Abstract

This paper presents a new method for three-dimensional (3D) scene acquisition via reconstruction with multispectral information and its Fourier-based encryption using computational integral imaging, by which the field of view, resolution, and information security are increased, respectively. The color imaging sensors covered with a Bayer color filter array captures elemental images (EI) at different spectral bands (400 and 700 nm intervals in the visible spectrum). Subsequently, double random phase encryption (DRPE) in the Fourier domain is employed on Bayer formatted EI to encrypt the captured 3D scene. Proper 3D object reconstruction only can be achieved by applying inverse decryption and a geometric ray backpropagation algorithm on the encrypted EI. Further, the high-resolution multispectral 3D scene can be visualized by using various adaptive interpolation algorithms. To objectively evaluate our proposed method, we carried out computational experiments for 3D object sensing, reconstruction, and digital simulations for DRPE. Experiment results validate the feasibility and robustness of our proposed approach, even under severe degradation.

© 2014 Optical Society of America

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2014 (1)

F. Yi, I. Moon, and Y. H. Lee, “A multispectral photon-counting double random phase encoding scheme for image authentication,” Sensors 14, 8877–8894 (2014).
[CrossRef]

2013 (4)

2012 (1)

2011 (1)

2010 (1)

M. Cho and B. Javidi, “Three-dimensional visualization of objects in turbid water using integral imaging,” J. Disp. Technol. 6, 544–547 (2010).
[CrossRef]

2009 (1)

Y.-R. Piao, D.-H. Shin, and E.-S. Kim, “Robust image encryption by combined use of integral imaging and pixel scrambling techniques,” Opt. Lasers Eng. 47, 1273–1281 (2009).
[CrossRef]

2007 (1)

2006 (5)

2005 (1)

2004 (3)

2003 (1)

2001 (2)

2000 (2)

1998 (1)

1995 (1)

1978 (1)

Y. Igarishi, H. Murata, and M. Ueda, “3D display system using a computer-generated integral photography,” Jpn. J. Appl. Phys. 17, 1683–1684 (1978).
[CrossRef]

1968 (1)

1931 (1)

1908 (1)

G. Lippmann, “La photographie integrale,” Comptes-Rendus Acad. Sci. 146, 446–451 (1908).

Arcos, S.

Arimoto, H.

Burckhardt, C.

Carmona, P. L.

Carnicer, A.

Cho, M.

Corral, M. M.

Cutler, R.

H. Malvar, L. He, and R. Cutler, “High-quality linear interpolation for demosaicing of Bayer-patterned color images,” in IEEE International Conference on Acoustics, Speech, and Signal Processing (IEEE, 2004), pp. 485–488.

Díaz, R. P.

Gopinathan, U.

He, L.

H. Malvar, L. He, and R. Cutler, “High-quality linear interpolation for demosaicing of Bayer-patterned color images,” in IEEE International Conference on Acoustics, Speech, and Signal Processing (IEEE, 2004), pp. 485–488.

Hong, S. H.

Hong, S.-H.

Hoshino, H.

Igarishi, Y.

Y. Igarishi, H. Murata, and M. Ueda, “3D display system using a computer-generated integral photography,” Jpn. J. Appl. Phys. 17, 1683–1684 (1978).
[CrossRef]

Isono, H.

Ives, H.

Jang, J.-S.

Javidi, B.

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

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

I. Moon, I. Muniraj, and B. Javidi, “3D visualization at low light levels using multispectral photon counting integral imaging,” J. Disp. Technol. 9, 51–55 (2013).
[CrossRef]

P. L. Carmona, E. S. Ortiga, X. Xiao, F. Pla, M. M. Corral, H. Navarro, G. Saavedra, and B. Javidi, “Multispectral integral imaging acquisition and processing using a monochrome camera and a liquid crystal tunable filter,” Opt. Express 20, 25960–25969 (2012).
[CrossRef]

E. Perez-Cabre, M. Cho, and B. Javidi, “Information authentication using photon counting double-random-phase encrypted images,” Opt. Lett. 36, 22–24 (2011).
[CrossRef]

M. Cho and B. Javidi, “Three-dimensional visualization of objects in turbid water using integral imaging,” J. Disp. Technol. 6, 544–547 (2010).
[CrossRef]

B. Javidi, R. P. Díaz, and S. H. Hong, “Three-dimensional recognition of occluded objects by using computational integral imaging,” Opt. Lett. 31, 1106–1108 (2006).
[CrossRef]

A. Stern and B. Javidi, “Three-dimensional image sensing, visualization, and processing using integral imaging,” Proc. IEEE 94, 591–607 (2006).
[CrossRef]

R. Martinez-Cuenca, A. Pons, G. Saavedra, M. Martinez-Corral, and B. Javidi, “Optically-corrected elemental images for undistorted integral image display,” Opt. Express 14, 9657–9663 (2006).
[CrossRef]

O. Matoba and B. Javidi, “Secure three-dimensional data transmission and display,” Appl. Opt. 43, 2285–2291 (2004).
[CrossRef]

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

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

H. Arimoto and B. Javidi, “Integrate three-dimensional imaging with computed reconstruction,” Opt. Lett. 26, 157–159 (2001).
[CrossRef]

E. Tajahuerce and B. Javidi, “Encrypting three-dimensional information with digital holography,” Appl. Opt. 39, 6595–6601 (2000).
[CrossRef]

P. Refregier and B. Javidi, “Optical-image encryption based on input plane and Fourier plane random encoding,” Opt. Lett. 20, 767–769 (1995).
[CrossRef]

Joseph, J.

Jung, S.

Juvells, I.

Kim, E.-S.

Y.-R. Piao, D.-H. Shin, and E.-S. Kim, “Robust image encryption by combined use of integral imaging and pixel scrambling techniques,” Opt. Lasers Eng. 47, 1273–1281 (2009).
[CrossRef]

Lee, B.

Lee, I. H.

Lee, Y. H.

F. Yi, I. Moon, and Y. H. Lee, “A multispectral photon-counting double random phase encoding scheme for image authentication,” Sensors 14, 8877–8894 (2014).
[CrossRef]

Lippmann, G.

G. Lippmann, “La photographie integrale,” Comptes-Rendus Acad. Sci. 146, 446–451 (1908).

Malvar, H.

H. Malvar, L. He, and R. Cutler, “High-quality linear interpolation for demosaicing of Bayer-patterned color images,” in IEEE International Conference on Acoustics, Speech, and Signal Processing (IEEE, 2004), pp. 485–488.

Martinez-Corral, M.

Martinez-Cuenca, R.

Matoba, O.

Min, S.-W.

Monaghan, D. S.

Moon, I.

F. Yi, I. Moon, and Y. H. Lee, “A multispectral photon-counting double random phase encoding scheme for image authentication,” Sensors 14, 8877–8894 (2014).
[CrossRef]

I. Moon, I. Muniraj, and B. Javidi, “3D visualization at low light levels using multispectral photon counting integral imaging,” J. Disp. Technol. 9, 51–55 (2013).
[CrossRef]

Muniraj, I.

I. Moon, I. Muniraj, and B. Javidi, “3D visualization at low light levels using multispectral photon counting integral imaging,” J. Disp. Technol. 9, 51–55 (2013).
[CrossRef]

I. Muniraj, “Multispectral image authentication method via photon counting Fourier optics,” M.S. thesis (Department of Computer Engineering, Chosun University, 2013).

Murata, H.

Y. Igarishi, H. Murata, and M. Ueda, “3D display system using a computer-generated integral photography,” Jpn. J. Appl. Phys. 17, 1683–1684 (1978).
[CrossRef]

Naughton, T. J.

Navarro, H.

Okano, F.

Ortiga, E. S.

Park, J.-H.

Peng, X.

Perez-Cabre, E.

Piao, Y.-R.

Y.-R. Piao, D.-H. Shin, and E.-S. Kim, “Robust image encryption by combined use of integral imaging and pixel scrambling techniques,” Opt. Lasers Eng. 47, 1273–1281 (2009).
[CrossRef]

Pla, F.

Pons, A.

Refregier, P.

Saavedra, G.

Sheridan, J. T.

Shin, D.-H.

Y.-R. Piao, D.-H. Shin, and E.-S. Kim, “Robust image encryption by combined use of integral imaging and pixel scrambling techniques,” Opt. Lasers Eng. 47, 1273–1281 (2009).
[CrossRef]

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

Singh, K.

Situ, G.

Stern, A.

Tajahuerce, E.

Ueda, M.

Y. Igarishi, H. Murata, and M. Ueda, “3D display system using a computer-generated integral photography,” Jpn. J. Appl. Phys. 17, 1683–1684 (1978).
[CrossRef]

Unnikrishnan, G.

Usategui, M. M.

Wei, H.

Xiao, X.

Yi, F.

F. Yi, I. Moon, and Y. H. Lee, “A multispectral photon-counting double random phase encoding scheme for image authentication,” Sensors 14, 8877–8894 (2014).
[CrossRef]

Yoo, H.

Yuyama, I.

Zhang, J.

Zhang, P.

Appl. Opt. (5)

Comptes-Rendus Acad. Sci. (1)

G. Lippmann, “La photographie integrale,” Comptes-Rendus Acad. Sci. 146, 446–451 (1908).

J. Disp. Technol. (2)

M. Cho and B. Javidi, “Three-dimensional visualization of objects in turbid water using integral imaging,” J. Disp. Technol. 6, 544–547 (2010).
[CrossRef]

I. Moon, I. Muniraj, and B. Javidi, “3D visualization at low light levels using multispectral photon counting integral imaging,” J. Disp. Technol. 9, 51–55 (2013).
[CrossRef]

J. Opt. Soc. Am. (2)

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

J. Opt. Soc. Korea (1)

Jpn. J. Appl. Phys. (1)

Y. Igarishi, H. Murata, and M. Ueda, “3D display system using a computer-generated integral photography,” Jpn. J. Appl. Phys. 17, 1683–1684 (1978).
[CrossRef]

Opt. Express (5)

Opt. Lasers Eng. (1)

Y.-R. Piao, D.-H. Shin, and E.-S. Kim, “Robust image encryption by combined use of integral imaging and pixel scrambling techniques,” Opt. Lasers Eng. 47, 1273–1281 (2009).
[CrossRef]

Opt. Lett. (9)

Proc. IEEE (1)

A. Stern and B. Javidi, “Three-dimensional image sensing, visualization, and processing using integral imaging,” Proc. IEEE 94, 591–607 (2006).
[CrossRef]

Sensors (1)

F. Yi, I. Moon, and Y. H. Lee, “A multispectral photon-counting double random phase encoding scheme for image authentication,” Sensors 14, 8877–8894 (2014).
[CrossRef]

Other (2)

I. Muniraj, “Multispectral image authentication method via photon counting Fourier optics,” M.S. thesis (Department of Computer Engineering, Chosun University, 2013).

H. Malvar, L. He, and R. Cutler, “High-quality linear interpolation for demosaicing of Bayer-patterned color images,” in IEEE International Conference on Acoustics, Speech, and Signal Processing (IEEE, 2004), pp. 485–488.

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Figures (9)

Fig. 1.
Fig. 1.

Optical schematic setup of DRPE technique (f denotes focal length of the lens). (a) Encryption process. (b) Decryption process.

Fig. 2.
Fig. 2.

Optical setup for pickup process (EI recording) in the MCII method.

Fig. 3.
Fig. 3.

Optical setup for 3D reconstruction process in the MCII method.

Fig. 4.
Fig. 4.

Captured 2D images of the sought 3D scene. (a) 2D image in Bayer (GRBG) format. (b) 2D image in RGB format.

Fig. 5.
Fig. 5.

Proposed multispectral 3D optical encryption scheme using MCII. (a) 3D encryption process. (b) 3D decryption process.

Fig. 6.
Fig. 6.

Subset of captured Bayer elemental images of the 3D scene.

Fig. 7.
Fig. 7.

Multispectral 3D sectional images using MCII. A gradient-corrected linear interpolation algorithm has been applied to the Bayer format sectional images. (a) Encrypted 2D EI in Bayer (GRBG) format. (b) Encrypted 2D EI in RGB format. (c) and (e) Properly decrypted 3D Bayer sectional images at two different distances: (c) first object is focused; (e) second object is focused. (d) and (f) Properly decrypted 3D RGB sectional images at two different distances: (d) first object is focused; (f) second object is focused. (g) and (h) decrypted 3D images with wrong Fourier phase keys: (g) decrypted Bayer image with wrong phase key; (h) decrypted RGB image with wrong phase key.

Fig. 8.
Fig. 8.

Encrypted image added with the additive zero-mean Gaussian noise having a variance of 0.3. (a) Encrypted image. (b) Encrypted image with added Gaussian noise. (c) Retrieved sectional image when first object is focused. (d) Retrieved sectional image when second object is focused.

Fig. 9.
Fig. 9.

Retrieved images with occluded portions of 25%, 50%, 75%: (a), (c), and (e) when Object 1 is focused and (b), (d), and (f) when Object 2 is focused, respectively.

Equations (9)

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ψB(x,y)=FT1[FT{Irs(x,y)exp[i2πp(x,y)]}exp{i2πb(μ,η)}],
ψB(x,y)=|ψ(x,y)|exp[iϕ(x,y)].
Irs(x,y)=|FT1{FT[ψB(x,y)]exp[i2πb(μ,η)]}|.
I(x,y,d0)=1RSr=0R1s=0S1Irs(x+(ShxM0)r,y+(ShyM0)s),
g^(x,y)=g^B(x,y)+αΔRed(x,y),
ΔRed(x,y)r(x,y)14r(x+m,y+n),
b^(x,y)=b^B(x,y)+βΔGreen(x,y),
b^(x,y)=b^B(x,y)+γΔRed(x,y).
PSNR=10·log10(Imax2MSE),

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