Abstract

We describe an electro-optical method of deciphering a watermark from a recently invented encoded image termed a concealogram. The watermark is revealed as a result of spatial correlation between two concealograms, one containing the watermark and the other containing the deciphering key. The two are placed side by side on the input plane of a modified joint-transform correlator. When the input plane is illuminated by a plane wave, the watermark image is reconstructed on part of the correlator’s output plane. The key function deciphers the concealed watermark from the visible picture only when the two specific concealograms are matched. To illustrate the system’s performance, both simulation and experimental results are presented.

© 2005 Optical Society of America

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References

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  1. W. Bender, D. Gruhl, N. Morimoto, L. Lu, “Techniques for data hiding,” IBM Syst. J. 35, 313–336 (1996).
    [CrossRef]
  2. D. Grover, “Steganography and watermarking of digital data,” Computer Law Security Rep. 17, 101–104 (2001).
    [CrossRef]
  3. N. F. Johnson, Z. Duric, S. Jajodia, Information Hiding: Steganography and Watermarking—Attacks and Countermeasures, Vol. 1 of Advances in Information Security, S. Jajodia, ed. (Kluwer Academic, Boston, Mass., 2001).
  4. G. C. Langelaar, I. Setyawan, R. L. Lagendijk, “Watermarking digital image and video data. A state of the art overview,” IEEE Signal Proc. Mag. 17, 20–46 (2000).
    [CrossRef]
  5. S. Kishk, B. Javidi, “3D object watermarking by a 3D hidden object,” Opt. Express 11, 874–888 (2003) http://www.opticsexpress.org .
    [CrossRef] [PubMed]
  6. J. Rosen, B. Javidi, “Hidden images in halftone pictures,” Appl. Opt. 40, 3346–3353 (2001).
    [CrossRef]
  7. J. Rosen, B. Javidi, H. Goldenfeld, S. Moshkovits, “Concealogram: an image within an image,” in Algorithms and Systems for Optical Information Processing VI, B. Javidi, D. Psaltis, eds., Proc. SPIE4789, 44–54 (2002).
    [CrossRef]
  8. O. Bryngdahl, T. Scheermesser, F. Wyrowski, “Digital halftoning: synthesis of binary images,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1994), Vol. 33, pp. 389–463.
    [CrossRef]
  9. D. Abookasis, O. Arazi, J. Rosen, B. Javidi, “Security optical systems based on a joint transform correlator with significant output images,” Opt. Eng. 40, 1584–1589 (2001).
    [CrossRef]
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    [CrossRef] [PubMed]

2003 (1)

2001 (3)

J. Rosen, B. Javidi, “Hidden images in halftone pictures,” Appl. Opt. 40, 3346–3353 (2001).
[CrossRef]

D. Abookasis, O. Arazi, J. Rosen, B. Javidi, “Security optical systems based on a joint transform correlator with significant output images,” Opt. Eng. 40, 1584–1589 (2001).
[CrossRef]

D. Grover, “Steganography and watermarking of digital data,” Computer Law Security Rep. 17, 101–104 (2001).
[CrossRef]

2000 (1)

G. C. Langelaar, I. Setyawan, R. L. Lagendijk, “Watermarking digital image and video data. A state of the art overview,” IEEE Signal Proc. Mag. 17, 20–46 (2000).
[CrossRef]

1996 (1)

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

1967 (1)

1966 (1)

1964 (1)

A. VanderLugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory IT-10, 139–146 (1964).

Abookasis, D.

D. Abookasis, O. Arazi, J. Rosen, B. Javidi, “Security optical systems based on a joint transform correlator with significant output images,” Opt. Eng. 40, 1584–1589 (2001).
[CrossRef]

Arazi, O.

D. Abookasis, O. Arazi, J. Rosen, B. Javidi, “Security optical systems based on a joint transform correlator with significant output images,” Opt. Eng. 40, 1584–1589 (2001).
[CrossRef]

Bender, W.

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

Bryngdahl, O.

O. Bryngdahl, T. Scheermesser, F. Wyrowski, “Digital halftoning: synthesis of binary images,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1994), Vol. 33, pp. 389–463.
[CrossRef]

Duric, Z.

N. F. Johnson, Z. Duric, S. Jajodia, Information Hiding: Steganography and Watermarking—Attacks and Countermeasures, Vol. 1 of Advances in Information Security, S. Jajodia, ed. (Kluwer Academic, Boston, Mass., 2001).

Goldenfeld, H.

J. Rosen, B. Javidi, H. Goldenfeld, S. Moshkovits, “Concealogram: an image within an image,” in Algorithms and Systems for Optical Information Processing VI, B. Javidi, D. Psaltis, eds., Proc. SPIE4789, 44–54 (2002).
[CrossRef]

Goodman, J. W.

Grover, D.

D. Grover, “Steganography and watermarking of digital data,” Computer Law Security Rep. 17, 101–104 (2001).
[CrossRef]

Gruhl, D.

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

Jajodia, S.

N. F. Johnson, Z. Duric, S. Jajodia, Information Hiding: Steganography and Watermarking—Attacks and Countermeasures, Vol. 1 of Advances in Information Security, S. Jajodia, ed. (Kluwer Academic, Boston, Mass., 2001).

Javidi, B.

S. Kishk, B. Javidi, “3D object watermarking by a 3D hidden object,” Opt. Express 11, 874–888 (2003) http://www.opticsexpress.org .
[CrossRef] [PubMed]

J. Rosen, B. Javidi, “Hidden images in halftone pictures,” Appl. Opt. 40, 3346–3353 (2001).
[CrossRef]

D. Abookasis, O. Arazi, J. Rosen, B. Javidi, “Security optical systems based on a joint transform correlator with significant output images,” Opt. Eng. 40, 1584–1589 (2001).
[CrossRef]

J. Rosen, B. Javidi, H. Goldenfeld, S. Moshkovits, “Concealogram: an image within an image,” in Algorithms and Systems for Optical Information Processing VI, B. Javidi, D. Psaltis, eds., Proc. SPIE4789, 44–54 (2002).
[CrossRef]

Johnson, N. F.

N. F. Johnson, Z. Duric, S. Jajodia, Information Hiding: Steganography and Watermarking—Attacks and Countermeasures, Vol. 1 of Advances in Information Security, S. Jajodia, ed. (Kluwer Academic, Boston, Mass., 2001).

Kishk, S.

Lagendijk, R. L.

G. C. Langelaar, I. Setyawan, R. L. Lagendijk, “Watermarking digital image and video data. A state of the art overview,” IEEE Signal Proc. Mag. 17, 20–46 (2000).
[CrossRef]

Langelaar, G. C.

G. C. Langelaar, I. Setyawan, R. L. Lagendijk, “Watermarking digital image and video data. A state of the art overview,” IEEE Signal Proc. Mag. 17, 20–46 (2000).
[CrossRef]

Lohmann, A. W.

Lu, L.

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

Morimoto, N.

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

Moshkovits, S.

J. Rosen, B. Javidi, H. Goldenfeld, S. Moshkovits, “Concealogram: an image within an image,” in Algorithms and Systems for Optical Information Processing VI, B. Javidi, D. Psaltis, eds., Proc. SPIE4789, 44–54 (2002).
[CrossRef]

Paris, D. P.

Rosen, J.

D. Abookasis, O. Arazi, J. Rosen, B. Javidi, “Security optical systems based on a joint transform correlator with significant output images,” Opt. Eng. 40, 1584–1589 (2001).
[CrossRef]

J. Rosen, B. Javidi, “Hidden images in halftone pictures,” Appl. Opt. 40, 3346–3353 (2001).
[CrossRef]

J. Rosen, B. Javidi, H. Goldenfeld, S. Moshkovits, “Concealogram: an image within an image,” in Algorithms and Systems for Optical Information Processing VI, B. Javidi, D. Psaltis, eds., Proc. SPIE4789, 44–54 (2002).
[CrossRef]

Scheermesser, T.

O. Bryngdahl, T. Scheermesser, F. Wyrowski, “Digital halftoning: synthesis of binary images,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1994), Vol. 33, pp. 389–463.
[CrossRef]

Setyawan, I.

G. C. Langelaar, I. Setyawan, R. L. Lagendijk, “Watermarking digital image and video data. A state of the art overview,” IEEE Signal Proc. Mag. 17, 20–46 (2000).
[CrossRef]

VanderLugt, A.

A. VanderLugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory IT-10, 139–146 (1964).

Weaver, C. S.

Wyrowski, F.

O. Bryngdahl, T. Scheermesser, F. Wyrowski, “Digital halftoning: synthesis of binary images,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1994), Vol. 33, pp. 389–463.
[CrossRef]

Appl. Opt. (3)

Computer Law Security Rep. (1)

D. Grover, “Steganography and watermarking of digital data,” Computer Law Security Rep. 17, 101–104 (2001).
[CrossRef]

IBM Syst. J. (1)

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

IEEE Signal Proc. Mag. (1)

G. C. Langelaar, I. Setyawan, R. L. Lagendijk, “Watermarking digital image and video data. A state of the art overview,” IEEE Signal Proc. Mag. 17, 20–46 (2000).
[CrossRef]

IEEE Trans. Inf. Theory (1)

A. VanderLugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory IT-10, 139–146 (1964).

Opt. Eng. (1)

D. Abookasis, O. Arazi, J. Rosen, B. Javidi, “Security optical systems based on a joint transform correlator with significant output images,” Opt. Eng. 40, 1584–1589 (2001).
[CrossRef]

Opt. Express (1)

Other (3)

N. F. Johnson, Z. Duric, S. Jajodia, Information Hiding: Steganography and Watermarking—Attacks and Countermeasures, Vol. 1 of Advances in Information Security, S. Jajodia, ed. (Kluwer Academic, Boston, Mass., 2001).

J. Rosen, B. Javidi, H. Goldenfeld, S. Moshkovits, “Concealogram: an image within an image,” in Algorithms and Systems for Optical Information Processing VI, B. Javidi, D. Psaltis, eds., Proc. SPIE4789, 44–54 (2002).
[CrossRef]

O. Bryngdahl, T. Scheermesser, F. Wyrowski, “Digital halftoning: synthesis of binary images,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1994), Vol. 33, pp. 389–463.
[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

Schematic of the system for revealing watermarks from concealograms.

Fig. 2
Fig. 2

Two concealograms displayed on the simulated modified JTC input plane.

Fig. 3
Fig. 3

Simulation results of the joint spectrum plane.

Fig. 4
Fig. 4

Simulation results of the JTC output plane in which the hidden watermark was revealed.

Fig. 5
Fig. 5

Two rotated concealograms displayed on SLM1 in the optical experiment.

Fig. 6
Fig. 6

Experimental results of the joint spectrum plane recorded by the CCD.

Fig. 7
Fig. 7

Experimental results of the reconstructed watermark observed by the CCD on the output plane of the modified JTC.

Equations (4)

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b ( x , y ) = k = M / 2 M / 2 B l = M / 2 M / 2 B × rect { ( x x 1 ) d [ k + θ g ( x k , y l ) / 2 π ] d [ | g ( x k , y l ) | ] 1 / 2 } × rect { ( y y 1 ) l d d [ | g ( x k , y l ) | ] 1 / 2 } + rect { ( x + x 1 ) d [ k + θ h ( x k , y l ) / 2 π ] d [ | h ( x k , y l ) | ] 1 / 2 } × rect { ( y + y 1 ) l d d [ | h ( x k , y l ) | ] 1 / 2 } ,
T ( f x , f y ) exp { i 2 π [ ( f x D x ) x 1 + f y y 1 ] } G ( f x D x , f y ) + exp i 2 π [ ( f x D x ) x 1 + f y y 1 ] } H ( f x D x , f y ) , ( | f x D x | , | f y | ) ( Π x 2 , Π y 2 ) ,
I ( f x , f y ) = | T ( f x , f y ) | 2 = | exp [ i 2 π ( x 1 f x + y 1 f y ) ] G ( f x , f y ) + exp [ i 2 π ( x 1 f x + y 1 f y ) ] H ( f x , f y ) | 2 = | G ( f x , f y ) | 2 + | H ( f x , f y ) | 2 + exp [ i 4 π ( x 1 f x + y 1 f y ) ] G ( f x , f y ) H * ( f x , f y ) + exp [ i 4 π ( x 1 f x + y 1 f y ) ] G * ( f x , f y ) H ( f x , f y ) ,
c ( x o , y o ) = g ( x o , y o ) g ( x o , y o ) + h ( x o , y o ) h ( x o , y o ) + g ( x o , y o ) h ( x o , y o ) * δ ( x o 2 x 1 , y o 2 y 1 ) + h ( x o , y o ) g ( x o , y o ) * δ ( x o + 2 x 1 , y o + 2 y 1 ) ,

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