Abstract

One of the common approaches to compensate for the grayscale performance limitation in time-multiplexing light field displays is to employ a halftone technique. We propose an ordered-dithering halftone algorithm based on a 3-dimension super-mask to increase the gray levels of the time-multiplexing light field display. Our method makes full use of the overlapping perceived pixels which are caused by the time-multiplexing design, such that effectively trading-off the spatial resolution and color performance. A real-time rendering time-multiplexing display prototype is built to validate the proposed halftone algorithm. We conducted a user study to evaluate the quality of display scenes dithered by different super-mask configuration, which showed the consistency with the parameters we pre-calculated. The 3D ordered-dithering algorithm is able to present better visual perception than the conventional halftone algorithms with respect to grayscale representation, and flexible to be applied in different time-multiplexing light field display systems.

© 2015 Optical Society of America

Full Article  |  PDF Article
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References

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    [Crossref]
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    [Crossref]
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  5. T. Kreis, P. Aswendt, and R. Hofling, “Hologram reconstruction using a digital micromirror device,” Opt. Eng. 40(6), 926–933 (2001).
    [Crossref]
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    [Crossref]
  7. X. Xia, X. Liu, H. Li, Z. Zheng, H. Wang, Y. Peng, and W. Shen, “A 360-degree floating 3D display based on light field regeneration,” Opt. Express 21(9), 11237–11247 (2013).
    [Crossref] [PubMed]
  8. J. Lee, J. Park, D. Nam, S. Choi, D. Park, and C. Kim, “32.1: Optimal projector configuration design for 300-Mpixel light-field 3D display,” SID Int. Symp. Dig. Tec. 44(1), 400–403(2013).
    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
  21. Y. Matsumoto and Y. Takaki, “Improvement of gray-scale representation of horizontally scanning holographic display using error diffusion,” Opt. Lett. 39(12), 3433–3436 (2014).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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  26. B. E. Bayer, “An optimum method for two-level rendition of continuous-tone pictures,” Proc. SPIE 154, 139–143 (1999).

2015 (1)

2014 (4)

A. Jones, K. Nagano, J. Liu, J. Busch, X. Yu, M. Bolas, and P. Debevec, “Interpolating vertical parallax for an autostereoscopic three-dimensional projector array,” J. Electron. Imaging 23(1), 011005 (2014).
[Crossref]

B. Chen, Q. Zhong, H. Li, X. Liu, and H. Xu, “Automatic geometrical calibration for multiprojector-type light field three-dimensional display,” Opt. Eng. 53(7), 073107 (2014).
[Crossref]

C. Su, X. Xia, H. Li, X. Liu, C. Kuang, J. Xia, and B. Wang, “A penetrable interactive 3D display based on motion recognition,” Chin. Opt. Lett. 12(6), 060007 (2014).
[Crossref]

Y. Matsumoto and Y. Takaki, “Improvement of gray-scale representation of horizontally scanning holographic display using error diffusion,” Opt. Lett. 39(12), 3433–3436 (2014).
[Crossref] [PubMed]

2013 (2)

2012 (1)

2010 (1)

2009 (3)

2007 (1)

A. Jones, I. McDowall, H. Yamada, M. Bolas, and P. Debevec, “Rendering for an interactive 360° light field display,” ACM Trans. Graph. 26(3), 40 (2007).
[Crossref]

2005 (2)

N. A. Dodgson, “Autostereoscopic 3D displays,” Computer 38(8), 31–36 (2005).
[Crossref]

G. E. Favalora, “Volumetric 3D displays and application infrastructure,” Computer 38(8), 37–44 (2005).
[Crossref]

2001 (1)

T. Kreis, P. Aswendt, and R. Hofling, “Hologram reconstruction using a digital micromirror device,” Opt. Eng. 40(6), 926–933 (2001).
[Crossref]

1999 (2)

O. Veryovka and J. Buchanan, “Comprehensive halftoning of 3D scenes,” Comput. Graph. Forum 18(3), 13–22 (1999).
[Crossref]

B. E. Bayer, “An optimum method for two-level rendition of continuous-tone pictures,” Proc. SPIE 154, 139–143 (1999).

1988 (1)

S. Weissbach, F. Wyrowski, and O. Bryngdahl, “Quantization noise in pulse density modulated holograms,” Opt. Commun. 67(3), 167–171 (1988).
[Crossref]

1974 (1)

C. N. Judice, J. F. Jarvis, and W. H. Ninke, “Using ordered dither to display continuous tone pictures on an AC Plasma Panel,” SID Int. Symp. Dig. Tec. 15(4), 161–169 (1974).

Aswendt, P.

T. Kreis, P. Aswendt, and R. Hofling, “Hologram reconstruction using a digital micromirror device,” Opt. Eng. 40(6), 926–933 (2001).
[Crossref]

Bayer, B. E.

B. E. Bayer, “An optimum method for two-level rendition of continuous-tone pictures,” Proc. SPIE 154, 139–143 (1999).

Bolas, M.

A. Jones, K. Nagano, J. Liu, J. Busch, X. Yu, M. Bolas, and P. Debevec, “Interpolating vertical parallax for an autostereoscopic three-dimensional projector array,” J. Electron. Imaging 23(1), 011005 (2014).
[Crossref]

A. Jones, M. Lang, G. Fyffe, X. Yu, J. Busch, I. McDowall, M. Bolas, and P. Debevec, “Achieving eye contact in a one-to-many 3D video teleconferencing system,” ACM Trans. Graph. 28(3), 64 (2009).
[Crossref]

A. Jones, I. McDowall, H. Yamada, M. Bolas, and P. Debevec, “Rendering for an interactive 360° light field display,” ACM Trans. Graph. 26(3), 40 (2007).
[Crossref]

Bryngdahl, O.

S. Weissbach, F. Wyrowski, and O. Bryngdahl, “Quantization noise in pulse density modulated holograms,” Opt. Commun. 67(3), 167–171 (1988).
[Crossref]

Buchanan, J.

O. Veryovka and J. Buchanan, “Comprehensive halftoning of 3D scenes,” Comput. Graph. Forum 18(3), 13–22 (1999).
[Crossref]

Busch, J.

A. Jones, K. Nagano, J. Liu, J. Busch, X. Yu, M. Bolas, and P. Debevec, “Interpolating vertical parallax for an autostereoscopic three-dimensional projector array,” J. Electron. Imaging 23(1), 011005 (2014).
[Crossref]

A. Jones, M. Lang, G. Fyffe, X. Yu, J. Busch, I. McDowall, M. Bolas, and P. Debevec, “Achieving eye contact in a one-to-many 3D video teleconferencing system,” ACM Trans. Graph. 28(3), 64 (2009).
[Crossref]

Callet, P.

P. Campisi, P. Callet, and E. Marini, “Stereoscopic images quality assessment,” in Proceedings of 15th European Signal Processing Conference (IEEE, 2007), pp. 2110–2114.

Campisi, P.

P. Campisi, P. Callet, and E. Marini, “Stereoscopic images quality assessment,” in Proceedings of 15th European Signal Processing Conference (IEEE, 2007), pp. 2110–2114.

Chen, B.

B. Chen, Q. Zhong, H. Li, X. Liu, and H. Xu, “Automatic geometrical calibration for multiprojector-type light field three-dimensional display,” Opt. Eng. 53(7), 073107 (2014).
[Crossref]

Debevec, P.

A. Jones, K. Nagano, J. Liu, J. Busch, X. Yu, M. Bolas, and P. Debevec, “Interpolating vertical parallax for an autostereoscopic three-dimensional projector array,” J. Electron. Imaging 23(1), 011005 (2014).
[Crossref]

A. Jones, M. Lang, G. Fyffe, X. Yu, J. Busch, I. McDowall, M. Bolas, and P. Debevec, “Achieving eye contact in a one-to-many 3D video teleconferencing system,” ACM Trans. Graph. 28(3), 64 (2009).
[Crossref]

A. Jones, I. McDowall, H. Yamada, M. Bolas, and P. Debevec, “Rendering for an interactive 360° light field display,” ACM Trans. Graph. 26(3), 40 (2007).
[Crossref]

Dodgson, N. A.

N. A. Dodgson, “Autostereoscopic 3D displays,” Computer 38(8), 31–36 (2005).
[Crossref]

Favalora, G. E.

G. E. Favalora, “Volumetric 3D displays and application infrastructure,” Computer 38(8), 37–44 (2005).
[Crossref]

Fyffe, G.

A. Jones, M. Lang, G. Fyffe, X. Yu, J. Busch, I. McDowall, M. Bolas, and P. Debevec, “Achieving eye contact in a one-to-many 3D video teleconferencing system,” ACM Trans. Graph. 28(3), 64 (2009).
[Crossref]

Hanrahan, P.

M. Levoy and P. Hanrahan, “Light Field Rendering,” in Proceedings of the 23rd annual conference on Computer graphics and interactive techniques (ACM, 1996), pp. 31–42.

Hofling, R.

T. Kreis, P. Aswendt, and R. Hofling, “Hologram reconstruction using a digital micromirror device,” Opt. Eng. 40(6), 926–933 (2001).
[Crossref]

Hong, K.

Hore, A.

A. Hore and D. Ziou, “Image quality metrics: PSNR vs. SSIM,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2010), pp. 2366–2369.

Inoue, T.

Jarvis, J. F.

C. N. Judice, J. F. Jarvis, and W. H. Ninke, “Using ordered dither to display continuous tone pictures on an AC Plasma Panel,” SID Int. Symp. Dig. Tec. 15(4), 161–169 (1974).

Jones, A.

A. Jones, K. Nagano, J. Liu, J. Busch, X. Yu, M. Bolas, and P. Debevec, “Interpolating vertical parallax for an autostereoscopic three-dimensional projector array,” J. Electron. Imaging 23(1), 011005 (2014).
[Crossref]

A. Jones, M. Lang, G. Fyffe, X. Yu, J. Busch, I. McDowall, M. Bolas, and P. Debevec, “Achieving eye contact in a one-to-many 3D video teleconferencing system,” ACM Trans. Graph. 28(3), 64 (2009).
[Crossref]

A. Jones, I. McDowall, H. Yamada, M. Bolas, and P. Debevec, “Rendering for an interactive 360° light field display,” ACM Trans. Graph. 26(3), 40 (2007).
[Crossref]

Judice, C. N.

C. N. Judice, J. F. Jarvis, and W. H. Ninke, “Using ordered dither to display continuous tone pictures on an AC Plasma Panel,” SID Int. Symp. Dig. Tec. 15(4), 161–169 (1974).

Kreis, T.

T. Kreis, P. Aswendt, and R. Hofling, “Hologram reconstruction using a digital micromirror device,” Opt. Eng. 40(6), 926–933 (2001).
[Crossref]

Kuang, C.

Lang, M.

A. Jones, M. Lang, G. Fyffe, X. Yu, J. Busch, I. McDowall, M. Bolas, and P. Debevec, “Achieving eye contact in a one-to-many 3D video teleconferencing system,” ACM Trans. Graph. 28(3), 64 (2009).
[Crossref]

Lee, B.

Levoy, M.

M. Levoy and P. Hanrahan, “Light Field Rendering,” in Proceedings of the 23rd annual conference on Computer graphics and interactive techniques (ACM, 1996), pp. 31–42.

Li, H.

Liu, J.

A. Jones, K. Nagano, J. Liu, J. Busch, X. Yu, M. Bolas, and P. Debevec, “Interpolating vertical parallax for an autostereoscopic three-dimensional projector array,” J. Electron. Imaging 23(1), 011005 (2014).
[Crossref]

Liu, X.

Lu, H.

Marini, E.

P. Campisi, P. Callet, and E. Marini, “Stereoscopic images quality assessment,” in Proceedings of 15th European Signal Processing Conference (IEEE, 2007), pp. 2110–2114.

Matsumoto, Y.

McDowall, I.

A. Jones, M. Lang, G. Fyffe, X. Yu, J. Busch, I. McDowall, M. Bolas, and P. Debevec, “Achieving eye contact in a one-to-many 3D video teleconferencing system,” ACM Trans. Graph. 28(3), 64 (2009).
[Crossref]

A. Jones, I. McDowall, H. Yamada, M. Bolas, and P. Debevec, “Rendering for an interactive 360° light field display,” ACM Trans. Graph. 26(3), 40 (2007).
[Crossref]

Nagano, K.

A. Jones, K. Nagano, J. Liu, J. Busch, X. Yu, M. Bolas, and P. Debevec, “Interpolating vertical parallax for an autostereoscopic three-dimensional projector array,” J. Electron. Imaging 23(1), 011005 (2014).
[Crossref]

Ninke, W. H.

C. N. Judice, J. F. Jarvis, and W. H. Ninke, “Using ordered dither to display continuous tone pictures on an AC Plasma Panel,” SID Int. Symp. Dig. Tec. 15(4), 161–169 (1974).

Okada, N.

Ostromoukhov, V.

V. Ostromoukhov, “A simple and efficient error-diffusion algorithm,” in Proceedings of the 28th annual conference on Computer graphics and interactive techniques (ACM, 2001), pp. 567–572.

Park, J.-H.

Peng, Y.

Shen, W.

Su, C.

Takaki, Y.

Uchida, S.

Veryovka, O.

O. Veryovka and J. Buchanan, “Comprehensive halftoning of 3D scenes,” Comput. Graph. Forum 18(3), 13–22 (1999).
[Crossref]

Wang, B.

Wang, H.

Weissbach, S.

S. Weissbach, F. Wyrowski, and O. Bryngdahl, “Quantization noise in pulse density modulated holograms,” Opt. Commun. 67(3), 167–171 (1988).
[Crossref]

Wyrowski, F.

S. Weissbach, F. Wyrowski, and O. Bryngdahl, “Quantization noise in pulse density modulated holograms,” Opt. Commun. 67(3), 167–171 (1988).
[Crossref]

Xia, J.

Xia, X.

Xu, H.

B. Chen, Q. Zhong, H. Li, X. Liu, and H. Xu, “Automatic geometrical calibration for multiprojector-type light field three-dimensional display,” Opt. Eng. 53(7), 073107 (2014).
[Crossref]

Yamada, H.

A. Jones, I. McDowall, H. Yamada, M. Bolas, and P. Debevec, “Rendering for an interactive 360° light field display,” ACM Trans. Graph. 26(3), 40 (2007).
[Crossref]

Yan, C.

Yokouchi, M.

Yu, X.

A. Jones, K. Nagano, J. Liu, J. Busch, X. Yu, M. Bolas, and P. Debevec, “Interpolating vertical parallax for an autostereoscopic three-dimensional projector array,” J. Electron. Imaging 23(1), 011005 (2014).
[Crossref]

A. Jones, M. Lang, G. Fyffe, X. Yu, J. Busch, I. McDowall, M. Bolas, and P. Debevec, “Achieving eye contact in a one-to-many 3D video teleconferencing system,” ACM Trans. Graph. 28(3), 64 (2009).
[Crossref]

Zheng, W.

Zheng, Z.

Zhong, Q.

B. Chen, Q. Zhong, H. Li, X. Liu, and H. Xu, “Automatic geometrical calibration for multiprojector-type light field three-dimensional display,” Opt. Eng. 53(7), 073107 (2014).
[Crossref]

Q. Zhong, Y. Peng, H. Li, C. Su, W. Shen, and X. Liu, “Multiview and light-field reconstruction algorithms for 360 degree multiple-projector-type 3D display,” Appl. Opt. 52(19), 4419–4425 (2013).
[Crossref] [PubMed]

Ziou, D.

A. Hore and D. Ziou, “Image quality metrics: PSNR vs. SSIM,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2010), pp. 2366–2369.

ACM Trans. Graph. (2)

A. Jones, I. McDowall, H. Yamada, M. Bolas, and P. Debevec, “Rendering for an interactive 360° light field display,” ACM Trans. Graph. 26(3), 40 (2007).
[Crossref]

A. Jones, M. Lang, G. Fyffe, X. Yu, J. Busch, I. McDowall, M. Bolas, and P. Debevec, “Achieving eye contact in a one-to-many 3D video teleconferencing system,” ACM Trans. Graph. 28(3), 64 (2009).
[Crossref]

Appl. Opt. (3)

Chin. Opt. Lett. (1)

Comput. Graph. Forum (1)

O. Veryovka and J. Buchanan, “Comprehensive halftoning of 3D scenes,” Comput. Graph. Forum 18(3), 13–22 (1999).
[Crossref]

Computer (2)

G. E. Favalora, “Volumetric 3D displays and application infrastructure,” Computer 38(8), 37–44 (2005).
[Crossref]

N. A. Dodgson, “Autostereoscopic 3D displays,” Computer 38(8), 31–36 (2005).
[Crossref]

J. Electron. Imaging (1)

A. Jones, K. Nagano, J. Liu, J. Busch, X. Yu, M. Bolas, and P. Debevec, “Interpolating vertical parallax for an autostereoscopic three-dimensional projector array,” J. Electron. Imaging 23(1), 011005 (2014).
[Crossref]

Opt. Commun. (1)

S. Weissbach, F. Wyrowski, and O. Bryngdahl, “Quantization noise in pulse density modulated holograms,” Opt. Commun. 67(3), 167–171 (1988).
[Crossref]

Opt. Eng. (2)

B. Chen, Q. Zhong, H. Li, X. Liu, and H. Xu, “Automatic geometrical calibration for multiprojector-type light field three-dimensional display,” Opt. Eng. 53(7), 073107 (2014).
[Crossref]

T. Kreis, P. Aswendt, and R. Hofling, “Hologram reconstruction using a digital micromirror device,” Opt. Eng. 40(6), 926–933 (2001).
[Crossref]

Opt. Express (4)

Opt. Lett. (1)

Proc. SPIE (1)

B. E. Bayer, “An optimum method for two-level rendition of continuous-tone pictures,” Proc. SPIE 154, 139–143 (1999).

SID Int. Symp. Dig. Tec. (1)

C. N. Judice, J. F. Jarvis, and W. H. Ninke, “Using ordered dither to display continuous tone pictures on an AC Plasma Panel,” SID Int. Symp. Dig. Tec. 15(4), 161–169 (1974).

Other (6)

A. Hore and D. Ziou, “Image quality metrics: PSNR vs. SSIM,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2010), pp. 2366–2369.

P. Campisi, P. Callet, and E. Marini, “Stereoscopic images quality assessment,” in Proceedings of 15th European Signal Processing Conference (IEEE, 2007), pp. 2110–2114.

R. W. Floyd and L. Steinberg, “An adaptive algorithm for spatial grey scale,” SID Int. Symp. Dig. Tec. 17, 75–77 (1976).

V. Ostromoukhov, “A simple and efficient error-diffusion algorithm,” in Proceedings of the 28th annual conference on Computer graphics and interactive techniques (ACM, 2001), pp. 567–572.

J. Lee, J. Park, D. Nam, S. Choi, D. Park, and C. Kim, “32.1: Optimal projector configuration design for 300-Mpixel light-field 3D display,” SID Int. Symp. Dig. Tec. 44(1), 400–403(2013).
[Crossref]

M. Levoy and P. Hanrahan, “Light Field Rendering,” in Proceedings of the 23rd annual conference on Computer graphics and interactive techniques (ACM, 1996), pp. 31–42.

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Figures (7)

Fig. 1
Fig. 1 The schematic of time-multiplexing light field displays, (a) with a tilted reflective screen. (b) with a flat microstructural transmitted screen.
Fig. 2
Fig. 2 The schematic diagram of planar overlapping of perceived pixels, and some of the displayed pixels are perceived appearing in the same location because of the human eye’s resolution limit.
Fig. 3
Fig. 3 The schematic diagram of temporal overlapping of perceived pixels. In the condition of the thin scanning line as (a) and (b), the consecutive projection images contain the perspective information and the reconstructed light field rays are directed to the viewers without crosstalk. In the condition of the extended scanning line as (c) and (d), the light field rays which originally represents Vn-1 and Vn + 1 are directed to Vn. Thus the temporal overlapping introduces crosstalk and decreases the angular resolution.
Fig. 4
Fig. 4 (a) The photographs and configuration of experimental system. (b) The captured picture and the Gaussian fitting of the extended scanning line.
Fig. 5
Fig. 5 Comparisons between the target scenes and the reconstructed scenes dithered by different super-masks.
Fig. 6
Fig. 6 User study evaluation result of the reconstructed 3D scene with different super-masks’ parameters (the higher score indicates better performance).
Fig. 7
Fig. 7 The comparison among the reconstructed 3D scenes with different state-of-the-art halftone algorithm.

Equations (6)

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

p = w r l δ w s
I A = k = N / 2 N / 2 ( I k A k d 0.5 d k d + 0.5 d G ( x ) d x )
Ξ dithered ( i , j , k ) = { 0 , Ξ raw ( i , j , k ) < M ( i % m , j % m , k % t ) 1 , Ξ raw ( i , j , k ) M ( i % m , j % m , k % t )
m = round ( p ) = round ( w r l δ w s )
I A ( t ) = k = ceil ( t 1 2 ) ceil ( t 1 2 ) ( I k A k d 0.5 d k d + 0.5 d G ( x ) d x ) = { 0.5 t d 0.5 t d G ( x ) d x when t is odd 0.5 ( t 1 ) d 0.5 ( t + 1 ) d G ( x ) d x when t is even
I A ( t ) I A ( t 1 ) I A ( t ) > ε

Metrics