Normalization cross correlation value of

IJRET: International Journal of Research in Engineering and Technology eISSN: 2319-1163 | pISSN: 2321-7308
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Volume: 03 Issue: 08 | Aug-2014, Available @ http://www.ijret.org 260
NORMALIZATION CROSS CORRELATION VALUE OF
ROTATIONAL ATTACK ON DIGITAL IMAGE WATERMARKING BY
USING SVD-DCT
Vikas Chaubey1, Komal Goyal2, Amita Garg3
1Asst. Professor, Computer Science Department, MVN University, Haryana, India
2Asst. Professor, Mathematics Department, MVN University, Haryana, India
3Research Scholar, Mathematics Department, Sharda University, Uttar Pradesh, India
Abstract
The WWW (World Wide Web) is a superb sales and distribution medium for digital image assets, but official document
compliance and important data can be a call to prove or justify it. Present days, digital image, audio and video used all over
world with or without agreement. In digital image watermarking answer let you add extra layer of protection (added logo) to
your digital image. By using Singular Value Decomposition - Discrete Cosine Transfer we are finding Normalization Cross
Correlation coefficient value of attacking (rotational attack) on digital image watermarking. The Normalization Cross
Correlation coefficient value depended on step size of digital image. If you change the value of step size than our results are
different.
Keywords: SVD, DCT, Orthogonal Matrix, NCC, Watermarking.
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1. INTRODUCTION
Maximum collection of data is transfer in digital format now
than ever and the growth in this field will not plane in the
likely further day. Digital collection of data is susceptible
[1][2] to having same creator at the same quality as the
original signal. Other word input signal is same as output
signal. Watermarking is possible to work on digital image,
audio and video it is a pattern of bits inserted into identifies
the file’s copyright collection of data. Digital image
watermarking is derived from the weakly visible marks
stamped on structural notepaper. Dissimilarly printed digital
watermarks, which are planned to be somewhat
visible(usually the actual light compass stamp watermarking
this report), digital image watermarking are designed to be
full proof invisible or in the case of audio clips, video clips
and inaudible clips.Digital Images that are misused can that
are leaked or misused can upset sale and distribution
marketing efforts, brand image. Other person one click on
your digital effect can be separate from your invisible
information so guarding brand and logical property.
2. DISCRETE COSINE TRANSFORM
Discrete Cosine Transform (DCT) is a new method for
converting digital signal into elementary frequency
components. It is maximums used in digital image
compression/decomposition. It is easy method to calculate
the Discrete Cosine Transform and to compress/de-compressdigital
image[2][3]. It is widely used for image
compression because of its high energy packing capabilities.
Discrete Cosine Transform has many useful properties and
involves only real components.
Discrete Cosine Transform of a 1D sequence of length N
can be given as
1
0
(2 1)
( ) ( ) ( ) cos
2
N
x
x u
C u W u f x
N
 

  
   
 

For u= 0,1,2….,N-1.
1 2
W(u) for u 0; for u 0
N N
 
    
 
When
1
0
1
0, (0) ( )
N
x
u C f x
N


   . This is called DC
component. For other value of u, the components obtained
are called AC coefficients. The inverse DCT is given below
1
0
(2 1)
( ) ( ) ( ) cos
2
N
u
x u
f x W u C u
N
 

  
    
 

The two dimensions DCT is an extension of 1-D DCT. It is
given as
     
1 1
0 0
(2 1) (2 1)
C u, v W u W v ( , ).
2 2
N N
x y
x u y v
f x y cos cos
N N
   
 
     
    
   

For u,v=0,1,2…..,N-1. W(u) and W(v) can be calculated as in
the case of one dimension. The inverse transformation is
given as

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1 1
0 0
(2 1) (2 1)
( , ) ( ) ( ) ( , )
2 2
N N
x y
x u y v
f x y W u W v C u v cos cos
N N
   
 
     
    
   

For x,y=0,1,2……N-1. The DCT is helpful in removing the
redundant data from an image. The energy compaction
efficiency of the DCT is higher than that of FFT in general.
The DCT is separable similar to FFT[9][10]. Since the
transforms for rows and columns are identical, the DCT can
be called as a symmetric transformation and can be
expressed as
g A F  A
where the symmetric transformation of matrix A is specified
as
1
,
0
(2 1)
( )
2
N
i j
j
j i
a W j cos
N


  
  
 

Here F is given image. The inverse DCT(IDCT) is given as
1 1 F A T A     
=
T T A T  A
The DCT can also be extended to higher dimensions.
3. SINGULAR VALUE DECOMPOSITION
The singular value decomposition of 푀 × 푁 matrix A is its
representation as A = U D V T, where U is an orthogonal
푀 × 푀 matrix, V - orthogonal 푁 × 푁 matrix. The diagonal
elements of matrix D are non-negative numbers in
descending order, all off-diagonal elements are zeros.
The matrix D consists mainly of zeros, so we only need the
first min(M,N) columns of matrixU to obtain matrix
A[4][5].Similarly, only the first min(M,N) rows of matrix V
T affect the product. These columns and rows are called left
and right singular vectors.
The expression A = U W V T, is known as SVD(Singular
value decomposition).
To decompose ‘A’ we require two orthogonal matrix “U’
and ‘V’ and one diagonal matrix ‘D’ which is formed by
square roots of eigen values of ‘퐴푇퐴′.
We need two equations to solve it :
푎 퐴푇퐴 = 푉퐷푇 퐷푉푇
푏 퐶푉 = 푈퐷.
We can understand it in better way using an example:
Let ‘A’ is any matrix,퐴 =
5 5
−1 7
Step I: Compute 퐴푇퐴 and find itseigen values.
퐴푇퐴 =
5 −1
5 7
5 5
−1 7
=
26 18
18 74
Eigen values of 퐴푇퐴 ,
Det 퐴푇퐴 − 휆퐼 = 퐷푒푡
26 − 휆 18
18 74 − 휆
=휆2 − 100휆 + 1600
= 휆 − 20 휆 − 80
Therefore, eigen values are 휆 = 20,80
Step II: To find eigen vectors of corresponding eigen values
to get V which is equal to 푉1, 푉2 .
Eigen vector of (퐴푇퐴 − 20퐼)푋 =
6 18
18 54
푥
푦
푉1 =
−3
10
1
10
Similarly, 퐴푇퐴 − 80퐼 =
−54 18
18 −6
푥
푦
푉2 =
1
10
3
10
Therefore,푉 =
−3
10
1
10
1
10
3
10
...............………………... (i)
Step III: To find 퐷 = 푒푖푔푒푛푣푎푙푢푒푠 .
Therefore 퐷 = 20 0
0 80
=
2 5 0
0 4 5
………………………………………. (ii)
Step IV: From (b) , we have ,
퐴푉 =
5 5
−1 7
−3
10
1
10
1
10
3
10
= 푈 2 5 0
0 4 5

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From this we get, 푈= −1 21 21 21 2 ……………………………... (iii) Thus, we get ‘U’ ‘D’ and ‘D’ to decompose any matrix ‘A’.
If a matrix ‘A’ has a matrix of eigenvectors ‘P’ that is not invertible (for example, the matrix 1101 , has the noninvertible system of eigenvectors 1000 , then ‘A’ does not have an eigen decomposition. The singular value decomposition has many useful properties [8]. For example, it can be used to: solve underdetermined and over determined systems of linear equations, matrix inversion and pseudo inversion, matrix condition number calculation, vector system orthogonalization and orthogonal complement calculation. 4. RESULTS AND DISCUSSION 4.1 NCC between Original Watermark and Extracted Watermark (i) To calculate the normalized cross correlation coefficient between the original and extracted watermark we use the concept of mathematical formula. (ii) First we take the multiplication between the original and extracted value for each element in the matrix. (iii) Then we normalize these values by dividing the value of (w*w) . Where w is the original watermark. Mathematically r = r + (w*W_h) c = c + (R*R) NCC = r/c Where r = 0; initially c = 0; initially w = original watermark W_h = extracted watermark from CH frequency sub band in resolution level ( l =1). As the same watermark is extracted from level 1 in CH frequency sub band so the value obtained is NCC = 1. 4.2 NCC Coefficient Calculation in case of Rotating Attack (i) Rotating attack is performed on watermarked image by rotating the watermarked image to 2 degree in anticlockwise direction.
(ii) The similarity between the watermarked image and attacked watermarked image is found by calculating the correlation over entire dimension of the attacked image.
(iii) The same procedure is applied as above.
Taking x3 = x3 + (w * W_h_r)
y3 = y3 + (w * w) P3 = (x3/y3) Where x3 = 0; initially y3 = 0; initially P3 = correlation coefficient w = original watermark W_h_r = watermark extracted from rotated image The value of correlation coefficient found in this case of rotated back is p1 = 0.6779 for step size of 15. the correlation value is less which shows that the watermarking scheme is not more robust for rotating attack also.

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The value of correlation coefficient found in this case of rotated back is p1 = 0.7044 for step size of 15. the correlation value is less which shows that the watermarking scheme is something robust for rotating attack from before. 5. CONCLUSIONS AND FUTURE WORK The correlation coefficient in the two different bit configuration 32*32 and 64*64. Both time you consider different value but these value are near by the 1.and also if you change the step size of image than also possible that you get different results on various step size of image. Digital Image processing operations can be applied both in the spatial domain as well as the frequency domain. The reason for performing these operations in the frequency domain is the speed and simplicity of operation in this domain.Digital Image Transforms are used to convert information from the spatial domain to the frequency domain and vice versa. Discrete Cosine Transform and Singular Value Decomposition both are together performing best result on digital image by the help of Normalization Cross Correlation Coefficient (NCCC). Limitation of this is we are not going to closer of 1 because if we are not getting closer value of 1 than you are not robust for rotating from before. REFERENCES [1]. Andreja SamˇcovićJán Turán,,Attacks On Digitalwavelet Imagewatermarks,Journal of ElectricalEngineering, Vol. 59, No. 3, 2008, 131–138. [2]. Carla D. Martin and Mason A. Porter,The Extraordinary SVD, The Mathematical Association Of America, December 2012, pp.838-851. [3]. Cox, I. J. Kilian, J., Leighton, T., and Shamoon, T., Secure spread spectrumwatermarking for images, audio, and video. Proceedings of the 1996 IEEEInternational Conference on Image Processing, 1996, 3, pp. 243–256.
[4]. Chih-Ch in La i, and Cheng-Chih Tsai,Digital Image Watermarking Using Discrete Wavelet Transform and Singular Value Decomposition,IEEE Transactions on Instrumentation and Measurement., Vol.59, no. 11, Nov. 2010, pp. 3060-3063.
[5]. Chih-Chin Lai, Member, IEEE, and Cheng-Chih Tsai, Digital Image Watermarking Using Discrete Wavelet Transform andSingular Value Decomposition, IEEE TTRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 59, NO. 11, NOVEMBER 2010. [6]. G. Bhatnagar and B. Ra man, A new robust reference watermarking scheme based on DWT-SVD, Comput. Standards Interfaces, Vol. 31, no. 5, Sep. 2009, pp. 1002– 1013,. [7]. Guru Prasad M. HEGDE and Cang YE, Singular Value Decomposition Filter: An Effective Method to Enhance the Swiss Ranger SR-3000’s Range Images ,International Journal Of Intelligent Control And Systems ,Vol. 13, No. 4, December 2008, 242-250 [8]. Harsh K Verma, Abhishek Narain Singh, Raman Kumar, Robustness of the Digital Image Watermarking Techniques againstBrightness and Rotation Attack,(IJCSIS) International Journal of Computer Science and Information Security. Vol. 5, No. 1,2009. [9]. H. C. Andrews and C. L. Patterson, Singular value decompositions and digital image processing, IEEE Transactions onAcoustics,Speech, and Signal Processing, Vol.ASSP-24, pp. 26–53, 1976. [10]. Jonathan K. Su, Frank Hartung, Bernd Girod,Digital Watermarking ofText, Image, and Video Documents. [11]. Van Schyndel, R. G., Tirkel, A. Z., and Osborne, C. F., A digital watermark.Proceedings of the 1994 IEEE International Conference on Image Processing, 1994, pp. 86–89. BIOGRAPHIES
He received M. Tech and B. Tech. Currently, he is working as an Assistant Professor in Computer Science Department at MVN University, Palwal. His areas of interest include Operating System, Computer Network and Object Oriented Programming, Digital Image Processing.
Komal Goyal received the M.Sc. degree in Mathematics in 2010. She is pursuing Ph.D. from Jaypee University, Noida. She is working as an Assistant Professor in a reputed University. She is mainly indulged in research of Fixed point theory and fractals. She has published two research papers in international Journals.

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Amita Garg received M.Sc. and M.Ed. degree from Dayalbagh Educational Institute. She is pursuing Ph.D. from Sharda University under the supervision of Dr. A. H. Siddiqi (Ex- Pro- vice chancellor of AMU). Her research area is inverse problems related to Partial differential equations. She has published two research papers in international Journals.

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