Abstract

In this paper, a novel secure optimal image watermarking scheme using an encrypted gyrator transform computer generated hologram (CGH) in the contourlet domain is presented. A new encrypted CGH technique, which is based on the gyrator transform, the random phase mask, the three-step phase-shifting interferometry and the Fibonacci transform, has been proposed to produce a hologram of a watermark first. With the huge key space of the encrypted CGH, the security strength of the watermarking system is enhanced. To achieve better imperceptibility, an improved quantization embedding algorithm is proposed to embed the encrypted CGH into the low frequency sub-band of the contourlet-transformed host image. In order to obtain the highest possible robustness without losing the imperceptibility, particle swarm optimization algorithm is employed to search the optimal embedding parameter of the watermarking system. In comparison with other method, the proposed watermarking scheme offers better performances for both imperceptibility and robustness. Experimental results demonstrate that the proposed image watermarking is not only secure and invisible, but also robust against a variety of attacks.

© 2014 Optical Society of America

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  1. C. C. Lai, “An improved SVD-based watermarking scheme using human visual characteristics,” Opt. Commun. 284(4), 938–944 (2011).
    [CrossRef]
  2. L. D. Li, B. L. Guo, “Localized image watermarking in spatial domain resistant to geometric attacks,” Int. J. Electron. Commun. 63(2), 123–131 (2009).
    [CrossRef]
  3. A. Poljicak, L. Mandic, D. Agic, “Discrete Fourier transform–based watermarking method with an optimal implementation radius,” J. Electron. Imaging 20(3), 033008 (2011).
    [CrossRef]
  4. A. Phadikar, S. P. Maity, B. Verma, “Region based QIM digital watermarking scheme for image database in DCT domain,” Comput. Electr. Eng. 37(3), 339–355 (2011).
    [CrossRef]
  5. P. Surekha, S. Sumathi, “Implementation of genetic algorithm for a dwt based image watermarking scheme,” IJSC 2(1), 244–252 (2011).
  6. P. Meerwald, A. Uhl, “A survey of wavelet-domain watermarking algorithms,” Proc. SPIE 4314, 505–516 (2001).
    [CrossRef]
  7. B. C. Mohan, S. S. Kumar, “Robust Digital Watermarking Scheme using Contourlet Transform,” IJCSNS 8(2), 43–51 (2008).
  8. M. N. Do, M. Vetterli, “The contourlet transform: An efficient directional multiresolution image representation,” IEEE Trans. Image Process. 14(12), 2091–2106 (2005).
    [CrossRef] [PubMed]
  9. O. Fındık, İ. Babaoğlu, E. Ülker, “A color image watermarking scheme based on hybrid classification method: Particle swarm optimization and k-nearest neighbor algorithm,” Opt. Commun. 283(24), 4916–4922 (2010).
    [CrossRef]
  10. Y. del Valle, G. K. Venayagamoorthy, S. Mohagheghi, J.-C. Hernandez, R. G. Harley, “Particle Swarm Optimization: Basic Concepts, Variants and Applications in Power Systems,” IEEE Trans. Evol. Comput. 12(2), 171–195 (2008).
    [CrossRef]
  11. N. Takai, Y. Mifune, “Digital watermarking by a holographic technique,” Appl. Opt. 41(5), 865–873 (2002).
    [CrossRef] [PubMed]
  12. H. T. Chang, C. L. Tsan, “Image watermarking by use of digital holography embedded in the discrete-cosine-transform domain,” Appl. Opt. 44(29), 6211–6219 (2005).
    [CrossRef] [PubMed]
  13. S. Z. Wang, S. J. Huang, X. P. Zhang, W. Wu, “Hologram-based watermarking capable of surviving print-scan process,” Appl. Opt. 49(7), 1170–1178 (2010).
    [CrossRef] [PubMed]
  14. O. E. Okman, G. B. Akar, “Quantization index modulation-based image watermarking using digital holography,” J. Opt. Soc. Am. A 24(1), 243–252 (2007).
    [CrossRef] [PubMed]
  15. J. Z. Li, “Robust image watermarking scheme against geometric attacks using a computer-generated hologram,” Appl. Opt. 49(32), 6302–6312 (2010).
    [CrossRef] [PubMed]
  16. L. Z. Cai, M. Z. He, Q. Liu, X. L. Yang, “Digital image encryption and watermarking by phase-shifting interferometry,” Appl. Opt. 43(15), 3078–3084 (2004).
    [CrossRef] [PubMed]
  17. M. Z. He, L. Z. Cai, Q. Liu, X. L. Yang, “Phase-only encryption and watermarking based on phase-shifting interferometry,” Appl. Opt. 44(13), 2600–2606 (2005).
    [CrossRef] [PubMed]
  18. L. Z. Cai, Q. Liu, X. L. Yang, “Phase-shift extraction and wave-front reconstruction in phase-shifting interferometry with arbitrary phase steps,” Opt. Lett. 28(19), 1808–1810 (2003).
    [CrossRef] [PubMed]
  19. P. Refregier, B. Javidi, “Optical image encryption based on input plane and Fourier plane random encoding,” Opt. Lett. 20(7), 767–769 (1995).
    [CrossRef] [PubMed]
  20. N. Singh, A. Sinha, “Gyrator transform-based optical image encryption, using chaos,” Opt. Lasers Eng. 47(5), 539–546 (2009).
    [CrossRef]
  21. M. M. Sathik, S. S. Sujatha, “A novel DWT based invisible watermarking technique for digital images,” Int. Arab J. e-Technol. 2(3), 167–172 (2012).
  22. Z. J. Liu, D. Z. Chen, J. P. Ma, S. Y. Wei, Y. L. Zhang, J. M. Dai, S. T. Liu, “Fast algorithm of discrete gyrator transform based on convolution operation,” Optik (Stuttg.) 122(10), 864–867 (2011).
    [CrossRef]
  23. S. Zhang, D. Van Der Weide, J. Oliver, “Superfast phase-shifting method for 3-D shape measurement,” Opt. Express 18(9), 9684–9689 (2010).
    [CrossRef] [PubMed]
  24. J. Kennedy and R. Eberhart, “Particle swarm optimization,” in Proceedings of IEEE International Conference on Neural Networks (Institute of Electrical and Electronics Engineers, New York, 1995), pp. 1942–1948.
    [CrossRef]
  25. M. Pluhacek, R. Senkerik, I. Zelinka, and D. Davendra, “Multiple choice strategy for PSO algorithm - performance analysis on shifted test functions,” in Proceedings of European Council for Modeling and Simulation,W. Rekdalsbakken, R. T. Bye and H. Zhang, ed. (Academic, Aalesund, Norway, 2013), pp. 393–397.
  26. Z. L. Yu and G. F. Jin, Computer-Generated Hologram (Tsinghua University Press, Beijing, 1984), Chap. 4.
  27. M. A. Qureshi, A. Aziz, B. Ahmed, A. Khalid, H. Munir, “Comparative Analysis and Implementation of Efficient Digital Image Watermarking Schemes,” Int. J. Comp. Elec. Eng. 4(4), 558–561 (2012).
    [CrossRef]
  28. H. Elazhary, “A fast, blind, transparent, and robust image watermarking algorithm with extended torus automorphism permutation,” Int. J. Comp. Appl. 32(4), 34–41 (2011).
  29. T. H. Chen, G. Horng, S. H. Wang, “A robust wavelet-based watermarking scheme using quantization and human visual system Model,” Pakistan Journal of Information and Technology 2(3), 213–230 (2003).
    [CrossRef]
  30. H. H. Song, S. Y. Yu, X. K. Yang, L. Song, C. Wang, “Contourlet-based image adaptive watermarking,” Signal Process-Image. 23(3), 162–178 (2008).
    [CrossRef]

2012

M. M. Sathik, S. S. Sujatha, “A novel DWT based invisible watermarking technique for digital images,” Int. Arab J. e-Technol. 2(3), 167–172 (2012).

M. A. Qureshi, A. Aziz, B. Ahmed, A. Khalid, H. Munir, “Comparative Analysis and Implementation of Efficient Digital Image Watermarking Schemes,” Int. J. Comp. Elec. Eng. 4(4), 558–561 (2012).
[CrossRef]

2011

H. Elazhary, “A fast, blind, transparent, and robust image watermarking algorithm with extended torus automorphism permutation,” Int. J. Comp. Appl. 32(4), 34–41 (2011).

Z. J. Liu, D. Z. Chen, J. P. Ma, S. Y. Wei, Y. L. Zhang, J. M. Dai, S. T. Liu, “Fast algorithm of discrete gyrator transform based on convolution operation,” Optik (Stuttg.) 122(10), 864–867 (2011).
[CrossRef]

A. Poljicak, L. Mandic, D. Agic, “Discrete Fourier transform–based watermarking method with an optimal implementation radius,” J. Electron. Imaging 20(3), 033008 (2011).
[CrossRef]

A. Phadikar, S. P. Maity, B. Verma, “Region based QIM digital watermarking scheme for image database in DCT domain,” Comput. Electr. Eng. 37(3), 339–355 (2011).
[CrossRef]

P. Surekha, S. Sumathi, “Implementation of genetic algorithm for a dwt based image watermarking scheme,” IJSC 2(1), 244–252 (2011).

C. C. Lai, “An improved SVD-based watermarking scheme using human visual characteristics,” Opt. Commun. 284(4), 938–944 (2011).
[CrossRef]

2010

2009

N. Singh, A. Sinha, “Gyrator transform-based optical image encryption, using chaos,” Opt. Lasers Eng. 47(5), 539–546 (2009).
[CrossRef]

L. D. Li, B. L. Guo, “Localized image watermarking in spatial domain resistant to geometric attacks,” Int. J. Electron. Commun. 63(2), 123–131 (2009).
[CrossRef]

2008

B. C. Mohan, S. S. Kumar, “Robust Digital Watermarking Scheme using Contourlet Transform,” IJCSNS 8(2), 43–51 (2008).

Y. del Valle, G. K. Venayagamoorthy, S. Mohagheghi, J.-C. Hernandez, R. G. Harley, “Particle Swarm Optimization: Basic Concepts, Variants and Applications in Power Systems,” IEEE Trans. Evol. Comput. 12(2), 171–195 (2008).
[CrossRef]

H. H. Song, S. Y. Yu, X. K. Yang, L. Song, C. Wang, “Contourlet-based image adaptive watermarking,” Signal Process-Image. 23(3), 162–178 (2008).
[CrossRef]

2007

2005

2004

2003

L. Z. Cai, Q. Liu, X. L. Yang, “Phase-shift extraction and wave-front reconstruction in phase-shifting interferometry with arbitrary phase steps,” Opt. Lett. 28(19), 1808–1810 (2003).
[CrossRef] [PubMed]

T. H. Chen, G. Horng, S. H. Wang, “A robust wavelet-based watermarking scheme using quantization and human visual system Model,” Pakistan Journal of Information and Technology 2(3), 213–230 (2003).
[CrossRef]

2002

2001

P. Meerwald, A. Uhl, “A survey of wavelet-domain watermarking algorithms,” Proc. SPIE 4314, 505–516 (2001).
[CrossRef]

1995

Agic, D.

A. Poljicak, L. Mandic, D. Agic, “Discrete Fourier transform–based watermarking method with an optimal implementation radius,” J. Electron. Imaging 20(3), 033008 (2011).
[CrossRef]

Ahmed, B.

M. A. Qureshi, A. Aziz, B. Ahmed, A. Khalid, H. Munir, “Comparative Analysis and Implementation of Efficient Digital Image Watermarking Schemes,” Int. J. Comp. Elec. Eng. 4(4), 558–561 (2012).
[CrossRef]

Akar, G. B.

Aziz, A.

M. A. Qureshi, A. Aziz, B. Ahmed, A. Khalid, H. Munir, “Comparative Analysis and Implementation of Efficient Digital Image Watermarking Schemes,” Int. J. Comp. Elec. Eng. 4(4), 558–561 (2012).
[CrossRef]

Babaoglu, I.

O. Fındık, İ. Babaoğlu, E. Ülker, “A color image watermarking scheme based on hybrid classification method: Particle swarm optimization and k-nearest neighbor algorithm,” Opt. Commun. 283(24), 4916–4922 (2010).
[CrossRef]

Cai, L. Z.

Chang, H. T.

Chen, D. Z.

Z. J. Liu, D. Z. Chen, J. P. Ma, S. Y. Wei, Y. L. Zhang, J. M. Dai, S. T. Liu, “Fast algorithm of discrete gyrator transform based on convolution operation,” Optik (Stuttg.) 122(10), 864–867 (2011).
[CrossRef]

Chen, T. H.

T. H. Chen, G. Horng, S. H. Wang, “A robust wavelet-based watermarking scheme using quantization and human visual system Model,” Pakistan Journal of Information and Technology 2(3), 213–230 (2003).
[CrossRef]

Dai, J. M.

Z. J. Liu, D. Z. Chen, J. P. Ma, S. Y. Wei, Y. L. Zhang, J. M. Dai, S. T. Liu, “Fast algorithm of discrete gyrator transform based on convolution operation,” Optik (Stuttg.) 122(10), 864–867 (2011).
[CrossRef]

del Valle, Y.

Y. del Valle, G. K. Venayagamoorthy, S. Mohagheghi, J.-C. Hernandez, R. G. Harley, “Particle Swarm Optimization: Basic Concepts, Variants and Applications in Power Systems,” IEEE Trans. Evol. Comput. 12(2), 171–195 (2008).
[CrossRef]

Do, M. N.

M. N. Do, M. Vetterli, “The contourlet transform: An efficient directional multiresolution image representation,” IEEE Trans. Image Process. 14(12), 2091–2106 (2005).
[CrossRef] [PubMed]

Elazhary, H.

H. Elazhary, “A fast, blind, transparent, and robust image watermarking algorithm with extended torus automorphism permutation,” Int. J. Comp. Appl. 32(4), 34–41 (2011).

Findik, O.

O. Fındık, İ. Babaoğlu, E. Ülker, “A color image watermarking scheme based on hybrid classification method: Particle swarm optimization and k-nearest neighbor algorithm,” Opt. Commun. 283(24), 4916–4922 (2010).
[CrossRef]

Guo, B. L.

L. D. Li, B. L. Guo, “Localized image watermarking in spatial domain resistant to geometric attacks,” Int. J. Electron. Commun. 63(2), 123–131 (2009).
[CrossRef]

Harley, R. G.

Y. del Valle, G. K. Venayagamoorthy, S. Mohagheghi, J.-C. Hernandez, R. G. Harley, “Particle Swarm Optimization: Basic Concepts, Variants and Applications in Power Systems,” IEEE Trans. Evol. Comput. 12(2), 171–195 (2008).
[CrossRef]

He, M. Z.

Hernandez, J.-C.

Y. del Valle, G. K. Venayagamoorthy, S. Mohagheghi, J.-C. Hernandez, R. G. Harley, “Particle Swarm Optimization: Basic Concepts, Variants and Applications in Power Systems,” IEEE Trans. Evol. Comput. 12(2), 171–195 (2008).
[CrossRef]

Horng, G.

T. H. Chen, G. Horng, S. H. Wang, “A robust wavelet-based watermarking scheme using quantization and human visual system Model,” Pakistan Journal of Information and Technology 2(3), 213–230 (2003).
[CrossRef]

Huang, S. J.

Javidi, B.

Khalid, A.

M. A. Qureshi, A. Aziz, B. Ahmed, A. Khalid, H. Munir, “Comparative Analysis and Implementation of Efficient Digital Image Watermarking Schemes,” Int. J. Comp. Elec. Eng. 4(4), 558–561 (2012).
[CrossRef]

Kumar, S. S.

B. C. Mohan, S. S. Kumar, “Robust Digital Watermarking Scheme using Contourlet Transform,” IJCSNS 8(2), 43–51 (2008).

Lai, C. C.

C. C. Lai, “An improved SVD-based watermarking scheme using human visual characteristics,” Opt. Commun. 284(4), 938–944 (2011).
[CrossRef]

Li, J. Z.

Li, L. D.

L. D. Li, B. L. Guo, “Localized image watermarking in spatial domain resistant to geometric attacks,” Int. J. Electron. Commun. 63(2), 123–131 (2009).
[CrossRef]

Liu, Q.

Liu, S. T.

Z. J. Liu, D. Z. Chen, J. P. Ma, S. Y. Wei, Y. L. Zhang, J. M. Dai, S. T. Liu, “Fast algorithm of discrete gyrator transform based on convolution operation,” Optik (Stuttg.) 122(10), 864–867 (2011).
[CrossRef]

Liu, Z. J.

Z. J. Liu, D. Z. Chen, J. P. Ma, S. Y. Wei, Y. L. Zhang, J. M. Dai, S. T. Liu, “Fast algorithm of discrete gyrator transform based on convolution operation,” Optik (Stuttg.) 122(10), 864–867 (2011).
[CrossRef]

Ma, J. P.

Z. J. Liu, D. Z. Chen, J. P. Ma, S. Y. Wei, Y. L. Zhang, J. M. Dai, S. T. Liu, “Fast algorithm of discrete gyrator transform based on convolution operation,” Optik (Stuttg.) 122(10), 864–867 (2011).
[CrossRef]

Maity, S. P.

A. Phadikar, S. P. Maity, B. Verma, “Region based QIM digital watermarking scheme for image database in DCT domain,” Comput. Electr. Eng. 37(3), 339–355 (2011).
[CrossRef]

Mandic, L.

A. Poljicak, L. Mandic, D. Agic, “Discrete Fourier transform–based watermarking method with an optimal implementation radius,” J. Electron. Imaging 20(3), 033008 (2011).
[CrossRef]

Meerwald, P.

P. Meerwald, A. Uhl, “A survey of wavelet-domain watermarking algorithms,” Proc. SPIE 4314, 505–516 (2001).
[CrossRef]

Mifune, Y.

Mohagheghi, S.

Y. del Valle, G. K. Venayagamoorthy, S. Mohagheghi, J.-C. Hernandez, R. G. Harley, “Particle Swarm Optimization: Basic Concepts, Variants and Applications in Power Systems,” IEEE Trans. Evol. Comput. 12(2), 171–195 (2008).
[CrossRef]

Mohan, B. C.

B. C. Mohan, S. S. Kumar, “Robust Digital Watermarking Scheme using Contourlet Transform,” IJCSNS 8(2), 43–51 (2008).

Munir, H.

M. A. Qureshi, A. Aziz, B. Ahmed, A. Khalid, H. Munir, “Comparative Analysis and Implementation of Efficient Digital Image Watermarking Schemes,” Int. J. Comp. Elec. Eng. 4(4), 558–561 (2012).
[CrossRef]

Okman, O. E.

Oliver, J.

Phadikar, A.

A. Phadikar, S. P. Maity, B. Verma, “Region based QIM digital watermarking scheme for image database in DCT domain,” Comput. Electr. Eng. 37(3), 339–355 (2011).
[CrossRef]

Poljicak, A.

A. Poljicak, L. Mandic, D. Agic, “Discrete Fourier transform–based watermarking method with an optimal implementation radius,” J. Electron. Imaging 20(3), 033008 (2011).
[CrossRef]

Qureshi, M. A.

M. A. Qureshi, A. Aziz, B. Ahmed, A. Khalid, H. Munir, “Comparative Analysis and Implementation of Efficient Digital Image Watermarking Schemes,” Int. J. Comp. Elec. Eng. 4(4), 558–561 (2012).
[CrossRef]

Refregier, P.

Sathik, M. M.

M. M. Sathik, S. S. Sujatha, “A novel DWT based invisible watermarking technique for digital images,” Int. Arab J. e-Technol. 2(3), 167–172 (2012).

Singh, N.

N. Singh, A. Sinha, “Gyrator transform-based optical image encryption, using chaos,” Opt. Lasers Eng. 47(5), 539–546 (2009).
[CrossRef]

Sinha, A.

N. Singh, A. Sinha, “Gyrator transform-based optical image encryption, using chaos,” Opt. Lasers Eng. 47(5), 539–546 (2009).
[CrossRef]

Song, H. H.

H. H. Song, S. Y. Yu, X. K. Yang, L. Song, C. Wang, “Contourlet-based image adaptive watermarking,” Signal Process-Image. 23(3), 162–178 (2008).
[CrossRef]

Song, L.

H. H. Song, S. Y. Yu, X. K. Yang, L. Song, C. Wang, “Contourlet-based image adaptive watermarking,” Signal Process-Image. 23(3), 162–178 (2008).
[CrossRef]

Sujatha, S. S.

M. M. Sathik, S. S. Sujatha, “A novel DWT based invisible watermarking technique for digital images,” Int. Arab J. e-Technol. 2(3), 167–172 (2012).

Sumathi, S.

P. Surekha, S. Sumathi, “Implementation of genetic algorithm for a dwt based image watermarking scheme,” IJSC 2(1), 244–252 (2011).

Surekha, P.

P. Surekha, S. Sumathi, “Implementation of genetic algorithm for a dwt based image watermarking scheme,” IJSC 2(1), 244–252 (2011).

Takai, N.

Tsan, C. L.

Uhl, A.

P. Meerwald, A. Uhl, “A survey of wavelet-domain watermarking algorithms,” Proc. SPIE 4314, 505–516 (2001).
[CrossRef]

Ülker, E.

O. Fındık, İ. Babaoğlu, E. Ülker, “A color image watermarking scheme based on hybrid classification method: Particle swarm optimization and k-nearest neighbor algorithm,” Opt. Commun. 283(24), 4916–4922 (2010).
[CrossRef]

Van Der Weide, D.

Venayagamoorthy, G. K.

Y. del Valle, G. K. Venayagamoorthy, S. Mohagheghi, J.-C. Hernandez, R. G. Harley, “Particle Swarm Optimization: Basic Concepts, Variants and Applications in Power Systems,” IEEE Trans. Evol. Comput. 12(2), 171–195 (2008).
[CrossRef]

Verma, B.

A. Phadikar, S. P. Maity, B. Verma, “Region based QIM digital watermarking scheme for image database in DCT domain,” Comput. Electr. Eng. 37(3), 339–355 (2011).
[CrossRef]

Vetterli, M.

M. N. Do, M. Vetterli, “The contourlet transform: An efficient directional multiresolution image representation,” IEEE Trans. Image Process. 14(12), 2091–2106 (2005).
[CrossRef] [PubMed]

Wang, C.

H. H. Song, S. Y. Yu, X. K. Yang, L. Song, C. Wang, “Contourlet-based image adaptive watermarking,” Signal Process-Image. 23(3), 162–178 (2008).
[CrossRef]

Wang, S. H.

T. H. Chen, G. Horng, S. H. Wang, “A robust wavelet-based watermarking scheme using quantization and human visual system Model,” Pakistan Journal of Information and Technology 2(3), 213–230 (2003).
[CrossRef]

Wang, S. Z.

Wei, S. Y.

Z. J. Liu, D. Z. Chen, J. P. Ma, S. Y. Wei, Y. L. Zhang, J. M. Dai, S. T. Liu, “Fast algorithm of discrete gyrator transform based on convolution operation,” Optik (Stuttg.) 122(10), 864–867 (2011).
[CrossRef]

Wu, W.

Yang, X. K.

H. H. Song, S. Y. Yu, X. K. Yang, L. Song, C. Wang, “Contourlet-based image adaptive watermarking,” Signal Process-Image. 23(3), 162–178 (2008).
[CrossRef]

Yang, X. L.

Yu, S. Y.

H. H. Song, S. Y. Yu, X. K. Yang, L. Song, C. Wang, “Contourlet-based image adaptive watermarking,” Signal Process-Image. 23(3), 162–178 (2008).
[CrossRef]

Zhang, S.

Zhang, X. P.

Zhang, Y. L.

Z. J. Liu, D. Z. Chen, J. P. Ma, S. Y. Wei, Y. L. Zhang, J. M. Dai, S. T. Liu, “Fast algorithm of discrete gyrator transform based on convolution operation,” Optik (Stuttg.) 122(10), 864–867 (2011).
[CrossRef]

Appl. Opt.

Comput. Electr. Eng.

A. Phadikar, S. P. Maity, B. Verma, “Region based QIM digital watermarking scheme for image database in DCT domain,” Comput. Electr. Eng. 37(3), 339–355 (2011).
[CrossRef]

IEEE Trans. Evol. Comput.

Y. del Valle, G. K. Venayagamoorthy, S. Mohagheghi, J.-C. Hernandez, R. G. Harley, “Particle Swarm Optimization: Basic Concepts, Variants and Applications in Power Systems,” IEEE Trans. Evol. Comput. 12(2), 171–195 (2008).
[CrossRef]

IEEE Trans. Image Process.

M. N. Do, M. Vetterli, “The contourlet transform: An efficient directional multiresolution image representation,” IEEE Trans. Image Process. 14(12), 2091–2106 (2005).
[CrossRef] [PubMed]

IJCSNS

B. C. Mohan, S. S. Kumar, “Robust Digital Watermarking Scheme using Contourlet Transform,” IJCSNS 8(2), 43–51 (2008).

IJSC

P. Surekha, S. Sumathi, “Implementation of genetic algorithm for a dwt based image watermarking scheme,” IJSC 2(1), 244–252 (2011).

Int. Arab J. e-Technol.

M. M. Sathik, S. S. Sujatha, “A novel DWT based invisible watermarking technique for digital images,” Int. Arab J. e-Technol. 2(3), 167–172 (2012).

Int. J. Comp. Appl.

H. Elazhary, “A fast, blind, transparent, and robust image watermarking algorithm with extended torus automorphism permutation,” Int. J. Comp. Appl. 32(4), 34–41 (2011).

Int. J. Comp. Elec. Eng.

M. A. Qureshi, A. Aziz, B. Ahmed, A. Khalid, H. Munir, “Comparative Analysis and Implementation of Efficient Digital Image Watermarking Schemes,” Int. J. Comp. Elec. Eng. 4(4), 558–561 (2012).
[CrossRef]

Int. J. Electron. Commun.

L. D. Li, B. L. Guo, “Localized image watermarking in spatial domain resistant to geometric attacks,” Int. J. Electron. Commun. 63(2), 123–131 (2009).
[CrossRef]

J. Electron. Imaging

A. Poljicak, L. Mandic, D. Agic, “Discrete Fourier transform–based watermarking method with an optimal implementation radius,” J. Electron. Imaging 20(3), 033008 (2011).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Commun.

C. C. Lai, “An improved SVD-based watermarking scheme using human visual characteristics,” Opt. Commun. 284(4), 938–944 (2011).
[CrossRef]

O. Fındık, İ. Babaoğlu, E. Ülker, “A color image watermarking scheme based on hybrid classification method: Particle swarm optimization and k-nearest neighbor algorithm,” Opt. Commun. 283(24), 4916–4922 (2010).
[CrossRef]

Opt. Express

Opt. Lasers Eng.

N. Singh, A. Sinha, “Gyrator transform-based optical image encryption, using chaos,” Opt. Lasers Eng. 47(5), 539–546 (2009).
[CrossRef]

Opt. Lett.

Optik (Stuttg.)

Z. J. Liu, D. Z. Chen, J. P. Ma, S. Y. Wei, Y. L. Zhang, J. M. Dai, S. T. Liu, “Fast algorithm of discrete gyrator transform based on convolution operation,” Optik (Stuttg.) 122(10), 864–867 (2011).
[CrossRef]

Pakistan Journal of Information and Technology

T. H. Chen, G. Horng, S. H. Wang, “A robust wavelet-based watermarking scheme using quantization and human visual system Model,” Pakistan Journal of Information and Technology 2(3), 213–230 (2003).
[CrossRef]

Proc. SPIE

P. Meerwald, A. Uhl, “A survey of wavelet-domain watermarking algorithms,” Proc. SPIE 4314, 505–516 (2001).
[CrossRef]

Signal Process-Image.

H. H. Song, S. Y. Yu, X. K. Yang, L. Song, C. Wang, “Contourlet-based image adaptive watermarking,” Signal Process-Image. 23(3), 162–178 (2008).
[CrossRef]

Other

J. Kennedy and R. Eberhart, “Particle swarm optimization,” in Proceedings of IEEE International Conference on Neural Networks (Institute of Electrical and Electronics Engineers, New York, 1995), pp. 1942–1948.
[CrossRef]

M. Pluhacek, R. Senkerik, I. Zelinka, and D. Davendra, “Multiple choice strategy for PSO algorithm - performance analysis on shifted test functions,” in Proceedings of European Council for Modeling and Simulation,W. Rekdalsbakken, R. T. Bye and H. Zhang, ed. (Academic, Aalesund, Norway, 2013), pp. 393–397.

Z. L. Yu and G. F. Jin, Computer-Generated Hologram (Tsinghua University Press, Beijing, 1984), Chap. 4.

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Figures (9)

Fig. 1
Fig. 1

The diagram of the generation and reconstruction processes of the encrypted hologram. (a) The generation procedure for the encrypted CGH. (b) The reconstruction procedure for the encrypted CGH.

Fig. 2
Fig. 2

PSO based optimization process of watermarking.

Fig. 3
Fig. 3

A sample watermark generated by computer. (a) image “STU” of size 32 × 64; (b), (c), (d) interferograms I1, I2 and I3, respectively. (e), (f) the amplitude and the normalized phase of the gyrator transform hologram. (g) reconstruction of the hologram with all correct keys.

Fig. 4
Fig. 4

The host images and watermark. (a) Gold hill. (b) Elaine. (c) Butterfly. (d) Scenic. (e) the watermark signal consisted of the amplitude and the phase of the encrypted hologram.

Fig. 5
Fig. 5

The PSO convergence history for the proposed method. The green line, the pink line, the blue line and the red line are the convergence curves for Goldhill, Elaine, Butterfly and Scienic, respectively.

Fig. 6
Fig. 6

The watermarked images and the corresponding reconstructions of the extracted mark holograms without any attacks. (a) The watermarked “Gold hill”(PSNR = 41.284). (b) reconstructed watermark of (a). (c) the watermarked “Elaine” (PSNR = 42.225). (d) reconstructed watermark of (c). (e) the watermarked “Butterfly” (PSNR = 40.456). (f) reconstructed watermark of (e). (g) the watermarked “Scenic” (PSNR = 42.481). (h) reconstructed watermark of (g).

Fig. 7
Fig. 7

The attacked watermarked images. (a) Gaussian low-pass filtering (PSNR = 26.28). (b) median filtering (PSNR = 28.34). (c) average filtering (PSNR = 30.47). (d) Gaussian noise (PSNR = 29.56). (e) salt & pepper noise (PSNR = 27.64). (f) JPEG (PSNR = 32.24). (g) JPEG2000 (PSNR = 34.88). (h) cropping (PSNR = 11.69). (i) unsharp (PSNR = 26.33). (j) horizontal motion (PSNR = 28.07). (k) circular average (PSNR = 24.63). (l) brighten (PSNR = 19.83). (m) darken (PSNR = 18.06). (n) rescaling (PSNR = 26.26). (o) painting (PSNR = 17.84).

Fig. 8
Fig. 8

The corresponding reconstructions of the holograms extracted from the distorted watermarked images in Fig. 7. (a) Gaussian low-pass filtering. (b) median filtering. (c) average filtering. (d) Gaussian noise. (e) salt & pepper noise. (f) JPEG. (g) JPEG2000. (h) cropping. (i) unsharp. (j) horizontal motion. (k) circular average. (l) brighten. (m) darken. (n) rescaling. (o)painting.

Fig. 9
Fig. 9

The reconstructions of the watermarks which were extracted from watermarked Goldhill. (a) reconstructed image with correct q(x1,y1), α1 and α2 and with D = D + 1; (b) reconstructed image with correct D, α1 and α2 when RPM R2 is not used; (c) reconstructed image with correct D, α1 and α2 when q(x1,y1) is shifted transversely by one pixel; (c) reconstructed image with correct D, q(x1,y1) and α2 when α1 has a relative error of 1.4%; (d) reconstructed image with correct D, q(x1,y1) and α1 when α2 has a relative error of 0.8%; (e) reconstructed image with correct D and q(x1,y1) when α1 and α2 both have relative errors of 0.6%.

Tables (2)

Tables Icon

Table 1 PSNR Values of Watermarks Extracting without Any Attacks Comparing between Proposed Method and Scheme in [15]

Tables Icon

Table 2 NCC Values of Watermarks Extracting under Attacks Comparing between Proposed Method and Scheme in [15]

Equations (29)

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G α (u,v)=G T α [f(x,y)]= f(x,y) |sinα| exp[i2π (xy+uv)cosαxvyu sinα ]dxdy,
I k (x,y) = A 2 (x,y)+2A(x,y) A r cos[φ(x,y) δ k ]+ A r 2 .
U(x,y) =[( I 1 I 3 )+i(2 I 2 I 1 I 3 )]/(4 A r ).
B m,n ' = B m,n /Δ Δ+λΔ w m,n ,
w m,n ' =( B m,n ' B m,n ' /Δ Δ)/(λΔ).
B m,n ' = B m,n ρ+λΔ w m,n .
w m,n ' =(X' X'/Δ Δ)/(λΔ)=( ( B m,n Δ)/Δ Δ+λΔ w m,n ( ( B m,n Δ)/Δ Δ+λΔ w m,n )/Δ Δ)/(λΔ) =( B m,n /Δ Δ+λΔ w m,n ( B m,n /Δ Δ+λΔ w m,n )/Δ Δ)/(λΔ)=( B m,n ' B m,n ' /Δ Δ)/(λΔ).
| B m,n X ' |=| B m,n ( X/Δ Δ+λΔ w m,n )|=| B m,n ( ( B m,n Δ)/Δ Δ+λΔ w m,n )| =| B m,n ( B m,n /Δ ΔΔ+λΔ w m,n )|=|Δ(ρ+λΔ w m,n )|.
| B m,n B m,n ' |=| B m,n ( B m,n /Δ Δ+λΔ w m,n )|=|(ρ+λΔ w m,n )|.
0<| B m,n X'|<Δ/2<| B m,n B m,n ' |<Δ.
w m,n ' =(Y' Y'/Δ Δ)/(λΔ)=( B m,n ' B m,n ' /Δ Δ)/(λΔ).
0<(| B m,n Y'|=|ρλΔ w m,n Δ|)<Δ/2<| B m,n B m,n ' |<Δ.
v id (it+1)=ω v id (it)+ c 1 rand()( p id x id (it))+ c 2 rand()( p gd x id (it)).
x id (it+1)= x id (it)+ v id (it+1).
ω(it)= ω start ( ω start ω end )it/i t max .
U 1 ( x 1 , y 1 )=G T α 1 {f( x 0 , y 0 )exp[i2πp( x 0 , y 0 )]}.
U 2 (u,v)=G T α 2 { U 1 ( x 1 , y 1 )exp[i2πq( x 1 , y 1 )]}=A'(u,v)exp[iφ'(u,v)],
I 1 =0.5A'(u,v) A r {1+cos[φ'(u,v) δ 1 ]}=0.5A'(u,v){1+cos[φ'(u,v)]}.
I 2 =0.5A'(u,v) A r {1+cos[φ'(u,v) δ 2 ]}=0.5A'(u,v){1+sin[φ'(u,v)]}.
I 3 =0.5A'(u,v) A r {1+cos[φ'(u,v) δ 3 ]}=0.5A'(u,v){1cos[φ'(u,v)]}.
U(u,v)=[( I 1 I 3 )+i(2 I 2 I 1 I 3 )]/(4 A r ) =[( I 1 I 3 )+i(2 I 2 I 1 I 3 )]/4 =A(u,v)exp[iφ(u,v)],
U'( x 0 , y 0 )=G T α 1 {G T α 2 [U(u,v)]exp[i2πq( x 1 , y 1 )]}.
wm=[ T Ψ ]=[ 1 A w φ w /(2π) ],
C L ξ,η ' ={ (C L ξ,η Δ)/Δ Δ+λΔw m ξ,η , if ρ+λΔw m ξ,η >Δ/2 (C L ξ,η +Δ)/Δ Δ+λΔw m ξ,η , if ρ+λΔw m ξ,η <Δ/2 C L ξ,η /Δ Δ+λΔw m ξ,η , otherwise ,
w m ξ,η ' =(C L ξ,η ' C L ξ,η ' /Δ )/(λΔ).
Fitness=PSNR/100+1.1×( j=1 5 NC C j )/5.
PSNR=10 log 10 (MaxP V 2 /MSE) (dB) ,
MSE=( m=1 M n=1 N ( H m,n H ' m,n ) 2 )/(M×N),
NCC= k=1 K l=1 L ( W k,l W ' k,l )/ k=1 K l=1 L ( W k,l ) 2 ,

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