Abstract

A blind robust watermarking scheme is proposed. A watermark is firstly transformed into a non-cascade iterative encrypted kinoform with non-cascade phase retrieve algorithm and random fractional Fourier transform (RFrFT). An iterative algorithm and Human Visual System (HVS) are both presented to adaptively embed the kinoform watermark into corresponding 2-level DWT coefficients of the cover image. The kinoform accounts for much less data amount to be embedded than regular computer-generated hologram (CGH). And the kinoform can be extracted with the only right phase key and right fractional order, and reconstructed to represent original watermark without original cover image. The experiments have shown the scheme’s high security, good imperceptibility, and robustness to resist attacks such as noise, compression, filtering, cropping.

© 2011 OSA

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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2009 (4)

2008 (1)

W.-H. Lin, S.-J. Horng, T.-W. Kao, P. Fan, C.-L. Lee, and Y. Pan, “An efficient watermarking method based on significant difference of wavelet coefficient quantization,” IEEE Trans. Multimed. 10(5), 746–757 (2008).
[CrossRef]

2007 (5)

N. Bi, Q. Sun, D. Huang, Z. Yang, and J. Huang, “Robust image watermarking based on multiband wavelets and empirical mode decomposition,” IEEE Trans. Image Process. 16(8), 1956–1966 (2007).
[CrossRef] [PubMed]

Z. Liu and S. Liu, “Random fractional Fourier transform,” Opt. Lett. 32(15), 2088–2090 (2007).
[CrossRef] [PubMed]

R. Tao, Y. Xin, and Y. Wang, “Double image encryption based on random phase encoding in the fractional Fourier domain,” Opt. Express 15(24), 16067–16079 (2007).
[CrossRef] [PubMed]

M. Liu, G. Yang, H. Xie, M. Xia, J. Hu, and H. Zha, “Computer-generated hologram watermarking resilient to rotation and scaling,” Opt. Eng. 46(6), 060501 (2007).
[CrossRef]

S. Deng, L. Liu, H. Lang, D. Zhao, and X. Liu, “Watermarks encrypted in the cascaded Fresnel digital hologram,” Optik (Stuttg.) 118, 302–305 (2007).
[CrossRef]

2006 (2)

S.-C. Pei and W.-L. Hsue, “The multiple-parameter discrete fractional Fourier transform,” IEEE Signal Process. Lett. 13(6), 329–332 (2006).
[CrossRef]

S. Deng, L. Liu, H. Lang, W. Pan, and D. Zhao, “Hiding an image in cascaded Fresnel digital holograms,” Chin. Opt. Lett. 4, 268–271 (2006).

2005 (2)

A. Reddy and B. Chatterji, “A new wavelet based logo-watermarking scheme,” Pattern Recognit. Lett. 26(7), 1019–1027 (2005).
[CrossRef]

P. Bao, “Xiaohu Ma, “Image adaptive watermarking using wavelet domain singular value decomposition,” IEEE Trans. Circ. Syst. Video Tech. 15, 96–102 (2005).
[CrossRef]

2003 (1)

H. Zhai, F. Liu, X. Yang, G. Mu, and P. Chavel, “Improving binary images reconstructed from kinoforms by amplitude adjustment,” Opt. Commun. 219(1-6), 81–85 (2003).
[CrossRef]

2002 (2)

2001 (2)

Y. Aoki, “Watermarking technique using computer-generated holograms,” Electron. Commun. Jpn. 84(1), 21–31 (2001).
[CrossRef]

M. Barni, F. Bartolini, and A. Piva, “Improved wavelet-based watermarking through pixel-wise masking,” IEEE Trans. Image Process. 10(5), 783–791 (2001).
[CrossRef]

2000 (1)

C. Candan, M. A. Kutay, and H. M. Ozaktas, “The discrete fractional Fourier transform,” IEEE Trans. Signal Process. 48(5), 1329–1337 (2000).
[CrossRef]

1995 (1)

Alam, M. S.

Aoki, Y.

Y. Aoki, “Watermarking technique using computer-generated holograms,” Electron. Commun. Jpn. 84(1), 21–31 (2001).
[CrossRef]

Bao, P.

P. Bao, “Xiaohu Ma, “Image adaptive watermarking using wavelet domain singular value decomposition,” IEEE Trans. Circ. Syst. Video Tech. 15, 96–102 (2005).
[CrossRef]

Barni, M.

M. Barni, F. Bartolini, and A. Piva, “Improved wavelet-based watermarking through pixel-wise masking,” IEEE Trans. Image Process. 10(5), 783–791 (2001).
[CrossRef]

Bartolini, F.

M. Barni, F. Bartolini, and A. Piva, “Improved wavelet-based watermarking through pixel-wise masking,” IEEE Trans. Image Process. 10(5), 783–791 (2001).
[CrossRef]

Bi, N.

N. Bi, Q. Sun, D. Huang, Z. Yang, and J. Huang, “Robust image watermarking based on multiband wavelets and empirical mode decomposition,” IEEE Trans. Image Process. 16(8), 1956–1966 (2007).
[CrossRef] [PubMed]

Candan, C.

C. Candan, M. A. Kutay, and H. M. Ozaktas, “The discrete fractional Fourier transform,” IEEE Trans. Signal Process. 48(5), 1329–1337 (2000).
[CrossRef]

Cao, L.

Chatterji, B.

A. Reddy and B. Chatterji, “A new wavelet based logo-watermarking scheme,” Pattern Recognit. Lett. 26(7), 1019–1027 (2005).
[CrossRef]

Chavel, P.

H. Zhai, F. Liu, X. Yang, G. Mu, and P. Chavel, “Improving binary images reconstructed from kinoforms by amplitude adjustment,” Opt. Commun. 219(1-6), 81–85 (2003).
[CrossRef]

Deng, S.

S. Deng, L. Liu, H. Lang, D. Zhao, and X. Liu, “Watermarks encrypted in the cascaded Fresnel digital hologram,” Optik (Stuttg.) 118, 302–305 (2007).
[CrossRef]

S. Deng, L. Liu, H. Lang, W. Pan, and D. Zhao, “Hiding an image in cascaded Fresnel digital holograms,” Chin. Opt. Lett. 4, 268–271 (2006).

Fan, P.

W.-H. Lin, S.-J. Horng, T.-W. Kao, P. Fan, C.-L. Lee, and Y. Pan, “An efficient watermarking method based on significant difference of wavelet coefficient quantization,” IEEE Trans. Multimed. 10(5), 746–757 (2008).
[CrossRef]

He, M.

He, Q.

Horng, S.-J.

W.-H. Lin, S.-J. Horng, T.-W. Kao, P. Fan, C.-L. Lee, and Y. Pan, “An efficient watermarking method based on significant difference of wavelet coefficient quantization,” IEEE Trans. Multimed. 10(5), 746–757 (2008).
[CrossRef]

Hsue, W.-L.

S.-C. Pei and W.-L. Hsue, “Random discrete fractional Fourier transform,” IEEE Signal Process. Lett. 16(12), 1015–1018 (2009).
[CrossRef]

S.-C. Pei and W.-L. Hsue, “The multiple-parameter discrete fractional Fourier transform,” IEEE Signal Process. Lett. 13(6), 329–332 (2006).
[CrossRef]

Hu, J.

M. Liu, G. Yang, H. Xie, M. Xia, J. Hu, and H. Zha, “Computer-generated hologram watermarking resilient to rotation and scaling,” Opt. Eng. 46(6), 060501 (2007).
[CrossRef]

Huang, D.

N. Bi, Q. Sun, D. Huang, Z. Yang, and J. Huang, “Robust image watermarking based on multiband wavelets and empirical mode decomposition,” IEEE Trans. Image Process. 16(8), 1956–1966 (2007).
[CrossRef] [PubMed]

Huang, J.

N. Bi, Q. Sun, D. Huang, Z. Yang, and J. Huang, “Robust image watermarking based on multiband wavelets and empirical mode decomposition,” IEEE Trans. Image Process. 16(8), 1956–1966 (2007).
[CrossRef] [PubMed]

Javidi, B.

Jin, G.

Kao, T.-W.

W.-H. Lin, S.-J. Horng, T.-W. Kao, P. Fan, C.-L. Lee, and Y. Pan, “An efficient watermarking method based on significant difference of wavelet coefficient quantization,” IEEE Trans. Multimed. 10(5), 746–757 (2008).
[CrossRef]

Kishk, S.

Kutay, M. A.

C. Candan, M. A. Kutay, and H. M. Ozaktas, “The discrete fractional Fourier transform,” IEEE Trans. Signal Process. 48(5), 1329–1337 (2000).
[CrossRef]

Lang, H.

S. Deng, L. Liu, H. Lang, D. Zhao, and X. Liu, “Watermarks encrypted in the cascaded Fresnel digital hologram,” Optik (Stuttg.) 118, 302–305 (2007).
[CrossRef]

S. Deng, L. Liu, H. Lang, W. Pan, and D. Zhao, “Hiding an image in cascaded Fresnel digital holograms,” Chin. Opt. Lett. 4, 268–271 (2006).

Lee, C.-L.

W.-H. Lin, S.-J. Horng, T.-W. Kao, P. Fan, C.-L. Lee, and Y. Pan, “An efficient watermarking method based on significant difference of wavelet coefficient quantization,” IEEE Trans. Multimed. 10(5), 746–757 (2008).
[CrossRef]

Li, J.

Lin, W.-H.

W.-H. Lin, S.-J. Horng, T.-W. Kao, P. Fan, C.-L. Lee, and Y. Pan, “An efficient watermarking method based on significant difference of wavelet coefficient quantization,” IEEE Trans. Multimed. 10(5), 746–757 (2008).
[CrossRef]

Liu, F.

H. Zhai, F. Liu, X. Yang, G. Mu, and P. Chavel, “Improving binary images reconstructed from kinoforms by amplitude adjustment,” Opt. Commun. 219(1-6), 81–85 (2003).
[CrossRef]

Liu, L.

S. Deng, L. Liu, H. Lang, D. Zhao, and X. Liu, “Watermarks encrypted in the cascaded Fresnel digital hologram,” Optik (Stuttg.) 118, 302–305 (2007).
[CrossRef]

S. Deng, L. Liu, H. Lang, W. Pan, and D. Zhao, “Hiding an image in cascaded Fresnel digital holograms,” Chin. Opt. Lett. 4, 268–271 (2006).

Liu, M.

M. Liu, G. Yang, H. Xie, M. Xia, J. Hu, and H. Zha, “Computer-generated hologram watermarking resilient to rotation and scaling,” Opt. Eng. 46(6), 060501 (2007).
[CrossRef]

Liu, S.

Liu, X.

S. Deng, L. Liu, H. Lang, D. Zhao, and X. Liu, “Watermarks encrypted in the cascaded Fresnel digital hologram,” Optik (Stuttg.) 118, 302–305 (2007).
[CrossRef]

Liu, Z.

Mifune, Y.

Mu, G.

H. Zhai, F. Liu, X. Yang, G. Mu, and P. Chavel, “Improving binary images reconstructed from kinoforms by amplitude adjustment,” Opt. Commun. 219(1-6), 81–85 (2003).
[CrossRef]

Ozaktas, H. M.

C. Candan, M. A. Kutay, and H. M. Ozaktas, “The discrete fractional Fourier transform,” IEEE Trans. Signal Process. 48(5), 1329–1337 (2000).
[CrossRef]

Pan, W.

Pan, Y.

W.-H. Lin, S.-J. Horng, T.-W. Kao, P. Fan, C.-L. Lee, and Y. Pan, “An efficient watermarking method based on significant difference of wavelet coefficient quantization,” IEEE Trans. Multimed. 10(5), 746–757 (2008).
[CrossRef]

Pei, S.-C.

S.-C. Pei and W.-L. Hsue, “Random discrete fractional Fourier transform,” IEEE Signal Process. Lett. 16(12), 1015–1018 (2009).
[CrossRef]

S.-C. Pei and W.-L. Hsue, “The multiple-parameter discrete fractional Fourier transform,” IEEE Signal Process. Lett. 13(6), 329–332 (2006).
[CrossRef]

Piva, A.

M. Barni, F. Bartolini, and A. Piva, “Improved wavelet-based watermarking through pixel-wise masking,” IEEE Trans. Image Process. 10(5), 783–791 (2001).
[CrossRef]

Reddy, A.

A. Reddy and B. Chatterji, “A new wavelet based logo-watermarking scheme,” Pattern Recognit. Lett. 26(7), 1019–1027 (2005).
[CrossRef]

Refregier, P.

Ren, X.

Sheng, Y.

Sun, Q.

N. Bi, Q. Sun, D. Huang, Z. Yang, and J. Huang, “Robust image watermarking based on multiband wavelets and empirical mode decomposition,” IEEE Trans. Image Process. 16(8), 1956–1966 (2007).
[CrossRef] [PubMed]

Takai, N.

Tan, Q.

Tao, R.

Wang, Y.

Xi, L.

Xia, M.

M. Liu, G. Yang, H. Xie, M. Xia, J. Hu, and H. Zha, “Computer-generated hologram watermarking resilient to rotation and scaling,” Opt. Eng. 46(6), 060501 (2007).
[CrossRef]

Xiao-Feng, L.

Xie, H.

M. Liu, G. Yang, H. Xie, M. Xia, J. Hu, and H. Zha, “Computer-generated hologram watermarking resilient to rotation and scaling,” Opt. Eng. 46(6), 060501 (2007).
[CrossRef]

Xin, Y.

Xin, Z.

Yang, G.

M. Liu, G. Yang, H. Xie, M. Xia, J. Hu, and H. Zha, “Computer-generated hologram watermarking resilient to rotation and scaling,” Opt. Eng. 46(6), 060501 (2007).
[CrossRef]

Yang, X.

H. Zhai, F. Liu, X. Yang, G. Mu, and P. Chavel, “Improving binary images reconstructed from kinoforms by amplitude adjustment,” Opt. Commun. 219(1-6), 81–85 (2003).
[CrossRef]

Yang, Z.

N. Bi, Q. Sun, D. Huang, Z. Yang, and J. Huang, “Robust image watermarking based on multiband wavelets and empirical mode decomposition,” IEEE Trans. Image Process. 16(8), 1956–1966 (2007).
[CrossRef] [PubMed]

Zha, H.

M. Liu, G. Yang, H. Xie, M. Xia, J. Hu, and H. Zha, “Computer-generated hologram watermarking resilient to rotation and scaling,” Opt. Eng. 46(6), 060501 (2007).
[CrossRef]

Zhai, H.

H. Zhai, F. Liu, X. Yang, G. Mu, and P. Chavel, “Improving binary images reconstructed from kinoforms by amplitude adjustment,” Opt. Commun. 219(1-6), 81–85 (2003).
[CrossRef]

Zhang, X.

Zhao, D.

S. Deng, L. Liu, H. Lang, D. Zhao, and X. Liu, “Watermarks encrypted in the cascaded Fresnel digital hologram,” Optik (Stuttg.) 118, 302–305 (2007).
[CrossRef]

S. Deng, L. Liu, H. Lang, W. Pan, and D. Zhao, “Hiding an image in cascaded Fresnel digital holograms,” Chin. Opt. Lett. 4, 268–271 (2006).

Appl. Opt. (3)

Chin. Opt. Lett. (1)

Electron. Commun. Jpn. (1)

Y. Aoki, “Watermarking technique using computer-generated holograms,” Electron. Commun. Jpn. 84(1), 21–31 (2001).
[CrossRef]

IEEE Signal Process. Lett. (2)

S.-C. Pei and W.-L. Hsue, “Random discrete fractional Fourier transform,” IEEE Signal Process. Lett. 16(12), 1015–1018 (2009).
[CrossRef]

S.-C. Pei and W.-L. Hsue, “The multiple-parameter discrete fractional Fourier transform,” IEEE Signal Process. Lett. 13(6), 329–332 (2006).
[CrossRef]

IEEE Trans. Circ. Syst. Video Tech. (1)

P. Bao, “Xiaohu Ma, “Image adaptive watermarking using wavelet domain singular value decomposition,” IEEE Trans. Circ. Syst. Video Tech. 15, 96–102 (2005).
[CrossRef]

IEEE Trans. Image Process. (2)

N. Bi, Q. Sun, D. Huang, Z. Yang, and J. Huang, “Robust image watermarking based on multiband wavelets and empirical mode decomposition,” IEEE Trans. Image Process. 16(8), 1956–1966 (2007).
[CrossRef] [PubMed]

M. Barni, F. Bartolini, and A. Piva, “Improved wavelet-based watermarking through pixel-wise masking,” IEEE Trans. Image Process. 10(5), 783–791 (2001).
[CrossRef]

IEEE Trans. Multimed. (1)

W.-H. Lin, S.-J. Horng, T.-W. Kao, P. Fan, C.-L. Lee, and Y. Pan, “An efficient watermarking method based on significant difference of wavelet coefficient quantization,” IEEE Trans. Multimed. 10(5), 746–757 (2008).
[CrossRef]

IEEE Trans. Signal Process. (1)

C. Candan, M. A. Kutay, and H. M. Ozaktas, “The discrete fractional Fourier transform,” IEEE Trans. Signal Process. 48(5), 1329–1337 (2000).
[CrossRef]

Opt. Commun. (1)

H. Zhai, F. Liu, X. Yang, G. Mu, and P. Chavel, “Improving binary images reconstructed from kinoforms by amplitude adjustment,” Opt. Commun. 219(1-6), 81–85 (2003).
[CrossRef]

Opt. Eng. (1)

M. Liu, G. Yang, H. Xie, M. Xia, J. Hu, and H. Zha, “Computer-generated hologram watermarking resilient to rotation and scaling,” Opt. Eng. 46(6), 060501 (2007).
[CrossRef]

Opt. Express (3)

Opt. Lett. (2)

Optik (Stuttg.) (1)

S. Deng, L. Liu, H. Lang, D. Zhao, and X. Liu, “Watermarks encrypted in the cascaded Fresnel digital hologram,” Optik (Stuttg.) 118, 302–305 (2007).
[CrossRef]

Pattern Recognit. Lett. (1)

A. Reddy and B. Chatterji, “A new wavelet based logo-watermarking scheme,” Pattern Recognit. Lett. 26(7), 1019–1027 (2005).
[CrossRef]

Other (1)

K. Deng, G. Yang, and C. Zhang, “Burch computer-generated hologram watermarking resilient to strong cropping attack,” Biomedical Optics and 3-D Imaging (BIOMED) Topical Meeting, OSA Optics and Photonics Congress, April 2010, in Miami, FL, USA.

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Figures (14)

Fig. 1
Fig. 1

(a) Cover image, (b) RFrFT amplitude image of the cover image (a), (c) RFrFT phase image of the cover image (a).

Fig. 2
Fig. 2

Reconstructed image (a) with wrong order, (b) with wrong phase key, (c) with right order and right phase key.

Fig. 3
Fig. 3

Kinoform watermark generation flowchart.

Fig. 4
Fig. 4

Blocks and 2-level DWT coefficients selection.

Fig. 5
Fig. 5

Kinoform watermark embedding flowchart.

Fig. 6
Fig. 6

(a) Original cover image (256✕256 pixels), (b) original watermark (64✕64 pixels).

Fig. 7
Fig. 7

(a) Non-cascade encrypted kinoform, (b) watermarked image (PSNR = 42.34), (c) extracted kinoform, (d) reconstructed watermark (NCC = 0.9592).

Fig. 8
Fig. 8

NMSE value and iterative loops for non-cascade encrypted kinoform generation.

Fig. 9
Fig. 9

Extracted watermark with right phase key and (a) withα = 0.15, NMSE = 0.9111, NCC = 0.2981, (b) with α = 0.8, NMSE = 0.6647, NCC = 0.5791, (c) with α = 0.8718, NMSE = 0.0757, NCC = 0.9614, (d) with α = 0.9, NMSE = 0.3738, NCC = 0.7913, (e) with α = 0.99, NMSE = 0.7327, NCC = 0.5170.

Fig. 11
Fig. 11

The NMSE value in kinoform reconstruction with different fractional order by the right phase key and wrong phase key.

Fig. 10
Fig. 10

Extracted watermark with wrong phase key and (a) with α = 0.15, NMSE = 0.9201, NCC = 0.2826, (b) with α = 0.8, NMSE = 0.9270, NCC = 0.2702, (c) with α = 0.8718, NMSE = 0.9257, NCC = 0.2726, (d) with α = 0.9, NMSE = 0.9230, NCC = 0.2775, (e) with α = 0.99, NMSE = 0.9178, NCC = 0.2867.

Fig. 12
Fig. 12

(a) Watermarked image suffering from 30% JPEG compression, P S N R = 27.38 d B , (b) watermarked image suffering from 5% JPEG Compression, P S N R = 23.70 d B , (c) extracted watermark from (a), N C C = 0.6885 , (d) extracted watermark from (b), N C C = 0.6132.

Fig. 13
Fig. 13

Robustness to resist cropping attack (a) column attack 50%, P S N R = 8.46 d B , (b) cross attack 44%, P S N R = 10.03 d B , (c) anonymous attack P S N R = 7.83 d B , (d) circle attack P S N R = 9.72 d B , (e) extracted watermark from (a) N C C = 0.7465 , (f) extracted watermark from (b) N C C = 0.7634 , (g) extracted watermark from (c) N C C = 0.7142 , (h) extracted watermark from (d) .

Fig. 14
Fig. 14

Reconstruction of extracted kinoform under different attacks (a) Gaussian noise (sigma = 0.001), (b) Salt and pepper noise (0.01), (c) Gaussian filtering (4✕4, sigma = 1), (d) Average filtering (4✕4), (e) Median filtering (4✕4), (f) Motion Blurring, (g) Histogram Equalization.

Tables (1)

Tables Icon

Table 1 Robust to Different Attacks

Equations (12)

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F α { f ( x ) } ( u ) = f ( x ) K α ( x ; u ) d x ,
K α ( x ; u ) = A α exp [ i π ( u 2 + x 2 tan θ α 2 x u sin θ α ) ] ,
A α = 1 i cot θ α ,
θ α = α π / 2.
α { f ( x ) } ( u ) = f ( x ) K ' α ( x ; u ) d x ,
{ A ( u , v ) e j ϕ ( u , v ) = α P { ω ( x , y ) e j φ ( x , y ) } ω ( x , y ) e j φ ( x , y ) = α P * { A ( u , v ) e j ϕ ( u , v ) } .
{ | C i ' | = | A i | + γ i K i m i Δ | C i ' C i | β i | C i | C i ' C i > 0 .
K i ' = | C i | | A i | + m i Δ γ i .
W ' ( x , y ) = | α P * { e j K ' ( u , v ) } | .
P S N R = 10 log 10 L 2 1 N x N y x = 1 N x y = 1 N y [ I o ( x , y ) I w ( x , y ) ] 2     d B ,
N C C = i j W i j W i j ' i j ( W i j ) 2 ,
N M S E = 1 N x N y x = 1 N x y = 1 N y [ I o ( x , y ) α I r ( x , y ) ] 2 ,

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