Abstract

In practical applications of three-dimensional integral imaging, the captured elemental image array (EIA) needs to be stored and delivered through the Internet. Therefore, there is an urgent need for protecting the copyright of EIA against piracy and malicious manipulation. In our work, we propose a copyright protection algorithm for EIA by combining the use of the modified hypercomplex Fourier transform (HFT) and the adaptive texturized holographic algorithm. The modified HFT can accurately extract the features from each elemental image. According to these features, we embed watermark into the visually less noticeable regions of the EIA to increase the visual perception. In addition, an adaptive texturized holographic algorithm is proposed to increase the robustness. Finally, the analytical performances are contrasted with simulation results where the imperceptibility and robustness of the proposed method are evaluated against standard attacks.

© 2017 Optical Society of America

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References

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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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2016 (2)

N. Zhou, S. Pan, S. Cheng, and Z. Zhou, “Image compression–encryption scheme based on hyper-chaotic system and 2D compressive sensing,” Opt. Laser Technol. 82, 121–133 (2016).
[Crossref]

X. Li, C. Li, and I.-K. Lee, “Chaotic image encryption using pseudo-random masks and pixel mapping,” Signal Process. 125, 48–63 (2016).
[Crossref]

2015 (1)

2014 (2)

2013 (5)

2012 (1)

2011 (1)

A. Aggoun, “Compression of 3D integral images using 3D wavelet transform,” J. Disp. Technol. 7(11), 586–592 (2011).
[Crossref]

2010 (1)

B. Lee, H. Kang, and E. Kim, “Occlusion removal method of partially occluded object using variance in computational integral imaging,” 3D Research 1(2), 6–10 (2010).
[Crossref]

2008 (2)

2007 (3)

2006 (1)

2005 (1)

2004 (2)

2003 (1)

2001 (2)

S. Liu, Y. Li, and B. Zhu, “Optical image encryption by cascaded fractional Fourier transforms with random phase filtering,” Opt. Commun. 187(3), 57–63 (2001).
[Crossref]

M. Hsieh, D. Tseng, and Y. Huang, “Hiding digital watermarks using multiresolution wavelet transform,” IEEE Trans. Ind. Electron. 48(5), 875–882 (2001).
[Crossref]

1998 (1)

L. Itti, C. Koch, and E. Niebur, “A model of saliency-based visual attention for rapid scene analysis,” IEEE Trans. Pattern Anal. Mach. Intell. 20(11), 1254–1259 (1998).
[Crossref]

Aggoun, A.

A. Aggoun, “Compression of 3D integral images using 3D wavelet transform,” J. Disp. Technol. 7(11), 586–592 (2011).
[Crossref]

An, X.

J. Li, M. D. Levine, X. An, X. Xu, and H. He, “Visual saliency based on scale-space analysis in the frequency domain,” IEEE Trans. Pattern Anal. Mach. Intell. 35(4), 996–1010 (2013).
[Crossref] [PubMed]

Castro, A.

Chen, Y.

Cheng, S.

N. Zhou, S. Pan, S. Cheng, and Z. Zhou, “Image compression–encryption scheme based on hyper-chaotic system and 2D compressive sensing,” Opt. Laser Technol. 82, 121–133 (2016).
[Crossref]

Cho, M.

Frauel, Y.

Gong, X.

H. Wu, J. Zhou, and X. Gong, “A novel image watermarking algorithm based on two-dimensional cellular automata transform,” in Proceedings of Conference of Information Technology and Artificial Intelligence (IEEE, 2011), pp. 206–210.
[Crossref]

Guo, B.

He, H.

J. Li, M. D. Levine, X. An, X. Xu, and H. He, “Visual saliency based on scale-space analysis in the frequency domain,” IEEE Trans. Pattern Anal. Mach. Intell. 35(4), 996–1010 (2013).
[Crossref] [PubMed]

Hong, S. H.

Horisaki, R.

Hsieh, M.

M. Hsieh, D. Tseng, and Y. Huang, “Hiding digital watermarks using multiresolution wavelet transform,” IEEE Trans. Ind. Electron. 48(5), 875–882 (2001).
[Crossref]

Huang, Y.

M. Hsieh, D. Tseng, and Y. Huang, “Hiding digital watermarks using multiresolution wavelet transform,” IEEE Trans. Ind. Electron. 48(5), 875–882 (2001).
[Crossref]

Hwang, D.

D. Hwang, D. Shin, and E. Kim, “A novel three-dimensional digital watermarking scheme basing on integral imaging,” Opt. Commun. 277(1), 40–49 (2007).
[Crossref]

Itti, L.

L. Itti, C. Koch, and E. Niebur, “A model of saliency-based visual attention for rapid scene analysis,” IEEE Trans. Pattern Anal. Mach. Intell. 20(11), 1254–1259 (1998).
[Crossref]

Jang, J. S.

Javidi, B.

Kang, H.

B. Lee, H. Kang, and E. Kim, “Occlusion removal method of partially occluded object using variance in computational integral imaging,” 3D Research 1(2), 6–10 (2010).
[Crossref]

Kang, H. H.

Kim, B.

Kim, E.

B. Lee, H. Kang, and E. Kim, “Occlusion removal method of partially occluded object using variance in computational integral imaging,” 3D Research 1(2), 6–10 (2010).
[Crossref]

D. Hwang, D. Shin, and E. Kim, “A novel three-dimensional digital watermarking scheme basing on integral imaging,” Opt. Commun. 277(1), 40–49 (2007).
[Crossref]

Kim, E. S.

Kim, S.

X. Li and S. Kim, “Optical 3D watermark based digital image watermarking for telemedicine,” Opt. Lasers Eng. 51(12), 1310–1320 (2013).
[Crossref]

Koch, C.

L. Itti, C. Koch, and E. Niebur, “A model of saliency-based visual attention for rapid scene analysis,” IEEE Trans. Pattern Anal. Mach. Intell. 20(11), 1254–1259 (1998).
[Crossref]

Lee, B.

B. Lee, H. Kang, and E. Kim, “Occlusion removal method of partially occluded object using variance in computational integral imaging,” 3D Research 1(2), 6–10 (2010).
[Crossref]

Lee, B. G.

Lee, I. K.

Lee, I.-K.

X. Li, C. Li, and I.-K. Lee, “Chaotic image encryption using pseudo-random masks and pixel mapping,” Signal Process. 125, 48–63 (2016).
[Crossref]

Lee, J. H.

Leval, J.

Levine, M. D.

J. Li, M. D. Levine, X. An, X. Xu, and H. He, “Visual saliency based on scale-space analysis in the frequency domain,” IEEE Trans. Pattern Anal. Mach. Intell. 35(4), 996–1010 (2013).
[Crossref] [PubMed]

Li, C.

X. Li, C. Li, and I.-K. Lee, “Chaotic image encryption using pseudo-random masks and pixel mapping,” Signal Process. 125, 48–63 (2016).
[Crossref]

Li, J.

J. Li, M. D. Levine, X. An, X. Xu, and H. He, “Visual saliency based on scale-space analysis in the frequency domain,” IEEE Trans. Pattern Anal. Mach. Intell. 35(4), 996–1010 (2013).
[Crossref] [PubMed]

Li, X.

X. Li, C. Li, and I.-K. Lee, “Chaotic image encryption using pseudo-random masks and pixel mapping,” Signal Process. 125, 48–63 (2016).
[Crossref]

X. Li and S. Kim, “Optical 3D watermark based digital image watermarking for telemedicine,” Opt. Lasers Eng. 51(12), 1310–1320 (2013).
[Crossref]

Li, X. W.

Li, Y.

S. Liu, Y. Li, and B. Zhu, “Optical image encryption by cascaded fractional Fourier transforms with random phase filtering,” Opt. Commun. 187(3), 57–63 (2001).
[Crossref]

Liu, S.

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

S. Liu, Y. Li, and B. Zhu, “Optical image encryption by cascaded fractional Fourier transforms with random phase filtering,” Opt. Commun. 187(3), 57–63 (2001).
[Crossref]

Liu, Z.

Muniraj, I.

Naughton, T. J.

Niebur, E.

L. Itti, C. Koch, and E. Niebur, “A model of saliency-based visual attention for rapid scene analysis,” IEEE Trans. Pattern Anal. Mach. Intell. 20(11), 1254–1259 (1998).
[Crossref]

Pan, S.

N. Zhou, S. Pan, S. Cheng, and Z. Zhou, “Image compression–encryption scheme based on hyper-chaotic system and 2D compressive sensing,” Opt. Laser Technol. 82, 121–133 (2016).
[Crossref]

Picart, P.

Ponce-Díaz, R.

Shin, D.

D. Hwang, D. Shin, and E. Kim, “A novel three-dimensional digital watermarking scheme basing on integral imaging,” Opt. Commun. 277(1), 40–49 (2007).
[Crossref]

Shin, D. H.

Situ, G.

Stern, A.

Tanida, J.

Tseng, D.

M. Hsieh, D. Tseng, and Y. Huang, “Hiding digital watermarks using multiresolution wavelet transform,” IEEE Trans. Ind. Electron. 48(5), 875–882 (2001).
[Crossref]

Wang, X.

Wu, H.

H. Wu, J. Zhou, and X. Gong, “A novel image watermarking algorithm based on two-dimensional cellular automata transform,” in Proceedings of Conference of Information Technology and Artificial Intelligence (IEEE, 2011), pp. 206–210.
[Crossref]

Xiao, X.

Xu, X.

J. Li, M. D. Levine, X. An, X. Xu, and H. He, “Visual saliency based on scale-space analysis in the frequency domain,” IEEE Trans. Pattern Anal. Mach. Intell. 35(4), 996–1010 (2013).
[Crossref] [PubMed]

Yeom, S.

Yoo, H.

Yu, S.

Zhang, J.

Zhang, Q.

Zhou, J.

H. Wu, J. Zhou, and X. Gong, “A novel image watermarking algorithm based on two-dimensional cellular automata transform,” in Proceedings of Conference of Information Technology and Artificial Intelligence (IEEE, 2011), pp. 206–210.
[Crossref]

Zhou, N.

N. Zhou, S. Pan, S. Cheng, and Z. Zhou, “Image compression–encryption scheme based on hyper-chaotic system and 2D compressive sensing,” Opt. Laser Technol. 82, 121–133 (2016).
[Crossref]

Zhou, Z.

N. Zhou, S. Pan, S. Cheng, and Z. Zhou, “Image compression–encryption scheme based on hyper-chaotic system and 2D compressive sensing,” Opt. Laser Technol. 82, 121–133 (2016).
[Crossref]

Zhu, B.

S. Liu, Y. Li, and B. Zhu, “Optical image encryption by cascaded fractional Fourier transforms with random phase filtering,” Opt. Commun. 187(3), 57–63 (2001).
[Crossref]

3D Research (1)

B. Lee, H. Kang, and E. Kim, “Occlusion removal method of partially occluded object using variance in computational integral imaging,” 3D Research 1(2), 6–10 (2010).
[Crossref]

Appl. Opt. (1)

IEEE Trans. Ind. Electron. (1)

M. Hsieh, D. Tseng, and Y. Huang, “Hiding digital watermarks using multiresolution wavelet transform,” IEEE Trans. Ind. Electron. 48(5), 875–882 (2001).
[Crossref]

IEEE Trans. Pattern Anal. Mach. Intell. (2)

J. Li, M. D. Levine, X. An, X. Xu, and H. He, “Visual saliency based on scale-space analysis in the frequency domain,” IEEE Trans. Pattern Anal. Mach. Intell. 35(4), 996–1010 (2013).
[Crossref] [PubMed]

L. Itti, C. Koch, and E. Niebur, “A model of saliency-based visual attention for rapid scene analysis,” IEEE Trans. Pattern Anal. Mach. Intell. 20(11), 1254–1259 (1998).
[Crossref]

J. Disp. Technol. (1)

A. Aggoun, “Compression of 3D integral images using 3D wavelet transform,” J. Disp. Technol. 7(11), 586–592 (2011).
[Crossref]

J. Opt. Soc. Am. A (1)

Opt. Commun. (2)

D. Hwang, D. Shin, and E. Kim, “A novel three-dimensional digital watermarking scheme basing on integral imaging,” Opt. Commun. 277(1), 40–49 (2007).
[Crossref]

S. Liu, Y. Li, and B. Zhu, “Optical image encryption by cascaded fractional Fourier transforms with random phase filtering,” Opt. Commun. 187(3), 57–63 (2001).
[Crossref]

Opt. Express (10)

S. Yeom, A. Stern, and B. Javidi, “Compression of 3D color integral images,” Opt. Express 12(8), 1632–1642 (2004).
[Crossref] [PubMed]

H. H. Kang, J. H. Lee, and E. S. Kim, “Enhanced compression rate of integral images by using motion-compensated residual images in three-dimensional integral-imaging,” Opt. Express 20(5), 5440–5459 (2012).
[Crossref] [PubMed]

S. H. Hong, J. S. Jang, and B. Javidi, “Three-dimensional volumetric object reconstruction using computational integral imaging,” Opt. Express 12(3), 483–491 (2004).
[Crossref] [PubMed]

H. Yoo, “Axially moving a lenslet array for high-resolution 3D images in computational integral imaging,” Opt. Express 21(7), 8873–8878 (2013).
[Crossref] [PubMed]

D. H. Shin and H. Yoo, “Scale-variant magnification for computational integral imaging and its application to 3D object correlator,” Opt. Express 16(12), 8855–8867 (2008).
[Crossref] [PubMed]

A. Stern and B. Javidi, “3-D computational synthetic aperture integral imaging (COMPSAII),” Opt. Express 11(19), 2446–2451 (2003).
[Crossref] [PubMed]

R. Horisaki, X. Xiao, J. Tanida, and B. Javidi, “Feasibility study for compressive multi-dimensional integral imaging,” Opt. Express 21(4), 4263–4279 (2013).
[Crossref] [PubMed]

Y. Chen, X. Wang, J. Zhang, S. Yu, Q. Zhang, and B. Guo, “Resolution improvement of integral imaging based on time multiplexing sub-pixel coding method on common display panel,” Opt. Express 22(15), 17897–17907 (2014).
[Crossref] [PubMed]

Y. Frauel, A. Castro, T. J. Naughton, and B. Javidi, “Resistance of the double random phase encryption against various attacks,” Opt. Express 15(16), 10253–10265 (2007).
[Crossref] [PubMed]

X. W. Li and I. K. Lee, “Robust copyright protection using multiple ownership watermarks,” Opt. Express 23(3), 3035–3046 (2015).
[Crossref] [PubMed]

Opt. Laser Technol. (1)

N. Zhou, S. Pan, S. Cheng, and Z. Zhou, “Image compression–encryption scheme based on hyper-chaotic system and 2D compressive sensing,” Opt. Laser Technol. 82, 121–133 (2016).
[Crossref]

Opt. Lasers Eng. (1)

X. Li and S. Kim, “Optical 3D watermark based digital image watermarking for telemedicine,” Opt. Lasers Eng. 51(12), 1310–1320 (2013).
[Crossref]

Opt. Lett. (4)

Signal Process. (1)

X. Li, C. Li, and I.-K. Lee, “Chaotic image encryption using pseudo-random masks and pixel mapping,” Signal Process. 125, 48–63 (2016).
[Crossref]

Other (2)

H. Wu, J. Zhou, and X. Gong, “A novel image watermarking algorithm based on two-dimensional cellular automata transform,” in Proceedings of Conference of Information Technology and Artificial Intelligence (IEEE, 2011), pp. 206–210.
[Crossref]

C. Li and Y. Hu, “Salient traffic sign detection based on multiscale hypercomplex Fourier transform,” in proceedings of IEEE International Congress on Image and Signal (IEEE 2011), pp.1963–1966.
[Crossref]

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Figures (21)

Fig. 1
Fig. 1

Analysis of self-correlation: (a) a usual image, (b) EIA generated by the usual image.

Fig. 2
Fig. 2

Procedure for computing saliency using the proposed HFT.

Fig. 3
Fig. 3

2D A ijkl basis function rule = 14, initial configuration = 11010100. A 00kl is the block at the extreme upper left corner. The top row denotes 0j<8, i=0. The left column is j=0, 0i<8.

Fig. 4
Fig. 4

Evolution of CAs with rules 30, 45, 82, 146, 182, 195 and 210.

Fig. 5
Fig. 5

Generating the HFT mask in the CA transform domains.

Fig. 6
Fig. 6

Block diagram of the stages used in HFT to generate the watermarked image.

Fig. 7
Fig. 7

Watermark extraction process.

Fig. 8
Fig. 8

The EIA capture device used in this experiment.

Fig. 9
Fig. 9

Responses to the elemental images of 3D scene ‘Doll’: The first row shows the original elemental images and corresponding saliency maps with three algorithms: (a) EIA of 3D scene ‘Doll’, (b) saliency map with Itti, (c) saliency map with HFT, (d) saliency map with our proposed HFT models; (e) correlation of EIA of 3D scene ‘Doll’, (f) correlation of saliency map with Itti, (g) correlation of saliency map with HFT, (h) correlation of saliency map with our proposed HFT models.

Fig. 10
Fig. 10

Responses to the elemental images of 3D scene ‘Cars’: The first row shows the original elemental images and corresponding saliency maps with three algorithms: (a) EIA of 3D scene ‘Cars’, (b) saliency map with Itti, (c) saliency map with HFT, (d) saliency map with our proposed HFT models; (e)-(f) correlations of EIA of ‘3D scene ‘Cars’, Itti, HFT, and our proposed HFT models.

Fig. 11
Fig. 11

Demonstration of adaptively texturizing a hologram to visually match the host EIA. First column: a sample texturized holograms before embedding. Second column: original EIA. Third column: watermarked EIA, all embedded with the same alpha map. Fourth column: enlarged watermarked EIA.

Fig. 12
Fig. 12

(Upper row) Imperceptibility test of method in [22]: watermarked image, SSIM map of the watermarked image, reconstructed 3D scene ‘Doll’, and SSIM map of 3D scene. (Lower row) Imperceptibility test of the proposed watermarking method.

Fig. 13
Fig. 13

(Upper row) Imperceptibility test of method in [22]: watermarked image, SSIM map of the watermarked image, reconstructed 3D scene ‘Cars’, and SSIM map of 3D scene. (Lower row) Imperceptibility test of the proposed watermarking method.

Fig. 14
Fig. 14

(a) Effects of attack type and reconstructed watermarks on robustness measured by BCR: (a) Gaussian noise with standard deviation of 0.12. (b) Salt & pepper with noise density 0.12. (c) Speckle noise with variance of 0.12. (d) Median filter with size of 3×3. (e) JPEG compression with the compression ratio of 40%. (f) Cropping attack with cropping size of 500×500pixels.

Fig. 15
Fig. 15

(a) Reconstructed watermarks on robustness: (a) our proposed method under Gaussian noise with standard deviation of 0.12, (b) the method of [21] with standard deviation of 0.12, (c) and (d) the method of [20] with standard deviation of 0.12 and 0.06, respectively; (e) our proposed method under salt & pepper with noise density of 0.12, (f) the method of [21] under salt & pepper with noise density of 0.12, (g) and (h) the method of [20] with noise density of 0.12 and 0.06, respectively; (i) our proposed method under speckle noise with variance of 0.12, (g) the method of [21] under speckle noise with variance of 0.12, (k) and (l) the method of [20] with variance of 0.12 and 0.06, respectively.

Fig. 16
Fig. 16

(a) Reconstructed watermarks on robustness: (a) our proposed method under Gaussian noise with median filter with size of 3×3, (b) the method of [21] under Gaussian noise with median filter with size of 3×3, (c) and (d) the method of [20] with the filter size of 3×3 and 2×2, respectively; (e) our proposed method with the compression ratio of 10%, (f) the method of [21] with the compression ratio of 10%, (g) and (h) the method of [20] with the compression ratio of 10% and 40%, respectively; (i) our proposed method with cropping size of 500×500, (g) the method of [21] with cropping size of 500×500, (k) and (l) the method of [20] with the cropping size of 500×500and 300×300, respectively.

Fig. 17
Fig. 17

(a) Reconstructed watermarks with Gaussian noise, salt & pepper, and speckle noise attack: the first column shows results of our proposed method; the second column shows results of the method of [22]; the third column shows results of the method in [24].

Fig. 18
Fig. 18

(a) Reconstructed watermarks with median filter, JPEG compression, and cropping attack: the first column shows results of our proposed method; the second column shows results of the method of [22]; the third column shows results of the method in [24].

Fig. 19
Fig. 19

(a) Effects of Gaussian noise and salt & pepper noise attacks on robustness measured by BCR: (a) Gaussian noise with the Gaussian standard deviations from 0.02 to 0.14. (b) Salt & pepper noise with the noise density from 0.02 to 0.14.

Fig. 20
Fig. 20

(a) Effects of speckle noise and median filter attacks on robustness measured by BCR: (a) speckle noise with the variance from 0.02 to 0.14. (b) Median filter with the window size from 2×2 to 5×5.

Fig. 21
Fig. 21

(a) Effects of JPEG compression and cropping attacks on robustness measured by BCR: (a) JPEG compression with the compression ratio from 10% to 90%. (b) Cropping with the size from 100×100 to 600×600.

Tables (3)

Tables Icon

Table 1 BCR values with Gaussian noise, salt & pepper, and speckle noise attack.

Tables Icon

Table 2 BCR values with median filter, JPEG compression, and cropping attack.

Tables Icon

Table 3 Average embedding/extraction speed of EIAs.

Equations (27)

Equations on this page are rendered with MathJax. Learn more.

s=H μ 1 +S μ 2 +V μ 3 ,
s= f 1 + f 2 μ 1 ,
f 1 =H μ 1 ,
f 2 =S+V μ 2 .
S(u,v)= F 1 (u,v)+ F 2 (u,v) μ 1 ,
F k (k=1,2) (u,v)= 1 MN x=0 M1 y=0 N1 e μ 1 2π(xu/M)+(yv/N)) f k (x,y) ,
f k (x,y)= 1 MN u=0 M1 v=0 N1 e μ 1 2π(xu/M)+(yv/N)) F k (u,v) .
S(u,v)= S(u,v) e μ 1 ϕ(u,v) ,
sM=g× S 1 (u,v) 2 ,
f o,l (x,y)= f o,l (x,y)+ α o,l sM( f o,l (x,y)) w o,l (x,y),
α o, l = (x,y) Max over all (o,l) (sM( f o,l (x,y)))sM( f o,l (x,y)) Max over all (o,l) (sM( f o,l (x,y))) .
f ij = k=0 N1 l=0 N1 c kl A ijkl ,
A ijkl =A A ik jl
A ik =α+β a ik a ki
c kl = f ij B ijkl ,
A(x,y)= A 0 (x,y)exp[j ψ 0 (x,y)],
O(x,y, d 0 )=A(x,y) i λ d 0 exp[ 2iπ d 0 λ ]×exp[ iπ λ d 0 ( x 2 + y 2 ) ],
r(x,y)= a R exp[2jπ( μ R x+ ν R y)+jΔψ(x,y)],
ψ(x,y)=exp[ j 2π λ ( k x x+ k y y) ]exp(jϕ(t)),
H(x,y, d 0 )= | O(x,y, d 0 ) | 2 + | r(x,y) | 2 + r (x,y)O(x,y, d 0 )+r(x,y) O (x,y, d 0 ).
( x y )=( 1 1 1 0 )( x y )(modN).
f (x,y)=f(x,y)×(1+β×n(x,y)),
SSIM(x,y)= (2 μ x μ y + c 1 )(2 σ xy + c 2 ) ( μ x 2 + μ y 2 + c 1 )( σ x 2 + σ y 2 + c 2 ) ,
c 1 = ( k 1 L) 2 , c 2 = ( k 2 L) 2
PSNR(O, O )=10 log 10 255 2 MSE(x,y) ,
MSE(x,y)= 1 MN x=0 M1 y=0 N1 [ O(x,y) O (x,y) ] 2 ,
BCR=( 1 i=1 L M w i w i L M ),

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