Abstract

We present an optical method for information watermarking of three-dimensional (3D) objects by digital holography. A hidden image is embedded by double phase encoding in a phase-shift digital hologram of the 3D object. We decode the watermarked hologram to reconstruct the hidden image and the 3D object. We use either the entire hologram or a part of it to decode the hidden image. Experiments are presented to illustrate the ability to recover both the 3D object and the decoded hidden image. Digital holograms of the 3D object are obtained by optical experiments. The watermarking process, 3D object reconstruction, and hidden image recovery are performed digitally. To the best of our knowledge, this is the first report of 3D object watermarking by use of a phase encoding technique and digital holography.

© 2003 Optical Society of America

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References

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  1. N. F. Johnson, Z. Duric, and S. Jajodia, Advances in Information Security, Vol. I of Information Hiding: Steganography and Watermarking—Attacks and Countermeasures (Kluwer Academic, Dordrecht, The Netherlands, 2001).
    [CrossRef]
  2. W. Bender, D. Gruhl, N. Morimoto, and L. Lu, IBM Syst. J. 35, 313 (1996).
    [CrossRef]
  3. J. Rosen and B. Javidi, Appl. Opt. 40, 3346 (2001).
    [CrossRef]
  4. G. C. Langelaar, I. Setyawan, and R. L. Lagendijk, IEEE Signal Process. Mag. 17(5), 20 (2000).
    [CrossRef]
  5. C. Hosinger and M. Rabbani, presented at the International Conference on Information Technology: Coding and Computing, Las Vegas, Nev., March 27–29, 2000.
  6. P. Refregier and B. Javidi, Opt. Lett. 20, 767 (1995).
    [CrossRef] [PubMed]
  7. S. Kishk and B. Javidi, Appl. Opt. 41, 5470 (2002).
  8. B. Javidi, A. Sergent, G. Zhang, and L. Guibert, Opt. Eng. 36, 992 (1997).
    [CrossRef]
  9. H. J. Caulfield, Handbook of Optical Holography (Academic, London, 1979).
  10. J. H. Bruninig, D. R. Herriott, J. E. Gallagher, D. P. Rosenfeld, A. D. White, and D. J. Brangaccio, Appl. Opt. 13, 2693 (1974).
    [CrossRef]
  11. I. Yamaguchi and T. Zhang, Opt. Lett. 22, 1268 (1997).
    [CrossRef] [PubMed]
  12. B. Javidi and E. Tajahuerce, Opt. Lett. 25, 610 (2000).
    [CrossRef]
  13. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1996).
  14. J. W. Goodman, Statistical Optics (Wiley, New York, 1985).

2002 (1)

S. Kishk and B. Javidi, Appl. Opt. 41, 5470 (2002).

2001 (1)

2000 (2)

G. C. Langelaar, I. Setyawan, and R. L. Lagendijk, IEEE Signal Process. Mag. 17(5), 20 (2000).
[CrossRef]

B. Javidi and E. Tajahuerce, Opt. Lett. 25, 610 (2000).
[CrossRef]

1997 (2)

I. Yamaguchi and T. Zhang, Opt. Lett. 22, 1268 (1997).
[CrossRef] [PubMed]

B. Javidi, A. Sergent, G. Zhang, and L. Guibert, Opt. Eng. 36, 992 (1997).
[CrossRef]

1996 (1)

W. Bender, D. Gruhl, N. Morimoto, and L. Lu, IBM Syst. J. 35, 313 (1996).
[CrossRef]

1995 (1)

1974 (1)

Bender, W.

W. Bender, D. Gruhl, N. Morimoto, and L. Lu, IBM Syst. J. 35, 313 (1996).
[CrossRef]

Brangaccio, D. J.

Bruninig, J. H.

Caulfield, H. J.

H. J. Caulfield, Handbook of Optical Holography (Academic, London, 1979).

Duric, Z.

N. F. Johnson, Z. Duric, and S. Jajodia, Advances in Information Security, Vol. I of Information Hiding: Steganography and Watermarking—Attacks and Countermeasures (Kluwer Academic, Dordrecht, The Netherlands, 2001).
[CrossRef]

Gallagher, J. E.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1996).

J. W. Goodman, Statistical Optics (Wiley, New York, 1985).

Gruhl, D.

W. Bender, D. Gruhl, N. Morimoto, and L. Lu, IBM Syst. J. 35, 313 (1996).
[CrossRef]

Guibert, L.

B. Javidi, A. Sergent, G. Zhang, and L. Guibert, Opt. Eng. 36, 992 (1997).
[CrossRef]

Herriott, D. R.

Hosinger, C.

C. Hosinger and M. Rabbani, presented at the International Conference on Information Technology: Coding and Computing, Las Vegas, Nev., March 27–29, 2000.

Jajodia, S.

N. F. Johnson, Z. Duric, and S. Jajodia, Advances in Information Security, Vol. I of Information Hiding: Steganography and Watermarking—Attacks and Countermeasures (Kluwer Academic, Dordrecht, The Netherlands, 2001).
[CrossRef]

Javidi, B.

Johnson, N. F.

N. F. Johnson, Z. Duric, and S. Jajodia, Advances in Information Security, Vol. I of Information Hiding: Steganography and Watermarking—Attacks and Countermeasures (Kluwer Academic, Dordrecht, The Netherlands, 2001).
[CrossRef]

Kishk, S.

S. Kishk and B. Javidi, Appl. Opt. 41, 5470 (2002).

Lagendijk, R. L.

G. C. Langelaar, I. Setyawan, and R. L. Lagendijk, IEEE Signal Process. Mag. 17(5), 20 (2000).
[CrossRef]

Langelaar, G. C.

G. C. Langelaar, I. Setyawan, and R. L. Lagendijk, IEEE Signal Process. Mag. 17(5), 20 (2000).
[CrossRef]

Lu, L.

W. Bender, D. Gruhl, N. Morimoto, and L. Lu, IBM Syst. J. 35, 313 (1996).
[CrossRef]

Morimoto, N.

W. Bender, D. Gruhl, N. Morimoto, and L. Lu, IBM Syst. J. 35, 313 (1996).
[CrossRef]

Rabbani, M.

C. Hosinger and M. Rabbani, presented at the International Conference on Information Technology: Coding and Computing, Las Vegas, Nev., March 27–29, 2000.

Refregier, P.

Rosen, J.

Rosenfeld, D. P.

Sergent, A.

B. Javidi, A. Sergent, G. Zhang, and L. Guibert, Opt. Eng. 36, 992 (1997).
[CrossRef]

Setyawan, I.

G. C. Langelaar, I. Setyawan, and R. L. Lagendijk, IEEE Signal Process. Mag. 17(5), 20 (2000).
[CrossRef]

Tajahuerce, E.

White, A. D.

Yamaguchi, I.

Zhang, G.

B. Javidi, A. Sergent, G. Zhang, and L. Guibert, Opt. Eng. 36, 992 (1997).
[CrossRef]

Zhang, T.

Appl. Opt. (3)

IBM Syst. J. (1)

W. Bender, D. Gruhl, N. Morimoto, and L. Lu, IBM Syst. J. 35, 313 (1996).
[CrossRef]

IEEE Signal Process. Mag. (1)

G. C. Langelaar, I. Setyawan, and R. L. Lagendijk, IEEE Signal Process. Mag. 17(5), 20 (2000).
[CrossRef]

Opt. Eng. (1)

B. Javidi, A. Sergent, G. Zhang, and L. Guibert, Opt. Eng. 36, 992 (1997).
[CrossRef]

Opt. Lett. (3)

Other (5)

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1996).

J. W. Goodman, Statistical Optics (Wiley, New York, 1985).

C. Hosinger and M. Rabbani, presented at the International Conference on Information Technology: Coding and Computing, Las Vegas, Nev., March 27–29, 2000.

N. F. Johnson, Z. Duric, and S. Jajodia, Advances in Information Security, Vol. I of Information Hiding: Steganography and Watermarking—Attacks and Countermeasures (Kluwer Academic, Dordrecht, The Netherlands, 2001).
[CrossRef]

H. J. Caulfield, Handbook of Optical Holography (Academic, London, 1979).

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Figures (4)

Fig. 1
Fig. 1

Phase-shifting interferometer for recording the digital hologram of a 3D object.

Fig. 2
Fig. 2

(a) Phase-shifting digital hologram of a 3D object. (b) Watermarked digital hologram of the same 3D object.

Fig. 3
Fig. 3

(a) Image to be hidden, (b) 3D object reconstructed without watermarking, (c) recovered hidden image, (d) 3D object reconstructed by use of the watermarked hologram.

Fig. 4
Fig. 4

Watermarking and verification by windowed digital holography: (a) 3D object reconstructed without watermarking, (b) recovered hidden image, (c) 3D object reconstructed by use of the watermarked hologram window.

Equations (11)

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Rx,y;α=AR expiϕR+α,
H0x,y=A0x,yexpiϕ0x,y,
Ix,y;α=H0x,y+Rx,y;α2.
HCx,y=ACx,yexpiϕCx,y.
AC=A0x,yAR=14Ix,y;0-Ix,y;-π2+Ix,y;-3π2-Ix,y;-π221/2,  
ϕC=arctanIx,y;-3π/2-Ix,y;π/2Ix,y;0-Ix,y;-π.
ψx,y=fx,yexpj2πpx,yhx,y,
HWx,y=HCx,y+aψx,y,
σ2=12×N×Mx=1N y=1Mfx,y2,
f˜x,y= afx,y+IFTHˆCv,wexp-j2πbv,w×exp-j2πpx,y,
MSE=Ex=0N-1y=0M-1fx,y-frx,y2x=0N-1y=0M-1fx,y2,

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