Abstract

The reconstruction of multiple depth images with a ray back-propagation algorithm in three-dimensional (3D) computational integral imaging is computationally burdensome. Further, a reconstructed depth image consists of a focus and an off-focus area. Focus areas are 3D points on the surface of an object that are located at the reconstructed depth, while off-focus areas include 3D points in free-space that do not belong to any object surface in 3D space. Generally, without being removed, the presence of an off-focus area would adversely affect the high-level analysis of a 3D object, including its classification, recognition, and tracking. Here, we use a graphics processing unit (GPU) that supports parallel processing with multiple processors to simultaneously reconstruct multiple depth images using a lookup table containing the shifted values along the x and y directions for each elemental image in a given depth range. Moreover, each 3D point on a depth image can be measured by analyzing its statistical variance with its corresponding samples, which are captured by the two-dimensional (2D) elemental images. These statistical variances can be used to classify depth image pixels as either focus or off-focus points. At this stage, the measurement of focus and off-focus points in multiple depth images is also implemented in parallel on a GPU. Our proposed method is conducted based on the assumption that there is no occlusion of the 3D object during the capture stage of the integral imaging process. Experimental results have demonstrated that this method is capable of removing off-focus points in the reconstructed depth image. The results also showed that using a GPU to remove the off-focus points could greatly improve the overall computational speed compared with using a CPU.

© 2014 Optical Society of America

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References

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  1. G. Lippmann, “La photographie intégrale,” C. R. Acad. Sci. 146, 446–451 (1908).
  2. B. Javidi, F. Okano, and J.-Y. Son, eds., Three-Dimensional Imaging, Visualization, and Display Technologies (Springer, 2009).
  3. T. Mishina, “3D television system based on integral photography,” in Picture Coding Symposium (PCS) (IEEE, 2010), p. 20.
  4. O. Matoba, E. Tajahuerce, and B. Javidi, “Real-time three-dimensional object recognition with multiple perspectives imaging,” Appl. Opt. 40, 3318–3325 (2001).
    [CrossRef]
  5. A. Stern and B. Javidi, “Three-dimensional image sensing, visualization, and processing using integral imaging,” Proc. IEEE 94, 591–607 (2006).
    [CrossRef]
  6. Y. Igarishi, H. Murata, and M. Ueda, “3D display system using a computer-generated integral photograph,” Jpn. J. Appl. Phys. 17, 1683–1684 (1978).
  7. R. Martinez-Cuenca, G. Saavedra, M. Martinez-Corral, and B. Javidi, “Progress in 3-D multiperspective display by integral imaging,” Proc. IEEE 97, 1067–1077 (2009).
    [CrossRef]
  8. M. Levoy, “Light fields and computational imaging,” Computer 39, 46–55 (2006).
    [CrossRef]
  9. H. Hoshino, F. Okano, H. Isono, and I. Yuyama, “Analysis of resolution limitation of integral photography,” J. Opt. Soc. Am. A 15, 2059–2065 (1998).
    [CrossRef]
  10. C. Burckhardt, “Optimum parameters and resolution limitation of integral photography,” J. Opt. Soc. Am. 58, 71–76 (1968).
    [CrossRef]
  11. F. Okano, J. Arai, K. Mitani, and M. Okui, “Real-time integral imaging based on extremely high resolution video system,” Proc. IEEE 94, 490–501 (2006).
    [CrossRef]
  12. F. Okano, H. Hoshino, J. Arai, and I. Yuyama, “Three-dimensional video system based on integral photography,” Opt. Eng. 38, 1072–1077 (1999).
    [CrossRef]
  13. M. Forman, N. Davies, and M. McCormick, “Continuous parallax in discrete pixelated integral three-dimensional displays,” J. Opt. Soc. Am. A 20, 411–420 (2003).
    [CrossRef]
  14. B. Javidi, I. Moon, and S. Yeom, “Three-dimensional identification of biological microorganism using integral imaging,” Opt. Express 14, 12096–12108 (2006).
    [CrossRef]
  15. M. Cho, M. Daneshpanah, I. Moon, and B. Javidi, “Three-dimensional optical sensing and visualization using integral imaging,” Proc. IEEE 99, 556–575 (2011).
    [CrossRef]
  16. X. Xiao, B. Javidi, M. Manuel, and A. Stern, “Advances in three-dimensional integral imaging: sensing, display and application,” Appl. Opt. 52, 546–560 (2013).
    [CrossRef]
  17. I. Moon and B. Javidi, “Three-dimensional visualization of objects in scattering medium by use of computational integral imaging,” Opt. Express 16, 13080–13089 (2008).
    [CrossRef]
  18. B. Tavakoli, B. Javidi, and E. Watson, “Three-dimensional visualization by photon counting computational integral imaging,” Opt. Express 16, 4426–4436 (2008).
    [CrossRef]
  19. J. Park, K. Hong, and B. Lee, “Recent progress in three-dimensional information processing based on integral imaging,” Appl. Opt. 48, H77–H94 (2009).
    [CrossRef]
  20. H. Tan, J. Xia, Y. He, and Y. Guan, “A system for capturing, rendering and multiplexing images on multi-view autostereoscopic display,” in International Conference on Cyberworlds (2010), pp. 325–330.
  21. Y. Taguchi, T. Koike, K. Takahashi, and T. Naemura, “TransCAIP: a live 3D TV system using a camera array and an integral photography display with interactive control of viewing parameters,” IEEE Trans. Vis. Comput. Graph. 15, 841–852 (2009).
    [CrossRef]
  22. D. Michael, “Signal processing and general-purpose computing on GPUs,” IEEE Signal Process. Mag. 24, 109–114 (2007).
    [CrossRef]
  23. T. Balogh and P. Kovacs, “Real-time 3D light field transmission,” Proc. SPIE 7724, 5–11 (2010).
  24. D. Luebke and G. Humphreys, “How GPUs work,” IEEE Computer Society 40, 96–100 (2007).
  25. F. Yi, I. Moon, J. A. Lee, and B. Javidi, “Fast 3D computational integral imaging using graphics processing unit,” J. Disp. Technol. 8, 714–722 (2012).
  26. X. Xiao, M. Daneshpanah, and B. Javidi, “Occlusion removal using depth mapping in three-dimensional integral imaging,” J. Disp. Technol. 8, 483–490 (2012).
  27. R. C. Gonzalez and R. E. Woods, Digital Imaging Processing (Prentice Hall, 2002).

2013 (1)

2012 (2)

F. Yi, I. Moon, J. A. Lee, and B. Javidi, “Fast 3D computational integral imaging using graphics processing unit,” J. Disp. Technol. 8, 714–722 (2012).

X. Xiao, M. Daneshpanah, and B. Javidi, “Occlusion removal using depth mapping in three-dimensional integral imaging,” J. Disp. Technol. 8, 483–490 (2012).

2011 (1)

M. Cho, M. Daneshpanah, I. Moon, and B. Javidi, “Three-dimensional optical sensing and visualization using integral imaging,” Proc. IEEE 99, 556–575 (2011).
[CrossRef]

2010 (1)

T. Balogh and P. Kovacs, “Real-time 3D light field transmission,” Proc. SPIE 7724, 5–11 (2010).

2009 (3)

Y. Taguchi, T. Koike, K. Takahashi, and T. Naemura, “TransCAIP: a live 3D TV system using a camera array and an integral photography display with interactive control of viewing parameters,” IEEE Trans. Vis. Comput. Graph. 15, 841–852 (2009).
[CrossRef]

R. Martinez-Cuenca, G. Saavedra, M. Martinez-Corral, and B. Javidi, “Progress in 3-D multiperspective display by integral imaging,” Proc. IEEE 97, 1067–1077 (2009).
[CrossRef]

J. Park, K. Hong, and B. Lee, “Recent progress in three-dimensional information processing based on integral imaging,” Appl. Opt. 48, H77–H94 (2009).
[CrossRef]

2008 (2)

2007 (2)

D. Michael, “Signal processing and general-purpose computing on GPUs,” IEEE Signal Process. Mag. 24, 109–114 (2007).
[CrossRef]

D. Luebke and G. Humphreys, “How GPUs work,” IEEE Computer Society 40, 96–100 (2007).

2006 (4)

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

M. Levoy, “Light fields and computational imaging,” Computer 39, 46–55 (2006).
[CrossRef]

F. Okano, J. Arai, K. Mitani, and M. Okui, “Real-time integral imaging based on extremely high resolution video system,” Proc. IEEE 94, 490–501 (2006).
[CrossRef]

B. Javidi, I. Moon, and S. Yeom, “Three-dimensional identification of biological microorganism using integral imaging,” Opt. Express 14, 12096–12108 (2006).
[CrossRef]

2003 (1)

2001 (1)

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]

1998 (1)

1978 (1)

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

1968 (1)

1908 (1)

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

Arai, J.

F. Okano, J. Arai, K. Mitani, and M. Okui, “Real-time integral imaging based on extremely high resolution video system,” Proc. IEEE 94, 490–501 (2006).
[CrossRef]

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

Balogh, T.

T. Balogh and P. Kovacs, “Real-time 3D light field transmission,” Proc. SPIE 7724, 5–11 (2010).

Burckhardt, C.

Cho, M.

M. Cho, M. Daneshpanah, I. Moon, and B. Javidi, “Three-dimensional optical sensing and visualization using integral imaging,” Proc. IEEE 99, 556–575 (2011).
[CrossRef]

Daneshpanah, M.

X. Xiao, M. Daneshpanah, and B. Javidi, “Occlusion removal using depth mapping in three-dimensional integral imaging,” J. Disp. Technol. 8, 483–490 (2012).

M. Cho, M. Daneshpanah, I. Moon, and B. Javidi, “Three-dimensional optical sensing and visualization using integral imaging,” Proc. IEEE 99, 556–575 (2011).
[CrossRef]

Davies, N.

Forman, M.

Gonzalez, R. C.

R. C. Gonzalez and R. E. Woods, Digital Imaging Processing (Prentice Hall, 2002).

Guan, Y.

H. Tan, J. Xia, Y. He, and Y. Guan, “A system for capturing, rendering and multiplexing images on multi-view autostereoscopic display,” in International Conference on Cyberworlds (2010), pp. 325–330.

He, Y.

H. Tan, J. Xia, Y. He, and Y. Guan, “A system for capturing, rendering and multiplexing images on multi-view autostereoscopic display,” in International Conference on Cyberworlds (2010), pp. 325–330.

Hong, K.

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]

H. Hoshino, F. Okano, H. Isono, and I. Yuyama, “Analysis of resolution limitation of integral photography,” J. Opt. Soc. Am. A 15, 2059–2065 (1998).
[CrossRef]

Humphreys, G.

D. Luebke and G. Humphreys, “How GPUs work,” IEEE Computer Society 40, 96–100 (2007).

Igarishi, Y.

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

Isono, H.

Javidi, B.

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

X. Xiao, M. Daneshpanah, and B. Javidi, “Occlusion removal using depth mapping in three-dimensional integral imaging,” J. Disp. Technol. 8, 483–490 (2012).

F. Yi, I. Moon, J. A. Lee, and B. Javidi, “Fast 3D computational integral imaging using graphics processing unit,” J. Disp. Technol. 8, 714–722 (2012).

M. Cho, M. Daneshpanah, I. Moon, and B. Javidi, “Three-dimensional optical sensing and visualization using integral imaging,” Proc. IEEE 99, 556–575 (2011).
[CrossRef]

R. Martinez-Cuenca, G. Saavedra, M. Martinez-Corral, and B. Javidi, “Progress in 3-D multiperspective display by integral imaging,” Proc. IEEE 97, 1067–1077 (2009).
[CrossRef]

I. Moon and B. Javidi, “Three-dimensional visualization of objects in scattering medium by use of computational integral imaging,” Opt. Express 16, 13080–13089 (2008).
[CrossRef]

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

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

B. Javidi, I. Moon, and S. Yeom, “Three-dimensional identification of biological microorganism using integral imaging,” Opt. Express 14, 12096–12108 (2006).
[CrossRef]

O. Matoba, E. Tajahuerce, and B. Javidi, “Real-time three-dimensional object recognition with multiple perspectives imaging,” Appl. Opt. 40, 3318–3325 (2001).
[CrossRef]

Koike, T.

Y. Taguchi, T. Koike, K. Takahashi, and T. Naemura, “TransCAIP: a live 3D TV system using a camera array and an integral photography display with interactive control of viewing parameters,” IEEE Trans. Vis. Comput. Graph. 15, 841–852 (2009).
[CrossRef]

Kovacs, P.

T. Balogh and P. Kovacs, “Real-time 3D light field transmission,” Proc. SPIE 7724, 5–11 (2010).

Lee, B.

Lee, J. A.

F. Yi, I. Moon, J. A. Lee, and B. Javidi, “Fast 3D computational integral imaging using graphics processing unit,” J. Disp. Technol. 8, 714–722 (2012).

Levoy, M.

M. Levoy, “Light fields and computational imaging,” Computer 39, 46–55 (2006).
[CrossRef]

Lippmann, G.

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

Luebke, D.

D. Luebke and G. Humphreys, “How GPUs work,” IEEE Computer Society 40, 96–100 (2007).

Manuel, M.

Martinez-Corral, M.

R. Martinez-Cuenca, G. Saavedra, M. Martinez-Corral, and B. Javidi, “Progress in 3-D multiperspective display by integral imaging,” Proc. IEEE 97, 1067–1077 (2009).
[CrossRef]

Martinez-Cuenca, R.

R. Martinez-Cuenca, G. Saavedra, M. Martinez-Corral, and B. Javidi, “Progress in 3-D multiperspective display by integral imaging,” Proc. IEEE 97, 1067–1077 (2009).
[CrossRef]

Matoba, O.

McCormick, M.

Michael, D.

D. Michael, “Signal processing and general-purpose computing on GPUs,” IEEE Signal Process. Mag. 24, 109–114 (2007).
[CrossRef]

Mishina, T.

T. Mishina, “3D television system based on integral photography,” in Picture Coding Symposium (PCS) (IEEE, 2010), p. 20.

Mitani, K.

F. Okano, J. Arai, K. Mitani, and M. Okui, “Real-time integral imaging based on extremely high resolution video system,” Proc. IEEE 94, 490–501 (2006).
[CrossRef]

Moon, I.

F. Yi, I. Moon, J. A. Lee, and B. Javidi, “Fast 3D computational integral imaging using graphics processing unit,” J. Disp. Technol. 8, 714–722 (2012).

M. Cho, M. Daneshpanah, I. Moon, and B. Javidi, “Three-dimensional optical sensing and visualization using integral imaging,” Proc. IEEE 99, 556–575 (2011).
[CrossRef]

I. Moon and B. Javidi, “Three-dimensional visualization of objects in scattering medium by use of computational integral imaging,” Opt. Express 16, 13080–13089 (2008).
[CrossRef]

B. Javidi, I. Moon, and S. Yeom, “Three-dimensional identification of biological microorganism using integral imaging,” Opt. Express 14, 12096–12108 (2006).
[CrossRef]

Murata, H.

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

Naemura, T.

Y. Taguchi, T. Koike, K. Takahashi, and T. Naemura, “TransCAIP: a live 3D TV system using a camera array and an integral photography display with interactive control of viewing parameters,” IEEE Trans. Vis. Comput. Graph. 15, 841–852 (2009).
[CrossRef]

Okano, F.

F. Okano, J. Arai, K. Mitani, and M. Okui, “Real-time integral imaging based on extremely high resolution video system,” Proc. IEEE 94, 490–501 (2006).
[CrossRef]

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

H. Hoshino, F. Okano, H. Isono, and I. Yuyama, “Analysis of resolution limitation of integral photography,” J. Opt. Soc. Am. A 15, 2059–2065 (1998).
[CrossRef]

Okui, M.

F. Okano, J. Arai, K. Mitani, and M. Okui, “Real-time integral imaging based on extremely high resolution video system,” Proc. IEEE 94, 490–501 (2006).
[CrossRef]

Park, J.

Saavedra, G.

R. Martinez-Cuenca, G. Saavedra, M. Martinez-Corral, and B. Javidi, “Progress in 3-D multiperspective display by integral imaging,” Proc. IEEE 97, 1067–1077 (2009).
[CrossRef]

Stern, A.

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

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

Taguchi, Y.

Y. Taguchi, T. Koike, K. Takahashi, and T. Naemura, “TransCAIP: a live 3D TV system using a camera array and an integral photography display with interactive control of viewing parameters,” IEEE Trans. Vis. Comput. Graph. 15, 841–852 (2009).
[CrossRef]

Tajahuerce, E.

Takahashi, K.

Y. Taguchi, T. Koike, K. Takahashi, and T. Naemura, “TransCAIP: a live 3D TV system using a camera array and an integral photography display with interactive control of viewing parameters,” IEEE Trans. Vis. Comput. Graph. 15, 841–852 (2009).
[CrossRef]

Tan, H.

H. Tan, J. Xia, Y. He, and Y. Guan, “A system for capturing, rendering and multiplexing images on multi-view autostereoscopic display,” in International Conference on Cyberworlds (2010), pp. 325–330.

Tavakoli, B.

Ueda, M.

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

Watson, E.

Woods, R. E.

R. C. Gonzalez and R. E. Woods, Digital Imaging Processing (Prentice Hall, 2002).

Xia, J.

H. Tan, J. Xia, Y. He, and Y. Guan, “A system for capturing, rendering and multiplexing images on multi-view autostereoscopic display,” in International Conference on Cyberworlds (2010), pp. 325–330.

Xiao, X.

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

X. Xiao, M. Daneshpanah, and B. Javidi, “Occlusion removal using depth mapping in three-dimensional integral imaging,” J. Disp. Technol. 8, 483–490 (2012).

Yeom, S.

Yi, F.

F. Yi, I. Moon, J. A. Lee, and B. Javidi, “Fast 3D computational integral imaging using graphics processing unit,” J. Disp. Technol. 8, 714–722 (2012).

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]

H. Hoshino, F. Okano, H. Isono, and I. Yuyama, “Analysis of resolution limitation of integral photography,” J. Opt. Soc. Am. A 15, 2059–2065 (1998).
[CrossRef]

Appl. Opt. (3)

C. R. Acad. Sci. (1)

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

Computer (1)

M. Levoy, “Light fields and computational imaging,” Computer 39, 46–55 (2006).
[CrossRef]

IEEE Computer Society (1)

D. Luebke and G. Humphreys, “How GPUs work,” IEEE Computer Society 40, 96–100 (2007).

IEEE Signal Process. Mag. (1)

D. Michael, “Signal processing and general-purpose computing on GPUs,” IEEE Signal Process. Mag. 24, 109–114 (2007).
[CrossRef]

IEEE Trans. Vis. Comput. Graph. (1)

Y. Taguchi, T. Koike, K. Takahashi, and T. Naemura, “TransCAIP: a live 3D TV system using a camera array and an integral photography display with interactive control of viewing parameters,” IEEE Trans. Vis. Comput. Graph. 15, 841–852 (2009).
[CrossRef]

J. Disp. Technol. (2)

F. Yi, I. Moon, J. A. Lee, and B. Javidi, “Fast 3D computational integral imaging using graphics processing unit,” J. Disp. Technol. 8, 714–722 (2012).

X. Xiao, M. Daneshpanah, and B. Javidi, “Occlusion removal using depth mapping in three-dimensional integral imaging,” J. Disp. Technol. 8, 483–490 (2012).

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (2)

Jpn. J. Appl. Phys. (1)

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

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 (3)

Proc. IEEE (4)

M. Cho, M. Daneshpanah, I. Moon, and B. Javidi, “Three-dimensional optical sensing and visualization using integral imaging,” Proc. IEEE 99, 556–575 (2011).
[CrossRef]

F. Okano, J. Arai, K. Mitani, and M. Okui, “Real-time integral imaging based on extremely high resolution video system,” Proc. IEEE 94, 490–501 (2006).
[CrossRef]

R. Martinez-Cuenca, G. Saavedra, M. Martinez-Corral, and B. Javidi, “Progress in 3-D multiperspective display by integral imaging,” Proc. IEEE 97, 1067–1077 (2009).
[CrossRef]

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

Proc. SPIE (1)

T. Balogh and P. Kovacs, “Real-time 3D light field transmission,” Proc. SPIE 7724, 5–11 (2010).

Other (4)

R. C. Gonzalez and R. E. Woods, Digital Imaging Processing (Prentice Hall, 2002).

B. Javidi, F. Okano, and J.-Y. Son, eds., Three-Dimensional Imaging, Visualization, and Display Technologies (Springer, 2009).

T. Mishina, “3D television system based on integral photography,” in Picture Coding Symposium (PCS) (IEEE, 2010), p. 20.

H. Tan, J. Xia, Y. He, and Y. Guan, “A system for capturing, rendering and multiplexing images on multi-view autostereoscopic display,” in International Conference on Cyberworlds (2010), pp. 325–330.

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Figures (13)

Fig. 1.
Fig. 1.

Schematic setup of image recording for integral imaging.

Fig. 2.
Fig. 2.

Schematic diagram of computational reconstruction in integral imaging.

Fig. 3.
Fig. 3.

Illustration of lookup table and shrunken back-projected elemental images.

Fig. 4.
Fig. 4.

Ray diagram for a 3D object point: (a) ray diagram for a 3D and free-space point and (b) ray diagram for an occluded 3D point.

Fig. 5.
Fig. 5.

Reconstruction of multiple depth images without off-focus points.

Fig. 6.
Fig. 6.

Illustration of the first depth image.

Fig. 7.
Fig. 7.

Pseudo-code for reconstructing multiple depth images in parallel.

Fig. 8.
Fig. 8.

3D scene used in the experiment.

Fig. 9.
Fig. 9.

Examples of 8×8 elemental images captured by the sensors.

Fig. 10.
Fig. 10.

Depth images reconstructed using a conventional ray back-propagation method at a distance of (a) 280 mm, (b) 298 mm, (c) 360 mm, (d) 382 mm, (e) 430 mm, and (f) 490 mm.

Fig. 11.
Fig. 11.

Depth images reconstructed without off-focus points using the proposed method at a distance of (a) 280 mm, (b) 298 mm, (c) 360 mm, (d) 382 mm, (e) 430 mm, and (f) 490 mm.

Fig. 12.
Fig. 12.

Computation time and speedup of a sequential CPU and parallel GPU when reconstructing multiple depth images without off-focus points: (a) CPU and GPU computation time comparison and (b) corresponding speedup based on the CPU and GPU computation times.

Fig. 13.
Fig. 13.

Computation time and speedup of a sequential CPU and parallel GPU with various elemental image sizes: (a) CPU and GPU computation time comparison and (b) corresponding speedup based on the CPU and GPU computation times.

Tables (2)

Tables Icon

Table 1. Comparison of Computing Times between a CPU and GPU for Reconstructing Multiple Depth Images

Tables Icon

Table 2. Comparison of Computing Time between the CPU and GPU for Reconstructing One Depth Image

Equations (5)

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

DI(x,y,z=d)=1o(x,y)×i=1Nxj=1NyEij[x+(px×fd)×(i1),y+(py×fd)×(j1)],
shx×sp=shx×cxsx=fd×pxshy×sp=shy×cysy=fd×py,
Depth image size=[shx×(Nx1)+sx,shy×(Ny1)+sy]×sp.
Dijm={0Iijm>thresholdI˜ijmIijmthreshold,
I˜ijm=average[nonzero(Bijm1,Bijm2,,BijmNxNy)]Iijm=variance[nonzero(Bijm1,Bijm2,,BijmNxNy)],

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