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\title{Novel Color Image Compression Algorithm Based on Quad tree}
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             \author[1]{Dr. A. A.  El-Harby}

             \author[2]{G. M.  Behery}

             \affil[1]{  Damietta University}

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\date{\small \em Received: 13 February 2012 Accepted: 29 February 2012 Published: 15 March 2012}

\maketitle


\begin{abstract}
        


This paper presents a novel algorithm having two image processing systems that have the ability to compress the colour image. The proposed systems divides the colour image into RGB components, each component is selected to be divided. The division processes of the component into blocks are based on quad tree method. For each selection, the other two components are divided using the same blocks coordinates of the selected divided component. In the first system, every block has three minimum values and three difference values. While the other system, every block has three minimum values and one average difference. From experiments, it is found that the division according to the G component is the best giving good visual quality of the compressed images with appropriate compression ratios. It is also noticed, the performance of the second system is better than the first one. The obtained compression ratios ofthe second system are between 1.3379 and 5.0495 at threshold value 0.1, and between 2.3476 and 8.9713 at threshold value 0.2.

\end{abstract}


\keywords{components, systems, algorithm}

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\let\tabcellsep& 	 	 		 
\section[{Introduction}]{Introduction}\par
any modern imaging systems are still producing gray-scale images, color images are more preferred due to the larger amount of information contained by them \hyperref[b0]{[1]}. There are many compression systems were used to compress the color images; these systems include those that use mathematical transforms such as Discrete Cosine Transform (DCT) transform \hyperref[b1]{[2]}\hyperref[b2]{[3]}\hyperref[b3]{[4]}, neural networks \hyperref[b4]{[5]}\hyperref[b5]{[6]}\hyperref[b6]{[7]}\hyperref[b7]{[8]}, wavelet transform \hyperref[b8]{[9]}\hyperref[b9]{[10]}\hyperref[b10]{[11]}, fractal \hyperref[b11]{[12]}\hyperref[b12]{[13]}\hyperref[b13]{[14]}, quad tree systems \hyperref[b14]{[15]}\hyperref[b15]{[16]}\hyperref[b16]{[17]}, and others \hyperref[b17]{[18]}\hyperref[b18]{[19]}\hyperref[b19]{[20]}\hyperref[b20]{[21]}\hyperref[b21]{[22]}. Data compression provides two advantages: reducing storage space and transmission time by finding the humanly imperceptible differences \hyperref[b22]{[23]}\hyperref[b23]{[24]}.\par
The quad tree algorithms are based on simple averages and comparisons. Quad-tree image compression is a method for splitting an image into homogenous sub-blocks. Defining the whole image as a single block, the method is performed according to some problem specific homogeneity criteria. Each block is examined to check whether it is homogenous or not. If it is not, then it will be split into four same-sized blocks. The method terminates when there is no other blocks to be split or when all blocks to be split are smaller than a pre-selected size. The minimum size of the blocks is set, to avoid over segmentation \hyperref[b24]{[25]}\hyperref[b25]{[26]}\hyperref[b26]{[27]}\hyperref[b27]{[28]}.A major advantage of the quad tree system for data compression is the simplicity of its approach. Unlike many other compression systems, a quad tree algorithm can compress images relatively quickly on a personal computer \hyperref[b28]{[29,}\hyperref[b29]{30]}.\par
Usually, distortion in images is measured by the PSNR (Peak-to-peak Signal to Noise Ratio). This ratio is often used as a quality measurement between the original and a compressed image. There is no standard way of defining distortion and PSNR for color images. The simplest way is to just average the distortions of the three RGB color components \hyperref[b30]{[31,} {\ref 32]}.\par
In this paper, an algorithm is applied on color images. The remainder of this paper is organized as follows: in Section 2, the proposed algorithm is illustrated. Experimental results and discussion are presented in Section 3 and finally, some conclusions are addressed in Section 4. 
\section[{II.}]{II.} 
\section[{Proposed algorithm}]{Proposed algorithm}\par
This algorithm contains two systems based on quad tree. Each one contains three different cases. The RGB color images are represented by three components. In gray-scale image there is a high correlation between neighbor pixels. In color image, in addition to this, there is also a high correlation between color components \hyperref[b1]{[2,}\hyperref[b2]{3]}. Therefore, the proposed systems are applied on the all components altogether. In the first system, one component is chosen to be divided using quad tree at specified threshold value. During the dividing of this component, even if the condition of quad tree division is not verified for the other two components, they are divided simultaneously using the same coordinates and block size of the chosen component. The condition is represented by difference value is greater than threshold value. There are three cases of this system are described as follows: 1. The image is divided according to the component R using quad tree. At the same time, the dividing process is applied on the other two components G and B respectively. After the dividing is completed, the three components will have the same numbers, sizes, and coordinates of all blocks. 2. This case is similar to the first one, except, the image is divided according to the second component G, and the dividing process is applied on the other two components R and B respectively. 3. The third case is similar to the previous two cases, except, the image is divided according to the third( D D D D ) F\textbf{2012}\par
Year component, and the dividing process is applied on the other two components R and G respectively.\par
In each case, the image is divided giving the following information for the three components: number of blocks, sizes, minimum value and difference between maximum and minimum values for each block. The three components have the same coordinates and sizes for all blocks. In the three components, any block has three min values and three diff values, one for each component.\par
The second system is similar to the first one including the above three cases, except, the three difference values are averaged for each block. The obtained information of every block is one coordinates, one size, three minimum values and one average difference value. The two systems are illustrated in details in the next sub section.\par
Several quality measures can be found in the open literature of the field. The most used measures are (distortion evaluation): The mean squared errors (MSE) and the popular peak signal to noise ratio (PSNR) \hyperref[b1]{[2]}.With gray level images, the PSNR is expressed by: MSE While, for color RGB images case [32], we have used the relation given in? ? ? ? ? ? ? ? + + × × = ) ( ) ( ) ( 3 255 log 10 PSNR 2 10 B MSE G MSE R MSE (2) ( ) 2 1 0 1 0 ij ij y X 1 ?? ? = ? = ? × = N i M j M N MSE (3)\par
and, : are, respectively, the original and reconstructed intensities belonging to R, G or B component. The compressed image is evaluated with the compression ratio (CR) or withthebite-rateperpixel(bpp) defined as follows:bits in image Compressed bits in size image color RGB Original CR = (4) CR bits 24 bpp = (5) a) Example\par
This example is proposed to describe the processes of the two systems. The example is applied on a sample of color image for size 8x8x3. The R component is firstly chosen to be divided using quad tree. The other two components will be divided using the same coordinates and block size of the chosen divided component, even if the condition of quad tree division is not verified for one or both components. In the first system, each block has three min values and three difference values, one for each component. For instance, the block of coordinates (4, 0) has the three minimum values (80, 25, and 11) and the three difference values (5, 77, and 6), see Fig.  {\ref 1} and table 1 for more details. While, the second system has three minimum values and one average difference. The above mentioned block of coordinates (4, 0) has the same three minimum values and one average difference value \hyperref[b28]{(29)}, see Fig.  {\ref 2}     
\section[{Experimental results and discussion}]{Experimental results and discussion}\par
In order to test the performance of the two proposed systems, they are applied using the same settings on four famous color images. These images are called Splash, Lena, Sailboat, and Pepper; see Fig.   {\ref -7}). The columns S1R, S1G, and S1B represent the three components of the color image for the first system.\par
The other forty eight experiments are carried out using the second system using the same threshold values that are proposed with the first system. The obtained results are shown in the second three columns of the Figures (  {\ref 4-7}). The columns S2R, S2G, and S2B are represented for the second system. The compression ratio is obtained by dividing the size of the original image file by the size of the compressed output file. From the above experiments of the two systems, Tables \hyperref[b1]{(2)}\hyperref[b2]{(3)}\hyperref[b3]{(4)}\hyperref[b4]{(5)} show the obtained compression ratios, bpp, PSNR and number of blocks in the compressed images. All programs are written using the Matlab software.\par
From figures (4-9) and Tables (2-5), it can be seen the following:\par
-In the two systems, the number of blocks decreases when the original image has low details (for instance Splash image); see Table \hyperref[tab_6]{5} and Figure \hyperref[b8]{(9)}.\par
-In the first system, the compression ratio is ranged between 1.0406:1 and 79.7275:1, while with the second system, the compression ratio is between 1.3379:1 and 102.5068:1. It is seen that the second system has the highest compression ratio.\par
-In the first system, the bpp is rangedbetween 23.0633 and 0.3010, while with the second system, the bpp is between 17.9381 and 0.2341. It is seen that the second system has the lowest bpp value.\par
-In the first system, the PSNR is rangedbetween 16.7784 and 10.7710, while with the second system, the PSNR is between 16.0773 and 15.5210.\par
-The visual quality of the compressed images and PSNR values are inversely proportional tothe compression ratio; see figures (4-7).\par
-In the two systems, the compression ratios increase when the original image has low details (for instance Splash image); see table 2 and Figure \hyperref[b7]{(8)}.\par
-\par
The compressed images quality increase when the image is divided according to the component G. 
\section[{-}]{-}\par
The compression ratios are proportional to the threshold values.\par
In Table \hyperref[tab_7]{6}, is presented comparative results among our proposed two systems and others, compression ratio is measured in terms of bpp and the image quality in terms of PSNR.          S1 R S1 G S1 B S2 R S2 G S2 B S1 R S1 G S1 B S2 R S2 G S2 B Image Name Threshold = 0.1 Threshold = 0.2 S1 R S1 G S1 B S2 R S2 G S2 B S1 R S1 G S1 B S2 R S2 G S2 B Sailboat 1. 
\section[{Conclusion}]{Conclusion}\par
This paper presents two efficient systems that have the ability to compress colour images in easy way. The division processes of image into blocks for the two systems are based on quad tree. At the dividing of one component, the other two components are divided using the same division even if the condition of quad tree division is not verified for them. After the division process is completed, the three components will have the same number and size of blocks. During the experimental results, the compression ratios, bit rate per pixel and PSNR are computed. The compression ratios of images are increased by increasing the value of threshold while the quality of the compressed images may be decreased. It was also noticed, the division according to the G component is the best giving good quality of the compressed images with appropriate compression ratios, and the performance of the second system is better than the first one. The compression ratios of the second system are ranged between 0.25 and 0.80 at threshold value 0.1, and between 0.78 and 0.94 at threshold value 0.2. \begin{figure}[htbp]
\noindent\textbf{12}\includegraphics[]{image-2.png}
\caption{\label{fig_1}Fig. 1 :Fig. 2 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{3}\includegraphics[]{image-3.png}
\caption{\label{fig_2}( 3 )}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{}\includegraphics[]{image-4.png}
\caption{\label{fig_3}}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{341563752}\includegraphics[]{image-5.png}
\caption{\label{fig_4}Fig. 3 :Fig. 4 : 1 Fig. 5 :Fig. 6 : 3 Fig. 7 : 5 Table 2 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{8}\includegraphics[]{image-6.png}
\caption{\label{fig_5}Fig. 8 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{9}\includegraphics[]{image-7.png}
\caption{\label{fig_6}Fig. 9 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{} \par 
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\caption{\label{tab_0}}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{1} \par 
\begin{longtable}{P{0.017461895294897282\textwidth}P{0.0022531477799867462\textwidth}P{0.04224652087475149\textwidth}P{0.596520874751491\textwidth}P{0.09857521537442014\textwidth}P{0.014082173624917163\textwidth}P{0.04393638170974155\textwidth}P{0.005069582504970179\textwidth}P{0.005632869449966865\textwidth}P{0.0022531477799867462\textwidth}P{0.021968190854870773\textwidth}}
\tabcellsep \tabcellsep \tabcellsep \tabcellsep \multicolumn{2}{l}{Minimum Values}\tabcellsep \multicolumn{4}{l}{Difference Values}\\
\tabcellsep \tabcellsep 0 1 2 3\tabcellsep 0 10 18 19 95 95 99 98 8 15 22 24 98 101 95 95 35 30 48 46 99 100102101 36 37 45 50 95 100102100\tabcellsep 0 10 18 8 15 30 45\tabcellsep 95\tabcellsep 0 0 0 0 7\tabcellsep 6 5\tabcellsep 7\tabcellsep \\
\tabcellsep \tabcellsep 4\tabcellsep 83 82 81 84 73 72 75 71\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
\tabcellsep \tabcellsep 5 6\tabcellsep 83 80 85 83 73 70 71 70 80 85 84 80 75 74 73 71\tabcellsep 80\tabcellsep 70\tabcellsep 5\tabcellsep \tabcellsep 5\tabcellsep \\
R\tabcellsep \tabcellsep 7\tabcellsep 81 81 80 80 75 75 75 70\tabcellsep (a)\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
RGB color\tabcellsep G\tabcellsep 0 1 2 3 4\tabcellsep 60 65 67 73 72 77 71 60 64 66 72 74 75 76 64 65 64 74 73 71 71 60 61 63 73 74 77 71 28 30 30 50 51 52 53\tabcellsep 60 65 66 60 64 60 62\tabcellsep 71\tabcellsep 0 0 0 0 5\tabcellsep 1 4\tabcellsep 6\tabcellsep \tabcellsep RGB compressed\\
image\tabcellsep \tabcellsep 6 5\tabcellsep 95 96 102 52 52 50 50 25 30 25 50 52 54 55\tabcellsep 25\tabcellsep 50\tabcellsep 77\tabcellsep \tabcellsep 7\tabcellsep \tabcellsep image\\
\tabcellsep \tabcellsep 7\tabcellsep 100 94 100101 51 54 56 57\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep (b)\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
B\tabcellsep \tabcellsep 0 2 3 1\tabcellsep 10 12 14 17 17 16 13 17 11 12 14 14 14 10 15 14 17 16 16 15 15 10 11 16 16 16 16 14\tabcellsep 10 12 14 11 12 10 11\tabcellsep 10\tabcellsep 0 0 6 0 0\tabcellsep 2 5\tabcellsep 7\tabcellsep \\
\tabcellsep \tabcellsep 4\tabcellsep 16 12 11 13 44 13 10\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
\tabcellsep \tabcellsep 5 6\tabcellsep 15 12 11 12 12 12 11 17 11 11 11 11 10 12\tabcellsep 11\tabcellsep 10\tabcellsep 6\tabcellsep \tabcellsep 34\tabcellsep \\
\tabcellsep \tabcellsep 7\tabcellsep 16 11 11 11 11 10 12\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep (c)\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
\tabcellsep \tabcellsep \tabcellsep 0 2 3 4 5 6 7\tabcellsep \multicolumn{2}{l}{Minimum Values}\tabcellsep \multicolumn{4}{l}{Average Difference}\\
\tabcellsep \tabcellsep 0 1 2 3\tabcellsep 0 10 18 19 95 95 99 98 8 15 22 24 98 101 95 95 35 30 48 46 99 100102101 36 37 45 50 95 100102100\tabcellsep 0 10 18 8 15 30 45\tabcellsep 95\tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
\tabcellsep \tabcellsep 4\tabcellsep 83 82 81 84 73 72 75 71\tabcellsep \tabcellsep 70\tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
\tabcellsep \tabcellsep 5 6\tabcellsep 83 80 85 83 73 70 71 70 80 85 84 80 75 74 73 71\tabcellsep 80\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
\tabcellsep R\tabcellsep 7\tabcellsep 81 81 80 80 75 75 75 70\tabcellsep \multicolumn{2}{l}{(a)}\tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
RGB color image\tabcellsep G\tabcellsep 0 1 2 3 4 6 5\tabcellsep 60 66 67 73 72 77 71 60 67 66 72 74 75 76 64 66 64 74 73 71 71 60 62 63 73 74 77 71 28 28 30 50 51 52 53 95 98 102 52 52 50 50 25 30 25 50 52 54 55\tabcellsep 60 65 66 60 64 60 62 25\tabcellsep 71 50\tabcellsep \multicolumn{2}{l}{0 0 0 0 6 29}\tabcellsep 3 5\tabcellsep 7 15\tabcellsep RGB compressed image\\
\tabcellsep \tabcellsep 7\tabcellsep 100 100101 51 54 56 57\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep \multicolumn{2}{l}{(b)}\tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
\tabcellsep B\tabcellsep 0 2 3 1\tabcellsep 10 15 14 17 17 16 13 17 13 12 14 14 14 10 15 16 17 16 16 15 15 10 17 16 16 16 16 14\tabcellsep 10 12 14 11 12 10 11\tabcellsep 10\tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
\tabcellsep \tabcellsep 4\tabcellsep 16 12 11 13 44 13 10\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
\tabcellsep \tabcellsep 5 6\tabcellsep 15 11 11 12 12 12 11 17 11 11 11 11 10 12\tabcellsep 11\tabcellsep 10\tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
\tabcellsep \tabcellsep 7\tabcellsep 16 12 11 11 11 10 12\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep \multicolumn{2}{l}{(c)}\tabcellsep \tabcellsep \tabcellsep \tabcellsep \end{longtable} \par
 
\caption{\label{tab_1}Table 1 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{3} \par 
\begin{longtable}{}
\end{longtable} \par
 
\caption{\label{tab_4}Table 3 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{4} \par 
\begin{longtable}{P{0.85\textwidth}}
2012\\
Year\\
19\\
Volume XII Issue XIII Version I\\
D D D D ) F\\
(\\
Global Journal of Computer Science and Technology\end{longtable} \par
  {\small\itshape [Note: © 2012 Global Journals Inc. (US)]} 
\caption{\label{tab_5}Table 4 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{5} \par 
\begin{longtable}{}
\end{longtable} \par
 
\caption{\label{tab_6}Table 5 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{6} \par 
\begin{longtable}{P{0.06485693323550991\textwidth}P{0.009977989728539985\textwidth}P{0.03866471019809244\textwidth}P{0.01995597945707997\textwidth}P{0.22076302274394718\textwidth}P{0.020579603815113718\textwidth}P{0.3012105649303008\textwidth}P{0.007483492296404989\textwidth}P{0.06735143066764489\textwidth}P{0.04490095377842993\textwidth}P{0.008730741012472487\textwidth}P{0.0024944974321349962\textwidth}P{0.020579603815113718\textwidth}P{0.018708730741012473\textwidth}P{0.0037417461482024943\textwidth}}
\tabcellsep \tabcellsep \tabcellsep \tabcellsep \multicolumn{10}{l}{Novel Color Image Compression Algorithm based on Quad tree}\\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep \multicolumn{2}{l}{Image Name}\tabcellsep \multicolumn{8}{l}{Threshold = 0.1 S1 R S1 G S1 B S2 R S2 G S2 B S1 R S1 G S1 B S2 R S2 G S2 B Threshold = 0.2}\\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep \multicolumn{2}{l}{Sailboat}\tabcellsep \multicolumn{8}{l}{30528 59800 50796 30528 59800 50796 7548 27240 27416 7548 27240 27416}\\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep \multicolumn{2}{l}{Lena}\tabcellsep \multicolumn{8}{l}{13972 22924 19012 13972 22924 19012 3912 8368 6536 3912 8368 6536}\\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep \multicolumn{10}{l}{Peppers 15556 22676 17548 15556 22676 17548 5612 10448 6888 5612 10448 6888}\\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep \multicolumn{2}{l}{Splash}\tabcellsep \multicolumn{8}{l}{4068 9248 8416 4068 9248 8416 2592 5940 5720 2592 5940 5720}\\
2012\tabcellsep \tabcellsep \tabcellsep \tabcellsep \multicolumn{2}{l}{Image Name Sailboat Lena}\tabcellsep \multicolumn{8}{l}{Threshold = 0.3 S1 R S1 G S1 B S2 R S2 G S2 B S1 R S1 G S1 B S2 R S2 G S2 B Threshold = 0.5 1084 9212 11152 1084 9212 11152 148 1756 1784 148 1756 1784 620 2324 1536 620 2324 1536 32 432 64 32 432 64}\\
Year\tabcellsep \tabcellsep \tabcellsep \tabcellsep \multicolumn{10}{l}{Peppers 2032 4964 2348 2032 4964 2348 732 2216 588 732 2216 588 Splash 1252 3868 3496 1252 3868 3496 380 1820 1136 380 1820 1136}\\
20\tabcellsep \tabcellsep 6\tabcellsep x 10 4\tabcellsep \tabcellsep \multicolumn{2}{l}{Threshold=0.1}\tabcellsep \tabcellsep S1 R\tabcellsep 3\tabcellsep 4 x 10\tabcellsep \tabcellsep \multicolumn{2}{l}{Threshold=0.2}\\
( D D D D ) F Volume XII Issue XIII Version I\tabcellsep Number of blocks\tabcellsep 0 1 5 4000 6000 8000 10000 12000 2 3 4 Number of blocks\tabcellsep Sailboot\tabcellsep Lena\tabcellsep \multicolumn{2}{l}{Pepper Threshold=0.3}\tabcellsep Splash\tabcellsep S1 G S1 B S2 R S2 G S2 B\tabcellsep 0 0.5 2.5 1000 1500 2000 2500 1 1.5 2 Number of blocks Number of blocks\tabcellsep Sailboot\tabcellsep Lena\tabcellsep \multicolumn{2}{l}{Pepper Threshold=0.5}\tabcellsep Splash\\
Global Journal of Computer Science and Technology\tabcellsep \tabcellsep 0 2000\tabcellsep Sailboot Image IV.\tabcellsep \multicolumn{3}{l}{Lena System1 Proposed Pepper System 2}\tabcellsep Splash\tabcellsep \multicolumn{5}{l}{Sailboot Other Systems Lena YCbCr [2] CBTC-PF[32] 0 500 JPEG [32] 1.5 30.47 1.47}\tabcellsep Pepper NNET [33] Splash ------\end{longtable} \par
  {\small\itshape [Note: © 2012 Global Journals Inc. (US)]} 
\caption{\label{tab_7}Table 6 :}\end{figure}
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\end{bibitemlist}
 			 		 	 
\end{document}
