSE and

Sample Hann Gaussian Median Wavelet PSNR values with different filtering techniques Input window Filtering Filtering based Images Fuzzy 5 CONCLUSION Filtering The additive noise removal is carried out using wavelet based Bird 16.82 16.25 14.56 3.63 fuzzy filtering techniques.The output of the wavelet based Tiger 192.98 129.65 25.66 18.45 fuzzy filtering techniques is compared with different other Bear 186.66 132.35 25.34 4.87 techniques based on MSE and PSNR values.The wavelet Elephant 64.92 25.32 22.45 9.67 based fuzzy filtering techniques gives the better accuracy in smoothing additive noise.

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