Abstract

A holographic technique is applied for digital watermarking by a computer. A digital-watermark image to be hidden is phase modulated in a random fashion, and its Fourier-transformed hologram is superposed on a content image. The watermark is reconstructed by means of a holographic-reconstruction technique from the bit-map image that hides it. In the study the processes of constructing and reconstructing a digital hologram are described on the basis of the theory of Fourier optics. The conditions for superposing the hologram onto the content images are investigated in detail. The validity of the present method is verified by changing the weighting of the hologram relative to that of the content image. The effect of image size is also discussed with respect to reconstruction of the watermark, and it is shown that watermark information in a form of a diffuse-type Fourier-transform hologram cannot be removed by cutting it out of the host image.

© 2002 Optical Society of America

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References

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  1. L. Cox, J. Kilian, T. Leighton, T. Shamoon, “Secure spread spectrum watermarking for multimedia,” Technical Report, 95–10 (NEC Research Institute, Princeton, N.J., 1995).
  2. W. Bender, D. Gruhl, N. Morimoto, A. Liu, “Techniques for data hiding,” IBM Syst. J., 35, 313–336 (1996).
    [CrossRef]
  3. P. Réfrégier, B. Javidi, “Optical image encryption based on input plane and Fourier plane random encoding,” Opt. Lett., 20, 767–769 (1995).
    [CrossRef] [PubMed]
  4. F. Goudail, F. Bollaro, B. Javidi, P. Réfrégier, “Influence of a perturbation in a double phase-encoding system,” J. Opt. Soc. Am. A 15, 2629–2638 (1998).
    [CrossRef]
  5. N. Towghi, B. Javidi, Z. Lou, “Fully phase encrypted image processor,” J. Opt. Soc. Am. A 16, 1915–1927 (1999).
    [CrossRef]
  6. B. Javidi, N. Towghi, N. Maghzi, S. C. Verall, “Error-reduction techniques and error analysis for phase- and amplitude-based encryption,” Appl. Opt. 38, 4117–4130 (2000).
    [CrossRef]
  7. J. W. Goodman, Introduction to Fourier Optics, Chap. 8, 198–254 (McGraw-Hill, San Francisco, 1968).
  8. M. Born, E. Wolf, Principles of Optics, Chap. 8, 412–516 (Cambridge U. Press, 7th ed., Cambridge, UK, 1999).
  9. I. Yamaguchi, T. Zhang, “Phase-shifting digital holography,” Opt. Lett. 22, 1268–1270 (1997).
    [CrossRef] [PubMed]
  10. T. Zhang, I. Yamaguchi, “Three-dimensional microscopy with phase-shifting digital holography,” Opt. Lett. 23, 1221–1223 (1998).
    [CrossRef]
  11. E. Tajahuerce, B. Javidi, “Encrypting three-dimensional information with digital holography,” Appl. Opt. 39, 6595–6601 (2000).
    [CrossRef]
  12. E. Tajahuerce, O. Matoba, S. C. Verrall, B. Javidi, “Optoelectronic information encryption with phase-shifting interferometry,” Appl. Opt. 39, 2313–2320 (2000).
    [CrossRef]

2000 (3)

E. Tajahuerce, B. Javidi, “Encrypting three-dimensional information with digital holography,” Appl. Opt. 39, 6595–6601 (2000).
[CrossRef]

E. Tajahuerce, O. Matoba, S. C. Verrall, B. Javidi, “Optoelectronic information encryption with phase-shifting interferometry,” Appl. Opt. 39, 2313–2320 (2000).
[CrossRef]

B. Javidi, N. Towghi, N. Maghzi, S. C. Verall, “Error-reduction techniques and error analysis for phase- and amplitude-based encryption,” Appl. Opt. 38, 4117–4130 (2000).
[CrossRef]

1999 (1)

1998 (2)

F. Goudail, F. Bollaro, B. Javidi, P. Réfrégier, “Influence of a perturbation in a double phase-encoding system,” J. Opt. Soc. Am. A 15, 2629–2638 (1998).
[CrossRef]

T. Zhang, I. Yamaguchi, “Three-dimensional microscopy with phase-shifting digital holography,” Opt. Lett. 23, 1221–1223 (1998).
[CrossRef]

1997 (1)

1996 (1)

W. Bender, D. Gruhl, N. Morimoto, A. Liu, “Techniques for data hiding,” IBM Syst. J., 35, 313–336 (1996).
[CrossRef]

1995 (1)

Bender, W.

W. Bender, D. Gruhl, N. Morimoto, A. Liu, “Techniques for data hiding,” IBM Syst. J., 35, 313–336 (1996).
[CrossRef]

Bollaro, F.

F. Goudail, F. Bollaro, B. Javidi, P. Réfrégier, “Influence of a perturbation in a double phase-encoding system,” J. Opt. Soc. Am. A 15, 2629–2638 (1998).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics, Chap. 8, 412–516 (Cambridge U. Press, 7th ed., Cambridge, UK, 1999).

Cox, L.

L. Cox, J. Kilian, T. Leighton, T. Shamoon, “Secure spread spectrum watermarking for multimedia,” Technical Report, 95–10 (NEC Research Institute, Princeton, N.J., 1995).

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, Chap. 8, 198–254 (McGraw-Hill, San Francisco, 1968).

Goudail, F.

F. Goudail, F. Bollaro, B. Javidi, P. Réfrégier, “Influence of a perturbation in a double phase-encoding system,” J. Opt. Soc. Am. A 15, 2629–2638 (1998).
[CrossRef]

Gruhl, D.

W. Bender, D. Gruhl, N. Morimoto, A. Liu, “Techniques for data hiding,” IBM Syst. J., 35, 313–336 (1996).
[CrossRef]

Javidi, B.

B. Javidi, N. Towghi, N. Maghzi, S. C. Verall, “Error-reduction techniques and error analysis for phase- and amplitude-based encryption,” Appl. Opt. 38, 4117–4130 (2000).
[CrossRef]

E. Tajahuerce, B. Javidi, “Encrypting three-dimensional information with digital holography,” Appl. Opt. 39, 6595–6601 (2000).
[CrossRef]

E. Tajahuerce, O. Matoba, S. C. Verrall, B. Javidi, “Optoelectronic information encryption with phase-shifting interferometry,” Appl. Opt. 39, 2313–2320 (2000).
[CrossRef]

N. Towghi, B. Javidi, Z. Lou, “Fully phase encrypted image processor,” J. Opt. Soc. Am. A 16, 1915–1927 (1999).
[CrossRef]

F. Goudail, F. Bollaro, B. Javidi, P. Réfrégier, “Influence of a perturbation in a double phase-encoding system,” J. Opt. Soc. Am. A 15, 2629–2638 (1998).
[CrossRef]

P. Réfrégier, B. Javidi, “Optical image encryption based on input plane and Fourier plane random encoding,” Opt. Lett., 20, 767–769 (1995).
[CrossRef] [PubMed]

Kilian, J.

L. Cox, J. Kilian, T. Leighton, T. Shamoon, “Secure spread spectrum watermarking for multimedia,” Technical Report, 95–10 (NEC Research Institute, Princeton, N.J., 1995).

Leighton, T.

L. Cox, J. Kilian, T. Leighton, T. Shamoon, “Secure spread spectrum watermarking for multimedia,” Technical Report, 95–10 (NEC Research Institute, Princeton, N.J., 1995).

Liu, A.

W. Bender, D. Gruhl, N. Morimoto, A. Liu, “Techniques for data hiding,” IBM Syst. J., 35, 313–336 (1996).
[CrossRef]

Lou, Z.

Maghzi, N.

Matoba, O.

E. Tajahuerce, O. Matoba, S. C. Verrall, B. Javidi, “Optoelectronic information encryption with phase-shifting interferometry,” Appl. Opt. 39, 2313–2320 (2000).
[CrossRef]

Morimoto, N.

W. Bender, D. Gruhl, N. Morimoto, A. Liu, “Techniques for data hiding,” IBM Syst. J., 35, 313–336 (1996).
[CrossRef]

Réfrégier, P.

F. Goudail, F. Bollaro, B. Javidi, P. Réfrégier, “Influence of a perturbation in a double phase-encoding system,” J. Opt. Soc. Am. A 15, 2629–2638 (1998).
[CrossRef]

P. Réfrégier, B. Javidi, “Optical image encryption based on input plane and Fourier plane random encoding,” Opt. Lett., 20, 767–769 (1995).
[CrossRef] [PubMed]

Shamoon, T.

L. Cox, J. Kilian, T. Leighton, T. Shamoon, “Secure spread spectrum watermarking for multimedia,” Technical Report, 95–10 (NEC Research Institute, Princeton, N.J., 1995).

Tajahuerce, E.

E. Tajahuerce, O. Matoba, S. C. Verrall, B. Javidi, “Optoelectronic information encryption with phase-shifting interferometry,” Appl. Opt. 39, 2313–2320 (2000).
[CrossRef]

E. Tajahuerce, B. Javidi, “Encrypting three-dimensional information with digital holography,” Appl. Opt. 39, 6595–6601 (2000).
[CrossRef]

Towghi, N.

Verall, S. C.

Verrall, S. C.

E. Tajahuerce, O. Matoba, S. C. Verrall, B. Javidi, “Optoelectronic information encryption with phase-shifting interferometry,” Appl. Opt. 39, 2313–2320 (2000).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics, Chap. 8, 412–516 (Cambridge U. Press, 7th ed., Cambridge, UK, 1999).

Yamaguchi, I.

T. Zhang, I. Yamaguchi, “Three-dimensional microscopy with phase-shifting digital holography,” Opt. Lett. 23, 1221–1223 (1998).
[CrossRef]

I. Yamaguchi, T. Zhang, “Phase-shifting digital holography,” Opt. Lett. 22, 1268–1270 (1997).
[CrossRef] [PubMed]

Zhang, T.

T. Zhang, I. Yamaguchi, “Three-dimensional microscopy with phase-shifting digital holography,” Opt. Lett. 23, 1221–1223 (1998).
[CrossRef]

I. Yamaguchi, T. Zhang, “Phase-shifting digital holography,” Opt. Lett. 22, 1268–1270 (1997).
[CrossRef] [PubMed]

Appl. Opt. (2)

E. Tajahuerce, B. Javidi, “Encrypting three-dimensional information with digital holography,” Appl. Opt. 39, 6595–6601 (2000).
[CrossRef]

E. Tajahuerce, O. Matoba, S. C. Verrall, B. Javidi, “Optoelectronic information encryption with phase-shifting interferometry,” Appl. Opt. 39, 2313–2320 (2000).
[CrossRef]

Appl. Opt. (1)

IBM Syst. J. (1)

W. Bender, D. Gruhl, N. Morimoto, A. Liu, “Techniques for data hiding,” IBM Syst. J., 35, 313–336 (1996).
[CrossRef]

J. Opt. Soc. Am. A (1)

F. Goudail, F. Bollaro, B. Javidi, P. Réfrégier, “Influence of a perturbation in a double phase-encoding system,” J. Opt. Soc. Am. A 15, 2629–2638 (1998).
[CrossRef]

J. Opt. Soc. Am. A (1)

Opt. Lett. (1)

T. Zhang, I. Yamaguchi, “Three-dimensional microscopy with phase-shifting digital holography,” Opt. Lett. 23, 1221–1223 (1998).
[CrossRef]

Opt. Lett. (2)

Other (3)

J. W. Goodman, Introduction to Fourier Optics, Chap. 8, 198–254 (McGraw-Hill, San Francisco, 1968).

M. Born, E. Wolf, Principles of Optics, Chap. 8, 412–516 (Cambridge U. Press, 7th ed., Cambridge, UK, 1999).

L. Cox, J. Kilian, T. Leighton, T. Shamoon, “Secure spread spectrum watermarking for multimedia,” Technical Report, 95–10 (NEC Research Institute, Princeton, N.J., 1995).

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Figures (12)

Fig. 1
Fig. 1

(a) Watermark pattern to be hidden and (b) content image. The size of images is 512 × 512 pixels.

Fig. 2
Fig. 2

Procedure for making a digital hologram.

Fig. 3
Fig. 3

Image reconstruction from holograms.

Fig. 4
Fig. 4

(a) Diffuse-type Fourier-transformed hologram of Fig. 1(a). (b) Image reconstructed from the hologram.

Fig. 5
Fig. 5

(a) Constant-level weighting; and (b) image-dependent weighting.

Fig. 6
Fig. 6

Configuration for separating g(x, y) and q(x, y).

Fig. 7
Fig. 7

Superposed images I(ξ, η) (upper rows) and the images reconstructed from them (lower rows) for constant-level weighting. α, weight of the hologram components.

Fig. 8
Fig. 8

Superposed images I(ξ, η) (upper rows) and the images reconstructed from them (lower rows) for image-dependent weighting. α, weight of the hologram components.

Fig. 9
Fig. 9

Dependence of the error parameter σ I of the reconstruction images on α.

Fig. 10
Fig. 10

Partial images (upper) and reconstructed watermarks (lower) for image-dependent weighting in the case α = 1/20. Image sizes are (a) 400 × 400, (b) 300 × 300, and (c) 200 × 200 pixels. Sized here to have the same printed dimensions.

Fig. 11
Fig. 11

(a) Spectral distribution of t(x, y) for the (256 × 256) window; (b) spectral distribution of q(x, y) for the content image.

Fig. 12
Fig. 12

Example of a digital watermark when the half-tone image (a) is used as a watermark. (b) Content image including the hologram component (a) with a weight of α = 1/5. (c) Image reconstructed from (b). Constant-level weighting scheme is used.

Equations (23)

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g 0 x ,   y = g mark x ,   y exp i ϕ x ,   y .
G mark ξ ,   η =   g 0 x ,   y exp - 2 π i ξ x + η y d x d y .
R ξ ,   η = R 0   exp 2 π i a ξ + b η ,
H 1 ξ ,   η = | G mark ξ ,   η + R ξ ,   η | 2 = | G mark ξ ,   η | 2 + | R ξ ,   η | 2 + G mark * ξ ,   η R ξ ,   η + G mark ξ ,   η R * ξ ,   η ,
H ξ ,   η = G mark * ξ ,   η R ξ ,   η + G mark ξ ,   η R * ξ ,   η .
S ξ ,   η = | S ξ ,   η | exp i ϕ S ξ ,   η ,
g R x ,   y =   H ξ ,   η exp 2 π i ξ x + η y d ξ d η .
g R x ,   y = g 0 * x - a ,   y - b + g 0 - x + a ,   - y + b .
| g R x ,   y | 2 = | g 0 * x - a ,   y - b | 2 + | g 0 - x + a ,   - y + b | 2 = | g mark x - a ,   y - b | 2 + | g mark - x + a ,   - y + b | 2 .
H ξ ,   η - H min H max - H min H ξ ,   η ,
Q ξ ,   η - Q min Q max - Q min Q ξ ,   η ,
0 H ξ ,   η 1 ,   0 Q ξ ,   η 1 .
I ξ ,   η = Q ξ ,   η + w ξ ,   η H ξ ,   η ,
w ξ ,   η = α α Q ξ ,   η ,
g x ,   y = q x ,   y + α g R x ,   y ,
q x ,   y =   Q ξ ,   η exp 2 π i x ξ + y η d ξ d η .
I ξ ,   η = Q ξ ,   η + α Q ξ ,   η H ξ ,   η .
g x ,   y = q x ,   y + α q x ,   y g R x ,   y ,
q x ,   y δ x ,   y ,
σ I = I - I α 2 1 / 2 I α
I t ξ ,   η = T ξ ,   η I ξ ,   η = T ξ ,   η Q ξ ,   η + α H ξ ,   η .
g t x ,   y = t x ,   y     q x ,   y + α g R x ,   y ,
t x ,   y = t 0 ,   0 sin π ax π ax sin π ay π ay .

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