Abstract

In this paper, we introduce a new multiresolution watermarking method for digital images. The method is based on the discrete wavelet transform (DWT). Pseudo-random codes are added to the large coefficients at the high and middle frequency bands of the DWT of an image. It is shown that this method is more robust to proposed methods to some common image distortions, such as the wavelet transform based image compression, image rescaling/stretching and image halftoning. Moreover, the method is hierarchical.

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  1. R. G. van Schyndel, A. Z. Tirkel, and C. F. Osborne, "A digital watermark," Proc. ICIP'94, 2, 86-90 (1994).
  2. I. J. Cox, J. Kilian, T. Leighton, and T. Shamoon, "Secure spread spectrum watermarking for images, audio and video," Proc. ICIP'96, 3, 243-246 (1996).
  3. J. Zhao and E. Koch, "Embedding robust labels into images for copyright protection," Proceedings of the International Congress on Intellectual Property Rights for Specialized Information, Knowledge and New Technologies, Vienna, Austria, August 21-25, 242-251 (1995).
  4. R. B. Wolfgang and E. J. Delp, "A watermark for digital images," Proc. ICIP'96, 3, 219-222 (1996).
  5. I. Pitas, "A method for signature casting on digital images," Proc. ICIP'96, 3, 215-218 (1996).
  6. N. Nikolaidis and I. Pitas, "Copyright protection of images using robust digital signatures," Proceedings of ICASSP'96, Atlanta, Georgia, May, 2168-2171 (1996).
  7. M. D. Swanson, B. Zhu, and A. H. Tewfik, "Transparent robust image watermarking," Proc. ICIP'96, 3, 211-214 (1996).
  8. M. Schneider and S.-F. Chang, "A robust content based digital signature for image authentication," Proc. ICIP'96, 3, 227-230 (1996).
  9. S. Mallat, "Multiresolution approximations and wavelet orthonormal bases of L 2 (R)," Trans. Amer. Math. Soc., 315, 69-87 (1989).
  10. I. Daubechies, "Orthonormal bases of compactly supported wavelets," Comm. on Pure and Appl. Math., 41, 909-996 (1988).
    [CrossRef]
  11. O. Rioul and M. Vetterli, "Wavelets and signal processing," IEEE Signal Processing Magazine, 14-38, (1991).
    [CrossRef]
  12. I. Daubechies, Ten Lectures on Wavelets, (SIAM, Philadelphia, 1992).
  13. P. P. Vaidyanathan, Multirate Systems and Filter Banks, (Prentice Hall, Englewood Cliffs, NJ, 1993).
  14. M. Vetterli and J. Kovacevic, Wavelets and Subband Coding, (Prentice Hall, Englewood Cliffs, NJ, 1995).
  15. G. Strang and T. Q. Nguyen, Wavelets and Filter Banks, (Wellesley-Cambridge Press, Cambridge, 1996).
  16. J. Shapiro, "Embedded image coding using zerotrees of wavelet coefficients," IEEE Trans. on Signal Processing, 41, 3445-3462 (1993).
    [CrossRef]
  17. R. Ulichney, Digital Halftoning, (MIT Press, Massachusetts, 1987).
  18. S. Craver, N. Memon, B-L Yeo, and M. M. Yeung, "Resolving rightful ownerships with invisible watermarking techniques: limitations, attacks, and implications," IBM Research Report (RC 20755), March 1997.

Other (18)

R. G. van Schyndel, A. Z. Tirkel, and C. F. Osborne, "A digital watermark," Proc. ICIP'94, 2, 86-90 (1994).

I. J. Cox, J. Kilian, T. Leighton, and T. Shamoon, "Secure spread spectrum watermarking for images, audio and video," Proc. ICIP'96, 3, 243-246 (1996).

J. Zhao and E. Koch, "Embedding robust labels into images for copyright protection," Proceedings of the International Congress on Intellectual Property Rights for Specialized Information, Knowledge and New Technologies, Vienna, Austria, August 21-25, 242-251 (1995).

R. B. Wolfgang and E. J. Delp, "A watermark for digital images," Proc. ICIP'96, 3, 219-222 (1996).

I. Pitas, "A method for signature casting on digital images," Proc. ICIP'96, 3, 215-218 (1996).

N. Nikolaidis and I. Pitas, "Copyright protection of images using robust digital signatures," Proceedings of ICASSP'96, Atlanta, Georgia, May, 2168-2171 (1996).

M. D. Swanson, B. Zhu, and A. H. Tewfik, "Transparent robust image watermarking," Proc. ICIP'96, 3, 211-214 (1996).

M. Schneider and S.-F. Chang, "A robust content based digital signature for image authentication," Proc. ICIP'96, 3, 227-230 (1996).

S. Mallat, "Multiresolution approximations and wavelet orthonormal bases of L 2 (R)," Trans. Amer. Math. Soc., 315, 69-87 (1989).

I. Daubechies, "Orthonormal bases of compactly supported wavelets," Comm. on Pure and Appl. Math., 41, 909-996 (1988).
[CrossRef]

O. Rioul and M. Vetterli, "Wavelets and signal processing," IEEE Signal Processing Magazine, 14-38, (1991).
[CrossRef]

I. Daubechies, Ten Lectures on Wavelets, (SIAM, Philadelphia, 1992).

P. P. Vaidyanathan, Multirate Systems and Filter Banks, (Prentice Hall, Englewood Cliffs, NJ, 1993).

M. Vetterli and J. Kovacevic, Wavelets and Subband Coding, (Prentice Hall, Englewood Cliffs, NJ, 1995).

G. Strang and T. Q. Nguyen, Wavelets and Filter Banks, (Wellesley-Cambridge Press, Cambridge, 1996).

J. Shapiro, "Embedded image coding using zerotrees of wavelet coefficients," IEEE Trans. on Signal Processing, 41, 3445-3462 (1993).
[CrossRef]

R. Ulichney, Digital Halftoning, (MIT Press, Massachusetts, 1987).

S. Craver, N. Memon, B-L Yeo, and M. M. Yeung, "Resolving rightful ownerships with invisible watermarking techniques: limitations, attacks, and implications," IBM Research Report (RC 20755), March 1997.

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Figures (18)

Figure 1.
Figure 1.

DWT for one dimensional signals.

Figure 2.
Figure 2.

DWT for two dimensional images.

Figure 3.
Figure 3.

DWT pyramid decomposition of an image.

Figure 4.
Figure 4.

Example of a DWT pyramid decomposition.

Figure 5.
Figure 5.

Watermarking in the DWT domain.

Figure 6.
Figure 6.

(a) Original “pepper” image; (b) Watermarked image using DWT.

Figure 7.
Figure 7.

(a) Watermarked image using DCT; (b) Watermarked image with low additive noise.

Figure 8.
Figure 8.

(a) Watermarked image with high additive noise; (b) Original “car” image.

Figure 9.
Figure 9.

Correlations for watermark detection for the “peppers” image: (a) DWT with HH 1 band for low additive noise; (b) DWT with HH 1 band for high additive noise; (d) DWT with HH 1 and LH 1 bands for high additive noise; (c) DCT for high additive noise.

Figure 10.
Figure 10.

Correlations for watermark detection for the “car” image: (a) DWT with HH 1 band for low additive noise; (b) DWT with HH 1 band for high additive noise; (d) DWT with HH 1 and LH 1 bands for high additive noise; (c) DCT for high additive noise.

Figure 11.
Figure 11.

Correlations for watermark detection for the rescaled “peppers” image: (a) and (b) piecewise constant interpolation in the rescaling and (a) DWT (b) DCT; (c) and (d) cubic spline interpolation in the rescaling and (c) DWT (d) DCT.

Figure 12.
Figure 12.

Correlations for watermark detection for the rescaled “car” image: (a) and (b) piecewise constant interpolation in the rescaling and (a) DWT (b) DCT; (c) and (d) cubic spline interpolation in the rescaling and (c) DWT (d) DCT.

Figure 13.
Figure 13.

Correlations for watermark detection for the stretched “peppers” image: (a) and (b) piecewise constant interpolation in the rescaling and (a) DWT (b) DCT; (c) and (d) cubic spline interpolation in the rescaling and (c) DWT (d) DCT.

Figure 14.
Figure 14.

Correlations for watermark detection for the stretched “car” image: (a) and (b) piecewise constant interpolation in the rescaling and (a) DWT (b) DCT; (c) and (d) cubic spline interpolation in the rescaling and (c) DWT (d) DCT.

Figure 15.
Figure 15.

Correlations for watermark detection for the stretched “peppers” image: (a) and (b) 1% stretching and (a) DWT (b) DCT; (c) and (d) 2% stretching and (c) DWT (d) DCT.

Figure 16.
Figure 16.

Correlations for watermark detection for the stretched “car” image: (a) and (b) 1% stretching and (a) DWT (b) DCT; (c) and (d) 2% stretching and (c) DWT (d) DCT.

Figure 17.
Figure 17.

Correlations for watermark detection for compressed images: (a) DWT; (b) DCT.

Figure 18.
Figure 18.

Correlations for watermark detection for halftoned images: (a) DWT; (b) DCT.

Equations (9)

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H ( ω ) = k h k e jkω , and G ( ω ) = k g k e jkω .
c j 1 , k = n h n 2 k c j , n
d j 1 , k = n g n 2 k c j , n
c j , n = k h n 2 k c j 1 , k + k g n 2 k d j 1 , k .
H ( ω ) 2 + G ( ω ) 2 = 1 .
H ( ω ) = 1 2 + 1 2 e j ω , and G ( ω ) = 1 2 1 2 e j ω ,
y ͂ [ m , n ] = y [ m , n ] + α y 2 [ m , n ] N [ m , n ] ,
x ̂ [ m , n ] = min ( max ( x [ m , n ] ) , max { x ͂ [ m , n ] , min ( x [ m , n ] ) } ) .
T = ( T j , k ) 4 × 4 = 16 ( 11 7 10 6 3 15 2 14 9 5 12 8 1 13 4 16 )

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