Abstract

A novel single-channel color-image watermarking with digital-optics means based on phase-shifting interferometry (PSI) and a neighboring pixel value subtraction algorithm in the discrete-cosine-transform (DCT) domain is proposed. The converted two-dimensional indexed image matrix from an original color image is encrypted to four interferograms by a PSI and double random-phase encoding technique. Then the interferograms are embedded in one chosen channel of an enlarged color host image in the DCT domain. The hidden color image can be retrieved by DCT, the improved neighboring pixel value subtraction algorithm, an inverse encryption process, and color image format conversion. The feasibility of this method and its robustness against some types of distortion and attacks from the superposed image with different weighting factors are verified and analyzed by computer simulations. This approach can avoid the cross-talk noise due to direct information superposition, enhance the imperceptibility of hidden data, and improve the efficiency of data transmission.

© 2007 Optical Society of America

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References

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  1. P. Refrégier and B. Javidi, "Optical image encryption based on input plane and Fourier plane random encoding," Opt. Lett. 20, 767-769 (1995).
    [CrossRef] [PubMed]
  2. B. Javidi, Optical and Digital Techniques for Information Security (Springer, 2005).
    [CrossRef]
  3. S. Kishk and B. Javidi, "Information hiding technique with double phase encoding," Appl. Opt. 41, 5462-5470 (2003).
    [CrossRef]
  4. N. Takai and Y. Mifune, "Digital watermarking by a holographic technique," Appl. Opt. 41, 865-873 (2002).
    [CrossRef] [PubMed]
  5. O. Matoba and B. Javidi, "Encrypted optical memory system using three-dimensional keys in the Fresnel domain," Opt. Lett. 24, 762-764 (1999).
    [CrossRef]
  6. T. Nomura, S. Mikan, Y. Morimoto, and B. Javidi, "Secure optical data storage with random phase key codes by use of a configuration of a joint transform correlator," Appl. Opt. 42, 1508-1514 (2003).
    [CrossRef] [PubMed]
  7. E. Tajahuerce and B. Javidi, "Encrypting three dimensional information with digital holography," Appl. Opt. 39, 6595-6601 (2000).
    [CrossRef]
  8. G. Unnikrishnan, J. Joseph, and K. Singh, "Optical encryption by double-random phase encoding in the fractional Fourier domain," Opt. Lett. 25, 887-889 (2000).
    [CrossRef]
  9. B. Hennelly and J. T. Sheridan, "Optical image encryption by random shifting in fractional Fourier domains," Opt. Lett. 28, 269-271 (2003).
    [CrossRef] [PubMed]
  10. H. Kim, D. H. Kim, and Y. H. Lee, "Encryption of digital hologram of 3-D object by virtual optics," Opt. Express 12, 4912-4921 (2004).
    [CrossRef] [PubMed]
  11. L. Z. Cai, M. Z. He, Q. Liu, and X. L. Yang, "Digital image encryption and watermarking by phase-shifting interferometry," Appl. Opt. 43, 3078-3084 (2004).
    [CrossRef] [PubMed]
  12. G. Situ and J. Zhang, "Image hiding with computer-generated phase codes for optical authentication," Opt. Commun. 245, 55-65 (2005).
    [CrossRef]
  13. H. T. Chang and C. L. Tsan, "Image watermarking by use of digital holography embedded in the discrete-cosine-transform domain," Appl. Opt. 44, 6211-6219 (2005).
    [CrossRef] [PubMed]
  14. X. Zhou and J. G. Chen, "Information hiding based on double-random phase encoding technology," J. Mod. Opt. 53, 1777-1783 (2006).
    [CrossRef]
  15. L. Chen and D. Zhao, "Optical color image encryption by wavelength multiplexing and lensless Fresnel transform holograms," Opt. Express 14, 8552-8560 (2004).
    [CrossRef]
  16. S. Zhang and M. A. Karim, "Color image encryption using double random phase encoding," Microwave Opt. Technol. Lett. 21, 318-323 (1999).
    [CrossRef]
  17. J. Nicolas, C. Lemmi, J. Compos, and M. J. Yzuel, "Optical encoding of color three-dimensional correlation," Opt. Commun. 209, 35-43 (2002).
    [CrossRef]
  18. X. F. Meng, L. Z. Cai, X. F. Xu, X. L. Yang, X. X. Shen, G. Y. Dong, and Y. R. Wang, "Two-step phase-shifting interferometry and its application in image encryption," Opt. Lett. 31, 1414-1416 (2006).
    [CrossRef] [PubMed]
  19. L. Z. Cai, Q. Liu, and X. L. Yang, "Phase-shift extraction and wave-front reconstruction in phase-shifting interferometry with arbitrary phase steps," Opt. Lett. 28, 1808-1810 (2003).
    [CrossRef] [PubMed]
  20. X. F. Meng, L. Z. Cai, X. L. Yang, X. X. Shen, and G. Y. Dong, "Information security system by iterative multiple-phase retrieval and pixel random permutation," Appl. Opt. 45, 3289-3297 (2006).
    [CrossRef] [PubMed]
  21. M. Z. He, L. Z. Cai, Q. Liu, and X. L. Yang, "Phase-only encryption and watermarking based on phase-shifting interferometry," Appl. Opt. 44, 2600-2606 (2005).
    [CrossRef] [PubMed]
  22. Y. Shi, G. Situ, and J. Zhang, "Optical image hiding in the Fresnel domain," J. Opt. A: Pure Appl. Opt. 8, 569-577 (2006).
    [CrossRef]

2006 (4)

2005 (3)

2004 (3)

2003 (4)

2002 (2)

N. Takai and Y. Mifune, "Digital watermarking by a holographic technique," Appl. Opt. 41, 865-873 (2002).
[CrossRef] [PubMed]

J. Nicolas, C. Lemmi, J. Compos, and M. J. Yzuel, "Optical encoding of color three-dimensional correlation," Opt. Commun. 209, 35-43 (2002).
[CrossRef]

2000 (2)

1999 (2)

O. Matoba and B. Javidi, "Encrypted optical memory system using three-dimensional keys in the Fresnel domain," Opt. Lett. 24, 762-764 (1999).
[CrossRef]

S. Zhang and M. A. Karim, "Color image encryption using double random phase encoding," Microwave Opt. Technol. Lett. 21, 318-323 (1999).
[CrossRef]

1995 (1)

Appl. Opt. (8)

J. Mod. Opt. (1)

X. Zhou and J. G. Chen, "Information hiding based on double-random phase encoding technology," J. Mod. Opt. 53, 1777-1783 (2006).
[CrossRef]

J. Opt. A: Pure Appl. Opt. (1)

Y. Shi, G. Situ, and J. Zhang, "Optical image hiding in the Fresnel domain," J. Opt. A: Pure Appl. Opt. 8, 569-577 (2006).
[CrossRef]

Microwave Opt. Technol. Lett. (1)

S. Zhang and M. A. Karim, "Color image encryption using double random phase encoding," Microwave Opt. Technol. Lett. 21, 318-323 (1999).
[CrossRef]

Opt. Commun. (2)

J. Nicolas, C. Lemmi, J. Compos, and M. J. Yzuel, "Optical encoding of color three-dimensional correlation," Opt. Commun. 209, 35-43 (2002).
[CrossRef]

G. Situ and J. Zhang, "Image hiding with computer-generated phase codes for optical authentication," Opt. Commun. 245, 55-65 (2005).
[CrossRef]

Opt. Express (2)

Opt. Lett. (6)

Other (1)

B. Javidi, Optical and Digital Techniques for Information Security (Springer, 2005).
[CrossRef]

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Figures (11)

Fig. 1
Fig. 1

(Color online) Schematic diagram of the encryption process: M, color map; RPM, random phase mask.

Fig. 2
Fig. 2

(Color online) Schematic diagram of (a) watermark embedding process and (b) watermark extraction process, where wavefield reconstruction is achieved by an improved NPVS algorithm and decryption is the inverse encryption process.

Fig. 3
Fig. 3

(Color online) (a) Original RGB image “Lena” to be hidden; (b) Original host image “baboon”; (c) one of the random phase masks; and (d) one of the interferograms.

Fig. 4
Fig. 4

(Color online) (a) Enlarged host image; (b)–(d) superposed image with weighting factors of 0.01, 0.05, and 0.1, respectively.

Fig. 5
Fig. 5

(Color online) (a) Decrypted color image with all the correct keys; (b)–(d) retrieved images obtained from only the real part, imaginary part, and the phase information of the diffraction field, respectively.

Fig. 6
Fig. 6

(Color online) Superposed image with weighting factor 0.01 cut by (a) 25% occlusion and (b) 50% occlusion; (c) and (d) the retrieved images from (a) and (b), respectively.

Fig. 7
Fig. 7

(Color online) CCs versus different weighting factors when using the real part, the imaginary part, a phase map of the diffraction field, and occluded information of the superposed image, respectively.

Fig. 8
Fig. 8

(Color online) (a)–(c) Retrieved RGB images when the superposed images with weighting factor 0.01 are quantized to 16, 8, and 4 bits, respectively.

Fig. 9
Fig. 9

(Color online) Fitted curves of CCs versus weighting factors for different quantization levels of the superposed image.

Fig. 10
Fig. 10

(Color online) Retrieved RGB images when the superposed image with weighting factor 0.05 is distorted by (a) multiplicative speckle noise with zero mean and variance 0.01, (b) additive salt and pepper noise with 0.01 density, and (c) additive Gaussian white noise of zero mean and standard deviation 0.01, respectively.

Fig. 11
Fig. 11

(Color online) Fitted curves of CCs versus weighting factors of the superposed images with attacks due to multiplicative speckle noise, additive salt and pepper noise, and additive Gaussian white noise.

Tables (1)

Tables Icon

Table 1 Calculation Results of Correlation Coefficients for the Retrieved RGB Images in Figs. 5, 6, 8, and 10

Equations (25)

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U ( x , y ) = FR { ( FR { f ( x 0 , y 0 ) exp [ i 2 π p ( x 0 , y 0 ) ] ; λ , z 1 } ) × exp [ i 2 π q ( x t , y t ) ] ; λ , z 2 } ,
U ( x , y ) = 1 4 A r { [ I 1 ( x , y ) I 3 ( x , y ) ] + i [ I 2 ( x , y ) I 4 ( x , y ) ] } ,
h ( 2 m 1 , 2 n 1 ) = o ( m , n ) , h ( 2 m 1 , 2 n ) = o ( m , n ) ,
h ( 2 m , 2 n 1 ) = o ( m , n ) , h ( 2 m , 2 n ) = o ( m , n ) .
m , n = 1 , 2 , … ,  N .
B ( ξ , η ) = 2 L K γ ( ξ ) γ ( η ) u = 0 L 1 v = 0 K 1 A ( u , v ) × cos [ ( 2 u + 1 ) ξ π 2 L ] cos [ ( 2 v + 1 ) η π 2 K ] ,
A ( u , v ) = 2 L K ξ = 0 L 1 η = 0 K 1 γ ( ξ ) γ ( η ) B ( ξ , η ) × cos [ ( 2 u + 1 ) ξ π 2 L ] cos [ ( 2 v + 1 ) η π 2 K ] ,
γ ( ξ ) = { 1 2 for   ξ = 0 1 for   ξ = 1 , 2 , … ,  L 1 ,
γ ( η ) = { 1 2 for   η = 0 1 for   η = 1 , 2 , … ,  K 1 .
D g ( 2 m 1 , 2 n 1 ) = D g ( 2 m 1 , 2 n ) ,
D g ( 2 m , 2 n 1 ) = D g ( 2 m , 2 n ) ,
m , n = 1 , 2 , … ,  N .
D g ( 2 m 1 , 2 n 1 ) = D g ( 2 m 1 , 2 n 1 ) + w I 1 ( m , n ) ,
D g ( 2 m 1 , 2 n ) = D g ( 2 m 1 , 2 n ) + w I 3 ( m , n ) ,
D g ( 2 m , 2 n 1 ) = D g ( 2 m , 2 n 1 ) + w I 2 ( m , n ) ,
D g ( 2 m , 2 n ) = D g ( 2 m , 2 n ) + w I 4 ( m , n ) ,
I 13 ( m , n ) = D g ( 2 m 1 , 2 n 1 ) D g ( 2 m 1 , 2 n ) = D g ( 2 m 1 , 2 n 1 ) + w I 1 ( m , n ) D g ( 2 m 1 , 2 n ) w I 3 ( m , n ) .
I 13 ( m , n ) = w [ I 1 ( m , n ) I 3 ( m , n ) ] ,
I 24 ( m , n ) = D g ( 2 m , 2 n 1 ) D g ( 2 m , 2 n ) = w [ I 2 ( m , n ) I 4 ( m , n ) ] .
U ( x , y ) = w ( I 13 i I 24 ) = w { [ I 1 ( x , y ) I 3 ( x , y ) ] + i [ I 2 ( x , y ) I 4 ( x , y ) ] } .
f ( x 0 , y 0 ) = abs { IFR { ( IFR { U ( x , y ) ; λ ,   z 2 } ) × exp [ i 2 π q ( x , y ) ] ; λ ,   z 1 } × exp [ i 2 π p ( x 0 , y 0 ) ] }
CC = COV ( h , h r ) σ h σ h r ,
COV ( h , h r ) = E { [ h E ( h ) ] [ h r E ( h r ) ] } ,
P { h = h k } = p k , k = 1 , 2 , 3 . . . ,
E ( h ) = k = 1 h k p k .

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