Abstract

In this paper, we present a novel volumetric computational reconstruction (VCR) method for improved 3D object correlator. Basically, VCR consists of magnification and superposition. This paper presents new scale-variant magnification as a technique for VCR. To introduce our technique, we discuss an interference problem among elemental images in VCR. We find that a large magnification causes interference among elemental images when they are applied to the superposition. Thus, the resolution of reconstructed images should be limited by this interference. To overcome the interference problem, we propose a method to calculate a minimum magnification factor while VCR is still valid. Magnification by a new factor enables the proposed method to reconstruct resolution-enhanced images. To confirm the feasibility of the proposed method, we apply our method to a VCR-based 3D object correlator. Experimental results indicate that our method outperforms the conventional VCR method.

© 2008 Optical Society of America

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2007

2006

2005

2004

2002

2001

1999

F. Okano, H. Hoshino, J. Arai, and I. Yuyama, "Three-dimensional video system based on integral photography," Opt. Eng. 38, 1072-1077 (1999).
[CrossRef]

1908

G. Lippmann, "La photographic integrale," C.R. Acad. Sci. 146, 446-451 (1908).

Arai, J.

F. Okano, H. Hoshino, J. Arai, and I. Yuyama, "Three-dimensional video system based on integral photography," Opt. Eng. 38, 1072-1077 (1999).
[CrossRef]

Frauel, Y.

Hong, S. -H.

Hoshino, H.

F. Okano, H. Hoshino, J. Arai, and I. Yuyama, "Three-dimensional video system based on integral photography," Opt. Eng. 38, 1072-1077 (1999).
[CrossRef]

Hwang, D.-C.

J.-S. Park, D.-C. Hwang, D.-H. Shin and E.-S. Kim, "Resolution-enhanced three-dimensional image correlator using computationally reconstructed integral images," Opt. Commun. 26, 72-79 (2007).
[CrossRef]

Jang, J. -S.

Jang, J.-S.

Javidi, B.

Jung, S. Y.

Kim, E. -S.

Kim, E.-S.

J.-S. Park, D.-C. Hwang, D.-H. Shin and E.-S. Kim, "Resolution-enhanced three-dimensional image correlator using computationally reconstructed integral images," Opt. Commun. 26, 72-79 (2007).
[CrossRef]

D.-H. Shin, E.-S. Kim and B. Lee, "Computational reconstruction technique of three-dimensional object in integral imaging using a lenslet array," Jpn. J. Appl. Phys. 44, 8016-8018 (2005).
[CrossRef]

Kim, J.

Lee, B.

Lippmann, G.

G. Lippmann, "La photographic integrale," C.R. Acad. Sci. 146, 446-451 (1908).

Martínez-Corral, M.

Martínez-Cuenca, R.

Min, S.-W.

Okano, F.

F. Okano, H. Hoshino, J. Arai, and I. Yuyama, "Three-dimensional video system based on integral photography," Opt. Eng. 38, 1072-1077 (1999).
[CrossRef]

Park, J.-H.

Park, J.-S.

J.-S. Park, D.-C. Hwang, D.-H. Shin and E.-S. Kim, "Resolution-enhanced three-dimensional image correlator using computationally reconstructed integral images," Opt. Commun. 26, 72-79 (2007).
[CrossRef]

Ponce-Díaz, R.

Saavedra, G.

Shin, D. -H.

Shin, D.-H.

J.-S. Park, D.-C. Hwang, D.-H. Shin and E.-S. Kim, "Resolution-enhanced three-dimensional image correlator using computationally reconstructed integral images," Opt. Commun. 26, 72-79 (2007).
[CrossRef]

D.-H. Shin, E.-S. Kim and B. Lee, "Computational reconstruction technique of three-dimensional object in integral imaging using a lenslet array," Jpn. J. Appl. Phys. 44, 8016-8018 (2005).
[CrossRef]

Yoo, H.

Yuyama, I.

F. Okano, H. Hoshino, J. Arai, and I. Yuyama, "Three-dimensional video system based on integral photography," Opt. Eng. 38, 1072-1077 (1999).
[CrossRef]

Appl. Opt.

C. R. Acad. Sci.

G. Lippmann, "La photographic integrale," C.R. Acad. Sci. 146, 446-451 (1908).

J. Opt. Soc. Am. A

Jpn. J. Appl. Phys.

D.-H. Shin, E.-S. Kim and B. Lee, "Computational reconstruction technique of three-dimensional object in integral imaging using a lenslet array," Jpn. J. Appl. Phys. 44, 8016-8018 (2005).
[CrossRef]

Opt. Commun.

J.-S. Park, D.-C. Hwang, D.-H. Shin and E.-S. Kim, "Resolution-enhanced three-dimensional image correlator using computationally reconstructed integral images," Opt. Commun. 26, 72-79 (2007).
[CrossRef]

Opt. Eng.

F. Okano, H. Hoshino, J. Arai, and I. Yuyama, "Three-dimensional video system based on integral photography," Opt. Eng. 38, 1072-1077 (1999).
[CrossRef]

Opt. Express

Opt. Lett.

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Figures (11)

Fig. 1.
Fig. 1.

(a) Conventional VCR method for an elemental image (b) Proposed VCR for an elemental image (c) Superposition of conventional VCR method for four 1D elemental images (d) Superposition of proposed VCR method for four 1D elemental images.

Fig. 2.
Fig. 2.

(a) Pickup (b) Pixel-to-pixel mapping (c) Conventional VCR method (d) Proposed VCR method.

Fig. 3.
Fig. 3.

(a) Ray formation of proposed VCR method. (b) Comparison of M(z) and Md (z).

Fig. 4.
Fig. 4.

Minimization process for calculating Md (z)=αmin according to the distance z.

Fig. 5.
Fig. 5.

(a) Experimental setup. (b) Three test images.

Fig. 6.
Fig. 6.

Average MSE results for three test images.

Fig. 7.
Fig. 7.

Comparison of reconstructed images (a) Conventional method (b) Proposed method.

Fig. 8.
Fig. 8.

(a) Experimental setups for optically recorded elemental images. (b) Elemental images (c) Correlation results between template and plane image.

Fig. 9.
Fig. 9.

Average curves of Cpeak (z) according to the distance for three test images when the test images are located at z=30 mm.

Fig. 10.
Fig. 10.

(a) Examples of plane images from the conventional method (b) Examples of plane images from the proposed method.

Fig. 11.
Fig. 11.

Correlation results according to the distance when the tree object is located at z=45 mm.

Equations (5)

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H n k ( z ) = kp z g nd ,
Δ H = H n 2 k 2 ( z ) H n 1 k 1 ( z ) = p ( k 2 k 1 ) z g ( n 2 n 1 ) d ·
α = Δ H d = N ( k 2 k 1 ) M ( n 2 n 1 ) ,
MSE ( O , R z ) = 1 u v x = 1 u y = 1 v [ O ( x , y ) R z ( x , y ) ] 2
C ( x c , y c ) = 1 u v x = 1 u y = 1 v [ R z * ( x , y ) O ( x c + x , y c + y ) ]

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