Abstract

In this paper, we propose an autocorrelation function (ACF) based watermarking scheme in the discrete wavelet transform (DWT) domain. Conventional ACF-based watermarking embeds a watermark in the spatial domain due to its detection mechanism. We show that the autocorrelation (AC) peaks, which play an important role in estimating the applied geometric attacks in ACF-based watermarking, can also be extracted by embedding the watermark in the DWT domain. In the proposed scheme, a periodic watermark is embedded in the DWT domain by considering the AC peak strength and noise visibility. The proposed scheme also deals efficiently with the image shift problem in the detection process by using the undecimated DWT. Experimental results show that the proposed scheme yields stronger AC peaks than the spatial domain scheme does and, as a result, shows improved robustness against combined geometric-removal attacks.

© 2005 Optical Society of America

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References

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  1. J. J. K. O’ Ruanaidh and T. Pun, “Rotation, scale and translation invariant spread spectrum digital image watermarking,” Signal Processing 66, 303-317 (1998).
    [CrossRef]
  2. M. Kutter, S. K. Bhattacharjee, and T. Ebrahimi, “Towards second generation watermarking schemes,” in Proceedings of IEEE Int. Conference on Image Processing (Institute of Electrical and Electronics Engineers, New York, 1999), pp. 320-323.
  3. S. Pereira and T. Pun, “Fast robust template matching for affine resistant image watermarking,” in International Workshop on Information Hiding, LNCS 1768 (Springer-Verlag, Berlin, Germany, 1999), pp. 200-210.
  4. M. Kutter, “Watermarking resisting to translation, rotation, and scaling,” in Multimedia systems and applications, Proc. SPIE 3528, 423-431 (1998).
  5. I. J. Cox, J. Kilian, F. T. Leighton, and T. Shamoon, “Secure spread spectrum watermarking for multimedia,” IEEE Trans. on Image Processing 6, 1673-1687 (1997).
    [CrossRef]
  6. M. Barni, F. Bartolini, V. Cappellini, and A. Piva, “A DCT-domain system for robust image watermarking,” Signal Processing 66, 357-372 (1998).
    [CrossRef]
  7. J. S. Lim, Two-dimensional signal and image processing (Prentice Hall, New Jersey, 1990).
  8. F. A. P. Petitcolas, R. J. Anderson, and M. G. Kuhn. “Attacks on copyright marking systems,” in International workshop on information hiding, LNCS 1525 (Springer-Verlag, Berlin, Germany, 1998), pp. 218-238.
    [CrossRef]
  9. R. Polikar, “The wavelet tutorial”, http://users.rowan.edu/˜polikar/WAVELETS/WTtutorial.html
  10. E. J. Stollnitz, T. D. DeRose, and D. H. Salesin, “Wavelets for computer graphics: A primer,” IEEE Computer Graphics and Applications 15, 76-84 (1995).
    [CrossRef]
  11. A.B. Watson, G.Y.Yang, J.A.Solomon, and J.Villasenor, “Visual thresholds for wavelet quantization error,” in Human Vision and Electronic Imaging, B. E. Rogowitz and J. P. Allebach, eds., Proc. SPIE 2657, 382-392 (1996).
  12. A. Gyaourova, C. Kamath, and I. K. Fodor, “Undecimated wavelet transforms for image de-noising,” Technical report, Lawrence Livermore National Laboratory, UCRL-ID-150931 (2002).
  13. G. Beylkin, “On the representation of operators in bases of compactly supported wavelets,” SIAM J. Numer. Anal. 29, 1716-1740, (1992).
    [CrossRef]
  14. M. Lang, H. Guo, J. E. Odegard, and C. S. Burrus, “Nonlinear processing of a shift invariant DWT for noise reduction,” in Mathematical Imaging: Wavelet Applications for Dual Use, Proc. SPIE 2491, 640-651 (1995).
  15. M. Kutter and F. A. P. Peticolas, “A fair benchmark for image watermarking systems,” in Security and Watermarking of Multimedia Contents, P. W. Wong and E. J. Delp, eds., Proc. SPIE 3657, 226-239 (1999).
  16. H. C. Huang, J. S. Pan, and H. M. Hang, “Watermarking based on transform domain,” in Intelligent Watermarking Techniques, J. S. Pan, H. C. Huang, and L. C. Jain, eds. (World Scientific, Singapore, 2004), pp.147-163.
  17. M. Barni, F. Bartolini, and A. Piva, “Improved wavelet-based watermarking through pixel-wise Masking,” IEEE Trans. on Image Processing 10, 783-791 (2001).
    [CrossRef]
  18. V. Darmstaedter, J.-F. Delaigle, J. J. Quisquater, and B. Macq, “Low Cost Spatial Watermarking,” Comput. & Graphics 22, 417-424 (1998).
    [CrossRef]
  19. W. Bender, D. Gruhl, N. Morimoto, and A. Lu, “Techniques for data hiding,” in Storage and Retrieval for Image and Video Database III, Proc. SPIE 2420, 165-173 (1995).
  20. C. I. Podilchuk and W. J. Zheng, “Image-adaptive watermarking using visual models,” IEEE Journal on Selected Areas in Communications 16, 525-539 (1998).
    [CrossRef]
  21. S. Voloshynovskiy, F. Deguillaume, and T. Pun, “Content adaptive watermarking based on a stochastic multiresolution image modeling,” in Tenth European Signal Processing Conference (EUSIPCO’2000), Tampere, Finland, Sept. 2000.
  22. S. Voloshynovskiy, A. Herrigel, N. Baumgartner, and T. Pun, “A stochastic approach to content adaptive digital image watermarking,” in International Workshop on Information Hiding, LNCS 1768 (Springer-Verlag, Berlin, Germany, 1999), pp. 212-236.
  23. I. J. Cox, M. L. Miller, and J. A. Bloom, Digital Watermarking (Morgan Kaufmann Publishers, San Francisco, Calif., 2002).
  24. T. Kalker, G. Depovere, J. Haitsma, and M. Maes, “A video watermarking system for broadcast monitoring,” in Security and Watermarking Multimedia Contents, P. W. Wong and E. J. Delp, eds., Proc. SPIE 3657, 103-112 (1999).

Comput. & Graphics (1)

V. Darmstaedter, J.-F. Delaigle, J. J. Quisquater, and B. Macq, “Low Cost Spatial Watermarking,” Comput. & Graphics 22, 417-424 (1998).
[CrossRef]

IEEE Computer Graphics and Applications (1)

E. J. Stollnitz, T. D. DeRose, and D. H. Salesin, “Wavelets for computer graphics: A primer,” IEEE Computer Graphics and Applications 15, 76-84 (1995).
[CrossRef]

IEEE Journal on Selected Areas in Commun (1)

C. I. Podilchuk and W. J. Zheng, “Image-adaptive watermarking using visual models,” IEEE Journal on Selected Areas in Communications 16, 525-539 (1998).
[CrossRef]

IEEE Trans. on Image Processing (2)

I. J. Cox, J. Kilian, F. T. Leighton, and T. Shamoon, “Secure spread spectrum watermarking for multimedia,” IEEE Trans. on Image Processing 6, 1673-1687 (1997).
[CrossRef]

M. Barni, F. Bartolini, and A. Piva, “Improved wavelet-based watermarking through pixel-wise Masking,” IEEE Trans. on Image Processing 10, 783-791 (2001).
[CrossRef]

Proc. SPIE (4)

A.B. Watson, G.Y.Yang, J.A.Solomon, and J.Villasenor, “Visual thresholds for wavelet quantization error,” in Human Vision and Electronic Imaging, B. E. Rogowitz and J. P. Allebach, eds., Proc. SPIE 2657, 382-392 (1996).

M. Kutter, “Watermarking resisting to translation, rotation, and scaling,” in Multimedia systems and applications, Proc. SPIE 3528, 423-431 (1998).

M. Lang, H. Guo, J. E. Odegard, and C. S. Burrus, “Nonlinear processing of a shift invariant DWT for noise reduction,” in Mathematical Imaging: Wavelet Applications for Dual Use, Proc. SPIE 2491, 640-651 (1995).

M. Kutter and F. A. P. Peticolas, “A fair benchmark for image watermarking systems,” in Security and Watermarking of Multimedia Contents, P. W. Wong and E. J. Delp, eds., Proc. SPIE 3657, 226-239 (1999).

SIAM J. Numer. Anal. (1)

G. Beylkin, “On the representation of operators in bases of compactly supported wavelets,” SIAM J. Numer. Anal. 29, 1716-1740, (1992).
[CrossRef]

Signal Processing (2)

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

M. Barni, F. Bartolini, V. Cappellini, and A. Piva, “A DCT-domain system for robust image watermarking,” Signal Processing 66, 357-372 (1998).
[CrossRef]

Other (12)

J. S. Lim, Two-dimensional signal and image processing (Prentice Hall, New Jersey, 1990).

F. A. P. Petitcolas, R. J. Anderson, and M. G. Kuhn. “Attacks on copyright marking systems,” in International workshop on information hiding, LNCS 1525 (Springer-Verlag, Berlin, Germany, 1998), pp. 218-238.
[CrossRef]

R. Polikar, “The wavelet tutorial”, http://users.rowan.edu/˜polikar/WAVELETS/WTtutorial.html

M. Kutter, S. K. Bhattacharjee, and T. Ebrahimi, “Towards second generation watermarking schemes,” in Proceedings of IEEE Int. Conference on Image Processing (Institute of Electrical and Electronics Engineers, New York, 1999), pp. 320-323.

S. Pereira and T. Pun, “Fast robust template matching for affine resistant image watermarking,” in International Workshop on Information Hiding, LNCS 1768 (Springer-Verlag, Berlin, Germany, 1999), pp. 200-210.

A. Gyaourova, C. Kamath, and I. K. Fodor, “Undecimated wavelet transforms for image de-noising,” Technical report, Lawrence Livermore National Laboratory, UCRL-ID-150931 (2002).

H. C. Huang, J. S. Pan, and H. M. Hang, “Watermarking based on transform domain,” in Intelligent Watermarking Techniques, J. S. Pan, H. C. Huang, and L. C. Jain, eds. (World Scientific, Singapore, 2004), pp.147-163.

S. Voloshynovskiy, F. Deguillaume, and T. Pun, “Content adaptive watermarking based on a stochastic multiresolution image modeling,” in Tenth European Signal Processing Conference (EUSIPCO’2000), Tampere, Finland, Sept. 2000.

S. Voloshynovskiy, A. Herrigel, N. Baumgartner, and T. Pun, “A stochastic approach to content adaptive digital image watermarking,” in International Workshop on Information Hiding, LNCS 1768 (Springer-Verlag, Berlin, Germany, 1999), pp. 212-236.

I. J. Cox, M. L. Miller, and J. A. Bloom, Digital Watermarking (Morgan Kaufmann Publishers, San Francisco, Calif., 2002).

T. Kalker, G. Depovere, J. Haitsma, and M. Maes, “A video watermarking system for broadcast monitoring,” in Security and Watermarking Multimedia Contents, P. W. Wong and E. J. Delp, eds., Proc. SPIE 3657, 103-112 (1999).

W. Bender, D. Gruhl, N. Morimoto, and A. Lu, “Techniques for data hiding,” in Storage and Retrieval for Image and Video Database III, Proc. SPIE 2420, 165-173 (1995).

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Figures (12)

Fig. 1.
Fig. 1.

AC peaks example of the Lena image marked in the DWT domain

Fig. 2.
Fig. 2.

Peak strength before and after JPEG compression by embedding a periodic watermark in the first-level sub-band

Fig. 3.
Fig. 3.

Peak strength before and after JPEG compression by embedding a periodic watermark in the second-level sub-band

Fig. 4.
Fig. 4.

Periodic watermark embedding in the DWT domain

Fig. 5.
Fig. 5.

Peak example for geometric transform estimation algorithm

Fig. 6.
Fig. 6.

Image decomposition by shift4 algorithm

Fig. 7.
Fig. 7.

Correlation based detection process in the second level subband

Fig. 8.
Fig. 8.

Distribution of AC peaks after JPEG quality 50% compression. (The histogram of non-peaks is scaled down vertically for better illustration.)

Fig. 9.
Fig. 9.

Distribution of the detector responses after JPEG 50% compression. (The histogram of the response from unmarked images is scaled down vertically for better illustration.)

Fig. 10.
Fig. 10.

Theoretical distribution models for detector responses and AC peaks. (a) Distribution model for detector response from DWT second level, (b) Distribution model for AC peak strength of the DWT watermarking.

Fig. 11.
Fig. 11.

ROC curves of the AC peak and watermark detection after JPEG quality 50% compression.

Fig. 12.
Fig. 12.

Test images for the watermark detection experiment

Tables (1)

Tables Icon

Table 1. Watermark detection results after Stirmark geometric attacks and JPEG 50% compression. The number in the parentesis is the total number of attacks for each attack class. For example, R-C Remove has 75 attacks (15 images×6 attacks).

Equations (23)

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I j θ ( x , y ) = I j θ ( x , y ) + α λ j θ ( x , y ) W j ( x , y )
N V F j θ ( x , y ) = 1 1 + D σ j max θ 2 σ j θ 2 ( x , y ) ,
Θ θ = { 2 if θ = 2 ( diagonal direction ) 1 otherwise .
λ j θ ( x , y ) = L j Θ θ [ ( 1 N V F j θ ( x , y ) ) · S + N V F j θ ( x , y ) · S 1 ] .
I ( x , y ) = μ ( x , y ) + σ 2 ( x , y ) s 2 σ 2 ( x , y ) ( I ( x , y ) μ ( x , y ) ) ,
E = I I .
A C F = I F F T ( F F T ( E ) · F F T ( E ) * ) E 2 ,
A C F ( x , y ) > μ acf + α acf σ acf ,
P f pAC = P ( AC non peak > μ acf + α acf σ acf ) = P ( X > α acf ) = α acf 1 2 π exp ( x 2 2 ) d x ,
Peak Ratio = Peak Count Expected Peak Count .
Weighted Peak Count = Peak Count × Peak Ratio .
N C j , k = I F F T ( F F T ( E j , k ) · F F T ( W r j ) * ) E j , k W r j .
D R j = max x , y , k { N C j , k ( x , y ) } .
D R 1 > τ 1 or D R 2 > τ 2 ,
τ j = μ n c j + α n c j σ n c j ,
P f p max = 1 ( 1 P f p N C ) R ,
b avg ( i , j ) = 1 N n = 1 N b n ( i , j ) , ( 1 i , j M ) .
I = I + α s λ s W s ,
λ s = ( 1 N V F ) · S + N V F · S 1 .
4 M 2 + 16 ( M 2 ) 2 + 3 × 4 × ( M 2 ) 2 log ( M 2 ) + 3 × 16 × ( M 4 ) 2 log ( M 4 )
= 8 M 2 + 3 M 2 ( log M log 2 ) + 3 M 2 ( log M log 4 )
= 6 M 2 log M M 2 .
PSNR = 20 log 10 ( 255 1 X Y ( I ( x , y ) I ( x , y ) ) 2 ) .

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