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\title{Sorted Pixel Value Difference on Fuzzy Watermarking Scheme}
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             \author[1]{S.Maruthu  Perumal}

             \author[2]{  V.Vijayakumar}

             \author[3]{  V.Vijayakumar}

             \affil[1]{  Dr.M.G.R. University}

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\date{\small \em Received: 5 April 2012 Accepted: 30 April 2012 Published: 15 May 2012}

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\begin{abstract}
        


 A robust watermark scheme for copyright protection is proposed in the present paper. The present method selects the pixel locations to insert the watermark by a new technique called fuzzy based wavelet approach. The watermark is embedded in the sorted pixel locations of fuzzy based wavelet approach by using pixel value difference method. The proposed approach overcomes the weak robustness problem of embedding the watermark in the spatia domain and also in pixel value difference method. Further the watermark extraction does not require the original image as in the case of many digital watermarking methods. The fuzzy logic approach in  the wavelet domain eliminates the requirement of repeated embedding process. The experimental results indicate the high image quality and robustness against various attacks when compared to several approaches.  

\end{abstract}


\keywords{Fuzzy Approach, Digital Image Watermarking, Sorted Pixel Value Difference (SPVD)}

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\let\tabcellsep& 	 	 		 \par
Abstract -A robust watermark scheme for copyright protection is proposed in the present paper. The present method selects the pixel locations to insert the watermark by a new technique called fuzzy based wavelet approach. The watermark is embedded in the sorted pixel locations of fuzzy based wavelet approach by using pixel value difference method. The proposed approach overcomes the weak robustness problem of embedding the watermark in the spatial domain and also in pixel value difference method. Further the watermark extraction does not require the original image as in the case of many digital watermarking methods. The fuzzy logic approach in the wavelet domain eliminates the requirement of repeated embedding process. The experimental results indicate the high image quality and robustness against various attacks when compared to several approaches.\par
Keywords : Fuzzy Approach, Digital Image Watermarking, Sorted Pixel Value Difference (SPVD).\par
n recent years, watermarking has become an attractive topic and many watermarking schemes have been proposed \hyperref[b7]{[3]}, \hyperref[b1]{[6]}. Many literatures have reported about watermarking based on spatial domain with different conventional extraction techniques \hyperref[b8]{[4]}. Watermarking in the frequency domain is more robust than watermarking in the spatial domain \hyperref[b5]{[1]}, because the watermark information can be spread out over the entire image \hyperref[b6]{[2]}. Transform domain watermarking techniques are more robust, due to the fact that when image is inverse wavelet transformed, watermark is distributed irregularly over the image, making the attacker difficult to read or modify.\par
In 2002, Joo et al. proposed a robust watermark scheme by embedding a watermark into wavelet low frequency sub-band \hyperref[b0]{[5]}. According to the embedding location, the watermark is extracted by comparing the two wavelet coefficients by three level wavelet transforms LL3 and LL3'. Finally, the extracted watermark is compared with the original watermark by similarity measure formula. Although the above scheme provides the characteristics of robustness and imperceptibility, but the embedding process is quite time-consuming. Besides, the original image is required in the watermark extraction process, which is impractical in real application. In one of the recent method \hyperref[b2]{[7]}, the original image is transformed into wavelet coefficients by one-level wavelet transform first. Then, three highfrequency sub-bands are modified and obtain its reference image by performing inverse wavelet transform. The watermark is embedded into the reference values between the original image and its reference image. In the watermark extraction process, the watermark extraction does not require the original image. This method suffers from poor identification of pixel locations where watermark is to be inserted. To overcome the above disadvantage, the proposed method initially locates the pixel locations by applying fuzzy logic on two level wavelet coefficients and further they are sorted to insert the watermark by PVD method \hyperref[b3]{[8]}. This makes the present method more powerful then earlier methods in breaking the watermark and also it gives high robustness.\par
The rest of this paper is organized as follows: The section 2 presents a brief introduction of the PVD; Section 3 describes the proposed method for embedding and extraction of watermark. The section four describes the experimental results. The conclusion is discussed in the final section.\par
The basic PVD scheme \hyperref[b3]{[8]} is meant for steganographic images. This scheme offers high imperceptibility to the stego image by selecting two consecutive pixels as the object of embedding. The payload is determined by the difference value between the pixels as given below. The basic PVD method, determines whether the two consecutive pixels belong to an edge or smooth area by checking out the difference value between two consecutive pixels. If the difference value is large, i.e. the two pixels are located in an edge area; more secret data can be hidden here. On the contrary, if the difference value is small, i.e. the two pixels are located in a smooth area, less secret data can be embedded. Therefore, this scheme produces stego images that are more similar to the original images than those produced by LSB substitution schemes, which directly embed secret data into the cover image without considering the differences between adjacent pixels.\par
Given a cover image I of size M×N, I i is a sub block of I that has two consecutive pixels broken down by partitioning I in raster scan order such that I=\{ I i /i=1,2,??..(M×N)/2\}. By definition each I i has two elements E (r,L) and E (r,R) . The pixel values of E (r,L) and E (r,R) are V (r,x) and V (r,y) respectively. The difference value d i of V (r,x) and V (r,y) can be derived by Equation \hyperref[b5]{(1)}.d i = |V(r,x) -V(r,y) |\textbf{(1)}\par
The range Table \hyperref[tab_1]{1} which consists of n contiguous sub ranges T j ; T= \{T j | j=1, 2,..n\}, provides major information about the hiding capacity of Ii. Each sub range T j has its lower and upper bound values, say l j and uj, so that it will have T j ? [l j , u j ]. The width w j of each T j is selected to be a power of 2, and can be computed by w j =u j -l j +1.Each sub block I i relates to its sub range T j from the range Table  {\ref 6}.1 such that T j =min(d i ,w j ) and d i ?[l j ,u j ]. This way, the hiding capacity of two consecutive pixels can be obtained by Equation \hyperref[b6]{(2)}. bi = log (w j )\par
Here, b i is the number of bits that can be hidden in I i . Table \hyperref[tab_1]{1} clearly indicates the number of bits of watermark to be selected. The PVD method selects bi bits from the binary secret data stream and transform bi into its decimal equivalent value bi'. Then it computes the remainder values E rem(r,x) , E rem(r,y) and I rem(r) of E (r,x), E (r,y) and sub block I i respectively by using the following Equations ( \hyperref[formula_2]{3}).E rem(r,x ) = E (r,y) mod 2 bi E rem(r,y) =E (r,y) mod2 bi\textbf{(3)}I rem(r) = (E (r,x) + E (r,y) ) mod 2 bi\par
After this the PVD embeds b i bits of secret data into I i by altering E (r,x) and E (r,y) . The optimal approach for altering the E (r,x) and E (r,y) to achieve the minimum distortion is as follows:Case1: I rem(r) > b i' , m?(2 bi )/2 , E (r,x) ) ? E (r,y) (E' (r,x) ,E' (r,y) )=(E (r,x) -m/2 ,E(r,y)-m/2 2) Case 2: I rem(r) > b i ', m<=(2 bi )/2, E (r,x) <E (r,y) (E' (r,x), E' (r,y) )=(E (r,x) -m/2 ,E (r,y) -m/2 2) Case 3: I rem(r) > b i ', m>(2 bi )/2, E (r,x) >=E (r,y) (E' (r,x), E (r,y) )=(E (r,x) + m 1 /2 , E (r,y) + m 1 /2 2) Case 4: I rem(r) > b i ', m>(2 bi )/2, E (r,x) <E (r,y) (E' (r,x) ,E'(r,y))=(E(r,x)+ m 1 /2 , E (r,y) + m 1 /2 2) Case 5: I rem(r) > b i ', m>(2 bi )/2, E (r,x) ?E (r,y) (E' (r,x), E' (r,y) )=(E (r,x) + m/2 2, E (r,y) + m/2 2) Case 6: I rem(r) ? b i ', m>(2 bi )/2, E (r,x) <E (r,y) (E (r,x) ,E' (r,y) )=(E (r,x) + m/2 2, E (r,y) + m/2 2) Case 7: I rem(r) ? b i' , m>(2 bi )/2, E (r,x) ?E (r,y) (E' (r,x) , E' (r,y) )= (E (r,x) -( m 1 /2 , E (r,y) -m 1 /2 2) Case 8: I rem(r) ? b i' , m>(2 bi )/2, E (r,x) ?E (r,y) (E' (r,x), E' (r,y))=( E (r,x) -m 1 /2 , E (r,y) -m 1 /2 2)\par
In the above approach, m=|I rem(r) -b i ' |, m 1 =2 bi -|I rem(r) -b i ' | and E' (r,x) , E' (r,y) are new pixels values after embedding bi bits of the secret data into sub block I i .\par
In the recovery process, the secret data is extracted quickly without using the original image. It is essential to use original range Table \hyperref[tab_1]{1} designed in the embedding phase in order to figure out the embedding capacity for each sub block I i . Given a sub block I i with two consecutive pixels from the watermarked image with their pixel values being E (r,x) and E (r,y) respectively, the difference value di of E (r,x) and E (r,y) can be derived by Equation \hyperref[b5]{(1)}. Each I i can be related to its optimal sub range T j from the original Table \hyperref[tab_1]{1} according to the difference value d i . Hence, the width of the sub range by w j =u j -l j +1is computed and the number of bits bi of secret data can be extracted from I i by Equation (1). The value of b i ' is computed by using the Equation (4). b i '=(E' (r,x) +E' (r,y) )mod2 bi (4)\par
Then transform b i ' value into a binary string with the length b i . If di value is zero or either or both of E' (r,x) , E' (r,y) overflows the boundary 0 or 255, consider the three situations below where the falling off boundary problem happens and revise the binary string with the length b i .\par
Case 1: if E (r,x) ? 0 , E (r,y) ? 0 and E' (r,x) < 0 or E' (r,y) < 0 , then re adjust E' (r,x) and E' (r,y) to be E" (r,x) and E" (r,y) by (E" (r,x) ,E" (r,y) ) = (E' (r,x) + (2 bi ) / 2 ), E' (r,y) + (2 bi ) / 2 ) 
\section[{Global Journal of Computer Science and Technology Volume XII Issue IV Version I}]{Global Journal of Computer Science and Technology Volume XII Issue IV Version I}\par
After that, the recovery process is accomplished.\par
The proposed watermark embedding scheme contains three basic steps. The block diagram of FWSPVD is given in the Figure \hyperref[fig_0]{1}. The proposed FW method modifies the original image into transform domain and selects the pixel locations to insert a watermark in the difference values between the original image and its reference image based on a novel fuzzy logic in step one.\par
Step 1: In the first step, a novel FW approach is determined based on the pixel locations where watermark is embedded. DWT decomposes an image into subbands having a bandwidth approximately equal on a logarithmic scale. To achieve imperceptibility, the lowest band of the image is left unmodified. The gray level image is transformed into a DWT of both vertical and horizontal directions, resulting in one low frequency subband (LL) and three higher frequency subbands (LH, HL and HH). The same is repeated on LL subband to generate the next level of decomposition. This process can be repeated to n level decomposition by considering the length of watermark, robustness, fidelity and so on. The determined LL n can be seen as a reduced version of the original image. Based on this a reference LLn' is prepared by inverse wavelet transforming the original LL n by initializing the three high frequency subbands (LH n+1 , HL n+1 and HH n+1 ) excluding LL n+1 as zeros. The proposed FW approach is not selecting all those pixels that have the difference in LL n ' and LL n . The difference between LL n and LL n ' mainly ranges from -1 to +1, because the error content in the wavelet transform is minimum, that is the reason one always obtains the original image by inverse transformation. In the proposed approach the fuzzy difference between LL n and LL n ' is obtained for selecting the pixel locations where watermark is embedded. The pixel locations to embed watermark are identified by taking the difference between (LL 2 ?LL 2 ') based on FW approach. The proposed FW approach divides the range -1 to +1 in to four regions as R0, R1, R2 and R3 as shown in the Figure  {\ref 2}. The pixel locations are selected based on the FW algorithm.\par
The pixel locations are selected for the embedding of watermark if they fall in the fuzzy region R1 and R2. Finally, the watermark information is embedded into the subband LL 2 . 
\section[{Fig.2. Representation based on fuzzy wavelet approach}]{Fig.2. Representation based on fuzzy wavelet approach} 
\section[{F ebruary}]{F ebruary}\par
Fuzzy Wavelet algorithm: begin for i =1 to n for j = 1 to m f(i,j)=LL n (i,j) -LL n '(i,j) if ((f(i,j) < 0.5) and (f(i,j)> -0.5))\par
then P(i,j) is considered for inserting the watermark else P i (i,j) is not considered for inserting the watermark end\par
Step 2 : The second step, groups only those pixel coordinates selected by step one based on their pixel values in ascending order. If two or more pixels are having same values then they will be sorted by row wise positions.\par
Step 3 : The pixel value differencing method only inserts watermarking bits in the adjacent pixels location based on pixel differences. By this it is easy to break or detect the watermark. To overcome this, the proposed method initially selects the pixel location where watermark is to be inserted based on FW approach. The watermark is inserted on the group of pixels in the sorted order by using SPVD method in the second level of wavelet transformed image as indicated in step two. By inserting watermark, the pixel value may be changed; and the sorted order may also be changed. The quality of the watermark is affected if the sorted order is changed after inserting the watermark bits by pixel value differencing method. To overcome this, in the proposed SPVD method watermark is inserted in the group of two pixels, if its values after inserting watermark are less than the next group of values. 
\section[{b) Watermark extraction process}]{b) Watermark extraction process}\par
Transform the watermarked image into wavelet coefficients by second level wavelet transformations. To extract the watermark signal, the sequences of embedding locations are utilized. Perform the inverse FWSPVD scheme to obtain the pixel locations and watermark contents.\par
Eight 256 × 256 sized cover images are used in the following experiments. As shown in Figure \hyperref[fig_1]{3}, those are Lena, Baboon, Pepper, House, Barbara, Milkdrop, F16 and Boat. The watermark considered for the experiments is logo SRRF GIET of size 32×32 as shown in Figure  {\ref 4}. Table \hyperref[tab_2]{2} shows the PNSR and NCC values for all the cover images. From the Table \hyperref[tab_2]{2} it is clearly evident that all the images shows high PSNR and NCC values which indicates robustness and high quality of image after watermark insertion.   
\section[{F ebruary}]{F ebruary}\par
The proposed method is tested with various attacks and the quality parameters are listed in tables. Table \hyperref[tab_3]{3} shows the PSNR and NCC values with various attacks using the proposed FWSPVD method on the watermark images with SRRF GIET respectively. The PSNR and NCC values of Table \hyperref[tab_3]{3} clearly indicate the robustness and quality of the image is not degraded for all attacks.\par
The resultant image after adding Gaussian (10\%), Salt and Pepper (10\%), and Poisson noise (10\%) to the watermarked image by the proposed FWSPVD is as shown in Figure  {\ref 5}, which demonstrates that FWSPVD scheme is significantly robust against these noises. Median filtering with different window sizes is applied to the watermarked images of the FWSPVD method and the resultant images are shown in Figure  {\ref 6}, which reflects the maximum detector response. Figure  {\ref 7} is the Gaussian blurred watermarked image by the FWSPVD method which demonstrates that FWSPVD scheme is significantly robust against this noise. Figure  {\ref 8} shows, the results after rotating the watermarked image by 2, 3 and 4 degrees in order to keep the same size as the original image by which four corners of the rotated image are cropped. The extraction algorithm extracted more than 50\% of the watermark.  \hyperref[tab_4]{4} compares the PSNR values after inserting the watermark without attacks by the proposed FWSPVD method with various other methods \hyperref[b2]{[7,}\hyperref[b3]{8,}\hyperref[b4]{9]}. Table \hyperref[tab_4]{4} clearly indicates the FWSPVD outperforms the other existing methods. A graph is also plotted in Figure \hyperref[fig_3]{9} which indicates the comparison of the proposed FWSPVD method with various other methods without attacks.  By transforming the original image in wavelet domain and embedding a watermark in the difference values based on fuzzy approach between the original image and its reference image, the proposed scheme overcomes the weak robustness problem of embedding watermark in the spatial domain. Our approach does not require the original image for watermark extraction. The experimental results on various images with various attacks show that the proposed technique provides good image quality and robustness when compared to other methods. This factor is clearly evident from the table 2, table 3 and table 4.\par
The authors would like to express their gratitude to Sri K.V.V. Satyanarayana Raju, Chairman, and Sri K. Sasi Kiran Varma, Managing Director, Chaitanya group of Institutions for providing necessary Infrastructure. Authors would like to thank the anonymous reviewers for their valuable comments. \begin{figure}[htbp]
\noindent\textbf{1}\includegraphics[]{image-2.png}
\caption{\label{fig_0}Fig. 1 .}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{3}\includegraphics[]{image-3.png}
\caption{\label{fig_1}Fig. 3}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{5678}\includegraphics[]{image-4.png}
\caption{\label{fig_2}Fig. 5 Fig. 6 Fig. 7 Fig. 8}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{9}\includegraphics[]{image-5.png}
\caption{\label{fig_3}Fig. 9}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{} \par 
\begin{longtable}{}
\end{longtable} \par
 
\caption{\label{tab_0}}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{1} \par 
\begin{longtable}{P{0.431640625\textwidth}P{0.09296875\textwidth}P{0.10625\textwidth}P{0.09296875\textwidth}P{0.126171875\textwidth}}
Range\tabcellsep l j\tabcellsep u j\tabcellsep w j\tabcellsep b i\\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep =log(w j )\\
T1=[0,7]\tabcellsep 0\tabcellsep 7\tabcellsep 8\tabcellsep 3\\
T2=[8,15]\tabcellsep 8\tabcellsep 15\tabcellsep 8\tabcellsep 3\\
T3=[16,31]\tabcellsep 16\tabcellsep 31\tabcellsep 16\tabcellsep 4\\
T4=[32,63]\tabcellsep 32\tabcellsep 63\tabcellsep 32\tabcellsep 5\\
T5=[64,127]\tabcellsep 64\tabcellsep 127\tabcellsep 64\tabcellsep 6\\
T6=[128,255]\tabcellsep 128\tabcellsep 255\tabcellsep 128\tabcellsep 7\end{longtable} \par
 
\caption{\label{tab_1}Table 1}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{2} \par 
\begin{longtable}{P{0.32125984251968503\textwidth}P{0.29448818897637796\textwidth}P{0.234251968503937\textwidth}}
Image\tabcellsep PSNR\tabcellsep NCC\\
Lena\tabcellsep 44.81\tabcellsep 0.96\\
Baboon\tabcellsep 46.79\tabcellsep 0.97\\
Pepper\tabcellsep 45.45\tabcellsep 0.99\\
House\tabcellsep 47.28\tabcellsep 0.98\\
Barbara\tabcellsep 44.70\tabcellsep 0.96\\
Milkdrop\tabcellsep 47.64\tabcellsep 0.97\\
F16\tabcellsep 49.81\tabcellsep 0.97\\
Boat\tabcellsep 47.37\tabcellsep 0.97\end{longtable} \par
  {\small\itshape [Note: Global Journal of Computer Science and Technology Volume XII Issue IV Version I 44 2012 © 2012 Global Journals Inc. (US)]} 
\caption{\label{tab_2}Table 2}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{3} \par 
\begin{longtable}{P{0.85\textwidth}}
2012\\
45 F ebruary\end{longtable} \par
 
\caption{\label{tab_3}Table 3}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{4} \par 
\begin{longtable}{P{0.016721311475409836\textwidth}P{0.1560655737704918\textwidth}P{0.17278688524590163\textwidth}P{0.17278688524590163\textwidth}P{0.17557377049180328\textwidth}P{0.1560655737704918\textwidth}}
\tabcellsep Test images\tabcellsep Jiang-Lung Liu Method\tabcellsep G.Thirug nanam Method\tabcellsep Method Chung Ming Wang\tabcellsep Proposed FWSPVD\\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep PSNR(dB)\tabcellsep \\
\tabcellsep Lena\tabcellsep 34.87\tabcellsep 39.98\tabcellsep 44.1\tabcellsep 44.81\\
2012\tabcellsep Baboon Pepper\tabcellsep 32.14 31.11\tabcellsep 34.45 36.56\tabcellsep 40.3 43.3\tabcellsep 46.79 45.45\\
\tabcellsep House\tabcellsep 30.49\tabcellsep 34.95\tabcellsep 43.5\tabcellsep 47.28\\
\tabcellsep Barbara\tabcellsep 33.15\tabcellsep 41.62\tabcellsep 42.5\tabcellsep 44.70\\
\tabcellsep Milk drop\tabcellsep 32.67\tabcellsep 39.14\tabcellsep 45.9\tabcellsep 47.64\\
46\tabcellsep F16\tabcellsep 33.72\tabcellsep 41.15\tabcellsep 43.5\tabcellsep 49.81\\
\tabcellsep Boat\tabcellsep 31.24\tabcellsep 40.32\tabcellsep 42.1\tabcellsep 47.37\end{longtable} \par
  {\small\itshape [Note: © 2012 Global Journals Inc. (US)]} 
\caption{\label{tab_4}Table 4}\end{figure}
 			\footnote{© 2012 Global Journals Inc. (US) Global Journal of Computer Science and Technology Volume XII Issue IV Version I 43} 		 		\backmatter  			  				\begin{bibitemlist}{1}
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