Abstract

This paper realizes an optical 3D images encryption and reconstruction by employing the geometric calibration algorithm to the monospectral synthetic aperture integral imaging system. This method has the simultaneous advantages of improving the quality of 3D images by eliminating the crosstalk from the unaligned cameras and increasing security of the multispectral 3D images encryption by importing the random generated maximum-length cellular automata into the Fresnel transform encoding algorithm. Furthermore, compared with the previous 3D images encryption methods of encrypting 3D multispectral information, the proposed method only encrypts monospectral data, which will greatly minimize the complexity. We present experimental results of 3D image encryption and volume pixel computational reconstruction to test and verify the performance of the proposed method. Experimental results validate the feasibility and robustness of our proposed approach, even under severe degradation.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
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References

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2018 (1)

X. Li, D. Xiao, and Q. Wang, “Error-free holographic frames encryption with CA pixel-permutation encoding algorithm,” Opt. Laser Eng. 100, 200–207 (2018).
[Crossref]

2017 (2)

2016 (5)

2015 (4)

Z. Xiong, Q. Wang, Y. Xing, H. Deng, and D. Li, “An active integral imaging system based on multiple structured light method,” Opt. Express 23(21), 27095–27104 (2015).
[Crossref]

X. Li and I. Lee, “Modified computational integral imaging-based double image encryption using fractional Fourier transform,” Opt. Laser Eng. 66, 112–121 (2015).
[Crossref]

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

Y. Wang, Y. Shen, Y. Lin, and B. Javidi, “Extended depth-of-field 3D endoscopy with synthetic aperture integral imaging using an electrically tunable focal-length liquid-crystal lens,” Opt. Lett. 40(15), 3564–3567 (2015).
[Crossref] [PubMed]

2014 (7)

2013 (6)

2012 (1)

2010 (2)

2009 (1)

A. Alfalou and C. Brosseau, “Optical image compression and encryption methods,” Adv. Opt. Photonics 1(3), 589–636 (2009)
[Crossref]

2008 (2)

W. Qin and X. Peng, “Asymmetric cryptosystem based on phase-truncated Fourier transforms,” Opt. Lett. 35(2), 581–583 (2008).

R. Tao, J. Lang, and Y. Wang, “Optical image encryption based on the multiple-parameter fractional Fourier transform,” Opt. Lett. 33(6), 581–583 (2008).
[Crossref] [PubMed]

2007 (3)

D. Shin and H. Yoo, “Image quality enhancement in 3D computational integral imaging by use of interpolation methods,” Opt. Express 15(19), 12039–12049 (2007).
[Crossref] [PubMed]

S. Liu, J. Xu, Y. Zhang, L. Chen, and C. Li, “General optical implementations of fractional Fourier transforms,” Opt. Lett. 20(9), 2088–2090 (2007).
[Crossref]

S. Cho, U. Choi, H. Kim, Y. Hwang, J. Kim, and S. Heo, “New synthesis of one-dimensional 90/150 linear hybrid group cellular automata,” IEEE Trans. Comput. AID D. 26(9), 1720–1724 (2007).
[Crossref]

2006 (3)

2005 (1)

2004 (2)

2003 (1)

2000 (1)

Z. Zhang, “A flexible new technique for camera calibration,” IEEE Trans. Pattern Anal. Machine Intell. 22(11), 1330–1334 (2000).
[Crossref]

1995 (1)

Ahmad, M.

Alfalou, A.

A. Alfalou and C. Brosseau, “Dual encryption scheme of images using polarized light,” Opt. Lett. 35(13), 2185–2187 (2010).
[Crossref] [PubMed]

A. Alfalou and C. Brosseau, “Optical image compression and encryption methods,” Adv. Opt. Photonics 1(3), 589–636 (2009)
[Crossref]

Brosseau, C.

A. Alfalou and C. Brosseau, “Dual encryption scheme of images using polarized light,” Opt. Lett. 35(13), 2185–2187 (2010).
[Crossref] [PubMed]

A. Alfalou and C. Brosseau, “Optical image compression and encryption methods,” Adv. Opt. Photonics 1(3), 589–636 (2009)
[Crossref]

Cao, L.

Chen, L.

S. Liu, J. Xu, Y. Zhang, L. Chen, and C. Li, “General optical implementations of fractional Fourier transforms,” Opt. Lett. 20(9), 2088–2090 (2007).
[Crossref]

L. Chen and D. Zhao, “Optical color image encryption by wavelength multiplexing and lensless Fresnel transform holograms,” Opt. Express 14(19), 8552–8560 (2006).
[Crossref] [PubMed]

Chen, W.

Chen, X.

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.

Cho, S.

S. Cho, U. Choi, H. Kim, Y. Hwang, J. Kim, and S. Heo, “New synthesis of one-dimensional 90/150 linear hybrid group cellular automata,” IEEE Trans. Comput. AID D. 26(9), 1720–1724 (2007).
[Crossref]

Choi, U.

S. Cho, U. Choi, H. Kim, Y. Hwang, J. Kim, and S. Heo, “New synthesis of one-dimensional 90/150 linear hybrid group cellular automata,” IEEE Trans. Comput. AID D. 26(9), 1720–1724 (2007).
[Crossref]

Deng, H.

Y. Xing, Q. Wang, Z. Xiong, and H. Deng, “Encrypting three-dimensional information system based on integral imaging and multiple chaotic maps,” Opt. Eng. 55(2), 023107 (2016).
[Crossref]

Z. Xiong, Q. Wang, Y. Xing, H. Deng, and D. Li, “An active integral imaging system based on multiple structured light method,” Opt. Express 23(21), 27095–27104 (2015).
[Crossref]

Gao, Q.

Gong, Q.

Guo, B.

Guo, Q.

Heo, S.

S. Cho, U. Choi, H. Kim, Y. Hwang, J. Kim, and S. Heo, “New synthesis of one-dimensional 90/150 linear hybrid group cellular automata,” IEEE Trans. Comput. AID D. 26(9), 1720–1724 (2007).
[Crossref]

Hong, K.

Hong, S.

Hwang, Y.

S. Cho, U. Choi, H. Kim, Y. Hwang, J. Kim, and S. Heo, “New synthesis of one-dimensional 90/150 linear hybrid group cellular automata,” IEEE Trans. Comput. AID D. 26(9), 1720–1724 (2007).
[Crossref]

Jang, J.

Javidi, B.

D. Kong, L. Cao, G. Jin, and B. Javidi, “Three-dimensional scene encryption and display based on computer-generated holograms,” Appl. Opt. 55(29), 8296–8300 (2016).
[Crossref] [PubMed]

Y. Wang, Y. Shen, Y. Lin, and B. Javidi, “Extended depth-of-field 3D endoscopy with synthetic aperture integral imaging using an electrically tunable focal-length liquid-crystal lens,” Opt. Lett. 40(15), 3564–3567 (2015).
[Crossref] [PubMed]

J. Wang, X. Xiao, and B. Javidi, “Three-dimensional integral imaging with flexible sensing,” Opt. Lett. 39(24), 6855–6858 (2014).
[Crossref] [PubMed]

A. Markman, J. Wang, and B. Javidi, “Three-dimensional integral imaging displays using a quick-response encoded elemental image array,” Optica 5(1), 332–335 (2014).
[Crossref]

W. Chen, B. Javidi, and X. Chen, “Advances in optical security systems,” Adv. Opt. Photonics 6(2), 120–155 (2014)
[Crossref]

M. Cho and B. Javidi, “Three-dimensional photon counting double-random-phase encryption,” Opt. Lett. 38(17), 3198–3201 (2013).
[Crossref] [PubMed]

M. Cho and B. Javidi, “Three-dimensional photon counting double-random-phase encryption,” Opt. Lett. 38(17), 3198–3201 (2013).
[Crossref] [PubMed]

X. Xiao, B. Javidi, M. Martinez-Corral, and A. Stern, “Advances in three-dimensional integral imaging: sensing, display, and applications,” Appl. Opt. 52(4), 546–560 (2013).
[Crossref] [PubMed]

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

A. Stern and B. Javidi, “Three-dimensional image sensing and reconstruction with time-division multiplexed computational integral imaging,” Appl. Opt. 42(35), 7036–7042 (2003).
[Crossref] [PubMed]

Jeong, Y.

Jin, G.

Jung, J.

Kim, B.

Kim, H.

S. Cho, U. Choi, H. Kim, Y. Hwang, J. Kim, and S. Heo, “New synthesis of one-dimensional 90/150 linear hybrid group cellular automata,” IEEE Trans. Comput. AID D. 26(9), 1720–1724 (2007).
[Crossref]

Kim, J.

J. Kim, J. Jung, Y. Jeong, K. Hong, and B. Lee, “Real-time integral imaging system for light field microscopy,” Opt. Express 22(9), 10210–10220 (2014).
[Crossref] [PubMed]

S. Cho, U. Choi, H. Kim, Y. Hwang, J. Kim, and S. Heo, “New synthesis of one-dimensional 90/150 linear hybrid group cellular automata,” IEEE Trans. Comput. AID D. 26(9), 1720–1724 (2007).
[Crossref]

Kim, S.

Kong, D.

Lang, J.

Lee, B.

Lee, I.

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

X. Li and I. Lee, “Modified computational integral imaging-based double image encryption using fractional Fourier transform,” Opt. Laser Eng. 66, 112–121 (2015).
[Crossref]

Li, C.

S. Liu, J. Xu, Y. Zhang, L. Chen, and C. Li, “General optical implementations of fractional Fourier transforms,” Opt. Lett. 20(9), 2088–2090 (2007).
[Crossref]

Li, D.

Z. Xiong, Q. Wang, Y. Xing, H. Deng, and D. Li, “An active integral imaging system based on multiple structured light method,” Opt. Express 23(21), 27095–27104 (2015).
[Crossref]

Li, H.

Li, L.

Li, T.

Li, X.

Lin, Y.

Liu, S.

Liu, Z.

Luo, Y.

Markman, A.

A. Markman, J. Wang, and B. Javidi, “Three-dimensional integral imaging displays using a quick-response encoded elemental image array,” Optica 5(1), 332–335 (2014).
[Crossref]

Martinez-Corral, M.

Muniraj, I.

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]

Peng, X.

W. Qin and X. Peng, “Asymmetric cryptosystem based on phase-truncated Fourier transforms,” Opt. Lett. 35(2), 581–583 (2008).

X. Peng, H. Wei, and P. Zhang, “Chosen-plaintext attack on lensless double-random phase encoding in the Fresnel domain,” Opt. Lett. 15(31), 3261–3263 (2006).
[Crossref]

X. Peng, P. Zhang, H. Wei, and B. Yu, “Known-plaintext attack on optical encryption based on double random phase keys,” Opt. Lett. 31(8), 1044–1046 (2006).
[Crossref] [PubMed]

Qin, W.

W. Qin and X. Peng, “Asymmetric cryptosystem based on phase-truncated Fourier transforms,” Opt. Lett. 35(2), 581–583 (2008).

Qin, Y.

Shen, Y.

Sheppard, C. JR

Shi, Y.

Shin, D.

Situ, G.

Stern, A.

Tao, R.

Wang, H.

Wang, J.

J. Wang, X. Xiao, and B. Javidi, “Three-dimensional integral imaging with flexible sensing,” Opt. Lett. 39(24), 6855–6858 (2014).
[Crossref] [PubMed]

A. Markman, J. Wang, and B. Javidi, “Three-dimensional integral imaging displays using a quick-response encoded elemental image array,” Optica 5(1), 332–335 (2014).
[Crossref]

Wang, Q.

X. Li, D. Xiao, and Q. Wang, “Error-free holographic frames encryption with CA pixel-permutation encoding algorithm,” Opt. Laser Eng. 100, 200–207 (2018).
[Crossref]

X. Li, S. Kim, and Q. Wang, “Copyright protection for elemental image array by hypercomplex Fourier transform and an adaptive texturized holographic algorithm,” Opt. Express 25(15), 17076–17098 (2017).
[Crossref] [PubMed]

X. Li, M. Zhao, Y. Xing, L. Li, S. Kim, X. Zhou, and Q. Wang, “Optical encryption via monospectral integral imaging,” Opt. Express 25(25), 31516–31527 (2017).
[Crossref] [PubMed]

Y. Xing, Q. Wang, Z. Xiong, and H. Deng, “Encrypting three-dimensional information system based on integral imaging and multiple chaotic maps,” Opt. Eng. 55(2), 023107 (2016).
[Crossref]

Z. Xiong, Q. Wang, Y. Xing, H. Deng, and D. Li, “An active integral imaging system based on multiple structured light method,” Opt. Express 23(21), 27095–27104 (2015).
[Crossref]

Wang, X.

Wang, Y.

Wang, Z.

Wei, H.

X. Peng, P. Zhang, H. Wei, and B. Yu, “Known-plaintext attack on optical encryption based on double random phase keys,” Opt. Lett. 31(8), 1044–1046 (2006).
[Crossref] [PubMed]

X. Peng, H. Wei, and P. Zhang, “Chosen-plaintext attack on lensless double-random phase encoding in the Fresnel domain,” Opt. Lett. 15(31), 3261–3263 (2006).
[Crossref]

Xiao, D.

X. Li, D. Xiao, and Q. Wang, “Error-free holographic frames encryption with CA pixel-permutation encoding algorithm,” Opt. Laser Eng. 100, 200–207 (2018).
[Crossref]

Xiao, X.

Xing, Y.

X. Li, M. Zhao, Y. Xing, L. Li, S. Kim, X. Zhou, and Q. Wang, “Optical encryption via monospectral integral imaging,” Opt. Express 25(25), 31516–31527 (2017).
[Crossref] [PubMed]

Y. Xing, Q. Wang, Z. Xiong, and H. Deng, “Encrypting three-dimensional information system based on integral imaging and multiple chaotic maps,” Opt. Eng. 55(2), 023107 (2016).
[Crossref]

Z. Xiong, Q. Wang, Y. Xing, H. Deng, and D. Li, “An active integral imaging system based on multiple structured light method,” Opt. Express 23(21), 27095–27104 (2015).
[Crossref]

Xiong, Z.

Y. Xing, Q. Wang, Z. Xiong, and H. Deng, “Encrypting three-dimensional information system based on integral imaging and multiple chaotic maps,” Opt. Eng. 55(2), 023107 (2016).
[Crossref]

Z. Xiong, Q. Wang, Y. Xing, H. Deng, and D. Li, “An active integral imaging system based on multiple structured light method,” Opt. Express 23(21), 27095–27104 (2015).
[Crossref]

Xu, H.

Xu, J.

S. Liu, J. Xu, Y. Zhang, L. Chen, and C. Li, “General optical implementations of fractional Fourier transforms,” Opt. Lett. 20(9), 2088–2090 (2007).
[Crossref]

Xu, L.

Xu, W.

Yoo, H.

Yu, B.

Yu, S.

Zhang, J.

Zhang, P.

X. Peng, P. Zhang, H. Wei, and B. Yu, “Known-plaintext attack on optical encryption based on double random phase keys,” Opt. Lett. 31(8), 1044–1046 (2006).
[Crossref] [PubMed]

X. Peng, H. Wei, and P. Zhang, “Chosen-plaintext attack on lensless double-random phase encoding in the Fresnel domain,” Opt. Lett. 15(31), 3261–3263 (2006).
[Crossref]

Zhang, Q.

Zhang, S.

Zhang, Y.

S. Liu, J. Xu, Y. Zhang, L. Chen, and C. Li, “General optical implementations of fractional Fourier transforms,” Opt. Lett. 20(9), 2088–2090 (2007).
[Crossref]

Zhang, Z.

Z. Zhang, “A flexible new technique for camera calibration,” IEEE Trans. Pattern Anal. Machine Intell. 22(11), 1330–1334 (2000).
[Crossref]

Zhao, D.

Zhao, M.

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, X.

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]

Adv. Opt. Photonics (2)

W. Chen, B. Javidi, and X. Chen, “Advances in optical security systems,” Adv. Opt. Photonics 6(2), 120–155 (2014)
[Crossref]

A. Alfalou and C. Brosseau, “Optical image compression and encryption methods,” Adv. Opt. Photonics 1(3), 589–636 (2009)
[Crossref]

Appl. Opt. (4)

IEEE Trans. Comput. AID D. (1)

S. Cho, U. Choi, H. Kim, Y. Hwang, J. Kim, and S. Heo, “New synthesis of one-dimensional 90/150 linear hybrid group cellular automata,” IEEE Trans. Comput. AID D. 26(9), 1720–1724 (2007).
[Crossref]

IEEE Trans. Pattern Anal. Machine Intell. (1)

Z. Zhang, “A flexible new technique for camera calibration,” IEEE Trans. Pattern Anal. Machine Intell. 22(11), 1330–1334 (2000).
[Crossref]

Opt. Eng. (1)

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Supplementary Material (1)

NameDescription
» Visualization 1       Optical 3D scene reconstruction by the improved integral imaging method.

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Figures (17)

Fig. 1
Fig. 1 Capturing process of the proposed monospectral SAII system.
Fig. 2
Fig. 2 The captured “chessboard” patterns and calibrated elemental image array.
Fig. 3
Fig. 3 The 1D case of the CA m-sequence with two groups CA rules.
Fig. 4
Fig. 4 The encryption process of the proposed method.
Fig. 5
Fig. 5 Experimental setup of the 3D images pickup system.
Fig. 6
Fig. 6 Encryption result of the monospectral elemental image array and its histogram.
Fig. 7
Fig. 7 Multispectral visualization of the reconstructed 3D images “Dices” and “Magic cube” from the calibrated monospectral elemental images at different depths (z).
Fig. 8
Fig. 8 Multispectral visualization of the reconstructed 3D images “Car” and “Magic cube” from the calibrated monospectral elemental images at different depths (z).
Fig. 9
Fig. 9 Reconstructed 3D images with three methods: (a) and (b) our proposed reconstructed 3D images at the distance of 600 mm and 500 mm, respectively, (c) and (d) reconstructed 3D images with the CII-based method [19] at the distance of 600 mm and 500 mm, respectively, (e) and (f) reconstructed 3D images with the SAII-based method [35] at the distance of 600 mm and 500 mm, respectively.
Fig. 10
Fig. 10 Reconstructed images of the previous method [33] with the different iterations: (a) 6th iteration, (b) 15th iteration.
Fig. 11
Fig. 11 Reconstructed 3D image with the uncalibrated elemental images.
Fig. 12
Fig. 12 Reconstructed 3D image with the partial incorrect keys (incorrect RGCM).
Fig. 13
Fig. 13 Our reconstructed 3D images “Dices” and “Magic cube” against attacks: (a) Gaussian noise (0.1) and the reconstruction depth 650 mm, (b) Gaussian noise (0.1) and the reconstruction depth 500 mm, (c) cropping attack (50%) and the reconstruction depth 650 mm, (d) cropping attack (50%) and the reconstruction depth 500 mm.
Fig. 14
Fig. 14 Our reconstructed 3D images “Car” and “Magic cube” against attacks: (a) Gaussian noise (0.1) and the reconstruction depth 650 mm, (b) Gaussian noise (0.1) and the reconstruction depth 500 mm, (c) cropping attack (50%) and the reconstruction depth 650 mm, (d) cropping attack (50%) and the reconstruction depth 500 mm.
Fig. 15
Fig. 15 Reconstructed 3D images “Dices” and “Magic cube” of the method [19] against attacks: (a) Gaussian noise (0.1) and the reconstruction depth 650 mm, (b) Gaussian noise (0.1) and the reconstruction depth 500 mm, (c) cropping attack (50%) and the reconstruction depth 650 mm, (d) cropping attack (50%) and the reconstruction depth 500 mm.
Fig. 16
Fig. 16 Reconstructed 3D images “Car” and “Magic cube” of the method [19] against attacks: (a) Gaussian noise (0.1) and the reconstruction depth 650 mm, (b) Gaussian noise (0.1) and the reconstruction depth 500 mm, (c) cropping attack (50%) and the reconstruction depth 650 mm, (d) cropping attack (50%) and the reconstruction depth 500 mm.
Fig. 17
Fig. 17 Different views of the optical reconstructed 3D images. In the video (see Visualization 1), we show the optical reconstruction of 3D images with different views.

Tables (2)

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Table 1 PSNR values of 3D images “Dices” and “Magic cube” with two different methods.

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Table 2 PSNR values of 3D images “Car” and “Magic cube” with two different methods.

Equations (14)

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H m , n = [ h 11 h 12 h 13 h 21 h 22 h 23 h 31 h 32 h 33 ] .
[ x i y i 1 ] m . n = s m , n H m , n [ x k y k 1 ] m , n ,
s i ( k + 1 ) = F ( s i 1 ( k ) , s i ( k ) , s i + 1 ( k ) ) ,
Rule 90 : s i ( k + 1 ) = s i 1 ( k ) s i + 1 ( k ) ,
Rule 150 : s i ( k + 1 ) = s i 1 ( k ) s i ( k ) s i + 1 ( k ) .
s i ( k + 1 ) = T ( r n ) s i ( k ) .
T ( r n ) = [ r 1 1 0 0 0 1 r 2 1 0 0 1 r 3 0 r n 2 1 0 0 1 r n 1 1 0 0 0 1 r n ]
r n = { 0 , rule 90 1 , rule 150
μ ( x , y ) = FT { E ( x , y ) M 1 ( r n ) } × h ( x ^ , y ^ ; z 1 ; λ ) ,
h ( x ^ , y ^ ; z 1 ; λ ) = exp [ j π λ z 1 × ( x ^ 2 + y ^ 2 ) ] ,
μ ( x , y ) = FT λ z 1 { ( E ( x , y ) M 1 ( r n ) ) } .
E ( x , y ) = FT λ z 2 { μ ( x , y ) M 2 ( r n ) } .
E ( x , y ) = FT λ z 1 { FT λ z 2 { E ( x , y ) M 2 ( r n ) } , M 1 ( r n ) } .
R ( x , y , z ) = 1 N o ( x , y ) k = 0 K 1 l = 0 L 1 E k l ( x k N x × p c x × z g , y l N y × p c y × z g ) ,

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