Abstract

In this paper we propose an image watermarking algorithm based on constraints in the Discrete Cosine Transform (DCT) domain. An image watermarking algorithm has two stages: signature casting (embedding) and signature detection. In the first stage it embeds an identifying label in the image. This is recognized in the second stage. The proposed algorithm has two processing steps. In the first step certain pixel blocks are selected using a set of parameters while in the second step a DCT coefficient constraint is embedded in the selected blocks. Two different constraint rules are suggested for the parametric modification of the DCT frequency coefficients. The first one embeds a linear constraint among certain selected DCT coefficients and the second defines circular detection regions according to the given parameters. The watermarks cast by the proposed algorithm are resistant to JPEG compression and filtering.

© 1998 Optical Society of America

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References

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  1. B. M. Macq and J.-J Quisquater, “ Cryptology for Digital TV Broadcasting,” Proc. of the IEEE,  vol. 83, no. 6, pp. 944–957, June 1995.
    [Crossref]
  2. W. Bender, D. Gruhl, and N. Morimoto, “Techniques for data hiding,” MIT Media Lab., Technical Report 1995.
  3. E. Koch and J. Zhao, “Towards robust and hidden image copyright labeling,” Proc. of IEEE Workshop on Nonlinear Signal and Image Processing, Neos Marmaras, Greece, pp. 452–455, 20-22 June 1995.
  4. O. Bruyndonckx, J.-J Quisquater, and B. Macq, “Spatial method for copyright labeling of digital images,” Proc. of IEEE Workshop on Nonlinear Signal and Image Processing, Neos Marmaras, Greece, pp. 456–459, 20-22 June 1995.
  5. M. Barni, F. Bartolini, V. Capellini, and A. Piva, “A DCT-domain system for robust image watermarking,” Signal Processing vol. 66, no. 3, pp. 357–372, 1998.
    [Crossref]
  6. I. Pitas and T. H. Kaskalis, “Applying signatures on digital images,” Proc. of IEEE Workshop on Nonlinear Signal and Image Processing, Neos Marmaras, Greece, pp. 460–463, 20-22 June 1995.
  7. A. G. Borş and I. Pitas, “Embedding parametric digital signatures in images,” European Signal Processing Conference, EUSIPCO’96, Trieste, Italy, Sep. 10-13, pp. 1701–1704, 1996.
  8. I. J. Cox, J. Kilian, T. Leighton, and T. Shamoon, “Secure Spread Spectrum Watermarking for Multimedia, IEEE Trans. on Image Processing,  vol. 6, no. 12, pp. 1673–1687, Dec. 1997.
    [Crossref]
  9. A. Papoulis, Probability and Statistics. Prentice Hall, 1990.
  10. S. A. Kassam, Signal detection in Non-Gaussian Noise, Springer-Verlag, 1988.
    [Crossref]
  11. G. K. Wallace, “The JPEG still picture compression standard,” IEEE Trans. on Consumer Electronics,  vol. 38, no. 1, pp. 18–34, Feb. 1992.
    [Crossref]
  12. A. K. Jain,Fundamentals of Digital Image Processing, Prentice Hall, 1989.
  13. A. C. Hung, “PVRG-JPEG CODEC 1.1,” Stanford University, Technical Report, 1993.
  14. A. V. Oppenheim and R. W. Schafer,Discrete-Time Signal Processing, Prentice-Hall, 1989.
  15. B. Widrow and S.D. Stearns, Adaptive Signal Processing. Englewood Cliffs, NJ: Prentice Hall, 1985.
  16. E. S. Chng, S. Chen, and B. Mulgrew, “Gradient radial basis function networks for nonlinear and nonstationary time series prediction,” IEEE Trans.on Neural Networks,  vol. 7, no. 1, pp. 190–194, Jan 1996.

1998 (1)

M. Barni, F. Bartolini, V. Capellini, and A. Piva, “A DCT-domain system for robust image watermarking,” Signal Processing vol. 66, no. 3, pp. 357–372, 1998.
[Crossref]

1997 (1)

I. J. Cox, J. Kilian, T. Leighton, and T. Shamoon, “Secure Spread Spectrum Watermarking for Multimedia, IEEE Trans. on Image Processing,  vol. 6, no. 12, pp. 1673–1687, Dec. 1997.
[Crossref]

1996 (1)

E. S. Chng, S. Chen, and B. Mulgrew, “Gradient radial basis function networks for nonlinear and nonstationary time series prediction,” IEEE Trans.on Neural Networks,  vol. 7, no. 1, pp. 190–194, Jan 1996.

1995 (2)

B. M. Macq and J.-J Quisquater, “ Cryptology for Digital TV Broadcasting,” Proc. of the IEEE,  vol. 83, no. 6, pp. 944–957, June 1995.
[Crossref]

E. Koch and J. Zhao, “Towards robust and hidden image copyright labeling,” Proc. of IEEE Workshop on Nonlinear Signal and Image Processing, Neos Marmaras, Greece, pp. 452–455, 20-22 June 1995.

1992 (1)

G. K. Wallace, “The JPEG still picture compression standard,” IEEE Trans. on Consumer Electronics,  vol. 38, no. 1, pp. 18–34, Feb. 1992.
[Crossref]

Barni, M.

M. Barni, F. Bartolini, V. Capellini, and A. Piva, “A DCT-domain system for robust image watermarking,” Signal Processing vol. 66, no. 3, pp. 357–372, 1998.
[Crossref]

Bartolini, F.

M. Barni, F. Bartolini, V. Capellini, and A. Piva, “A DCT-domain system for robust image watermarking,” Signal Processing vol. 66, no. 3, pp. 357–372, 1998.
[Crossref]

Bender, W.

W. Bender, D. Gruhl, and N. Morimoto, “Techniques for data hiding,” MIT Media Lab., Technical Report 1995.

Bors, A. G.

A. G. Borş and I. Pitas, “Embedding parametric digital signatures in images,” European Signal Processing Conference, EUSIPCO’96, Trieste, Italy, Sep. 10-13, pp. 1701–1704, 1996.

Bruyndonckx, O.

O. Bruyndonckx, J.-J Quisquater, and B. Macq, “Spatial method for copyright labeling of digital images,” Proc. of IEEE Workshop on Nonlinear Signal and Image Processing, Neos Marmaras, Greece, pp. 456–459, 20-22 June 1995.

Capellini, V.

M. Barni, F. Bartolini, V. Capellini, and A. Piva, “A DCT-domain system for robust image watermarking,” Signal Processing vol. 66, no. 3, pp. 357–372, 1998.
[Crossref]

Chen, S.

E. S. Chng, S. Chen, and B. Mulgrew, “Gradient radial basis function networks for nonlinear and nonstationary time series prediction,” IEEE Trans.on Neural Networks,  vol. 7, no. 1, pp. 190–194, Jan 1996.

Chng, E. S.

E. S. Chng, S. Chen, and B. Mulgrew, “Gradient radial basis function networks for nonlinear and nonstationary time series prediction,” IEEE Trans.on Neural Networks,  vol. 7, no. 1, pp. 190–194, Jan 1996.

Cox, I. J.

I. J. Cox, J. Kilian, T. Leighton, and T. Shamoon, “Secure Spread Spectrum Watermarking for Multimedia, IEEE Trans. on Image Processing,  vol. 6, no. 12, pp. 1673–1687, Dec. 1997.
[Crossref]

Gruhl, D.

W. Bender, D. Gruhl, and N. Morimoto, “Techniques for data hiding,” MIT Media Lab., Technical Report 1995.

Hung, A. C.

A. C. Hung, “PVRG-JPEG CODEC 1.1,” Stanford University, Technical Report, 1993.

Jain, A. K.

A. K. Jain,Fundamentals of Digital Image Processing, Prentice Hall, 1989.

Kaskalis, T. H.

I. Pitas and T. H. Kaskalis, “Applying signatures on digital images,” Proc. of IEEE Workshop on Nonlinear Signal and Image Processing, Neos Marmaras, Greece, pp. 460–463, 20-22 June 1995.

Kassam, S. A.

S. A. Kassam, Signal detection in Non-Gaussian Noise, Springer-Verlag, 1988.
[Crossref]

Kilian, J.

I. J. Cox, J. Kilian, T. Leighton, and T. Shamoon, “Secure Spread Spectrum Watermarking for Multimedia, IEEE Trans. on Image Processing,  vol. 6, no. 12, pp. 1673–1687, Dec. 1997.
[Crossref]

Koch, E.

E. Koch and J. Zhao, “Towards robust and hidden image copyright labeling,” Proc. of IEEE Workshop on Nonlinear Signal and Image Processing, Neos Marmaras, Greece, pp. 452–455, 20-22 June 1995.

Leighton, T.

I. J. Cox, J. Kilian, T. Leighton, and T. Shamoon, “Secure Spread Spectrum Watermarking for Multimedia, IEEE Trans. on Image Processing,  vol. 6, no. 12, pp. 1673–1687, Dec. 1997.
[Crossref]

Macq, B.

O. Bruyndonckx, J.-J Quisquater, and B. Macq, “Spatial method for copyright labeling of digital images,” Proc. of IEEE Workshop on Nonlinear Signal and Image Processing, Neos Marmaras, Greece, pp. 456–459, 20-22 June 1995.

Macq, B. M.

B. M. Macq and J.-J Quisquater, “ Cryptology for Digital TV Broadcasting,” Proc. of the IEEE,  vol. 83, no. 6, pp. 944–957, June 1995.
[Crossref]

Morimoto, N.

W. Bender, D. Gruhl, and N. Morimoto, “Techniques for data hiding,” MIT Media Lab., Technical Report 1995.

Mulgrew, B.

E. S. Chng, S. Chen, and B. Mulgrew, “Gradient radial basis function networks for nonlinear and nonstationary time series prediction,” IEEE Trans.on Neural Networks,  vol. 7, no. 1, pp. 190–194, Jan 1996.

Oppenheim, A. V.

A. V. Oppenheim and R. W. Schafer,Discrete-Time Signal Processing, Prentice-Hall, 1989.

Papoulis, A.

A. Papoulis, Probability and Statistics. Prentice Hall, 1990.

Pitas, I.

I. Pitas and T. H. Kaskalis, “Applying signatures on digital images,” Proc. of IEEE Workshop on Nonlinear Signal and Image Processing, Neos Marmaras, Greece, pp. 460–463, 20-22 June 1995.

A. G. Borş and I. Pitas, “Embedding parametric digital signatures in images,” European Signal Processing Conference, EUSIPCO’96, Trieste, Italy, Sep. 10-13, pp. 1701–1704, 1996.

Piva, A.

M. Barni, F. Bartolini, V. Capellini, and A. Piva, “A DCT-domain system for robust image watermarking,” Signal Processing vol. 66, no. 3, pp. 357–372, 1998.
[Crossref]

Quisquater, J.-J

B. M. Macq and J.-J Quisquater, “ Cryptology for Digital TV Broadcasting,” Proc. of the IEEE,  vol. 83, no. 6, pp. 944–957, June 1995.
[Crossref]

O. Bruyndonckx, J.-J Quisquater, and B. Macq, “Spatial method for copyright labeling of digital images,” Proc. of IEEE Workshop on Nonlinear Signal and Image Processing, Neos Marmaras, Greece, pp. 456–459, 20-22 June 1995.

Schafer, R. W.

A. V. Oppenheim and R. W. Schafer,Discrete-Time Signal Processing, Prentice-Hall, 1989.

Shamoon, T.

I. J. Cox, J. Kilian, T. Leighton, and T. Shamoon, “Secure Spread Spectrum Watermarking for Multimedia, IEEE Trans. on Image Processing,  vol. 6, no. 12, pp. 1673–1687, Dec. 1997.
[Crossref]

Stearns, S.D.

B. Widrow and S.D. Stearns, Adaptive Signal Processing. Englewood Cliffs, NJ: Prentice Hall, 1985.

Wallace, G. K.

G. K. Wallace, “The JPEG still picture compression standard,” IEEE Trans. on Consumer Electronics,  vol. 38, no. 1, pp. 18–34, Feb. 1992.
[Crossref]

Widrow, B.

B. Widrow and S.D. Stearns, Adaptive Signal Processing. Englewood Cliffs, NJ: Prentice Hall, 1985.

Zhao, J.

E. Koch and J. Zhao, “Towards robust and hidden image copyright labeling,” Proc. of IEEE Workshop on Nonlinear Signal and Image Processing, Neos Marmaras, Greece, pp. 452–455, 20-22 June 1995.

IEEE Trans. (1)

E. S. Chng, S. Chen, and B. Mulgrew, “Gradient radial basis function networks for nonlinear and nonstationary time series prediction,” IEEE Trans.on Neural Networks,  vol. 7, no. 1, pp. 190–194, Jan 1996.

IEEE Trans. on Consumer Electronics (1)

G. K. Wallace, “The JPEG still picture compression standard,” IEEE Trans. on Consumer Electronics,  vol. 38, no. 1, pp. 18–34, Feb. 1992.
[Crossref]

IEEE Trans. on Image Processing (1)

I. J. Cox, J. Kilian, T. Leighton, and T. Shamoon, “Secure Spread Spectrum Watermarking for Multimedia, IEEE Trans. on Image Processing,  vol. 6, no. 12, pp. 1673–1687, Dec. 1997.
[Crossref]

Proc. of the IEEE (1)

B. M. Macq and J.-J Quisquater, “ Cryptology for Digital TV Broadcasting,” Proc. of the IEEE,  vol. 83, no. 6, pp. 944–957, June 1995.
[Crossref]

Signal Processing (1)

M. Barni, F. Bartolini, V. Capellini, and A. Piva, “A DCT-domain system for robust image watermarking,” Signal Processing vol. 66, no. 3, pp. 357–372, 1998.
[Crossref]

Other (11)

I. Pitas and T. H. Kaskalis, “Applying signatures on digital images,” Proc. of IEEE Workshop on Nonlinear Signal and Image Processing, Neos Marmaras, Greece, pp. 460–463, 20-22 June 1995.

A. G. Borş and I. Pitas, “Embedding parametric digital signatures in images,” European Signal Processing Conference, EUSIPCO’96, Trieste, Italy, Sep. 10-13, pp. 1701–1704, 1996.

A. Papoulis, Probability and Statistics. Prentice Hall, 1990.

S. A. Kassam, Signal detection in Non-Gaussian Noise, Springer-Verlag, 1988.
[Crossref]

W. Bender, D. Gruhl, and N. Morimoto, “Techniques for data hiding,” MIT Media Lab., Technical Report 1995.

E. Koch and J. Zhao, “Towards robust and hidden image copyright labeling,” Proc. of IEEE Workshop on Nonlinear Signal and Image Processing, Neos Marmaras, Greece, pp. 452–455, 20-22 June 1995.

O. Bruyndonckx, J.-J Quisquater, and B. Macq, “Spatial method for copyright labeling of digital images,” Proc. of IEEE Workshop on Nonlinear Signal and Image Processing, Neos Marmaras, Greece, pp. 456–459, 20-22 June 1995.

A. K. Jain,Fundamentals of Digital Image Processing, Prentice Hall, 1989.

A. C. Hung, “PVRG-JPEG CODEC 1.1,” Stanford University, Technical Report, 1993.

A. V. Oppenheim and R. W. Schafer,Discrete-Time Signal Processing, Prentice-Hall, 1989.

B. Widrow and S.D. Stearns, Adaptive Signal Processing. Englewood Cliffs, NJ: Prentice Hall, 1985.

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Figures (8)

Figure 1.
Figure 1.

The processing blocks for watermark embedding and detection.

Figure 2.
Figure 2.

The selection of a block site using a Gaussian network where the selected blocks are black.

Figure 3.
Figure 3.

Watermarking Baboon image: (a) Original image; (b) chosen image blocks for embedding the watermark

Figure 4.
Figure 4.

Watermarking results: (a) when the DCT coefficient constraint is linear; (b) when embedding circular detection regions in the DCT domain.

Figure 5.
Figure 5.

Watermark detection results after JPEG compression; (a) linear DCT constraint; (b) circular detection regions.

Figure 6.
Figure 6.

Compressed watermarked color images; (a) original color Lenna image; (b) image watermarked based on the linear constraint in the DCT coefficients; (c) image watermarked based on the circular detection regions in the DCT coefficients.

Figure 7.
Figure 7.

Watermark detection results in the case of color images; (a) linear constraint in the DCT coefficients; (b) circular detection regions in the DCT coefficients.

Figure 8.
Figure 8.

Watermark detection results after filtering; (a) median filter; (b) moving average filter.

Equations (22)

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S k = [ L k , C k ]
G ( x ) = i = 1 L λ i exp [ j = 1 N ( x j w i , j ) 2 r i , j 2 ]
G ( x ) > α
w i , j = w ( i + 1 ) mod L , j 1
r i , j = r ( i + 1 ) mod L , j 1
{ w i , N T i , N < x N < w i , N + T i , N } where
T i , N = r i , N ln 1 α j = 1 N 1 ( d j w i , j r i , j ) 2 .
min { w i , j 1 , w i + 1 , j } > T i , j > 1 , for j = 2 , , N , i = 1 , , L .
MRL 64 i = 1 L ( w i , N T i , N ) > n > MRL 64 i = 1 L ( w i , N + T i , N ) ,
64 i = 1 L ( w i , N T i , N ) < s k < 64 i = 1 L ( w i , N + T i , N )
F j ( u , v ) = 1 4 C ( u ) C ( v ) [ k = 0 7 l = 0 7 f j ( k , l ) cos ( 2 k + 1 ) u π 16 cos ( 2 l + 1 ) v π 16 ]
C ( u ) , C ( v ) = 1 2 for u , v = 0 and C ( u ) , C ( v ) = 1 otherwise
( u i , v i ) { ( 1,1 ) , ( 1,2 ) , ( 2,1 ) , ( 3,1 ) , ( 2,2 , ) , ( 1,3 ) } , i = 1 , , K .
Y = F Q
F Q k 2 = min i = 1 H F Q i 2 then F = Q k ,
g j ( k , l ) = 1 4 u = 0 7 v = 0 7 C ( u ) C ( v ) F j ( u , v ) cos ( 2 k + 1 ) u π 16 cos ( 2 l + 1 ) 16
k = arg min j = b + w j , N T j , N b + w j , N + T j , N x = 0 7 y = 0 7 f i ( x , y ) g i ( x , y ) ,
P ( x , y g , S k ) P ( x y , g , L k ) P ( y g , C k ) ,
D y , L k = { y IR y F Q < D L } ,
D y , C k = { y IR | F Q i 2 < D C 2 , i = 1 , , K } .
D x k D y k P ( x , y g , S k ) dxdy D x k D y k q ( x , y g , S k ) dxdy i = 1 p s i MR > c ,
SNR = 10 log i = 0 M j = 0 R f ( i , j ) 2 i = 0 M j = 0 R ( f ( i , j ) g ( i , j ) ) 2 ,

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