Abstract

In this paper, we introduce an improved signal analysis of the computational integral imaging (CII) system having a pickup process of three-dimensional object and a volumetric computational reconstruction (VCR) process. We propose a signal model for the CII system. From the signal model and its analysis, we can define a granular noise caused by the non-uniform overlapping. We also analyze the characteristics of the granular noise. According to our model and analysis, there is a condition that the granular noise cancels out. To show the feasibility of our model, the preliminary experiments are carried out and the result is presented. This is the first time, to our knowledge, that a signal model for the analysis of CII systems is provided.

© 2007 Optical Society of America

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  1. G. Lippmann, "La photographic integrale," C. R. Acad. Sci. 146, 446-451 (1908).
  2. F. Okano, H. Hoshino, J. Arai, and I. Yuyama, "Three-dimensional video system based on integral photography," Opt. Eng. 38, 1072-1077 (1999).
    [CrossRef]
  3. B. Javidi and F. Okano, eds., Three dimensional television, video, and display technologies, (Springer Verlag Berlin, 2002).
  4. J.-S. Jang and B. Javidi, "Improved viewing resolution of three- dimensional integral imaging by use of nonstationary micro-optics," Opt. Lett. 27, 324-326 (2002).
    [CrossRef]
  5. B. Lee, S. Y. Jung, S.-W. Min, and J.-H. Park, "Three-dimensional display by use of integral photography with dynamically variable image planes," Opt. Lett. 26, 1481-1482 (2001).
    [CrossRef]
  6. M. Martínez-Corral, B. Javidi, R. Martínez-Cuenca, and G. Saavedra, "Multifacet structure of observed reconstructed integral images," J. Opt. Soc. Am. A 22, 597-603 (2005).
    [CrossRef]
  7. A. Stern and B. Javidi, "3D image sensing, visualization, and processing using integral imaging," Proc. of IEEE 94, 591-608 (2006).
    [CrossRef]
  8. J. S. Jang and B. Javidi, "Depth and size control of three-dimensional images in projection integral imaging," Opt. Express 12, 3778-3790 (2004).
    [CrossRef] [PubMed]
  9. D. -H. Shin, B. Lee, and E. -S. Kim, "Multidirectional curved integral imaging with large depth by additional use of a large-aperture lens," Appl. Opt. 45, 7375-7381 (2006).
    [CrossRef] [PubMed]
  10. H. Arimoto and B. Javidi, "Integral three-dimensional imaging with digital reconstruction," Opt. Lett. 26, 157-159 (2001).
    [CrossRef]
  11. A. Stern and B. Javidi, "3D image sensing and reconstruction with time-division multiplexed computational integral imaging," Appl. Opt. 42, 7036-7042 (2003).
    [CrossRef] [PubMed]
  12. 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] [PubMed]
  13. 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]
  14. S. -H. Hong and B. Javidi, "Improved resolution 3D object reconstruction using computational integral imaging with time multiplexing," Opt. Express 12, 4579-4588 (2004).
    [CrossRef] [PubMed]
  15. B. Javidi, R. Ponce-Díaz, and S. -H. Hong, "Three-dimensional recognition of occluded objects by using computational integral imaging," Opt. Lett. 31, 1106-1108 (2006).
    [CrossRef] [PubMed]
  16. S. -H. Hong and B. Javidi, "Distortion-tolerant 3D recognition of occluded objects using computational integral imaging," Opt. Express 14, 12085-12095 (2006).
    [CrossRef] [PubMed]
  17. 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]

2007

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]

2006

2005

M. Martínez-Corral, B. Javidi, R. Martínez-Cuenca, and G. Saavedra, "Multifacet structure of observed reconstructed integral images," J. Opt. Soc. Am. A 22, 597-603 (2005).
[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]

2004

2003

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]

Arimoto, H.

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.

Jang, J.-S.

Javidi, B.

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

A. Stern and B. Javidi, "3D image sensing, visualization, and processing using integral imaging," Proc. of IEEE 94, 591-608 (2006).
[CrossRef]

S. -H. Hong and B. Javidi, "Distortion-tolerant 3D recognition of occluded objects using computational integral imaging," Opt. Express 14, 12085-12095 (2006).
[CrossRef] [PubMed]

M. Martínez-Corral, B. Javidi, R. Martínez-Cuenca, and G. Saavedra, "Multifacet structure of observed reconstructed integral images," J. Opt. Soc. Am. A 22, 597-603 (2005).
[CrossRef]

J. S. Jang and B. Javidi, "Depth and size control of three-dimensional images in projection integral imaging," Opt. Express 12, 3778-3790 (2004).
[CrossRef] [PubMed]

S. -H. Hong and B. Javidi, "Improved resolution 3D object reconstruction using computational integral imaging with time multiplexing," Opt. Express 12, 4579-4588 (2004).
[CrossRef] [PubMed]

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] [PubMed]

A. Stern and B. Javidi, "3D image sensing and reconstruction with time-division multiplexed computational integral imaging," Appl. Opt. 42, 7036-7042 (2003).
[CrossRef] [PubMed]

J.-S. Jang and B. Javidi, "Improved viewing resolution of three- dimensional integral imaging by use of nonstationary micro-optics," Opt. Lett. 27, 324-326 (2002).
[CrossRef]

H. Arimoto and B. Javidi, "Integral three-dimensional imaging with digital reconstruction," Opt. Lett. 26, 157-159 (2001).
[CrossRef]

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]

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]

Stern, A.

A. Stern and B. Javidi, "3D image sensing, visualization, and processing using integral imaging," Proc. of IEEE 94, 591-608 (2006).
[CrossRef]

A. Stern and B. Javidi, "3D image sensing and reconstruction with time-division multiplexed computational integral imaging," Appl. Opt. 42, 7036-7042 (2003).
[CrossRef] [PubMed]

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.

Proc. of IEEE

A. Stern and B. Javidi, "3D image sensing, visualization, and processing using integral imaging," Proc. of IEEE 94, 591-608 (2006).
[CrossRef]

Other

B. Javidi and F. Okano, eds., Three dimensional television, video, and display technologies, (Springer Verlag Berlin, 2002).

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Figures (6)

Fig. 1.
Fig. 1.

The CII system. (a) Pickup process (b) VCR process.

Fig. 2.
Fig. 2.

Signal model for the analysis of the CII system.

Fig. 3.
Fig. 3.

Illustration of relationship between fz (x) and rz (x).

Fig. 4.
Fig. 4.

(a). Illustration of the sum of nine SWFs, (b). Lower uniform component and positive granular component and (c). Upper uniform component and negative granular component of the signal Sπ (x) of the non-transition region.

Fig. 5.
Fig. 5.

Experimental results: (a) Set of elemental images (b) reconstructed image at distance z=3.5g with the granular noise and the original object “tree” is located at z=3.5g (c) reconstructed image at distance z=4g without the granular noise but it is slightly defocused.

Fig. 6.
Fig. 6.

Graph of Power of (a) the granular noise and (b) the uniform component (c) USNR along the z-axis.

Equations (7)

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r z ( x ) = i = 0 N 1 f z ( x ) π i ( x w ) = f z ( x ) i = 0 N 1 π i ( x w ) = f z ( x ) S π ( x ) ,
π i ( x w ) = π 0 ( ( x s ) w ) ,
w = na + b = a ( n + b a ) ,
w = a z g = aM .
f z ( x ) = r z ( x ) S π ( x ) .
gn ( x ) = { S π ( x ) w a , 0 < b 0.5 a w a S π ( x ) , 0.5 a b < a .
USNR = 10 log 10 P U P gn = 10 log 10 round ( w a ) 2 1 a 0 a gn ( x ) 2 dx ,

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