Abstract

The optimum condition for watermarking the digital hologram of a 3-D host object is analyzed. It is shown in the experiment that the digital hologram watermarked with the optimum weighting factor produces the least errors in the reconstructed 3-D host object and the decoded watermark even in the presence of an occlusion attack.

© 2005 Optical Society of America

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References

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Appl. Opt.

IBM Syst. J.

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

IEEE T. Image Process.

G. C. Langelaar and R. L. Lagendijk, �??Optimal differential energy watermarking of DCT encoded images and video,�?? IEEE T. Image Process. 6, 148-158 (2001).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Commun.

X. Peng, L. Yu, and L. Cai, �??Digital watermarking in three-dimensional space with a virtual-optics imaging modality,�?? Opt. Commun. 226, 155-165 (2003).
[CrossRef]

L. Yu, X. Peng, and L. Cai, �??Parameterized multi-dimensional data encryption by digital optics,�?? Opt. Commun. 203, 67-77 (2002).
[CrossRef]

Opt. Express

Opt. Lett.

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Figures (7)

Fig. 1.
Fig. 1.

(a) Digital hologram of 3-D host object at CCD plane is optically obtained by phase-shifting digital holography and (b) the watermark to be hidden is encrypted on a computer by double-random phase encoding. FT Lenses represent Fourier transforming Lenses.

Fig. 2.
Fig. 2.

The digital hologram of the toy car: (a) real and (b) imaginary parts. (c) The reconstructed host object. The watermarked hologram: (d) real and (e) imaginary parts. (f) Original watermark.

Fig. 3.
Fig. 3.

Decoded watermarks and reconstructed host objects from the watermarked hologram. First column, w=0.2; second column, w=0.59(optimum); third column, w=1.0.

Fig. 4.
Fig. 4.

Decoded watermarks and reconstructed host objects from watermarked encrypted-hologram. First column, w=0.2; second column, w=0.75(optimum); third column, w=1.0.

Fig. 5.
Fig. 5.

Measured MSE versus weighting factor for (a) watermarked digital hologram and (b) watermarked encrypted-hologram.

Fig. 6.
Fig. 6.

Occlusion attack of 25%: (a) real and (b) imaginary parts of the watermarked hologram. Total occlusion of the imaginary part: (c) and (d). Decoded watermarks and reconstructed host objects: (e) and (f), 25% occlusion; (g) and (h), total occlusion of the imaginary part. w=0.59.

Fig. 7.
Fig. 7.

Total MSE versus weighting factor with no loss, 25% and 50% occlusion attacks. (a) Watermarked hologram. (b) Watermarked encrypted-hologram.

Equations (9)

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G ( x , y ) = F r T { g ( x o , y o ; z ) } z = d o ,
F ( x , y ) = IFT [ FT { f ( x 1 , y 1 ) exp [ j p ( x 1 , y 1 ) ] } exp [ j b ( u , v ) ] ] ,
H ( x , y ) = G ( x , y ) + w F ( x , y ) ,
g r ( x o , y o ; z = d o ) = I F r T [ H ( x , y ) ] z = d o = g ( x o , y o ; z = d o ) + w n f ( x o , y o ) ,
f d ( x 1 , y 1 ) = IFT { F T [ H ( x , y ) ] exp [ j b ( u , v ) ] } exp [ j p ( x 1 , y 1 ) ] = n g ( x 1 , y 1 ) + w f ( x 1 , y 1 ) ,
E ( w ) = 1 N x N y [ x o = 1 N x y o = 1 N y g ( x o , y o ; z = d o ) g r ( x o , y o ; z = d o ) 2 + x 1 = 1 N x y 1 = 1 N y [ f ( x 1 , y 1 ) f d ( x 1 , y 1 ) ] 2 ]
1 N x N y x = 1 N x y = 1 N y [ n f ( x , y ) 2 w 2 + ( 1 w ) 2 f 2 ( x , y ) + n g ( x , y ) 2 ] .
w opt = x = 1 N x y = 1 N y [ f 2 ( x , y ) ] x = 1 N x y = 1 N y [ f 2 ( x , y ) + n f ( x , y ) 2 ] .
G e ( x e , y e ) = F r T { G ( x , y ) exp [ j ϕ e ( x , y ) ] } z = d e .

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