Abstract

Many proposed image watermarking techniques are sensitive to geometric distortions, such as rotation, scaling and translation. Geometric distortions, even by slight amount, can make watermark decoder disable. In this paper, a geometric invariant blind image watermarking is designed by utilizing the invariant Tchebichef moments. The detailed construction of invariant Tchebichef moments is described. Watermark is generated independent to the original image and inserted into the perceptually significant invariant Tchebichef moments of original image. The watermark decoder extracts watermark blindly utilizing Independent Component Analysis (ICA). The computational aspects of the proposed watermarking are also discussed in detail. Experimental results have demonstrated that the proposed watermarking technique is robust against geometric distortions and other attacks performed by popular watermark benchmark-Stirmark, such as filtering, image compression, additive noise, random geometric distortions.

© 2007 Optical Society of America

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References

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  1. S. Voloshynovskiy, S. Pereira, T. Pun, J. J. Eggers, and J. K. Su, "Attacks on digital watermarks: classification, estimation-based attacks and benchmarks," IEEE Communications Magazine 8, 2~10 (2001).
  2. C.-H. Lee, H.-K. Lee, "Geometric attack resistant watermarking in wavelet transform domain," Opt. Express 13,1307-1321 (2005).
    [CrossRef] [PubMed]
  3. M. Alghoniemy, A. H. Tewfik, "Geometric invariants in image watermarking," IEEE Transactions on Image Processing 13, 145-153 (2004).
    [CrossRef] [PubMed]
  4. Y. Xin, S. Liao, M. Pawlak, "Geometrically robust image watermarking via pseudo-Zernike moments," IEEE Canadian Conference on Electrical and Computer Engineering 2, 939-942 (2004).
  5. Y. Xin, S. Liao, M. Pawlak, "A multibit geometrically robust image watermark based on Zernike moments," International Conference on Pattern Recognition IV, 861-864 (2004).
  6. S. Pereira, T. Pun, "Robust template matching for affine resistant image watermarks," IEEE Transations on Image Processing 9, 1123-1129 (2000).
    [CrossRef]
  7. M. Kutter, "Performance improvement of spread spectrum based image watermarking schemes through M-ary modulation," Lecture Notes in Computer Science 1728, 238-250 (1999).
  8. P. Dong and N. P. Galasanos, "Affine transform resistant watermarking based on image normalization," IEEE Int. Conf. Image Pro. 489-492 (2002).
  9. J. O'Ruanaidh and T. Pun, "Rotation, scale and translation invariant spread spectrum digital image watermarking," Signal Processing 66, 303-317 (1998).
    [CrossRef]
  10. H. S. Kim and H. K, Lee. "Invariant image watermark using Zernike moments," IEEE Trans.Circuits and Systems for Vid. 13, 766-775 (2003).
    [CrossRef]
  11. M. R. Teague, "Image analysis via the general theory of moments," J. Opt. Soc. Amer. 70, 920-930 (1980).
    [CrossRef]
  12. C. Kan and M. D. Srinath, "Invariant character recognition with Zernike and orthogonal Fourier-Mellin moments," Pattern Recognition 35, 143-154 (2002)
    [CrossRef]
  13. R. Mukundan, S. H. Ong, and P. A. Lee, "Image analysis by Tchebichef moments," IEEE Trans, Image Processing 10, 1357-1364 (2001).
    [CrossRef]
  14. R. Mukundan, "Some computational aspects of discrete orthonormal moments," IEEE Transactions on Image Processing 13, 1055 - 1059 (2004).
    [CrossRef] [PubMed]
  15. M. K. Hu, "Visual pattern recognition by moment invariants," IRE Trans. Information Theory IT-8, 179-187 (1962).
  16. A. Hyvarinen and E. Oja, "Independent component analysis: A tutorial. Notes for International Joint Conference on Neural Networks (IJCNN’99)," Washington D. C., http://www.cis.hut.fi/projects/ica/ (1999)
  17. S. Pereira and T Pun, "Robust template matching for affine resistant image watermarks," IEEE Transactions on Image Processing 9, 1123 -1129 (2000).
    [CrossRef]
  18. D. Yu, F. Sattar, and K. K. Ma, "Watermark detection and extraction using independent component analysis method," EURASIP Journal on Applied Signal Processing 1, 92-104 (2002).

2005

C.-H. Lee, H.-K. Lee, "Geometric attack resistant watermarking in wavelet transform domain," Opt. Express 13,1307-1321 (2005).
[CrossRef] [PubMed]

2004

M. Alghoniemy, A. H. Tewfik, "Geometric invariants in image watermarking," IEEE Transactions on Image Processing 13, 145-153 (2004).
[CrossRef] [PubMed]

R. Mukundan, "Some computational aspects of discrete orthonormal moments," IEEE Transactions on Image Processing 13, 1055 - 1059 (2004).
[CrossRef] [PubMed]

2003

H. S. Kim and H. K, Lee. "Invariant image watermark using Zernike moments," IEEE Trans.Circuits and Systems for Vid. 13, 766-775 (2003).
[CrossRef]

2002

C. Kan and M. D. Srinath, "Invariant character recognition with Zernike and orthogonal Fourier-Mellin moments," Pattern Recognition 35, 143-154 (2002)
[CrossRef]

D. Yu, F. Sattar, and K. K. Ma, "Watermark detection and extraction using independent component analysis method," EURASIP Journal on Applied Signal Processing 1, 92-104 (2002).

2001

S. Voloshynovskiy, S. Pereira, T. Pun, J. J. Eggers, and J. K. Su, "Attacks on digital watermarks: classification, estimation-based attacks and benchmarks," IEEE Communications Magazine 8, 2~10 (2001).

R. Mukundan, S. H. Ong, and P. A. Lee, "Image analysis by Tchebichef moments," IEEE Trans, Image Processing 10, 1357-1364 (2001).
[CrossRef]

2000

S. Pereira, T. Pun, "Robust template matching for affine resistant image watermarks," IEEE Transations on Image Processing 9, 1123-1129 (2000).
[CrossRef]

S. Pereira and T Pun, "Robust template matching for affine resistant image watermarks," IEEE Transactions on Image Processing 9, 1123 -1129 (2000).
[CrossRef]

1999

M. Kutter, "Performance improvement of spread spectrum based image watermarking schemes through M-ary modulation," Lecture Notes in Computer Science 1728, 238-250 (1999).

1998

J. O'Ruanaidh and T. Pun, "Rotation, scale and translation invariant spread spectrum digital image watermarking," Signal Processing 66, 303-317 (1998).
[CrossRef]

1980

M. R. Teague, "Image analysis via the general theory of moments," J. Opt. Soc. Amer. 70, 920-930 (1980).
[CrossRef]

1962

M. K. Hu, "Visual pattern recognition by moment invariants," IRE Trans. Information Theory IT-8, 179-187 (1962).

Alghoniemy, M.

M. Alghoniemy, A. H. Tewfik, "Geometric invariants in image watermarking," IEEE Transactions on Image Processing 13, 145-153 (2004).
[CrossRef] [PubMed]

Hu, M. K.

M. K. Hu, "Visual pattern recognition by moment invariants," IRE Trans. Information Theory IT-8, 179-187 (1962).

Kim, H. S.

H. S. Kim and H. K, Lee. "Invariant image watermark using Zernike moments," IEEE Trans.Circuits and Systems for Vid. 13, 766-775 (2003).
[CrossRef]

Kutter, M.

M. Kutter, "Performance improvement of spread spectrum based image watermarking schemes through M-ary modulation," Lecture Notes in Computer Science 1728, 238-250 (1999).

Lee, P. A.

R. Mukundan, S. H. Ong, and P. A. Lee, "Image analysis by Tchebichef moments," IEEE Trans, Image Processing 10, 1357-1364 (2001).
[CrossRef]

Ma, K. K.

D. Yu, F. Sattar, and K. K. Ma, "Watermark detection and extraction using independent component analysis method," EURASIP Journal on Applied Signal Processing 1, 92-104 (2002).

Mukundan, R.

R. Mukundan, "Some computational aspects of discrete orthonormal moments," IEEE Transactions on Image Processing 13, 1055 - 1059 (2004).
[CrossRef] [PubMed]

R. Mukundan, S. H. Ong, and P. A. Lee, "Image analysis by Tchebichef moments," IEEE Trans, Image Processing 10, 1357-1364 (2001).
[CrossRef]

Ong, S. H.

R. Mukundan, S. H. Ong, and P. A. Lee, "Image analysis by Tchebichef moments," IEEE Trans, Image Processing 10, 1357-1364 (2001).
[CrossRef]

O'Ruanaidh, J.

J. O'Ruanaidh and T. Pun, "Rotation, scale and translation invariant spread spectrum digital image watermarking," Signal Processing 66, 303-317 (1998).
[CrossRef]

Pereira, S.

S. Voloshynovskiy, S. Pereira, T. Pun, J. J. Eggers, and J. K. Su, "Attacks on digital watermarks: classification, estimation-based attacks and benchmarks," IEEE Communications Magazine 8, 2~10 (2001).

S. Pereira, T. Pun, "Robust template matching for affine resistant image watermarks," IEEE Transations on Image Processing 9, 1123-1129 (2000).
[CrossRef]

S. Pereira and T Pun, "Robust template matching for affine resistant image watermarks," IEEE Transactions on Image Processing 9, 1123 -1129 (2000).
[CrossRef]

Pun, T

S. Pereira and T Pun, "Robust template matching for affine resistant image watermarks," IEEE Transactions on Image Processing 9, 1123 -1129 (2000).
[CrossRef]

Pun, T.

S. Voloshynovskiy, S. Pereira, T. Pun, J. J. Eggers, and J. K. Su, "Attacks on digital watermarks: classification, estimation-based attacks and benchmarks," IEEE Communications Magazine 8, 2~10 (2001).

S. Pereira, T. Pun, "Robust template matching for affine resistant image watermarks," IEEE Transations on Image Processing 9, 1123-1129 (2000).
[CrossRef]

J. O'Ruanaidh and T. Pun, "Rotation, scale and translation invariant spread spectrum digital image watermarking," Signal Processing 66, 303-317 (1998).
[CrossRef]

Sattar, F.

D. Yu, F. Sattar, and K. K. Ma, "Watermark detection and extraction using independent component analysis method," EURASIP Journal on Applied Signal Processing 1, 92-104 (2002).

Teague, M. R.

M. R. Teague, "Image analysis via the general theory of moments," J. Opt. Soc. Amer. 70, 920-930 (1980).
[CrossRef]

Tewfik, A. H.

M. Alghoniemy, A. H. Tewfik, "Geometric invariants in image watermarking," IEEE Transactions on Image Processing 13, 145-153 (2004).
[CrossRef] [PubMed]

Voloshynovskiy, S.

S. Voloshynovskiy, S. Pereira, T. Pun, J. J. Eggers, and J. K. Su, "Attacks on digital watermarks: classification, estimation-based attacks and benchmarks," IEEE Communications Magazine 8, 2~10 (2001).

Yu, D.

D. Yu, F. Sattar, and K. K. Ma, "Watermark detection and extraction using independent component analysis method," EURASIP Journal on Applied Signal Processing 1, 92-104 (2002).

Circuits and Systems for Vid.

H. S. Kim and H. K, Lee. "Invariant image watermark using Zernike moments," IEEE Trans.Circuits and Systems for Vid. 13, 766-775 (2003).
[CrossRef]

EURASIP Journal on Applied Signal Processing

D. Yu, F. Sattar, and K. K. Ma, "Watermark detection and extraction using independent component analysis method," EURASIP Journal on Applied Signal Processing 1, 92-104 (2002).

IEEE Communications Magazine

S. Voloshynovskiy, S. Pereira, T. Pun, J. J. Eggers, and J. K. Su, "Attacks on digital watermarks: classification, estimation-based attacks and benchmarks," IEEE Communications Magazine 8, 2~10 (2001).

IEEE Trans, Image Processing

R. Mukundan, S. H. Ong, and P. A. Lee, "Image analysis by Tchebichef moments," IEEE Trans, Image Processing 10, 1357-1364 (2001).
[CrossRef]

IEEE Transactions on Image Processing

R. Mukundan, "Some computational aspects of discrete orthonormal moments," IEEE Transactions on Image Processing 13, 1055 - 1059 (2004).
[CrossRef] [PubMed]

S. Pereira and T Pun, "Robust template matching for affine resistant image watermarks," IEEE Transactions on Image Processing 9, 1123 -1129 (2000).
[CrossRef]

M. Alghoniemy, A. H. Tewfik, "Geometric invariants in image watermarking," IEEE Transactions on Image Processing 13, 145-153 (2004).
[CrossRef] [PubMed]

IEEE Transations on Image Processing

S. Pereira, T. Pun, "Robust template matching for affine resistant image watermarks," IEEE Transations on Image Processing 9, 1123-1129 (2000).
[CrossRef]

IRE Trans. Information Theory

M. K. Hu, "Visual pattern recognition by moment invariants," IRE Trans. Information Theory IT-8, 179-187 (1962).

J. Opt. Soc. Amer.

M. R. Teague, "Image analysis via the general theory of moments," J. Opt. Soc. Amer. 70, 920-930 (1980).
[CrossRef]

Lecture Notes in Computer Science

M. Kutter, "Performance improvement of spread spectrum based image watermarking schemes through M-ary modulation," Lecture Notes in Computer Science 1728, 238-250 (1999).

OPTICS EXPRESS

C.-H. Lee, H.-K. Lee, "Geometric attack resistant watermarking in wavelet transform domain," Opt. Express 13,1307-1321 (2005).
[CrossRef] [PubMed]

Pattern Recognition

C. Kan and M. D. Srinath, "Invariant character recognition with Zernike and orthogonal Fourier-Mellin moments," Pattern Recognition 35, 143-154 (2002)
[CrossRef]

Signal Processing

J. O'Ruanaidh and T. Pun, "Rotation, scale and translation invariant spread spectrum digital image watermarking," Signal Processing 66, 303-317 (1998).
[CrossRef]

Other

A. Hyvarinen and E. Oja, "Independent component analysis: A tutorial. Notes for International Joint Conference on Neural Networks (IJCNN’99)," Washington D. C., http://www.cis.hut.fi/projects/ica/ (1999)

P. Dong and N. P. Galasanos, "Affine transform resistant watermarking based on image normalization," IEEE Int. Conf. Image Pro. 489-492 (2002).

Y. Xin, S. Liao, M. Pawlak, "Geometrically robust image watermarking via pseudo-Zernike moments," IEEE Canadian Conference on Electrical and Computer Engineering 2, 939-942 (2004).

Y. Xin, S. Liao, M. Pawlak, "A multibit geometrically robust image watermark based on Zernike moments," International Conference on Pattern Recognition IV, 861-864 (2004).

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Figures (4)

Fig.  1.
Fig. 1.

Original image, watermark and watermarked image. (a)original image (b)watermark (c)permuted watermark (d)watermarked image

Fig. 2.
Fig. 2.

Experimental results of robust against geometric distortions. (a)NC due to scaling attack (b) NC due to rotation attacks

Fig. 3.
Fig. 3.

Experimental results of robustness against filtering. (a)NC due to low pass filtering (b)NC due to median filtering

Fig. 4.
Fig. 4.

NC comparison (scaling and rotation).

Tables (4)

Tables Icon

Table 1. Robust to additive noise

Tables Icon

Table 2. Robust to JPEG compression produced by Stirmark

Tables Icon

Table 3. Robustness against attacks produced by Stirmark

Tables Icon

Table 4. Experimental results compared to [17] and two commercial watermarking

Equations (41)

Equations on this page are rendered with MathJax. Learn more.

T pq = 1 ρ p N ρ q N x = 0 N 1 y = 0 N 1 t p ( x ) t p ( x ) f x y , p , q = 0,1,2 , , N 1
t n ( x ) = n ! k = 0 n ( 1 ) n k ( N 1 k n k ) ( n + k n ) ( x k )
f x y = p = 0 N 1 q = 0 N 1 T pq t p ( x ) t q ( y )
t ˜ n ( x ) = t n ( x ) β n N = k = 0 n c k , n , N x k
t ˜ 0 x N = 1
t ˜ 1 x N = 1 N N + 2 N x
t ˜ 2 x N = N 2 3 N + 2 N 2 + 6 ( 1 N ) N 2 x + 6 N 2 x 2
t ˜ 3 x N = N 3 + 6 N 2 11 N + 6 N 3 + 12 N 2 30 N + 22 N 3 x + 30 ( 1 N ) N 3 x 2 + 20 N 3 x 3
c 0 , 0 , N = 1
c 0,1 , N = 1 N N c 1,1 , N = 2 N
c 0,2 , N = N 2 3 N + 2 N 2 c 1,2 . N = 6 ( 1 N ) N 2 c 2,2 , N = 6 N 2
c 0,3 , N = N 3 + 6 N 2 11 N + 6 N 3 c 1,3 , N = 12 N 2 30 N + 22 N 3 c 2,3 , N = 30 ( 1 N ) N 3 c 3,3 , N = 20 N N 3
T pq = 1 ρ ˜ p N ρ ˜ q N x = 0 N 1 y = 0 N 1 ( i = 0 p c i , p , N x i ) ( j = 0 q c j , q , N x j ) f ( x , y )
m pq = x = 0 N 1 y = 0 N 1 x p y q f x y
T pq = 1 ρ ˜ p N ρ ˜ q N i = 0 p j = 0 q c j , q , N c i , p , N m i , j
T 00 = m 00 N 2 T 10 = 6 m 10 + 3 ( 1 N ) m 00 N ( N 2 1 ) T 01 = 6 m 01 + 3 ( 1 N ) m 00 N ( N 2 1 )
T 20 = 30 m 20 + 30 ( 1 N ) m 10 + 5 ( 1 N ) ( 2 N ) m 00 ( N 2 1 ) ( N 2 2 ) T 02 = 30 m 02 + 30 ( 1 N ) m 01 + 5 ( 1 N ) ( 2 N ) m 00 ( N 2 1 ) ( N 2 2 )
T 11 = 36 m 11 + 18 ( 1 N ) ( m 10 + m 01 ) + 9 ( 1 N 2 ) m 00 ( N 2 1 ) 2
μ nm = ( x x ¯ ) n ( x y ¯ ) m f ( x , y ) dxdy
g x + N 2 y + N 2 = f x ¯ + x cos θ y sin θ α y ¯ + y cos θ x sin θ α
m ̅ nm = x = 0 N 1 x = 0 N 1 α 2 f x y { α [ ( x x ¯ ) cos θ + ( y y ¯ ) sin θ ] + N 2 } n × { α [ ( y y ¯ ) cos θ ( x x ¯ ) sin θ ] + N 2 } m
m
m
T ̅ pq = 1 ρ ˜ p N ρ ˜ q N i = 0 p j = 0 q c j , q , N c i , P , N m ¯ i , j
T ¯ pq = x = 0 N 1 y = 0 N 1 N 2 2 m 00 f x y { [ ( x x ¯ ) cos θ + ( y y ¯ ) sin θ ] N 2 2 m 00 + N 2 } p { [ ( y y ¯ ) cos θ ( x x ¯ ) sin θ ] N 2 2 m 00 + N 2 } q
T ̂ m i , n i = T om i , n i + a m i n i T wm i , n i
x j = a j 1 s 1 + a j 2 s 2 + + a jn s n for all j = 1 . . n
t ˜ n ( N 1 x ) = ( 1 ) n t ˜ n ( x )
T pq = 1 ρ ˜ p N ρ ˜ q N x = 0 N 2 1 y = 0 N 2 1 t ˜ p ( x ) t ˜ q ( y ) { f x y + ( 1 ) p f ( N 1 x , y ) + ( 1 ) q f ( x , N 1 y ) + ( 1 ) p + q f ( N 1 x , N 1 y ) }
f x y = { m = 0 N 1 n = 0 N 1 T mn t ˜ m ( x ) t ˜ n ( y ) x , y < ( N 2 ) m = 0 N 1 n = 0 N 1 ( 1 ) m T mn t ˜ m ( N 1 x ) t ˜ n ( y ) y < ( N 2 ) ; x ( N 2 ) m = 0 N 1 n = 0 N 1 ( 1 ) m T mn t ˜ m ( x ) t ˜ n ( N 1 y ) x < ( N 2 ) ; y ( N 2 ) m = 0 N 1 n = 0 N 1 ( 1 ) m + n T mn t ˜ m ( N 1 x ) t ˜ n ( N 1 y ) x , y ( N 2 )
T = CFC T
T = { T i , j } i , j = 0 N 1 , N 1 .
F = { f i j } i , j = 0 N 1 , N 1 .
C = { t i , j } i , j = 0 N 1 , N 1 .
F = C T TC
1 3 ( p + q ) 3 + ( p + q ) 2 + 2 3 ( p + q )
PSNR = 10 log ( f ( x , y ) max 2 / ( N 2 x = 0 N 1 y = 0 N 1 ( f ( x , y ) z ( x , y ) ) 2 ) )
NC ( w , w ) = i w ( i ) w ´ ( i ) / ( i w 2 ( i ) i w 2 ( i ) )
f ̂ ( x , y ) = f x y + v ( x , y )
p ( V = v ) = 1 2 π σ exp ( ( v μ ´ ) 2 2 σ 2 )
v x y = λ f x y

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