Abstract

In this paper we present a method to watermark a 3D object with another hidden 3D object using digital holography. The watermark or the hidden information is a 3D object that is embedded in the digital hologram of a 3D host object. The digital holograms are obtained optically by phase shift interferometery. The hologram of the hidden 3D object is double phase encoded before embedding it to the host 3D object hologram. Then, the watermarked hologram is double phase encoded again using different set of codes. The resultant watermarked hologram is very secure because of the multi-key nature of the watermarking process. We discuss the effect of distortion caused by hologram quantization and occlusion of some of the hologram pixels. We present tests to illustrate the effect of using a window of the hologram to reconstruct the hidden 3D object and the host 3D object. Both mathematical analysis and simulations are presented to illustrate the system performance. To the best of our knowledge, this is the first report of embedding a 3D objects within another 3D object.

© 2003 Optical Society of America

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References

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  1. N. F. Johnson, Z. Duric, and S. Jajodia, Information Hiding : Steganography and Watermarking �?? Attacks and Countermeasures (Advances in Information Security, Volume 1, Kluwer Academic 2001).
  2. W. Bender, D. Gruhl, N. Morimoto and L. Lu, �??Techniques for data hiding,�?? IBM Systems J. 35, 313-336 (1996).
    [CrossRef]
  3. G. C. Langelaar, I. Setyawan and, R. L. Lagendijk, "Watermarking Digital Image and Video Data. A state of the Art overview,�?? IEEE Signal Processing Magazine 17, 20-46 (2000).
    [CrossRef]
  4. S. Kishk, and B. Javidi, "Information Hiding Technique using Double Phase Encoding,�?? Appl. Opt. 41, 5470-5482 (2002).
    [CrossRef]
  5. Chuan-Fu Wu; Wen-Shyong Hsieh, "Digital watermarking using zerotree of DCT,�?? IEEE Trans. Consumer Electron. 46, 87-94 (2000)
    [CrossRef]
  6. Joseph Rosen, Bahram Javidi, �??Hiding images in Halftone Pictures,�?? Appl. Opt. 40, 3346 (2001)
    [CrossRef]
  7. C. Hosinger and M. Rabbani, �??Data Embedding using Phase Dispersion, "The International Conference on Information Technology: Coding and Computing (ITCC 2000), Las Vegas, Nev. 27-29 March (2000).
  8. Po-Chyi Su,C.-C. Jay Kuo,Houng-jyh Wang, "Wavelet-Based Digital Image Watermarking,�?? Opt. Express 3, 491-496 (1998), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-3-12-491">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-3-12-491</a>
    [CrossRef] [PubMed]
  9. S. Kishk and B. Javidi �??Watermarking of a 3D Object Using Digital Holography,�?? Opt. Lett. 28, 167-169 (2003).
    [CrossRef]
  10. R. Ohbuchi,A. ukaiyama,S. Takahashi �??A frequency-domain approach to watermarking 3D shapes,�?? Computer Graphics Forum 21, 373-382 Sp. Iss. SI(2002).
    [CrossRef]
  11. P. Refregier and B. Javidi, �??Optical image encryption using input plane and Fourier plane random encoding,�?? Opt. Lett. 20, 767-769 (1995).
    [CrossRef]
  12. R. K. Wang, I. A. Watson, and C. Chatwin, �??Random phase encoding for optical secutity,�?? Opt. Eng. 35, 2464-2460 (1996).
    [CrossRef]
  13. F. Goudail, F. Bollaro, B. Javidi, and P. Refregier, �??Influence of perturbation in a double phase-encoding system,�?? J. Opt. Soc. Am. A 15, 2629-2638 (1998).
    [CrossRef]
  14. H. J. Caulfield, Handbook of Optical Holography, (Academic press, London, 1979).
  15. J. W. Goodman, Introduction to Fourier Optics, (McGraw-Hill, New York, NY, 1996).
  16. U. Schnars, and W. P. O. Jüptner, �??Direct recording of holograms by a CCD target and numerical reconstruction,�?? Appl. Opt. 33, 179-181 (1994).
    [CrossRef] [PubMed]
  17. I Yamaguchi, and T Zhang, �??Phase-Shifting Digital Holography,�?? Opt. Lett. 22, 1268-1270 (1997)
    [CrossRef] [PubMed]
  18. J. H. Bruninig, D. R. Herriott, J. E. Gallagher, D. P. Rosenfeld, A. D. White, and D. J. Brangaccio, �??Digital Wavefront measuring interferometer for Testing Optical Surfaces and Lenses,�?? Appl. Opt. 13, 2693 (1974).
    [CrossRef]
  19. J. Schwider, �??Advanced Evaluation Techniques in Interferometry,�?? in Progress in Optics, E. Wolf, ed (North Holland, Amesterdam) XXVIII, 271-359 (1990)
  20. T. Naughton, Y. Frauel, B. Javidi, and E. Tajahuerce, "Compression of digital holograms for three dimensional object reconstruction and recognition,�?? Appl. Opt. 11, 4124-4132 (2002).
    [CrossRef]

Appl. Opt. (5)

S. Kishk, and B. Javidi, "Information Hiding Technique using Double Phase Encoding,�?? Appl. Opt. 41, 5470-5482 (2002).
[CrossRef]

U. Schnars, and W. P. O. Jüptner, �??Direct recording of holograms by a CCD target and numerical reconstruction,�?? Appl. Opt. 33, 179-181 (1994).
[CrossRef] [PubMed]

T. Naughton, Y. Frauel, B. Javidi, and E. Tajahuerce, "Compression of digital holograms for three dimensional object reconstruction and recognition,�?? Appl. Opt. 11, 4124-4132 (2002).
[CrossRef]

J. H. Bruninig, D. R. Herriott, J. E. Gallagher, D. P. Rosenfeld, A. D. White, and D. J. Brangaccio, �??Digital Wavefront measuring interferometer for Testing Optical Surfaces and Lenses,�?? Appl. Opt. 13, 2693 (1974).
[CrossRef]

Joseph Rosen, Bahram Javidi, �??Hiding images in Halftone Pictures,�?? Appl. Opt. 40, 3346 (2001)
[CrossRef]

Computer Graphics Forum (1)

R. Ohbuchi,A. ukaiyama,S. Takahashi �??A frequency-domain approach to watermarking 3D shapes,�?? Computer Graphics Forum 21, 373-382 Sp. Iss. SI(2002).
[CrossRef]

IBM Systems J. (1)

W. Bender, D. Gruhl, N. Morimoto and L. Lu, �??Techniques for data hiding,�?? IBM Systems J. 35, 313-336 (1996).
[CrossRef]

IEEE Signal Processing Magazine (1)

G. C. Langelaar, I. Setyawan and, R. L. Lagendijk, "Watermarking Digital Image and Video Data. A state of the Art overview,�?? IEEE Signal Processing Magazine 17, 20-46 (2000).
[CrossRef]

IEEE Trans. Consumer Electron. (1)

Chuan-Fu Wu; Wen-Shyong Hsieh, "Digital watermarking using zerotree of DCT,�?? IEEE Trans. Consumer Electron. 46, 87-94 (2000)
[CrossRef]

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

Opt. Eng. (1)

R. K. Wang, I. A. Watson, and C. Chatwin, �??Random phase encoding for optical secutity,�?? Opt. Eng. 35, 2464-2460 (1996).
[CrossRef]

Opt. Express (1)

Opt. Lett. (3)

Other (5)

N. F. Johnson, Z. Duric, and S. Jajodia, Information Hiding : Steganography and Watermarking �?? Attacks and Countermeasures (Advances in Information Security, Volume 1, Kluwer Academic 2001).

J. Schwider, �??Advanced Evaluation Techniques in Interferometry,�?? in Progress in Optics, E. Wolf, ed (North Holland, Amesterdam) XXVIII, 271-359 (1990)

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

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

C. Hosinger and M. Rabbani, �??Data Embedding using Phase Dispersion, "The International Conference on Information Technology: Coding and Computing (ITCC 2000), Las Vegas, Nev. 27-29 March (2000).

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Figures (14)

Fig. 1.
Fig. 1.

Phase shifting interferometer

Fig. 2.
Fig. 2.

Block diagram of the proposed system (a) Transmitter (b) Receiver

Fig. 3.
Fig. 3.

3D object reconstructed at different distances from the output plane

Fig. 4.
Fig. 4.

The original host and hidden 3D objects.

Fig. 5.
Fig. 5.

(a) The autocorrelation for the watermarked hologram without using the second double phase encoding process. (b) The autocorrelation for the watermarked hologram when using the second double phase encoding process.

Fig. 6.
Fig. 6.

The Reconstructed 3D objects from the double phase encoded watermarked hologram without distortions (a) the 3D host object(b) The 3D hidden object

Fig. 7.
Fig. 7.

The reconstructed 3D host object using uniform quantization (a) 8 bits (b) 2 bits

Fig. 8.
Fig. 8.

The reconstructed 3D hidden object using uniform quantization (a) 8 bits (b) 2 bits

Fig. 9.
Fig. 9.

The reconstructed 3D objects using different portions of the digital holograms using quantized watermarked hologram. (a,b) 1/16 of the hologram area and 8 bits quantization (c,d) 1/4 of the hologram area and 4 bits quantization (e,f) 1/2 of the hologram area and 2 bits quantization

Fig. 10.
Fig. 10.

(a) The transmitted hologram having 50% occlusion and 4 bits quantization (b) The transmitted hologram having 75% occlusion and 4 bits quantization (c) The reconstructed 3D host object using the hologram in a (d) The reconstructed 3D hidden object using the hologram in a (e) The reconstructed 3D host object using the hologram in b (f) The reconstructed 3D hidden object using the hologram in b.

Fig. 11.
Fig. 11.

The effect of number of quantization levels and occluding parts of the transmitted double phase encoded watermarked hologram when using a uniform quantizer

Fig. 12.
Fig. 12.

The reconstructed 3D objects using an optimum quantizer with 4 bits quantization and 25% of the holograms (a) host object (b) hidden object

Fig. 13.
Fig. 13.

The error when using an optimum quantizer compared to the error when using a uniform quantizer, 25% of the hologram is used.

Fig. 14.
Fig. 14.

Effect of blind decoding on the hidden object (a) only the hidden object spatial domain phase code is unknown. (b) only the hidden object Fourier domain phase code is unknown.

Tables (2)

Tables Icon

Table 1. error when using a uniform quantizer

Tables Icon

Table 2. Error when using only 25% of the hologram and a uniform quantizer

Equations (48)

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D ( x , y ) = A ( x , y ) exp ( j ϕ ( x , y ) )
R ( x , y ; α ) = A R exp j ( ϕ R + α )
I ( x , y ; α ) = A 2 ( x , y ) + A R 2 + 2 A ( x , y ) A R cos [ ϕ ( x , y ) ϕ R α ] .
ϕ O ( x , y ) = arctan [ I 4 ( x , y ) I 2 ( x , y ) I 1 ( x , y ) I 3 ( x , y ) ] ,
A O ( x , y ) = 1 4 { [ I 1 ( x , y ) I 3 ( x , y ) ] 2 + [ I 2 ( x , y ) I 4 ( x , y ) ] 2 } 1 2
H O ( x , y ) = A O ( x , y ) exp [ j ϕ O ( x , y ) ]
H d ( x , y ) = { H ( x , y ) ψ 1 ( x , y ) } IFT [ ψ 2 ( ξ , γ ) ]
σ 2 = 1 N . M y = 0 M 1 x = 0 N 1 H ( x , y ) H * ( x , y )
H w ( x , y ) = { [ H host ( x , y ) + α [ H hidden ( x , y ) ψ 1 ( x , y ) ψ 2 ( x , y ) ] ] ψ 1 ( x , y ) } ψ 2 ( x , y )
σ w 2 = 1 2 . N . M y = 0 M 1 x = 0 N 1 H hidden ( x , y ) H hidden * ( x , y )
H ˜ hidden ( x , y ) = α H hidden ( x , y ) + IFT { H ̂ host ( ξ , γ ) ψ * 2 ( ξ , γ ) } ψ * 1 ( x , y )
σ w 2 = 1 N . M y = 0 M 1 x = 0 N 1 H host ( x , y ) H host * ( x , y )
O ˜ d ( u , v ; d 1 ) = exp [ j π λ d 1 ( Δ u 2 u 2 + Δ v 2 v 2 ) ] x = 0 N 1 y = 0 M 1 { H ˜ hidden ( x , y )
exp [ j π λ d 1 ( Δ x 2 x + Δ y 2 y ) ] exp [ j 2 π ( x u N + y v M ) ] }
Δ u = λ d 1 N Δ x , and
Δ v = λ d 1 M Δ y
O ˜ d ( u , v ; d 1 ) = α O d ( u , v ; d 1 ) + exp [ j π λ d 1 ( Δ u 2 u 2 + Δ v 2 v 2 ) ] .
x = 0 N 1 y = 0 M 1 { ( IFT { H ˜ host ( ξ , γ ) ψ * 2 ( ξ , γ ) } ψ 1 * ( x , y ) )
exp [ j π λ d 1 ( Δ x 2 x + Δ y 2 y ) ] exp [ j 2 π ( x u N + y v M ) ] }
O ˜ h ( u , v ; d 2 ) = O h ( u , v ; d 2 ) + exp [ j π λ d 2 ( Δ u 2 u 2 + Δ v 2 v 2 ) ]
x = 0 N 1 = 01 M 1 { α [ H hidden ( x , y ) ψ * 1 ( x , y ) ψ * 2 ( x , y ) ]
exp [ j π λ d 2 ( Δ x 2 x + Δ y 2 y ) ] exp [ j 2 π ( x u N + y v M ) ] }
σ host 2 = α 2 N . M y = 0 M 1 x = 0 N 1 H hidden ( x , y ) H hidden * ( x , y )
H ˜ w ( x , y ) = H w ( x , y ) + Δ H w ( x , y )
O ˜ d ( u , v ; d 1 ) = α O d ( u , v ; d 1 ) + exp [ λ d 1 ( Δ u 2 u 2 + Δ v 2 v 2 ) ] .
{ x = 0 N 1 y = 0 M 1 ( IFT { H ˜ host ( ξ , γ ) ψ 2 * ( ξ , γ ) } ψ 1 * ( x , y ) ) .
exp [ j π λ d 1 ( Δ x 2 x + Δ y 2 y ) ] exp [ j 2 π ( x u N + y v M ) ] +
x = 0 N 1 y = 0 M 1 Δ H w ( x , y ) exp [ j π λ d ( Δ x 2 x + Δ y 2 y ) ] exp [ j 2 π ( x u N + y v M ) ] } .
O ˜ d ( u , v ; d 2 ) = O d ( u , v ; d 2 ) + exp [ j π λ d 2 ( Δ u 2 u 2 + Δ v 2 v 2 ) ] .
{ u = 0 N 1 v = 0 M 1 α [ H hidden ( x , y ) ψ 1 ( x , y ) ψ 2 ( x , y ) ] .
exp [ j π λ d 2 ( Δ x 2 x + Δ y 2 y ) ] exp [ j 2 π ( x u N + y v M ) ] +
x = 0 N 1 y = 0 M 1 Δ H w ( x , y ) exp [ λ d 2 ( Δ x 2 x + Δ y 2 y ) ] exp [ j 2 π ( x u N + y v M ) ] }
σ host 2 = α 2 N . M y = 0 M 1 x = 0 N 1 H hidden ( x , y ) H hidden * ( x , y ) + Δ 2 12
σ w 2 = 1 N . M y = 0 M 1 x = 0 N 1 H host ( x , y ) H host * ( x , y ) + Δ 2 12
H w o ( x , y ) = H w ( x , y ) ( 1 W ( x , y ) ) = H w ( x , y ) H w ( x , y ) W ( x , y )
O d ( u , v ; d ) = exp [ j 2 π λ ( z d ) ] λ ( z d ) exp [ j π λ ( z d ) ( u 2 + v 2 ) ] ·
O ( x , y , z ) exp [ j π λ ( z d ) ( x 2 + y 2 ) ]
exp [ j 2 π λ ( z d ) ( x u + y v ) ] dx dy dz
error = 1 P p = 1 P 1 N × M y = 0 M 1 x = 0 N 1 [ O d ( u , v ; d ( p ) ) O ( u , v ; d ( p ) ) ] 2 O ( u , v ; d ( p ) )
X ( u ) exp [ j π λ d ( Δ u 2 u 2 ) ] · x = 0 N 1 ( IFT { H ̂ host ( ξ ) ψ 2 ( ξ ) } ψ 1 ( x ) ) exp [ j π λ d ( Δ x 2 x ) ] exp [ j 2 π ( x u N ) ] .
R x ( u , u ) = E X * ( u ) X ( u )
R x ( u , u ) = E [ exp [ j π λ d ( Δ u 2 u 2 ) ] x = 0 N 1 ξ = 0 N 1 1 N H ̂ host * ( ξ ) ψ 2 * ( ξ ) ψ 1 * ( x ) exp [ j π λ d ( Δ x 2 x ) ] exp [ j 2 π ( x u N ) ] . exp [ j π λ d ( Δ u 2 u 2 ) ] x = 0 N 1 ξ = 0 N 1 1 N H ̂ host ( ξ ) ψ 2 ( ξ ) ψ 1 ( x ) exp [ j π λ d ( Δ x 2 x ) ] exp [ j 2 π ( x u N ) ] ]
R x ( u , u ) = 1 N 2 E [ exp [ j π λ d Δ u 2 ( u 2 u 2 ) ] x = 0 N 1 x = 0 N 1 ξ = 0 N 1 ξ N 1 H * ( ζ ) H ( ξ ) ψ 2 ( ξ ) ψ 2 ( ξ ' ) ψ 1 ( x ) ψ 1 ( x ) exp [ j π λ d Δ x 2 ( x x ) ] exp [ j 2 π ( x u N x u N ) ] ]
R x ( u , u ) = 1 N 2 exp [ j π λ d Δ u 2 ( u 2 u 2 ) ] x = 0 N 1 x = 0 N 1 ξ = 0 N 1 ξ N 1 H * ( ζ ) H ( ξ ) E n 2 [ ψ 2 ( ξ ) ψ 2 ( ξ ) ] E n 1 [ ψ 1 ( x ) ψ 12 ( x ) ]
exp [ j π λ d Δ x 2 ( x x ) ] exp [ j 2 π ( x u N x u N ) ]
R ( u , u ) = 1 N 2 exp [ j π λ d Δ u 2 ( u 2 u 2 ) ] x = 0 N 1 ζ = 0 N 1 H ( ξ ) 2 exp [ j 2 π x ( u N u N ) ] .
R ( u , u ) = 1 N exp [ j π λ d Δ u 2 ( u 2 u 2 ) ξ = 0 N 1 H ( ξ ) 2 δ ( u u ) ]
R ( u , u ) = 1 N ξ = 0 N 1 H ( ξ ) 2 δ ( u u )

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