Abstract

In this paper, we propose an improved analysis on the signal property of curved computational integral imaging reconstruction (C-CIIR). In the proposed model and analysis, we explain a general analysis of computational integral imaging by introducing a curvature effect that is obtained by the additional use of a large-aperture (LA) lens. Based on the proposed signal model in C-CIIR, we analyze the characteristics of the granular noise (GN) and conduct preliminary experiments to show the feasibility of our model. Experimental results indicate that the GN caused by the nonuniform overlapping gets reduced and that the GN is diminished as the focal length of the additional LA lens used decreases in C-CIIR. Also, the proposed model and analysis are considered to be generalized versions of the signal model and analysis of the previous computational integral imaging systems.

© 2009 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  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. 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]
  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. 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]
  6. A. Stern and B. Javidi, “3D image sensing, visualization, and processing using integral imaging,” Proc. IEEE 94, 591-608(2006).
    [CrossRef]
  7. 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]
  8. H. Arimoto and B. Javidi, “Integral three-dimensional imaging with digital reconstruction,” Opt. Lett. 26, 157-159(2001).
    [CrossRef]
  9. 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]
  10. 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]
  11. 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]
  12. 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]
  13. 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]
  14. 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]
  15. 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. 276, 72-79 (2007).
    [CrossRef]
  16. Y. Hwang, S. Hong, and B. Javidi, “Free view 3-D visualization of occluded objects by using computational synthetic aperture integral imaging,” J. Display Technol. 3, 64-70(2007).
    [CrossRef]
  17. 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] [PubMed]
  18. H. Yoo and D.-H. Shin, “Improved analysis on the signal property of computational integral imaging system,” Opt. Express 15, 14107-14114 (2007).
    [CrossRef] [PubMed]
  19. J.-B. Hyun, D.-C. Hwang, D.-H. Shin, and E.-S. Kim, “Curved computational integral imaging reconstruction technique for resolution-enhanced display of three-dimensional object images,” Appl. Opt. 46, 7697-7708 (2007).
    [CrossRef] [PubMed]
  20. B. Tavakoli, B. Javidi, and E. Watson, “Three dimensional visualization by photon counting computational integral imaging,” Opt. Express 16, 4426-4436 (2008).
    [CrossRef] [PubMed]
  21. D.-C. Hwang, K.-J. Lee, S.-C. Kim, and E.-S. Kim, “Extraction of location coordinates of 3-D objects from computationally reconstructed integral images basing on a blur metric,” Opt. Express 16, 3623-3635 (2008).
    [CrossRef] [PubMed]
  22. D. Shin and H. Yoo, “Scale-variant magnification for computational integral imaging and its application to 3D object correlator,” Opt. Express 16, 8855-8867 (2008).
    [CrossRef] [PubMed]
  23. D.-H. Shin, B.-G. Lee, and J.-J. Lee, “Occlusion removal method of partially occluded 3D object using sub-image block matching in computational integral imaging,” Opt. Express 16, 16294-16304 (2008).
    [CrossRef] [PubMed]

2008 (4)

2007 (5)

2006 (4)

2005 (2)

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]

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]

2004 (2)

2003 (1)

2002 (1)

2001 (2)

1999 (1)

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 (1)

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.

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.

Hwang, Y.

Hyun, J.-B.

Jang, J.-S.

Javidi, B.

B. Tavakoli, B. Javidi, and E. Watson, “Three dimensional visualization by photon counting computational integral imaging,” Opt. Express 16, 4426-4436 (2008).
[CrossRef] [PubMed]

Y. Hwang, S. Hong, and B. Javidi, “Free view 3-D visualization of occluded objects by using computational synthetic aperture integral imaging,” J. Display Technol. 3, 64-70(2007).
[CrossRef]

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. 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]

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, S.-C.

Lee, B.

Lee, B.-G.

Lee, J.-J.

Lee, K.-J.

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. 276, 72-79 (2007).
[CrossRef]

Ponce-Díaz, R.

Saavedra, G.

Shin, D.

Shin, D.-H.

Stern, A.

A. Stern and B. Javidi, “3D image sensing, visualization, and processing using integral imaging,” Proc. 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]

Tavakoli, B.

Watson, E.

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. (3)

C. R. Acad. Sci. (1)

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

J. Display Technol. (1)

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

Jpn. J. Appl. Phys. (1)

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. (1)

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. 276, 72-79 (2007).
[CrossRef]

Opt. Eng. (1)

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 (9)

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]

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

D.-C. Hwang, K.-J. Lee, S.-C. Kim, and E.-S. Kim, “Extraction of location coordinates of 3-D objects from computationally reconstructed integral images basing on a blur metric,” Opt. Express 16, 3623-3635 (2008).
[CrossRef] [PubMed]

B. Tavakoli, B. Javidi, and E. Watson, “Three dimensional visualization by photon counting computational integral imaging,” Opt. Express 16, 4426-4436 (2008).
[CrossRef] [PubMed]

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

D.-H. Shin, B.-G. Lee, and J.-J. Lee, “Occlusion removal method of partially occluded 3D object using sub-image block matching in computational integral imaging,” Opt. Express 16, 16294-16304 (2008).
[CrossRef] [PubMed]

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] [PubMed]

H. Yoo and D.-H. Shin, “Improved analysis on the signal property of computational integral imaging system,” Opt. Express 15, 14107-14114 (2007).
[CrossRef] [PubMed]

Opt. Lett. (4)

Proc. IEEE (1)

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

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (11)

Fig. 1
Fig. 1

(a) Computational integral imaging with the CIIR process. (b) Ray diagram for the CIIR process.

Fig. 2
Fig. 2

(a) Pickup of the 3D object using curved integral imaging. (b) Ray diagram for the C-CIIR process.

Fig. 3
Fig. 3

Signal model for the analysis of computational integral imaging using the C-CIIR process.

Fig. 4
Fig. 4

Relationship between f z ( x ) and r z ( x ) .

Fig. 5
Fig. 5

Sum of nine SWFs.

Fig. 6
Fig. 6

Graph of the power of the GN: (a) previous CIIR process and (b) C-CIIR process ( f = 90 mm ).

Fig. 7
Fig. 7

Graph of the power of the GN according to the focal length of the LA lens: (a)  180 mm , (b)  150 mm , (c)  120 mm , and (d)  90 mm .

Fig. 8
Fig. 8

Experimental structure for performance evaluation using the Gaussian image.

Fig. 9
Fig. 9

MSE results in C-CIIR when f = 150 mm .

Fig. 10
Fig. 10

Reconstructed Gaussian images at different distances.

Fig. 11
Fig. 11

Experimental results for real objects: (a) elemental images, (b) reconstructed images with GN before compensation processing, and (c) reconstructed images without GN after compensation processing.

Equations (9)

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

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 ) = π 0 ( ( x i a ( f ) ) / w ) ,
a ( f ) = a 0 ( f z ) / f .
w = n a ( f ) + b ( f ) = a ( f ) [ n + b ( f ) a ( f ) ] ,
b ( f ) a 0 = min | { z g n ( f - z ) f } | .
z = f n g f + n g .
f z ( x ) = r z ( x ) S π ( x ) .
G ( x , y ) = e ( x 2 + y 2 ) / 2 .
MSE = 1 K 2 x = 1 K y = 1 K | G ( x , y ) R ( x , y ) | 2 .

Metrics