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.

© 1998 Optical Society of America

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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 L2(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. Kovačević, 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.

1996 (5)

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).

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).

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).

1994 (1)

R. G. van Schyndel, A. Z. Tirkel, and C. F. Osborne, “A digital watermark,” Proc. ICIP’94,  2, 86–90 (1994).

1993 (1)

J. Shapiro, “Embedded image coding using zerotrees of wavelet coefficients,” IEEE Trans. on Signal Processing,  41, 3445–3462 (1993).
[Crossref]

1991 (1)

O. Rioul and M. Vetterli, “Wavelets and signal processing,” IEEE Signal Processing Magazine, 14–38, (1991).
[Crossref]

1989 (1)

S. Mallat, “Multiresolution approximations and wavelet orthonormal bases of L2(R),” Trans. Amer. Math. Soc.,  315, 69–87 (1989).

1988 (1)

I. Daubechies, “Orthonormal bases of compactly supported wavelets,” Comm. on Pure and Appl. Math.,  41, 909–996 (1988).
[Crossref]

Chang, S.-F.

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

Cox, I. J.

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).

Craver, S.

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.

Daubechies, I.

I. Daubechies, “Orthonormal bases of compactly supported wavelets,” Comm. on Pure and Appl. Math.,  41, 909–996 (1988).
[Crossref]

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

Delp, E. J.

R. B. Wolfgang and E. J. Delp, “A watermark for digital images,” Proc. ICIP‘96,  3, 219–222 (1996).

Kilian, J.

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).

Koch, E.

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).

Kovacevic, J.

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

Leighton, T.

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).

Mallat, S.

S. Mallat, “Multiresolution approximations and wavelet orthonormal bases of L2(R),” Trans. Amer. Math. Soc.,  315, 69–87 (1989).

Memon, N.

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.

Nguyen, T. Q.

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

Nikolaidis, N.

N. Nikolaidis and I. Pitas, “Copyright protection of images using robust digital signatures,” Proceedings of ICASSP’96, Atlanta, Georgia, May, 2168–2171 (1996).

Osborne, C. F.

R. G. van Schyndel, A. Z. Tirkel, and C. F. Osborne, “A digital watermark,” Proc. ICIP’94,  2, 86–90 (1994).

Pitas, I.

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).

Rioul, O.

O. Rioul and M. Vetterli, “Wavelets and signal processing,” IEEE Signal Processing Magazine, 14–38, (1991).
[Crossref]

Schneider, M.

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

Shamoon, T.

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).

Shapiro, J.

J. Shapiro, “Embedded image coding using zerotrees of wavelet coefficients,” IEEE Trans. on Signal Processing,  41, 3445–3462 (1993).
[Crossref]

Strang, G.

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

Swanson, M. D.

M. D. Swanson, B. Zhu, and A. H. Tewfik, “Transparent robust image watermarking,” Proc. ICIP’96,  3, 211–214 (1996).

Tewfik, A. H.

M. D. Swanson, B. Zhu, and A. H. Tewfik, “Transparent robust image watermarking,” Proc. ICIP’96,  3, 211–214 (1996).

Tirkel, A. Z.

R. G. van Schyndel, A. Z. Tirkel, and C. F. Osborne, “A digital watermark,” Proc. ICIP’94,  2, 86–90 (1994).

Ulichney, R.

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

Vaidyanathan, P. P.

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

van Schyndel, R. G.

R. G. van Schyndel, A. Z. Tirkel, and C. F. Osborne, “A digital watermark,” Proc. ICIP’94,  2, 86–90 (1994).

Vetterli, M.

O. Rioul and M. Vetterli, “Wavelets and signal processing,” IEEE Signal Processing Magazine, 14–38, (1991).
[Crossref]

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

Wolfgang, R. B.

R. B. Wolfgang and E. J. Delp, “A watermark for digital images,” Proc. ICIP‘96,  3, 219–222 (1996).

Yeo, B-L

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.

Yeung, M. M.

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.

Zhao, J.

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).

Zhu, B.

M. D. Swanson, B. Zhu, and A. H. Tewfik, “Transparent robust image watermarking,” Proc. ICIP’96,  3, 211–214 (1996).

Comm. on Pure and Appl. Math. (1)

I. Daubechies, “Orthonormal bases of compactly supported wavelets,” Comm. on Pure and Appl. Math.,  41, 909–996 (1988).
[Crossref]

IEEE Signal Processing Magazine (1)

O. Rioul and M. Vetterli, “Wavelets and signal processing,” IEEE Signal Processing Magazine, 14–38, (1991).
[Crossref]

IEEE Trans. on Signal Processing (1)

J. Shapiro, “Embedded image coding using zerotrees of wavelet coefficients,” IEEE Trans. on Signal Processing,  41, 3445–3462 (1993).
[Crossref]

Proc. ICIP‘96 (1)

R. B. Wolfgang and E. J. Delp, “A watermark for digital images,” Proc. ICIP‘96,  3, 219–222 (1996).

Proc. ICIP’94 (1)

R. G. van Schyndel, A. Z. Tirkel, and C. F. Osborne, “A digital watermark,” Proc. ICIP’94,  2, 86–90 (1994).

Proc. ICIP’96 (4)

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).

I. Pitas, “A method for signature casting on digital images,” Proc. ICIP’96,  3, 215–218 (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).

Trans. Amer. Math. Soc. (1)

S. Mallat, “Multiresolution approximations and wavelet orthonormal bases of L2(R),” Trans. Amer. Math. Soc.,  315, 69–87 (1989).

Other (8)

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.

N. Nikolaidis and I. Pitas, “Copyright protection of images using robust digital signatures,” Proceedings of ICASSP’96, Atlanta, Georgia, May, 2168–2171 (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).

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. Kovačević, 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).

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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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