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\title{Implementation of Impulse Noise Reduction Method to Color Images using Fuzzy Logic}
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             \author[1]{G Venkateswara  Rao}

             \affil[1]{  JNTU}

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\date{\small \em Received: 12 November 2011 Accepted: 2 December 2011 Published: 13 December 2011}

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\begin{abstract}
        


Image Processing is a technique to enhance raw images received from cameras/sensors placed on satellites, space probes and aircrafts or pictures taken in normal day-to-day life for various applications. Impulse noise reduction method is one of the critical techniques to reduce the noise in color images. In this paper the impulse noise reduction method for color images by using Fuzzy Logic is implemented. Generally Grayscale algorithm is used to filter the impulse noise in corrupted color images by separate the each color component or using a vector-based approach where each pixel is considered as a single vector. In this paper the concepts of Fuzzy logic has been used in order to distinguish between noise and image characters and filter only the corrupted pixels while preserving the color and the edge sharpness. Due to this a good noise reduction performance is achieved. The main difference between this method and other classical noise reduction methods is that the color information is taken into account to develop a better impulse noise detection a noise reduction that filters only the corrupted pixels while preserving the color and the edge sharpness. The Fuzzy based impulse noise reduction method is implemented on set of selected images and the obtained results are presented.

\end{abstract}


\keywords{Image Processing, Impulse noise, Fuzzy logic.}

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\let\tabcellsep& 	 	 		 
\section[{INTRODUCTION}]{INTRODUCTION}\par
rocessing of images which are digital in nature by a digital computer is called as digital image processing. Image Processing is a technique to enhance raw images received from cameras/sensors placed on satellites, space probes and aircrafts or pictures taken in normal day-to-day life for various applications. Various techniques have been developed in Image Processing during the last four to five decades. Most of the techniques are developed for enhancing images obtained from unmanned spacecrafts, space probes and military reconnaissance flights. Image Processing systems are becoming popular due to easy availability of powerful personnel computers, large size memory devices, graphics software etc. Image Processing is used in various applications such as remote sensing, medical imaging, film industry, military, etc.\par
Author ? : Asst. Professor, in MCA Department, Gayatri Vidya Parishad College for PG Courses, Rushikonda, Visakhapatnam, A.P., India. E-mail : venkyintouch@gmail.com Author ? : Asst. Professor, in CSE Department, Avanthi College of Engg \& Tech, Tamaram, Visakhapatnam, A.P., India. E-mail : balasriram1982@gmail.com a) Color Models\par
The purpose of a color model is to facilitate the specification of colors in some standard, generally accepted way. In essence, a color model is a specification of a co-ordinate system and a subspace within that system where each color is represented by a single point. 
\section[{b) Fuzzy Logic}]{b) Fuzzy Logic}\par
In this paper Fuzzy logic concept has been used in order to distinguish between noise and image characters and filter only the corrupted pixels while preserving the color and the edge sharpness. Fuzzy set theory and fuzzy logic offer us powerful tools to represent and process human knowledge represented as fuzzy if-then rules. Fuzzy image processing has three main stages: 1) image fuzzification, 2) modification of membership values, and 3) image defuzzification. The fuzzification and defuzzification steps are due to the fact that we do not yet possess fuzzy hardware. Therefore, the coding of image data (fuzzification) and decoding of the results (defuzzification) are steps that make it possible to process images with fuzzy techniques. The main power of fuzzy image processing lies in the second step (modification of membership values). 
\section[{II.}]{II.} 
\section[{METHOD a) Implementing Filter to Remove Noise}]{METHOD a) Implementing Filter to Remove Noise}\par
This method consists of two phases viz., the Detection phase and De-noising phase. The result of the detection method is used to calculate the noise-free color component differences of each pixel. These differences are used by the noise reduction method so that the color component differences are preserved. We use the red-green-blue (RGB) color space as basic color space. 1) to the neighbors in the same color band and 2) to the color components of the two other color bands. if F i denotes the input noisy image and O i the original noise-free image at pixel position , then we can express the random-value impulse noise as?? ?? ?????? = ? ?? ?? ?????? , ??????? ?????????????????????? 1 ? ?? ?? ?? ?????? , ??????? ?????????????????????? ??\par
Where ? I col is an identically distributed, independent random process with an arbitrary underlying probability density function. We consider the most used distribution: namely the uniform distribution,  the neighbors in the same color band and 2. Whether the value differences in each color band corresponds to the value differences in the other bands. Since we are using the RGB color-space, the color of the image pixel at position i is denoted as the vector F i which comprises its red (R), green (G), and blue (B) component, soF i = (F i R , F i G , F i B\par
). Let us consider the use of a sliding filter window of size nxn, , with n = 2c+1 and c E N, which should be centered at the pixel under processing, denoted as F o . For a 3 x3 window, we will denote the neighboring pixels as F 1 to F 8 (i.e., from left to right and upper to lower corner). The color pixel under processing is always represented byF o = (F 0 R , F 0 G , F 0 B )\par
The Detection phase consists of the following seven steps a) Calculation of absolute differential matrix First, we compute the absolute value differences between the central pixel F o and each color neighbor as follows:?F k R = | F o R -F k R |, ?F k G = | F o G -F k G | and ?F k B = | F o B -F k B |\par
where k = 1,?,n 2 -1 and ?F k R , ?F k G and ?F k B denote the value difference with the color at position in the R, G, and B component, respectively.\par
b) Compute the fuzzy set S1 (membership degrees) for these differences Now, we want to check if these differences can be considered as small. Since small is a linguistic term, it can be represented as a fuzzy set. Fuzzy sets, in turn, can be represented by a membership function. In order to compute the membership degree in the fuzzy set small we have to know the desired behavior, i.e., if the difference is relatively small then we want to have a large membership degree (the membership degree should decrease slowly), but after a certain point, we want to decrease the membership degree faster for each larger difference. Therefore, we have chosen the 1-Smembership function over other possible functions. This function is defined as follows:1 ? ??(??) ? ? ? ? ? 1, ???? ?? ? ?? 1 1 ? 2 ? ?? ? ?? 1 ?? 1 ? ?? 1 ? 2 , ???? ?? 1 < ?? ? ?? 1 + ?? 1 2 2 ? ?? ? ?? 1 ?? 1 ? ?? 1 ? 2 , ???? ?? 1 + ?? 1 2 < ?? ? ?? 1 0, ???? ?? > ?? 1\par
where it has been experimentally found that ? 1 =10 and ? 1 =70 receive satisfying results in terms of noise detection. In this case, we denote 1-S by S 1 , so that S 1 (?F k R ), S 1 (?F k G ), S 1 (?F k B ) denote the membership degrees in the fuzzy set small 1 of the computed differences with respect to the color at position k . ?? ?? = ? ?? 1 ?Î?"?? (?? ) ?? ? ?? ?? =1\par
where µ R denotes the degree of similarity between F 0 R and K the -nearest neighbors.d) From S1 calculate S1(RG, GB, BR) i.e differences among R, G, B components\par
Besides the first step of the detection method, i.e., checking if the central pixel is similar to its local neighborhood or not, we investigate whether the color components are correlated which each other or not. In other words, we determine whether the local differences in the R component neighborhood corresponds to the differences in the G and B component. we compute the absolute value of the difference between the membership degrees in the fuzzy set small 1 for the red and the green and for the red and the blue components, i.e., | S 1 (?F k R )-S 1 (?F k G ) and | S 1 (?F k R )-S 1 (?F k B ) | where k = 1,?,n 2 -1 , respectively. e) Compute the fuzzy set S2 (membership degrees) for these differences Now, in order to see if the computed differences are small we compute their fuzzy membership degrees in the fuzzy set small 2 .The 1-S membership function is also used but now we used ? 2 =0.01 and ? 2 =0.15 and , which also have been determined experimentally. In this case we denote the membership function as S 2 f) Calculate the joint similarity µ RG µ RB µ BG we calculate?? ?? ???? = ?? 2 ???? 1 ?Î?"?? ?? ?? ? ? ?? 1 ?Î?"?? ?? ?? ??? ?? ?? ???? = ?? 2 ???? 1 ?Î?"?? ?? ?? ? ? ?? 1 ?Î?"?? ?? ?? ???\par
where the noise was added to each color component independently. The indexes i and col indicate the 2-D where µ RG k and µ RB k denote the degree in which the local difference (between the center pixel and the pixel at position ) in the red component is similar to the local difference in the green and blue components. The obtained degrees µ RG k and µ RB k are sorted again sorted in descending order, where µ RG (J) and µ RB (J) denote the values ranked at the k th position. Consequently, the joint similarity with respect to k neighbors is computed as?? ???? = ? ?? (?? ) ???? ?? ?? =1 , ?? ???? = ? ?? (?? ) ???? ?? ?? =1\par
where µ RG and µ GB denote the degree in which the local differences for the red component are similar to the local differences in the green and blue components, respectively. Notice that if A color component is considered as noise-free if 1) it is similar to some of its neighbor values (µ R ) and 2) the local differences with respect to some of its neighbors are similar to the local differences in some of the other color components (µ RG and µ GB ).F o R is\par
In fuzzy logic, triangular norms and co-norms are used to represent conjunctions and disjunctions respectively. Since we use the product triangular norm to represent the fuzzy AND (conjunction) operator and the probabilistic sum co-norm to represent the fuzzy OR (disjunction) operator the noise-free degree of F o R which we denote as NF F R 0 is computed as follows???? ?? 0 ?? = ?? ?? ?? ???? ?? ?? + ?? ?? ?? ???? ?? ?? ? ?? ?? ?? ???? ?? ?? ?? ?? ?? ???? ?? ??\par
Analogously to the calculation of noise-free degree for the red component described above, we obtain the noise-free degrees of  
\section[{Algorithm for Impulse Noise Generator}]{Algorithm for Impulse Noise Generator}\par
Step1: Read the pixels from image ,we take some temporary variable initialize to zero. 
\section[{Step2: For Red}]{Step2: For Red}\par
Step 2.1: check the condition if temporary variable equal to zero assign color code 0x00ff0000.\par
Step 2.2: check the condition if temporary variable equal to one assign color code 0xff00ffff.\par
Step 2.  
\section[{RESULTS ANALYSIS}]{RESULTS ANALYSIS}\par
Different images as inputs are taken and apply this algorithm on these images and obtained the PSNR values .All these values are tabulated in table:1. Table  {\ref 1} : PSNR Valued of lena image corrupted with ( RIN \& FIN both ranging from 1 to 10) 
\section[{CONCLUSION}]{CONCLUSION}\par
In this paper, a new fuzzy filter for impulse noise reduction in color images is presented. The main difference between the proposed method (denoted as INR) and other classical noise reduction method is that IV.\par
the color information is taken into account in a more appropriate way .This method also illustrates that color images should be treated differently than grayscale images in order to increase the visual performance.    
\section[{REFERENCES RÉFÉRENCES REFERENCIAS}]{REFERENCES RÉFÉRENCES REFERENCIAS}\begin{figure}[htbp]
\noindent\textbf{2011}\includegraphics[]{image-2.png}
\caption{\label{fig_0}P © 2011}\end{figure}
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\noindent\textbf{}\includegraphics[]{image-3.png}
\caption{\label{fig_1}}\end{figure}
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\noindent\textbf{}\includegraphics[]{image-4.png}
\caption{\label{fig_2}c)}\end{figure}
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\noindent\textbf{}\includegraphics[]{image-5.png}
\caption{\label{fig_3}}\end{figure}
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\noindent\textbf{}\includegraphics[]{image-6.png}
\caption{\label{fig_4}}\end{figure}
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\noindent\textbf{1}\includegraphics[]{image-7.png}
\caption{\label{fig_5}Figure 1 :}\end{figure}
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\noindent\textbf{}\includegraphics[]{image-8.png}
\caption{\label{fig_6}}\end{figure}
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\noindent\textbf{} \par 
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\end{longtable} \par
 
\caption{\label{tab_1}}\end{figure}
 			\footnote{© 2011 Global Journals Inc. (US) Global Journal of Computer Science and Technology Volume XI Issue XXII Version I} 			\footnote{DecemberImplementation of Impulse Noise Reduction Method to Color Images using Fuzzy Logic} 			\footnote{DecemberImplementation of Impulse Noise Reduction Method to Color Images using Fuzzy Logic III.} 			\footnote{DecemberImplementation of Impulse Noise Reduction Method to Color Images using Fuzzy Logic} 		 		\backmatter  			  				\begin{bibitemlist}{1}
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\end{document}
