Abstract

A method of concealing an image in a different halftone image is proposed. Continuous-tone levels of the visible images are represented by the area of the halftone dots. However, the hidden image is encoded by the dots’ positions inside their cells. Only a spatial correlator with a unique filter function can reveal the hidden image from the halftone picture. The technique and its robustness to noise and distortions are demonstrated.

© 2001 Optical Society of America

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References

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  1. 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]
  2. D. Kermisch, P. G. Roetling, “Fourier spectrum of halftone images,” J. Opt. Soc. Am. A 65, 716–723 (1975).
    [CrossRef]
  3. B. Javidi, “Securing information with optical technologies,” Phys. Today 50(3), 27–32 (1997).
  4. F. A. P. Petitcolas, R. J. Anderson, M. G. Kuhn, “Information hiding—survey,” Proc. IEEE 87, 1062–1077 (1999).
    [CrossRef]
  5. F. Hartung, M. Kutter, “Watermarking digital image and video data,” IEEE Signal Proc. Mag. 17(5), 20–46 (2000).
  6. R. L. van Renesse, ed. Optical Document Security, 2nd ed. (Artech House, Boston, Mass., 1998), Chap. 18, p. 427.
  7. J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996), Chap. 8, p. 232.
  8. A. B. VanderLugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory IT-10, 139–145 (1964).
  9. Ref. 7, Chap. 8, p. 243.
  10. Ref. 7, Chap. 8, p. 282.
  11. J. Rosen, “Learning in correlators based on projections onto constraint sets,” Opt. Lett. 18, 1183–1185 (1993).
    [CrossRef] [PubMed]
  12. O. Bryngdahl, F. Wyrowski, “Digital holography/computer-generated holograms,” in Progress In Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1990), Vol. 28, pp. 1–86.
  13. A. W. Lohmann, D. P. Paris, “Binary Fraunhofer holograms generated by computer,” Appl. Opt. 6, 1739–1748 (1967).
    [CrossRef] [PubMed]
  14. A. K. Jennison, J. P. Allebach, D. W. Sweeney, “Iterative approaches to computer-generated holography,” Opt. Eng. 28, 629–637 (1989).
  15. Ref. 7, Chap. 7, p. 184.
  16. Y. Li, K. Kreske, J. Rosen, “Security and encryption optical systems based on a correlator with significant output images,” Appl. Opt. 39, 5295–5301 (2000).
    [CrossRef]

2000 (2)

F. Hartung, M. Kutter, “Watermarking digital image and video data,” IEEE Signal Proc. Mag. 17(5), 20–46 (2000).

Y. Li, K. Kreske, J. Rosen, “Security and encryption optical systems based on a correlator with significant output images,” Appl. Opt. 39, 5295–5301 (2000).
[CrossRef]

1999 (1)

F. A. P. Petitcolas, R. J. Anderson, M. G. Kuhn, “Information hiding—survey,” Proc. IEEE 87, 1062–1077 (1999).
[CrossRef]

1997 (1)

B. Javidi, “Securing information with optical technologies,” Phys. Today 50(3), 27–32 (1997).

1993 (1)

1989 (1)

A. K. Jennison, J. P. Allebach, D. W. Sweeney, “Iterative approaches to computer-generated holography,” Opt. Eng. 28, 629–637 (1989).

1975 (1)

D. Kermisch, P. G. Roetling, “Fourier spectrum of halftone images,” J. Opt. Soc. Am. A 65, 716–723 (1975).
[CrossRef]

1967 (1)

1964 (1)

A. B. VanderLugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory IT-10, 139–145 (1964).

Allebach, J. P.

A. K. Jennison, J. P. Allebach, D. W. Sweeney, “Iterative approaches to computer-generated holography,” Opt. Eng. 28, 629–637 (1989).

Anderson, R. J.

F. A. P. Petitcolas, R. J. Anderson, M. G. Kuhn, “Information hiding—survey,” Proc. IEEE 87, 1062–1077 (1999).
[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]

O. Bryngdahl, F. Wyrowski, “Digital holography/computer-generated holograms,” in Progress In Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1990), Vol. 28, pp. 1–86.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996), Chap. 8, p. 232.

Hartung, F.

F. Hartung, M. Kutter, “Watermarking digital image and video data,” IEEE Signal Proc. Mag. 17(5), 20–46 (2000).

Javidi, B.

B. Javidi, “Securing information with optical technologies,” Phys. Today 50(3), 27–32 (1997).

Jennison, A. K.

A. K. Jennison, J. P. Allebach, D. W. Sweeney, “Iterative approaches to computer-generated holography,” Opt. Eng. 28, 629–637 (1989).

Kermisch, D.

D. Kermisch, P. G. Roetling, “Fourier spectrum of halftone images,” J. Opt. Soc. Am. A 65, 716–723 (1975).
[CrossRef]

Kreske, K.

Kuhn, M. G.

F. A. P. Petitcolas, R. J. Anderson, M. G. Kuhn, “Information hiding—survey,” Proc. IEEE 87, 1062–1077 (1999).
[CrossRef]

Kutter, M.

F. Hartung, M. Kutter, “Watermarking digital image and video data,” IEEE Signal Proc. Mag. 17(5), 20–46 (2000).

Li, Y.

Lohmann, A. W.

Paris, D. P.

Petitcolas, F. A. P.

F. A. P. Petitcolas, R. J. Anderson, M. G. Kuhn, “Information hiding—survey,” Proc. IEEE 87, 1062–1077 (1999).
[CrossRef]

Roetling, P. G.

D. Kermisch, P. G. Roetling, “Fourier spectrum of halftone images,” J. Opt. Soc. Am. A 65, 716–723 (1975).
[CrossRef]

Rosen, J.

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]

Sweeney, D. W.

A. K. Jennison, J. P. Allebach, D. W. Sweeney, “Iterative approaches to computer-generated holography,” Opt. Eng. 28, 629–637 (1989).

VanderLugt, A. B.

A. B. VanderLugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory IT-10, 139–145 (1964).

Wyrowski, F.

O. Bryngdahl, F. Wyrowski, “Digital holography/computer-generated holograms,” in Progress In Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1990), Vol. 28, pp. 1–86.

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. (2)

IEEE Signal Proc. Mag. (1)

F. Hartung, M. Kutter, “Watermarking digital image and video data,” IEEE Signal Proc. Mag. 17(5), 20–46 (2000).

IEEE Trans. Inf. Theory (1)

A. B. VanderLugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory IT-10, 139–145 (1964).

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

D. Kermisch, P. G. Roetling, “Fourier spectrum of halftone images,” J. Opt. Soc. Am. A 65, 716–723 (1975).
[CrossRef]

Opt. Eng. (1)

A. K. Jennison, J. P. Allebach, D. W. Sweeney, “Iterative approaches to computer-generated holography,” Opt. Eng. 28, 629–637 (1989).

Opt. Lett. (1)

Phys. Today (1)

B. Javidi, “Securing information with optical technologies,” Phys. Today 50(3), 27–32 (1997).

Proc. IEEE (1)

F. A. P. Petitcolas, R. J. Anderson, M. G. Kuhn, “Information hiding—survey,” Proc. IEEE 87, 1062–1077 (1999).
[CrossRef]

Other (7)

R. L. van Renesse, ed. Optical Document Security, 2nd ed. (Artech House, Boston, Mass., 1998), Chap. 18, p. 427.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996), Chap. 8, p. 232.

Ref. 7, Chap. 8, p. 243.

Ref. 7, Chap. 8, p. 282.

O. Bryngdahl, F. Wyrowski, “Digital holography/computer-generated holograms,” in Progress In Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1990), Vol. 28, pp. 1–86.

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]

Ref. 7, Chap. 7, p. 184.

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Figures (7)

Fig. 1
Fig. 1

Block diagram of the POCS algorithm used in the first stage of halftone production.

Fig. 2
Fig. 2

Schematic of a single cell from an entire halftone picture.

Fig. 3
Fig. 3

Spatial spectrum of a typical halftone picture. The area surrounded by the white square is the region that is multiplied by the filter.

Fig. 4
Fig. 4

Optical correlator that can be used to reveal the hidden image in the halftone picture.

Fig. 5
Fig. 5

(a) Original set of gray-tone pictures used as the visible images. (b) Original set of binary pictures used as the hidden images. (c) The resultant halftone images. (d) The hidden images revealed by the correlation between the set in (c) and the key function.

Fig. 6
Fig. 6

Enlarged region of a halftone picture (a) with and (b) without dot-position modulation.

Fig. 7
Fig. 7

(a) Set of halftone pictures covered by a zero-valued square with area values that vary from 11% of the picture area at the rightmost figure to 55% at the leftmost figure. (b) Correlation results between the set in (a) and the key function. (c) Set of halftone pictures in which various amounts of their pixel values have been randomly flipped from their original values shown in Fig. 5(c). The number of flipped pixels is varied from 8% at the rightmost figure to 40% at the leftmost figure. (d) Correlation results between the set in (c) and the key function.

Equations (8)

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cξ, η=fx, yexpiθx, yh*-x, -y=IFTFTgx, yexpiϕu, v,
gx, y=IFTFTcξ, ηHu, v=IFTFTcξ, ηexp-iϕu, v.
P1cjξ, η=aξ, ηexpiψjξ, ηξ, ηWcjξ, ηotherwise,
P2gjx, y=fx, yexpiθjx, y,
ec,j=1MW2  |P1cjξ, η-cjξ, η|2dξdη=1MW2  |aξ, η-|cjξ, η2dξdη, eg,j=1M2  |P2gjx, y-gjx, y|2dxdy=1M2  |fx, y-|gjx, y2dxdy,
bx, y=Bk=-M/2M/2Bl=-M/2M/2rectx-dk+θnxk, yl/2πd|gnxk, yl|1/2×recty-ldd|gnxk, yl|1/2,
Bu, vGnu, v,  |u-MΔu|MΔu/2,|v|MΔv/2,
cξ, ηIFTGnu, vHu, v,

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