Abstract

Digital holography techniques can be utilized to implement image watermarking schemes. In a previous method proposed by Takai and Mifune [ Appl. Opt. 41, 865 ( 2002)], a watermark image is transformed into a digital Fourier hologram, which then is directly superposed onto a content image to perform the embedding process. In the detection stage, the watermark is extracted based on the inverse Fourier transform and optical holography techniques. A method in which the hologram is superposed on the discrete-cosine-transform domain of the content image is proposed to significantly improve Takai and Mifune’s method. The proposed method can greatly reduce the degradation on the superposed image, which is the major drawback in Takai and Mifune’s method. Simulation results also demonstrate that the watermark can be successfully extracted under different kinds of attack.

© 2005 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. L. Cox, J. Kilian, T. Leighton, T. Shamoon, “Secure spread spectrum watermarking for multimedia,” (NEC Research Institute, 1995).
  2. C. I. Podilchuk, E. J. Delp, “Digital watermarking: algorithms and application,” IEEE Signal Process. Mag. 18, 33–46 (2001).
    [CrossRef]
  3. N. Towghi, B. Javidi, Z. Lou, “Fully phase encrypted image processor,” J. Opt. Soc. Am. A 16, 1915–1927 (1999).
    [CrossRef]
  4. C. H. Yeh, H. T. Chang, H. C. Chien, C. J. Kuo, “Design of cascaded phase keys for a hierarchical security system,” Appl. Opt. 41, 6128–6134 (2002).
    [CrossRef] [PubMed]
  5. H. T. Chang, W. C. Lu, C. J. Kuo, “Multiple-phase retrieval for optical security systems by use of random-phase encoding,” Appl. Opt. 41, 4825–4834 (2002).
    [CrossRef] [PubMed]
  6. K. H. Lin, H. T. Chang, W. N. Lai, C. H. Chuang, “A public-key-based optical image cryptosystem with data embedding techniques,” Opt. Eng. 42, 2331–2339 (2003).
    [CrossRef]
  7. Y. C. Chang, H. T. Chang, C. J. Kuo, “Hybrid image cryptosystem based on dyadic phase displacement in the Fourier domain,” Opt. Commun. 236, 245–257 (2004).
    [CrossRef]
  8. N. Takai, Y. Mifune, “Digital watermarking by a holographic technique,” Appl. Opt. 41, 865–873 (2002).
    [CrossRef] [PubMed]
  9. J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996), Chap. 8, pp. 198–254.
  10. I. Yamaguchi, T. Zhang, “Phase-shifting digital holography,” Opt. Lett. 22, 1268–1270 (1997).
    [CrossRef] [PubMed]
  11. E. Tajahuerce, O. Matoba, S. C. Verrall, B. Javidi, “Opto-electronic information encyption with phase-shifting interferometry,” Appl. Opt. 39, 2313–2320 (2000).
    [CrossRef]
  12. J.-R. Ohm, Multimedia Communication Technology (Springer, 2004), Chap. 4, p. 118.

2004

Y. C. Chang, H. T. Chang, C. J. Kuo, “Hybrid image cryptosystem based on dyadic phase displacement in the Fourier domain,” Opt. Commun. 236, 245–257 (2004).
[CrossRef]

2003

K. H. Lin, H. T. Chang, W. N. Lai, C. H. Chuang, “A public-key-based optical image cryptosystem with data embedding techniques,” Opt. Eng. 42, 2331–2339 (2003).
[CrossRef]

2002

2001

C. I. Podilchuk, E. J. Delp, “Digital watermarking: algorithms and application,” IEEE Signal Process. Mag. 18, 33–46 (2001).
[CrossRef]

2000

1999

1997

Chang, H. T.

Y. C. Chang, H. T. Chang, C. J. Kuo, “Hybrid image cryptosystem based on dyadic phase displacement in the Fourier domain,” Opt. Commun. 236, 245–257 (2004).
[CrossRef]

K. H. Lin, H. T. Chang, W. N. Lai, C. H. Chuang, “A public-key-based optical image cryptosystem with data embedding techniques,” Opt. Eng. 42, 2331–2339 (2003).
[CrossRef]

C. H. Yeh, H. T. Chang, H. C. Chien, C. J. Kuo, “Design of cascaded phase keys for a hierarchical security system,” Appl. Opt. 41, 6128–6134 (2002).
[CrossRef] [PubMed]

H. T. Chang, W. C. Lu, C. J. Kuo, “Multiple-phase retrieval for optical security systems by use of random-phase encoding,” Appl. Opt. 41, 4825–4834 (2002).
[CrossRef] [PubMed]

Chang, Y. C.

Y. C. Chang, H. T. Chang, C. J. Kuo, “Hybrid image cryptosystem based on dyadic phase displacement in the Fourier domain,” Opt. Commun. 236, 245–257 (2004).
[CrossRef]

Chien, H. C.

Chuang, C. H.

K. H. Lin, H. T. Chang, W. N. Lai, C. H. Chuang, “A public-key-based optical image cryptosystem with data embedding techniques,” Opt. Eng. 42, 2331–2339 (2003).
[CrossRef]

Cox, L.

L. Cox, J. Kilian, T. Leighton, T. Shamoon, “Secure spread spectrum watermarking for multimedia,” (NEC Research Institute, 1995).

Delp, E. J.

C. I. Podilchuk, E. J. Delp, “Digital watermarking: algorithms and application,” IEEE Signal Process. Mag. 18, 33–46 (2001).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996), Chap. 8, pp. 198–254.

Javidi, B.

Kilian, J.

L. Cox, J. Kilian, T. Leighton, T. Shamoon, “Secure spread spectrum watermarking for multimedia,” (NEC Research Institute, 1995).

Kuo, C. J.

Lai, W. N.

K. H. Lin, H. T. Chang, W. N. Lai, C. H. Chuang, “A public-key-based optical image cryptosystem with data embedding techniques,” Opt. Eng. 42, 2331–2339 (2003).
[CrossRef]

Leighton, T.

L. Cox, J. Kilian, T. Leighton, T. Shamoon, “Secure spread spectrum watermarking for multimedia,” (NEC Research Institute, 1995).

Lin, K. H.

K. H. Lin, H. T. Chang, W. N. Lai, C. H. Chuang, “A public-key-based optical image cryptosystem with data embedding techniques,” Opt. Eng. 42, 2331–2339 (2003).
[CrossRef]

Lou, Z.

Lu, W. C.

Matoba, O.

Mifune, Y.

Ohm, J.-R.

J.-R. Ohm, Multimedia Communication Technology (Springer, 2004), Chap. 4, p. 118.

Podilchuk, C. I.

C. I. Podilchuk, E. J. Delp, “Digital watermarking: algorithms and application,” IEEE Signal Process. Mag. 18, 33–46 (2001).
[CrossRef]

Shamoon, T.

L. Cox, J. Kilian, T. Leighton, T. Shamoon, “Secure spread spectrum watermarking for multimedia,” (NEC Research Institute, 1995).

Tajahuerce, E.

Takai, N.

Towghi, N.

Verrall, S. C.

Yamaguchi, I.

Yeh, C. H.

Zhang, T.

Appl. Opt.

IEEE Signal Process. Mag.

C. I. Podilchuk, E. J. Delp, “Digital watermarking: algorithms and application,” IEEE Signal Process. Mag. 18, 33–46 (2001).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Commun.

Y. C. Chang, H. T. Chang, C. J. Kuo, “Hybrid image cryptosystem based on dyadic phase displacement in the Fourier domain,” Opt. Commun. 236, 245–257 (2004).
[CrossRef]

Opt. Eng.

K. H. Lin, H. T. Chang, W. N. Lai, C. H. Chuang, “A public-key-based optical image cryptosystem with data embedding techniques,” Opt. Eng. 42, 2331–2339 (2003).
[CrossRef]

Opt. Lett.

Other

J.-R. Ohm, Multimedia Communication Technology (Springer, 2004), Chap. 4, p. 118.

L. Cox, J. Kilian, T. Leighton, T. Shamoon, “Secure spread spectrum watermarking for multimedia,” (NEC Research Institute, 1995).

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996), Chap. 8, pp. 198–254.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (16)

Fig. 1
Fig. 1

(a) Procedure used to make a digital hologram H(ξ, η); (b) watermark image reconstructed from a digital hologram. FT, Fourier transform; IFT, inverse FT.

Fig. 2
Fig. 2

Schematic diagram of Takai and Mifune’s method: (a) watermark embedding; (b) watermark extraction.

Fig. 3
Fig. 3

Watermark positions in the reconstruction plane.

Fig. 4
Fig. 4

Schematic diagram of the proposed method: (a) watermark embedding; (b) watermark extraction. DCT, discrete cosine transform; IDCT, inverse DCT.

Fig. 5
Fig. 5

Region of median-frequency coefficients for embedding the digital hologram.

Fig. 6
Fig. 6

(a) Watermark image to be embedded and (b)–(d) the content images.

Fig. 7
Fig. 7

(a) Digital hologram in which the watermark has been hidden; (b) watermark images reconstructed from the hologram.

Fig. 8
Fig. 8

Simulation results of Takai and Mifune’s method. The upper row shows the supposed image f(ξ, η) and the lower row shows the reconstructed images gr(x, y). (a) α = 1/1, σI = 0.38; (b) α = 1/5, σI = 0.51; (c) αI = 1310, σI = 1.56; (d) α = 1/50, ′I = 7.64.

Fig. 9
Fig. 9

Simulation results of the proposed method. The upper row shows the superposed images f′(u, v) and the lower row shows the reconstructed images gr(x, y). (a) α = 1/1, σI = 0.37; (b) α = 1/5, σI = 0.51; (c) α = 1310, σI = 1.43; (d) α = 1/50, σI = 7.19.

Fig. 10
Fig. 10

(a) Watermarked baboon image with the weighting factor α = 1; (b) the reconstructed watermark images, σI = 0.55; (c) the watermarked image with the weighting factor α = 1/50; (d) the reconstructed watermark images, σI = 7.81.

Fig. 11
Fig. 11

(a) Halftone image used as a watermark; (b) the experimental result of the extracted watermark, σI = 0.5.

Fig. 12
Fig. 12

Experimental result under Gaussian noise attack: (a) α = 1/1, σI = 8.41; (b) α = 1350, σI = 9.87.

Fig. 13
Fig. 13

Modified image suffering from tampering modifications; (a) the extracted watermark from the experimental result; (b) the reconstructed watermark images, σI = 8.98.

Fig. 14
Fig. 14

Simulation result of the proposed method: (a) lower half-image is lost; (b) the reconstructed watermark images, σI = 10.58.

Fig. 15
Fig. 15

(a) Superposed image after low-pass filter; (b) the watermark reconstructed from the superposed image, σI = 8.95.

Fig. 16
Fig. 16

(a) Brightened image; (b) the watermark reconstructed from the brightened image, σI = 8.87; (c) the darkened image; (d) the watermark reconstructed from the darkened image, σI = 8.62.

Tables (2)

Tables Icon

Table 1 Peak Signal-to-Noise Ratio (PSNR) (in Decibels) and σI Comparisons under Different α Values for the Sailor Image

Tables Icon

Table 2 Peak Signal-to-Noise Ratio (in Decibels) and σI Comparisons under Different α Values for the Baboon Image

Equations (23)

Equations on this page are rendered with MathJax. Learn more.

g 0 ( x , y ) = g mark ( x , y ) exp [ i 2 π ϕ ( x , y ) ] ,
G mark ( ξ , η ) = - - g 0 ( x , y ) × exp [ - i 2 π ( ξ x + η y ) ] d x d y .
R ( ξ , η ) = R 0 exp [ i 2 π ( 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 ) ,
g r ( x , y ) = - - H ( ξ , η ) exp [ i 2 π ( 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 LP ( ξ , η ) - q min q max - q min q ( ξ , η ) .
0 H ( ξ , η ) 1 ,             0 q ( ξ , η ) 1.
f ( ξ , η ) = q LP ( ξ , η ) + α H ( ξ , η ) .
g w ( x , y ) = Q LP ( x , y ) + α g r ( x , y ) ,
σ I = ( I - I α ) 2 1 / 2 I α 1 / 2 ,
Q ( ξ , η ) = 2 M N γ ( ξ ) γ ( η ) u = 1 M - 1 v = 0 N - 1 q ( u , v ) × cos [ ( 2 u + 1 ) ξ π 2 M ] cos [ ( 2 v + 1 ) η π 2 N ] ,
q ( u , v ) = 2 M N ξ = 0 M - 1 η = 0 N - 1 γ ( ξ ) γ ( η ) Q ( ξ , η ) × cos [ ( 2 u + 1 ) ξ π 2 M ] cos [ ( 2 v + 1 ) η π 2 N ] ,
γ ( ξ ) = { 1 2 , for ξ = 0 1 , for ξ = 1 , 2 , , M - 1 , γ ( η ) = { 1 2 , for η = 0 1 , for η = 1 , 2 , , N - 1 .
Q MED ( ξ , η ) = Q MED ( ξ , η ) + α H ( ξ , η ) .
Q ( ξ , η ) = Q LOW ( ξ , η ) + Q MED ( ξ , η ) + Q HIGH ( ξ , η ) ,
f ( u , v ) = 2 M N ξ = 0 M - 1 η = 0 N - 1 γ ( ξ ) γ ( η ) Q ( ξ , η ) × cos [ ( 2 ξ + 1 ) u π 2 M ] cos [ ( 2 η + 1 ) v π 2 N ] = q ( u , v ) + IDCT { α H ( ξ , η ) } ,
Q ( ξ , η ) = 2 M N γ ( ξ ) γ ( η ) ξ = 1 M - 1 η = 0 N - 1 f ( u , v ) × cos [ ( 2 ξ + 1 ) u π 2 M ] cos [ ( 2 η + 1 ) v π 2 N ] .
g w ( x , y ) = IFT [ Q MED ( ξ , η ) ] = IFT [ Q MED ( ξ , η ) ] + α g r ( x , y ) .
PSNR = 10 log 10 255 2 1 M N ξ = 0 M - 1 η = 0 N - 1 f ( ξ , η ) - f ( ξ , η ) 2 dB ,

Metrics