An optimized watermarking scheme using an encrypted gyrator transform computer generated hologram based on particle swarm optimization Jianzhong Li* Department of mathematics and statistics, Hanshan Normal University, Chaozhou, Guangdong, 521041, China * [email protected]
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 contourlettransformed 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 OCIS codes: (090.1760) Computer holography; (100.2000) Digital image processing; (060.4785) Optical security and encryption; (070.2590) ABCD transforms.
References and links 1.
C. C. Lai, “An improved SVD-based watermarking scheme using human visual characteristics,” Opt. Commun. 284(4), 938–944 (2011). 2. L. D. Li and B. L. Guo, “Localized image watermarking in spatial domain resistant to geometric attacks,” Int. J. Electron. Commun. 63(2), 123–131 (2009). 3. A. Poljicak, L. Mandic, and D. Agic, “Discrete Fourier transform–based watermarking method with an optimal implementation radius,” J. Electron. Imaging 20(3), 033008 (2011). 4. A. Phadikar, S. P. Maity, and B. Verma, “Region based QIM digital watermarking scheme for image database in DCT domain,” Comput. Electr. Eng. 37(3), 339–355 (2011). 5. P. Surekha and S. Sumathi, “Implementation of genetic algorithm for a dwt based image watermarking scheme,” IJSC 2(1), 244–252 (2011). 6. P. Meerwald and A. Uhl, “A survey of wavelet-domain watermarking algorithms,” Proc. SPIE 4314, 505–516 (2001). 7. B. C. Mohan and S. S. Kumar, “Robust Digital Watermarking Scheme using Contourlet Transform,” IJCSNS 8(2), 43–51 (2008). 8. M. N. Do and M. Vetterli, “The contourlet transform: An efficient directional multiresolution image representation,” IEEE Trans. Image Process. 14(12), 2091–2106 (2005). 9. O. Fındık, İ. Babaoğlu, and 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). 10. Y. del Valle, G. K. Venayagamoorthy, S. Mohagheghi, J.-C. Hernandez, and R. G. Harley, “Particle Swarm Optimization: Basic Concepts, Variants and Applications in Power Systems,” IEEE Trans. Evol. Comput. 12(2), 171–195 (2008). 11. N. Takai and Y. Mifune, “Digital watermarking by a holographic technique,” Appl. Opt. 41(5), 865–873 (2002).
#204029 - $15.00 USD (C) 2014 OSA
Received 3 Jan 2014; revised 2 Apr 2014; accepted 10 Apr 2014; published 18 Apr 2014 21 April 2014 | Vol. 22, No. 8 | DOI:10.1364/OE.22.010002 | OPTICS EXPRESS 10002
12. H. T. Chang and C. L. Tsan, “Image watermarking by use of digital holography embedded in the discrete-cosinetransform domain,” Appl. Opt. 44(29), 6211–6219 (2005). 13. S. Z. Wang, S. J. Huang, X. P. Zhang, and W. Wu, “Hologram-based watermarking capable of surviving printscan process,” Appl. Opt. 49(7), 1170–1178 (2010). 14. O. E. Okman and G. B. Akar, “Quantization index modulation-based image watermarking using digital holography,” J. Opt. Soc. Am. A 24(1), 243–252 (2007). 15. J. Z. Li, “Robust image watermarking scheme against geometric attacks using a computer-generated hologram,” Appl. Opt. 49(32), 6302–6312 (2010). 16. L. Z. Cai, M. Z. He, Q. Liu, and X. L. Yang, “Digital image encryption and watermarking by phase-shifting interferometry,” Appl. Opt. 43(15), 3078–3084 (2004). 17. 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(13), 2600–2606 (2005). 18. 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(19), 1808–1810 (2003). 19. P. Refregier and B. Javidi, “Optical image encryption based on input plane and Fourier plane random encoding,” Opt. Lett. 20(7), 767–769 (1995). 20. N. Singh and A. Sinha, “Gyrator transform-based optical image encryption, using chaos,” Opt. Lasers Eng. 47(5), 539–546 (2009). 21. M. M. Sathik and 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, and S. T. Liu, “Fast algorithm of discrete gyrator transform based on convolution operation,” Optik (Stuttg.) 122(10), 864–867 (2011). 23. S. Zhang, D. Van Der Weide, and J. Oliver, “Superfast phase-shifting method for 3-D shape measurement,” Opt. Express 18(9), 9684–9689 (2010). 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. 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, and H. Munir, “Comparative Analysis and Implementation of Efficient Digital Image Watermarking Schemes,” Int. J. Comp. Elec. Eng. 4(4), 558–561 (2012). 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, and 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). 30. H. H. Song, S. Y. Yu, X. K. Yang, L. Song, and C. Wang, “Contourlet-based image adaptive watermarking,” Signal Process-Image. 23(3), 162–178 (2008).
1. Introduction With the rapid development of the information technology and the growth of the Internet, acquisition, exchange, and transmission of digital multimedia have become quite convenient. Meanwhile, digital media can be manipulated or reproduced easily without the loss of information, and even illegally distributed through the Internet. Hence, the copyright protection of digital multimedia has become an important issue. In order to prevent any copyright forgery, misuse or violation, digital watermarking, which allows for the imperceptibly embedding information in an original multimedia data, provides a promising way for the copyright protection of digital media [1–5]. In the past ten decade, lots of image watermarking methods have been proposed [2–7]. According to the domain in which the watermark is applied, the watermark can be classified into two categories: spatial domain or transform domain (such as discrete Fourier transform (DFT), discrete cosine transform (DCT), and discrete wavelet transform (DWT)) [2–5]. Compared with transform domain watermarking techniques, spatial domain methods are simple and fast, but are not robust against attacks. Among the transform domain techniques, DWT-based techniques are more popular, since DWT has a number of advantages over other transforms including space-frequency multiresolution representation, localization, superior HVS modeling, linear complexity, and adaptivity [6]. Even though DWT is popular, powerful, and familiar among watermarking methods, it has its own limitations in capturing the directional information such as smooth contours and the directional edges of the image [7]. This problem is addressed by contourlet transform (CT) proposed by Do et al. [8]. The CT possesses multiscale and time frequency localization properties of wavelet in addition to
#204029 - $15.00 USD (C) 2014 OSA
Received 3 Jan 2014; revised 2 Apr 2014; accepted 10 Apr 2014; published 18 Apr 2014 21 April 2014 | Vol. 22, No. 8 | DOI:10.1364/OE.22.010002 | OPTICS EXPRESS 10003
directionality and anisotropy [7]. Hence CT is considered as an improvement over wavelet in terms of efficiency. Therefore, we focus on CT domain watermarking in this work. In general, the characteristics of digital watermarking are as follows [1]: (1) robustness, (2) imperceptibility, (3) capacity, (4) security, and (5) verifiability. However, in the watermarking system, there exist conflict requirements between the two major properties – robustness and imperceptibility which are essential in preserving the security of multimedia data from unauthorized usage [5]. In other words, if the watermarking is wanted to be more robust, then the quality of the watermarked digital data may be sacrificed. The design of an optimal watermarking always involves a trade-off between these requirements. Therefore, watermarking problem can be considered as an optimization problem. But most of existing watermarking methods usually employ pre-defined embedding rules and determine their embedding parameters, such as embedding strengths or thresholds, either empirically or experimentally. However, it is difficult to determine optimal watermarking parameters empirically or experimentally since watermarking methods have larger parameter space. As a result, these watermarking techniques do not exhibit desirable performance. Recently, many watermarking methods which employ intelligent optimization techniques, such as genetic algorithm (GA) [5] and particle swarm optimization (PSO) [9], to optimize the robustness and imperceptibility have been proposed. These watermarking methods have attracted much attention because of their promising performance. Compared with other similar optimization techniques, such as GA which suffers from important limitations of high computational costs which eventually results in low convergence speed [10], PSO has some advantages as the following [10]: 1) PSO is easier to implement and there are fewer parameters to adjust; 2) PSO has a more effective memory capability since every particle remembers its own previous best value as well as the neighborhood best; 3) Because all the particles use the information related to the most successful particle, PSO is more efficient in maintaining the diversity of the swarm. In order to achieve a tradeoff between imperceptibility and robustness, PSO is utilized to search the optimal embedding parameter in this study. In recent years, a new approach which uses digital holograms as the watermark signal has been investigated [11–17]. Takai and Mifune proposed that the Fourier transform hologram is added to the spatial domain of the host image [11].The major drawback of this method is that the host image must be low-pass filtered to remove the high-frequency components before the superposition stage. Therefore the quality of the watermarked image is seriously degraded. To achieve the high quality of the watermarked image, Chang and Tsan proposed that the hologram is superposed on the DCT middle frequency coefficients of the host image [12]. But the method is weak in resisting a JPEG compression attack [12]. Wang et al. developed a method that the computer generated hologram (CGH) is also inserted into the DCT domain of the image [13]. This method also cannot resist the compression attack effectively. With quantization index modulation technique, Okman and Akar proposed that the hologram is added to the wavelet domain of the host image [14]. But the watermarking quantizers are determined experimentally in this method. Based on the geometric correction method, we presented a geometric robust watermarking scheme which embeds the CGH into the wavelettransformed image [15]. However, the image quality may be decreased when the absolute values of the variations of the embedded wavelet coefficients are greater than half of the quantization step. Furthermore, the security of the methods mentioned above is less investigated and seriously affected. To increase the security, Cai et al. proposed that the holograms, which are obtained by three-step phase-shifting interferometry (PSI) [18] and encrypted using the random phase mask (RPM) [19], are added to the host images in the spatial domain after multiplying by a weighting factor [16]. But it is inconvenient for the copyright protection of an image because three interferograms are needed to be inserted into three same or different host images by using this watermarking method. To avoid the above drawback, the effect of embedding only real, imaginary, or phase parts of the hologram is studied in [17]. However, the quality of reconstruction of the extracted watermark is seriously
#204029 - $15.00 USD (C) 2014 OSA
Received 3 Jan 2014; revised 2 Apr 2014; accepted 10 Apr 2014; published 18 Apr 2014 21 April 2014 | Vol. 22, No. 8 | DOI:10.1364/OE.22.010002 | OPTICS EXPRESS 10004
degraded. In addition, the both above methods are less concerned with either the watermarked image quality or the robustness criteria. In this paper, a secure optimized CGH-based image watermarking scheme is presented to guarantee high security, good imperceptibility, and robustness to withstand attacks. To obtain the high security of the watermarking scheme, based on the gyrator transform (GT) [20], the RPM, the three-step PSI and the Fibonacci transform [21], a novel encrypted CGH method which offers a huge key space is developed to generate a hologram of a watermark. In the embedding procedure, the encrypted CGH is inserted into the host image using the proposed improved quantization embedding algorithm which offers better imperceptibility. Different from the previously suggested holography-based methods, the mark hologram is inserted into the image in the contourlet transform domain. Moreover, to achieve the highest possible robustness without losing the imperceptibility, PSO is utilized to find the optimal embedding parameter which can satisfy the both imperceptibility and robustness requirements of the watermarking system. Compared with the method in [15], the proposed watermarking scheme not only provides better performance for imperceptibility, but also can resist most of common attacks more effectively. The experimental results demonstrate that the proposed watermarking scheme is not only secure and invisible, but also robust against different attacks. 2. Related background 2.1 Gyrator transform The GT is a linear canonical integral transform which produces the rotation in the twisted position-spatial frequency planes of phase space [20]. Mathematically, the GT of a twodimensional function f(x,y) can be expressed as Gα (u, v) = GT α [ f ( x, y )] =
f ( x, y ) ( xy + uv) cos α − xv − yu exp[i 2π ]dxdy, (1) | sin α | sin α
where the Gα(u,v) and f(x,y) are the output and input of the transform, respectively. The symbol GTα represents gyrator operator. α is the transformation angle. The GT can be achieved either by using an optical system [20] or by using a fast algorithm [22]. 2.2 Phase-shifting interferometry Phase-shifting interferometry is an effective way to record complex wave field digitally. A variety of PSI techniques have been developed, including three-step, four-step, etc [23]. Let A(x,y)exp[iφ(x,y)] and Arexp(iδk) be the complex amplitude distribution of the object wave in the recording plane and the reference wave in that plane at the kth exposure, respectively. Here, Ar is a constant, δk is the phase shift of the reference wave between two adjacent steps and k = 1,2,…,N. The kth interference pattern Ik(x,y) can be represented as [18], I k ( x, y ) = A2 ( x, y ) + 2 A( x, y ) Ar cos[ϕ ( x, y ) − δ k ] + Ar2 . (2) For a known set {δk}(k = 1,2,...,N), the expression of U(x,y) which is a digital hologram can be derived as a function {Ik} and {δk} [18]. In the three-frame case, N is 3. When δ1 = 0, δ2 = π/2 and δ3 = π, a digital hologram U(x,y) from the three interferograms I1, I2 and I3 can be expressed as [16,18] U ( x, y ) = [( I1 − I 3 ) + i (2 I 2 − I1 − I 3 )] / (4 Ar ).
(3)
2.3 Watermarking scheme in [15] In the previous work [15], the mark hologram is suggested embedding into the DWT low frequency sub-band using the following formula.
Bm' , n = Bm , n / Δ Δ + λΔwm , n ,
#204029 - $15.00 USD (C) 2014 OSA
(4)
Received 3 Jan 2014; revised 2 Apr 2014; accepted 10 Apr 2014; published 18 Apr 2014 21 April 2014 | Vol. 22, No. 8 | DOI:10.1364/OE.22.010002 | OPTICS EXPRESS 10005
where Bm,n is the (m,n)th pixel of the low frequency sub-band, 0≤wm,n≤1 is the (m,n)th element of the normalized hologram, ⋅ is the floor operation, Δ>0 is the quantization step and 0Δ/2. The reason is analyzed as follows. From |-ρ + λΔwm,n|>Δ/2, –ρ + λΔwm,n>Δ/2 and –ρ + λΔwm,nΔ/2 case, let X = Bm,n–Δ firstly. Then embed wm,n into X to obtain X ' = X / Δ Δ + λΔwm , n using Eq. (4). The watermark signal w’m,n can be extracted using Eq. (5). wm' , n = ( X '− X '/ Δ Δ ) / (λΔ ) = ( ( Bm , n − Δ ) / Δ Δ + λΔwm , n − ( ( Bm , n − Δ ) / Δ Δ + λΔwm , n ) / Δ Δ ) / (λΔ ) = ( Bm , n / Δ Δ + λΔwm , n − ( Bm , n / Δ Δ + λΔwm , n ) / Δ Δ ) / (λΔ ) = ( Bm' , n − Bm' , n / Δ Δ ) / (λΔ ). (7) It can be observed from Eq. (5) and Eq. (7) that the extracted signals are the same from B’m,n and X’m,n which were embedded with wm,n, respectively. On the other hand, the variation between Bm,n and X’, and that between Bm,n and B’m,n can be calculated as follows.
| Bm , n − X ' |=| Bm , n − ( X / Δ Δ + λΔwm , n ) |=| Bm , n − ( ( Bm , n − Δ) / Δ Δ + λΔwm , n ) | (8) =| Bm , n − ( Bm , n / Δ Δ − Δ + λΔwm , n ) |=| Δ − (− ρ + λΔwm , n ) | .
(9) | Bm , n − Bm' ,n |=| Bm , n − ( Bm , n / Δ Δ + λΔwm , n ) |=| −(− ρ + λΔwm , n ) | . Since 0≤ρ0, 0
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 contourlettransformed 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 OCIS codes: (090.1760) Computer holography; (100.2000) Digital image processing; (060.4785) Optical security and encryption; (070.2590) ABCD transforms.
References and links 1.
C. C. Lai, “An improved SVD-based watermarking scheme using human visual characteristics,” Opt. Commun. 284(4), 938–944 (2011). 2. L. D. Li and B. L. Guo, “Localized image watermarking in spatial domain resistant to geometric attacks,” Int. J. Electron. Commun. 63(2), 123–131 (2009). 3. A. Poljicak, L. Mandic, and D. Agic, “Discrete Fourier transform–based watermarking method with an optimal implementation radius,” J. Electron. Imaging 20(3), 033008 (2011). 4. A. Phadikar, S. P. Maity, and B. Verma, “Region based QIM digital watermarking scheme for image database in DCT domain,” Comput. Electr. Eng. 37(3), 339–355 (2011). 5. P. Surekha and S. Sumathi, “Implementation of genetic algorithm for a dwt based image watermarking scheme,” IJSC 2(1), 244–252 (2011). 6. P. Meerwald and A. Uhl, “A survey of wavelet-domain watermarking algorithms,” Proc. SPIE 4314, 505–516 (2001). 7. B. C. Mohan and S. S. Kumar, “Robust Digital Watermarking Scheme using Contourlet Transform,” IJCSNS 8(2), 43–51 (2008). 8. M. N. Do and M. Vetterli, “The contourlet transform: An efficient directional multiresolution image representation,” IEEE Trans. Image Process. 14(12), 2091–2106 (2005). 9. O. Fındık, İ. Babaoğlu, and 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). 10. Y. del Valle, G. K. Venayagamoorthy, S. Mohagheghi, J.-C. Hernandez, and R. G. Harley, “Particle Swarm Optimization: Basic Concepts, Variants and Applications in Power Systems,” IEEE Trans. Evol. Comput. 12(2), 171–195 (2008). 11. N. Takai and Y. Mifune, “Digital watermarking by a holographic technique,” Appl. Opt. 41(5), 865–873 (2002).
#204029 - $15.00 USD (C) 2014 OSA
Received 3 Jan 2014; revised 2 Apr 2014; accepted 10 Apr 2014; published 18 Apr 2014 21 April 2014 | Vol. 22, No. 8 | DOI:10.1364/OE.22.010002 | OPTICS EXPRESS 10002
12. H. T. Chang and C. L. Tsan, “Image watermarking by use of digital holography embedded in the discrete-cosinetransform domain,” Appl. Opt. 44(29), 6211–6219 (2005). 13. S. Z. Wang, S. J. Huang, X. P. Zhang, and W. Wu, “Hologram-based watermarking capable of surviving printscan process,” Appl. Opt. 49(7), 1170–1178 (2010). 14. O. E. Okman and G. B. Akar, “Quantization index modulation-based image watermarking using digital holography,” J. Opt. Soc. Am. A 24(1), 243–252 (2007). 15. J. Z. Li, “Robust image watermarking scheme against geometric attacks using a computer-generated hologram,” Appl. Opt. 49(32), 6302–6312 (2010). 16. L. Z. Cai, M. Z. He, Q. Liu, and X. L. Yang, “Digital image encryption and watermarking by phase-shifting interferometry,” Appl. Opt. 43(15), 3078–3084 (2004). 17. 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(13), 2600–2606 (2005). 18. 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(19), 1808–1810 (2003). 19. P. Refregier and B. Javidi, “Optical image encryption based on input plane and Fourier plane random encoding,” Opt. Lett. 20(7), 767–769 (1995). 20. N. Singh and A. Sinha, “Gyrator transform-based optical image encryption, using chaos,” Opt. Lasers Eng. 47(5), 539–546 (2009). 21. M. M. Sathik and 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, and S. T. Liu, “Fast algorithm of discrete gyrator transform based on convolution operation,” Optik (Stuttg.) 122(10), 864–867 (2011). 23. S. Zhang, D. Van Der Weide, and J. Oliver, “Superfast phase-shifting method for 3-D shape measurement,” Opt. Express 18(9), 9684–9689 (2010). 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. 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, and H. Munir, “Comparative Analysis and Implementation of Efficient Digital Image Watermarking Schemes,” Int. J. Comp. Elec. Eng. 4(4), 558–561 (2012). 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, and 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). 30. H. H. Song, S. Y. Yu, X. K. Yang, L. Song, and C. Wang, “Contourlet-based image adaptive watermarking,” Signal Process-Image. 23(3), 162–178 (2008).
1. Introduction With the rapid development of the information technology and the growth of the Internet, acquisition, exchange, and transmission of digital multimedia have become quite convenient. Meanwhile, digital media can be manipulated or reproduced easily without the loss of information, and even illegally distributed through the Internet. Hence, the copyright protection of digital multimedia has become an important issue. In order to prevent any copyright forgery, misuse or violation, digital watermarking, which allows for the imperceptibly embedding information in an original multimedia data, provides a promising way for the copyright protection of digital media [1–5]. In the past ten decade, lots of image watermarking methods have been proposed [2–7]. According to the domain in which the watermark is applied, the watermark can be classified into two categories: spatial domain or transform domain (such as discrete Fourier transform (DFT), discrete cosine transform (DCT), and discrete wavelet transform (DWT)) [2–5]. Compared with transform domain watermarking techniques, spatial domain methods are simple and fast, but are not robust against attacks. Among the transform domain techniques, DWT-based techniques are more popular, since DWT has a number of advantages over other transforms including space-frequency multiresolution representation, localization, superior HVS modeling, linear complexity, and adaptivity [6]. Even though DWT is popular, powerful, and familiar among watermarking methods, it has its own limitations in capturing the directional information such as smooth contours and the directional edges of the image [7]. This problem is addressed by contourlet transform (CT) proposed by Do et al. [8]. The CT possesses multiscale and time frequency localization properties of wavelet in addition to
#204029 - $15.00 USD (C) 2014 OSA
Received 3 Jan 2014; revised 2 Apr 2014; accepted 10 Apr 2014; published 18 Apr 2014 21 April 2014 | Vol. 22, No. 8 | DOI:10.1364/OE.22.010002 | OPTICS EXPRESS 10003
directionality and anisotropy [7]. Hence CT is considered as an improvement over wavelet in terms of efficiency. Therefore, we focus on CT domain watermarking in this work. In general, the characteristics of digital watermarking are as follows [1]: (1) robustness, (2) imperceptibility, (3) capacity, (4) security, and (5) verifiability. However, in the watermarking system, there exist conflict requirements between the two major properties – robustness and imperceptibility which are essential in preserving the security of multimedia data from unauthorized usage [5]. In other words, if the watermarking is wanted to be more robust, then the quality of the watermarked digital data may be sacrificed. The design of an optimal watermarking always involves a trade-off between these requirements. Therefore, watermarking problem can be considered as an optimization problem. But most of existing watermarking methods usually employ pre-defined embedding rules and determine their embedding parameters, such as embedding strengths or thresholds, either empirically or experimentally. However, it is difficult to determine optimal watermarking parameters empirically or experimentally since watermarking methods have larger parameter space. As a result, these watermarking techniques do not exhibit desirable performance. Recently, many watermarking methods which employ intelligent optimization techniques, such as genetic algorithm (GA) [5] and particle swarm optimization (PSO) [9], to optimize the robustness and imperceptibility have been proposed. These watermarking methods have attracted much attention because of their promising performance. Compared with other similar optimization techniques, such as GA which suffers from important limitations of high computational costs which eventually results in low convergence speed [10], PSO has some advantages as the following [10]: 1) PSO is easier to implement and there are fewer parameters to adjust; 2) PSO has a more effective memory capability since every particle remembers its own previous best value as well as the neighborhood best; 3) Because all the particles use the information related to the most successful particle, PSO is more efficient in maintaining the diversity of the swarm. In order to achieve a tradeoff between imperceptibility and robustness, PSO is utilized to search the optimal embedding parameter in this study. In recent years, a new approach which uses digital holograms as the watermark signal has been investigated [11–17]. Takai and Mifune proposed that the Fourier transform hologram is added to the spatial domain of the host image [11].The major drawback of this method is that the host image must be low-pass filtered to remove the high-frequency components before the superposition stage. Therefore the quality of the watermarked image is seriously degraded. To achieve the high quality of the watermarked image, Chang and Tsan proposed that the hologram is superposed on the DCT middle frequency coefficients of the host image [12]. But the method is weak in resisting a JPEG compression attack [12]. Wang et al. developed a method that the computer generated hologram (CGH) is also inserted into the DCT domain of the image [13]. This method also cannot resist the compression attack effectively. With quantization index modulation technique, Okman and Akar proposed that the hologram is added to the wavelet domain of the host image [14]. But the watermarking quantizers are determined experimentally in this method. Based on the geometric correction method, we presented a geometric robust watermarking scheme which embeds the CGH into the wavelettransformed image [15]. However, the image quality may be decreased when the absolute values of the variations of the embedded wavelet coefficients are greater than half of the quantization step. Furthermore, the security of the methods mentioned above is less investigated and seriously affected. To increase the security, Cai et al. proposed that the holograms, which are obtained by three-step phase-shifting interferometry (PSI) [18] and encrypted using the random phase mask (RPM) [19], are added to the host images in the spatial domain after multiplying by a weighting factor [16]. But it is inconvenient for the copyright protection of an image because three interferograms are needed to be inserted into three same or different host images by using this watermarking method. To avoid the above drawback, the effect of embedding only real, imaginary, or phase parts of the hologram is studied in [17]. However, the quality of reconstruction of the extracted watermark is seriously
#204029 - $15.00 USD (C) 2014 OSA
Received 3 Jan 2014; revised 2 Apr 2014; accepted 10 Apr 2014; published 18 Apr 2014 21 April 2014 | Vol. 22, No. 8 | DOI:10.1364/OE.22.010002 | OPTICS EXPRESS 10004
degraded. In addition, the both above methods are less concerned with either the watermarked image quality or the robustness criteria. In this paper, a secure optimized CGH-based image watermarking scheme is presented to guarantee high security, good imperceptibility, and robustness to withstand attacks. To obtain the high security of the watermarking scheme, based on the gyrator transform (GT) [20], the RPM, the three-step PSI and the Fibonacci transform [21], a novel encrypted CGH method which offers a huge key space is developed to generate a hologram of a watermark. In the embedding procedure, the encrypted CGH is inserted into the host image using the proposed improved quantization embedding algorithm which offers better imperceptibility. Different from the previously suggested holography-based methods, the mark hologram is inserted into the image in the contourlet transform domain. Moreover, to achieve the highest possible robustness without losing the imperceptibility, PSO is utilized to find the optimal embedding parameter which can satisfy the both imperceptibility and robustness requirements of the watermarking system. Compared with the method in [15], the proposed watermarking scheme not only provides better performance for imperceptibility, but also can resist most of common attacks more effectively. The experimental results demonstrate that the proposed watermarking scheme is not only secure and invisible, but also robust against different attacks. 2. Related background 2.1 Gyrator transform The GT is a linear canonical integral transform which produces the rotation in the twisted position-spatial frequency planes of phase space [20]. Mathematically, the GT of a twodimensional function f(x,y) can be expressed as Gα (u, v) = GT α [ f ( x, y )] =
f ( x, y ) ( xy + uv) cos α − xv − yu exp[i 2π ]dxdy, (1) | sin α | sin α
where the Gα(u,v) and f(x,y) are the output and input of the transform, respectively. The symbol GTα represents gyrator operator. α is the transformation angle. The GT can be achieved either by using an optical system [20] or by using a fast algorithm [22]. 2.2 Phase-shifting interferometry Phase-shifting interferometry is an effective way to record complex wave field digitally. A variety of PSI techniques have been developed, including three-step, four-step, etc [23]. Let A(x,y)exp[iφ(x,y)] and Arexp(iδk) be the complex amplitude distribution of the object wave in the recording plane and the reference wave in that plane at the kth exposure, respectively. Here, Ar is a constant, δk is the phase shift of the reference wave between two adjacent steps and k = 1,2,…,N. The kth interference pattern Ik(x,y) can be represented as [18], I k ( x, y ) = A2 ( x, y ) + 2 A( x, y ) Ar cos[ϕ ( x, y ) − δ k ] + Ar2 . (2) For a known set {δk}(k = 1,2,...,N), the expression of U(x,y) which is a digital hologram can be derived as a function {Ik} and {δk} [18]. In the three-frame case, N is 3. When δ1 = 0, δ2 = π/2 and δ3 = π, a digital hologram U(x,y) from the three interferograms I1, I2 and I3 can be expressed as [16,18] U ( x, y ) = [( I1 − I 3 ) + i (2 I 2 − I1 − I 3 )] / (4 Ar ).
(3)
2.3 Watermarking scheme in [15] In the previous work [15], the mark hologram is suggested embedding into the DWT low frequency sub-band using the following formula.
Bm' , n = Bm , n / Δ Δ + λΔwm , n ,
#204029 - $15.00 USD (C) 2014 OSA
(4)
Received 3 Jan 2014; revised 2 Apr 2014; accepted 10 Apr 2014; published 18 Apr 2014 21 April 2014 | Vol. 22, No. 8 | DOI:10.1364/OE.22.010002 | OPTICS EXPRESS 10005
where Bm,n is the (m,n)th pixel of the low frequency sub-band, 0≤wm,n≤1 is the (m,n)th element of the normalized hologram, ⋅ is the floor operation, Δ>0 is the quantization step and 0Δ/2. The reason is analyzed as follows. From |-ρ + λΔwm,n|>Δ/2, –ρ + λΔwm,n>Δ/2 and –ρ + λΔwm,nΔ/2 case, let X = Bm,n–Δ firstly. Then embed wm,n into X to obtain X ' = X / Δ Δ + λΔwm , n using Eq. (4). The watermark signal w’m,n can be extracted using Eq. (5). wm' , n = ( X '− X '/ Δ Δ ) / (λΔ ) = ( ( Bm , n − Δ ) / Δ Δ + λΔwm , n − ( ( Bm , n − Δ ) / Δ Δ + λΔwm , n ) / Δ Δ ) / (λΔ ) = ( Bm , n / Δ Δ + λΔwm , n − ( Bm , n / Δ Δ + λΔwm , n ) / Δ Δ ) / (λΔ ) = ( Bm' , n − Bm' , n / Δ Δ ) / (λΔ ). (7) It can be observed from Eq. (5) and Eq. (7) that the extracted signals are the same from B’m,n and X’m,n which were embedded with wm,n, respectively. On the other hand, the variation between Bm,n and X’, and that between Bm,n and B’m,n can be calculated as follows.
| Bm , n − X ' |=| Bm , n − ( X / Δ Δ + λΔwm , n ) |=| Bm , n − ( ( Bm , n − Δ) / Δ Δ + λΔwm , n ) | (8) =| Bm , n − ( Bm , n / Δ Δ − Δ + λΔwm , n ) |=| Δ − (− ρ + λΔwm , n ) | .
(9) | Bm , n − Bm' ,n |=| Bm , n − ( Bm , n / Δ Δ + λΔwm , n ) |=| −(− ρ + λΔwm , n ) | . Since 0≤ρ0, 0
