Abstract

We propose a depth extraction method by using the correlation between an elemental image and a periodic function in computational integral imaging. Because each elemental image corresponds to a different perspective of the three-dimensional (3-D) object, an elemental image is regarded as the sum of the periodic spatial frequencies depending on the depth of a 3-D object. In this regard, we analyze the property of correlation between the same periodic functions and vice versa. To show the feasibility of the proposed method, we carried out our experiment and presented the results.

© 2012 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. M. McCormick and N. Davies, “Full natural color 3-D optical models by integral imaging,” in Fourth International Conference on Holographic Systems, Components, and Applications (Institute of Electrical Engineers, 1993), pp. 237–242.
  3. N. Davies, M. McCormick, and M. Brewin, “Design and analysis of an image transfer system using microlens arrays,” Opt. Eng. 33, 3624–3633 (1994).
    [CrossRef]
  4. F. Okano, H. Hoshino, J. Arai, and I. Yuyama, “Real-time pickup method for a three-dimensional image based on integral photography,” Appl. Opt. 36, 1598–1603 (1997).
    [CrossRef]
  5. S. Manolache, A. Aggoun, M. McCormick, N. Davies, and S.-Y. Kung, “Analytical model of a three-dimensional integral image recording system that uses circular- and hexagonal-based spherical surface microlenses,” J. Opt. Soc. Am. A 18, 1814–1821 (2001).
    [CrossRef]
  6. M. C. Forman, N. Davies, and M. McCormick, “Continuous parallax in discrete pixilated integral three-dimensional displays,” J. Opt. Soc. Am. A 20, 411–420 (2003).
    [CrossRef]
  7. D.-C. Hwang, K.-H. Shin, S.-C. Kim, and E.-S. Kim, “Depth extraction of three-dimensional objects in space by the computational integral imaging reconstruction technique,” Appl. Opt. 47, D128–D135 (2008).
    [CrossRef]
  8. G. Saavedra, R. Martínez-Cuenca, M. Martínez-Corral, H. Navarro, M. Daneshpanah, and B. Javidi, “Digital slicing of 3-D scenes by Fourier filtering of integral images,” Opt. Express 16, 17154–17160 (2008).
    [CrossRef]
  9. J.-H. Park, H.-R. Kim, Y. Kim, J. Kim, J. Hong, S.-D. Lee, and B. Lee, “Depth-enhanced three-dimensional-two-dimensional convertible display based on modified integral imaging,” Opt. Lett. 29, 2734–2736 (2004).
    [CrossRef]
  10. J. Kim, S.-W. Min, and B. Lee, “Viewing window expansion of integral floating display,” Appl. Opt. 48, 862–867 (2009).
    [CrossRef]
  11. H. Kim, J. Hahn, and B. Lee, “The use of a negative index planoconcave lens array for wide-viewing angle integral imaging,” Opt. Express 16, 21865–21880 (2008).
    [CrossRef]
  12. J.-Y. Jang, H.-S. Lee, S. Cha, and S.-H Shin, “Viewing angle enhanced integral imaging display by using a high refractive index medium,” Appl. Opt. 50, B71–B76 (2011).
    [CrossRef]
  13. J.-S. Jang and B. Javidi, “Improvement of viewing angle in integral imaging by use of moving lenslet arrays with low fill factor,” Appl. Opt. 42, 1996–2002 (2003).
    [CrossRef]
  14. M. DaneshPanah and B. Javidi, “Profilometry and optical slicing by passive three-dimensional imaging,” Opt. Lett. 34, 1105–1107 (2009).
    [CrossRef]
  15. J.-I. Ser, S. Cha, and S.-H. Shin, “Distortion correction of reconstructed three-dimensional image in an integral imaging system combined with a single imaging lens,” Appl. Opt. 48, 3108–3119 (2009).
    [CrossRef]
  16. J. Hong, J.-H. Park, S. Jung, and B. Lee, “Depth-enhanced integral imaging by use of optical path control,” Opt. Lett. 29, 1790–1792 (2004).
    [CrossRef]
  17. J.-I. Ser, J.-Y. Jang, S. Cha, and S.-H. Shin, “Applicability of diffraction grating to parallax image array generation in integral imaging,” Appl. Opt. 49, 2429–2433 (2010).
    [CrossRef]
  18. Y.-T. Lim, J.-H. Park, K.-C. Kwon, and N. Kim, “Resolution-enhanced integral imaging microscopy that uses lens array shifting,” Opt. Express 17, 19253–19263 (2009).
    [CrossRef]
  19. J.-H. Park, S. Jung, H. Choi, Y. Kim, and B. Lee, “Depth extraction by use of a rectangular lens array and one-dimensional elemental image modification,” Appl. Opt. 43, 4882–4895 (2004).
    [CrossRef]
  20. Y. Frauel, E. Tajahuerce, O. Matoba, A. Castro, and B. Javidi, “Comparison of passive ranging integral imaging and active imaging digital holography for three-dimensional object recognition,” Appl. Opt. 43, 452–462 (2004).
    [CrossRef]
  21. S.-H. Hong and B. Javidi, “Distortion-tolerant 3-D recognition of occluded objects using computational integral imaging,” Opt. Express 14, 12085–12095 (2006).
    [CrossRef]
  22. D.-H. Shin, B.-G. Lee, and J.-J. Lee, “Occlusion removal method of partially occluded 3-D object using sub-image block matching in computational integral imaging,” Opt. Express 16, 16294–16304 (2008).
    [CrossRef]
  23. M. Zhang, Y. Piao, and E.-S. Kim, “Occlusion-removed scheme using depth-reversed method in computational integral imaging,” Appl. Opt. 49, 2571–2580 (2010).
    [CrossRef]
  24. J.-J. Lee, B.-G. Lee, and H. Yoo, “Image quality enhancement of computational integral imaging reconstruction for partially occluded objects using binary weighting mask on occlusion areas,” Appl. Opt. 50, 1889–1893 (2011).
    [CrossRef]
  25. F. Okano, H. Hoshino, J. Arai, and I. Yuyama, “Real-time pickup method for a three-dimensional image based on integral photography,” Appl. Opt. 36, 1598–1603 (1997).
    [CrossRef]
  26. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).

2011

2010

2009

2008

2006

2004

2003

2001

1997

1994

N. Davies, M. McCormick, and M. Brewin, “Design and analysis of an image transfer system using microlens arrays,” Opt. Eng. 33, 3624–3633 (1994).
[CrossRef]

1908

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

Aggoun, A.

Arai, J.

Brewin, M.

N. Davies, M. McCormick, and M. Brewin, “Design and analysis of an image transfer system using microlens arrays,” Opt. Eng. 33, 3624–3633 (1994).
[CrossRef]

Castro, A.

Cha, S.

Choi, H.

DaneshPanah, M.

Davies, N.

M. C. Forman, N. Davies, and M. McCormick, “Continuous parallax in discrete pixilated integral three-dimensional displays,” J. Opt. Soc. Am. A 20, 411–420 (2003).
[CrossRef]

S. Manolache, A. Aggoun, M. McCormick, N. Davies, and S.-Y. Kung, “Analytical model of a three-dimensional integral image recording system that uses circular- and hexagonal-based spherical surface microlenses,” J. Opt. Soc. Am. A 18, 1814–1821 (2001).
[CrossRef]

N. Davies, M. McCormick, and M. Brewin, “Design and analysis of an image transfer system using microlens arrays,” Opt. Eng. 33, 3624–3633 (1994).
[CrossRef]

M. McCormick and N. Davies, “Full natural color 3-D optical models by integral imaging,” in Fourth International Conference on Holographic Systems, Components, and Applications (Institute of Electrical Engineers, 1993), pp. 237–242.

Forman, M. C.

Frauel, Y.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).

Hahn, J.

Hong, J.

Hong, S.-H.

Hoshino, H.

Hwang, D.-C.

Jang, J.-S.

Jang, J.-Y.

Javidi, B.

Jung, S.

Kim, E.-S.

Kim, H.

Kim, H.-R.

Kim, J.

Kim, N.

Kim, S.-C.

Kim, Y.

Kung, S.-Y.

Kwon, K.-C.

Lee, B.

Lee, B.-G.

Lee, H.-S.

Lee, J.-J.

Lee, S.-D.

Lim, Y.-T.

Lippmann, G.

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

Manolache, S.

Martínez-Corral, M.

Martínez-Cuenca, R.

Matoba, O.

McCormick, M.

M. C. Forman, N. Davies, and M. McCormick, “Continuous parallax in discrete pixilated integral three-dimensional displays,” J. Opt. Soc. Am. A 20, 411–420 (2003).
[CrossRef]

S. Manolache, A. Aggoun, M. McCormick, N. Davies, and S.-Y. Kung, “Analytical model of a three-dimensional integral image recording system that uses circular- and hexagonal-based spherical surface microlenses,” J. Opt. Soc. Am. A 18, 1814–1821 (2001).
[CrossRef]

N. Davies, M. McCormick, and M. Brewin, “Design and analysis of an image transfer system using microlens arrays,” Opt. Eng. 33, 3624–3633 (1994).
[CrossRef]

M. McCormick and N. Davies, “Full natural color 3-D optical models by integral imaging,” in Fourth International Conference on Holographic Systems, Components, and Applications (Institute of Electrical Engineers, 1993), pp. 237–242.

Min, S.-W.

Navarro, H.

Okano, F.

Park, J.-H.

Piao, Y.

Saavedra, G.

Ser, J.-I.

Shin, D.-H.

Shin, K.-H.

Shin, S.-H

Shin, S.-H.

Tajahuerce, E.

Yoo, H.

Yuyama, I.

Zhang, M.

Appl. Opt.

F. Okano, H. Hoshino, J. Arai, and I. Yuyama, “Real-time pickup method for a three-dimensional image based on integral photography,” Appl. Opt. 36, 1598–1603 (1997).
[CrossRef]

D.-C. Hwang, K.-H. Shin, S.-C. Kim, and E.-S. Kim, “Depth extraction of three-dimensional objects in space by the computational integral imaging reconstruction technique,” Appl. Opt. 47, D128–D135 (2008).
[CrossRef]

J. Kim, S.-W. Min, and B. Lee, “Viewing window expansion of integral floating display,” Appl. Opt. 48, 862–867 (2009).
[CrossRef]

J.-Y. Jang, H.-S. Lee, S. Cha, and S.-H Shin, “Viewing angle enhanced integral imaging display by using a high refractive index medium,” Appl. Opt. 50, B71–B76 (2011).
[CrossRef]

J.-S. Jang and B. Javidi, “Improvement of viewing angle in integral imaging by use of moving lenslet arrays with low fill factor,” Appl. Opt. 42, 1996–2002 (2003).
[CrossRef]

J.-I. Ser, S. Cha, and S.-H. Shin, “Distortion correction of reconstructed three-dimensional image in an integral imaging system combined with a single imaging lens,” Appl. Opt. 48, 3108–3119 (2009).
[CrossRef]

J.-H. Park, S. Jung, H. Choi, Y. Kim, and B. Lee, “Depth extraction by use of a rectangular lens array and one-dimensional elemental image modification,” Appl. Opt. 43, 4882–4895 (2004).
[CrossRef]

Y. Frauel, E. Tajahuerce, O. Matoba, A. Castro, and B. Javidi, “Comparison of passive ranging integral imaging and active imaging digital holography for three-dimensional object recognition,” Appl. Opt. 43, 452–462 (2004).
[CrossRef]

M. Zhang, Y. Piao, and E.-S. Kim, “Occlusion-removed scheme using depth-reversed method in computational integral imaging,” Appl. Opt. 49, 2571–2580 (2010).
[CrossRef]

J.-J. Lee, B.-G. Lee, and H. Yoo, “Image quality enhancement of computational integral imaging reconstruction for partially occluded objects using binary weighting mask on occlusion areas,” Appl. Opt. 50, 1889–1893 (2011).
[CrossRef]

F. Okano, H. Hoshino, J. Arai, and I. Yuyama, “Real-time pickup method for a three-dimensional image based on integral photography,” Appl. Opt. 36, 1598–1603 (1997).
[CrossRef]

J.-I. Ser, J.-Y. Jang, S. Cha, and S.-H. Shin, “Applicability of diffraction grating to parallax image array generation in integral imaging,” Appl. Opt. 49, 2429–2433 (2010).
[CrossRef]

C. R. Acad. Sci.

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

J. Opt. Soc. Am. A

Opt. Eng.

N. Davies, M. McCormick, and M. Brewin, “Design and analysis of an image transfer system using microlens arrays,” Opt. Eng. 33, 3624–3633 (1994).
[CrossRef]

Opt. Express

Opt. Lett.

Other

M. McCormick and N. Davies, “Full natural color 3-D optical models by integral imaging,” in Fourth International Conference on Holographic Systems, Components, and Applications (Institute of Electrical Engineers, 1993), pp. 237–242.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).

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 (8)

Fig. 1.
Fig. 1.

Geometrical relation between a point object and imaging points in the lens array method.

Fig. 2.
Fig. 2.

δ-function arrays and correlation results. (a) δ-function array whose spatial period is 330 pixels. (b) Autocorrelation result of δ-function array in (a). (c) δ-function array whose spatial period is 331 pixels. (d) Correlation result of between different periodic δ-function arrays. (e) Sum of δ-function arrays in (a) and (c). (f) Correlation result between sum of δ-function arrays in (e) and δ-function array whose spatial period is 330 pixels in (a).

Fig. 3.
Fig. 3.

Depth resolution of proposed method. (a) When individual elemental image in elemental image array consists of 100×100, 200×200, and 300×300pixels. (b) Scaled graph of (a) when individual elemental image consists of 300×300pixels and the object depth from 130 to 230 mm.

Fig. 4.
Fig. 4.

Experimental setup for computationally picked up elemental image.

Fig. 5.
Fig. 5.

Object and elemental image. (a) Objects “3” and “D” located 155 and 205 mm from lens array, respectively. (b) Elemental image computationally picking up by using 10×10 lens array and the resolution is 3000×3000.

Fig. 6.
Fig. 6.

Depth extraction result. (a) Correlation result between elemental image and 2-D δ-function array whose spatial period is 332 pixels. (b) Magnified image of the correlation result. (c) Intensity map of (b).

Fig. 7.
Fig. 7.

Depth extraction result. (a) Correlation result between elemental image and 2-D δ-function array whose spatial period is 319 pixels. (b) Magnified image of the correlation result. (c) Intensity map of (b).

Fig. 8.
Fig. 8.

Depth extraction results from 145 to 215 mm.

Equations (9)

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

xEk=xO+zOnzOn+f[(k12)PxO].
{xO>P(K1)2fKzOn+(K12)P,xO<P(K1)fKzOn+P2,zOn<0,
g(xE)|zOn=f(xE)|zOn*h(xE)|zOn.
f(xE)|zOn=|zEnzOn|fO(xE)|zOn.
h(xE)|zOn=k=1Kδ(xExEk|zOn),
g(xE)|zOn=|zEnzOn|fO(xE)|zOn*k=1Kδ(xExEk|zOn).
XZOn=ceil[|xEsxE(s1)|×number of pixelP×number of lens],
h(xE)|zOnh(xE)|zOm=k=1Kδ(xExEk|zOn)*k=1Kδ(xExEk|zOm).
ΔzO=Nf(XZonN)(XZon+1N),

Metrics