Abstract

In full-parallax three-dimensional (3-D) imaging systems, the pixel cells often have the shape of a rhombus. Proper arrangement of pixels in these rhombic-shaped cells is important to maximize the quality of displayable 3-D images with a given display panel. The possible number of pixel arrangements in a rhombic cell with a definite dimension is found by considering the number of possible crossings between parallel line families forming the pixel cells, when the slopes of the lines are approximated by the ratio between the number of pixels in the vertical and horizontal directions. To make the rhombic cell have a uniquely defined pixel arrangement, its horizontal and vertical dimensions should be equal to the even multiple of the pixel dimension in their corresponding direction.

© 2006 Optical Society of America

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References

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  1. J.-Y. Son, V. V. Saveljev, Y.-J. Choi, J.-E. Bahn, S.-K. Kim, and H.-H. Choi, " Parameters for designing autostereoscopic imaging systems based on lenticular, parallax barrier and IP plates," Opt. Eng. 42, 3326- 3333 ( 2003).
    [CrossRef]
  2. M. Brewin, M. Forman, and N. Davis, " Electronic capture and display of full parallax 3D images," in Proc. SPIE 2409, 118- 124 ( 1995).
    [CrossRef]
  3. J.-Y. Son and B. Javidi, " 3-dimensional imaging systems based on multiview images," J. Display Technol. 1, 125- 140 ( 2005).
    [CrossRef]
  4. F. Okano, H. Hoshino, J. Arai, M. Yamada, and I. Yuyama, " Three-dimensional television system based on integral photography," in Three-Dimensional Television, Video, and Display Technology, B.Javidi and F.Okano, eds. (Springer, 2002), Chap. 4, pp. 101- 123.
  5. J. Ren, A. Aggoun, and M. McCormick, " Computer generation of integral 3D images with maximum effective viewing," in Proc. SPIE 5006, 65- 73 ( 2003).
    [CrossRef]
  6. J.-S. Jang and B. Javidi, " Improved viewing resolution of three-dimensional integral imaging with nonstationsary micro-optics," Opt. Lett. 28, 324- 326 ( 2003).
  7. I. Amidror, The Theory of the Moire Phenomenon (Kluwer Academic, 2000), pp. 42-57, 60-61.
    [CrossRef]
  8. J.-Y. Son, V. Saveljev, S.-H. Shin, Y.-J. Choi, and S.-S. Kim, " Moire pattern reduction in full-parallax autostereoscopic imaging systems using two crossed lenticular plates as a viewing zone forming optics," in Proceedings of the Ninth International Display Workshop (IDWOS, 2003), pp. 1401- 1404.
  9. J.-Y. Son, V. V. Saveljev, Y.-J. Choi, and S.-S. Kim, " Full parallax images with a diamond shaped pixel cell," in Proc. SPIE 5006, 58- 64 ( 2003).
    [CrossRef]

2005 (1)

2003 (4)

J. Ren, A. Aggoun, and M. McCormick, " Computer generation of integral 3D images with maximum effective viewing," in Proc. SPIE 5006, 65- 73 ( 2003).
[CrossRef]

J.-S. Jang and B. Javidi, " Improved viewing resolution of three-dimensional integral imaging with nonstationsary micro-optics," Opt. Lett. 28, 324- 326 ( 2003).

J.-Y. Son, V. V. Saveljev, Y.-J. Choi, and S.-S. Kim, " Full parallax images with a diamond shaped pixel cell," in Proc. SPIE 5006, 58- 64 ( 2003).
[CrossRef]

J.-Y. Son, V. V. Saveljev, Y.-J. Choi, J.-E. Bahn, S.-K. Kim, and H.-H. Choi, " Parameters for designing autostereoscopic imaging systems based on lenticular, parallax barrier and IP plates," Opt. Eng. 42, 3326- 3333 ( 2003).
[CrossRef]

1995 (1)

M. Brewin, M. Forman, and N. Davis, " Electronic capture and display of full parallax 3D images," in Proc. SPIE 2409, 118- 124 ( 1995).
[CrossRef]

Aggoun, A.

J. Ren, A. Aggoun, and M. McCormick, " Computer generation of integral 3D images with maximum effective viewing," in Proc. SPIE 5006, 65- 73 ( 2003).
[CrossRef]

Amidror, I.

I. Amidror, The Theory of the Moire Phenomenon (Kluwer Academic, 2000), pp. 42-57, 60-61.
[CrossRef]

Arai, J.

F. Okano, H. Hoshino, J. Arai, M. Yamada, and I. Yuyama, " Three-dimensional television system based on integral photography," in Three-Dimensional Television, Video, and Display Technology, B.Javidi and F.Okano, eds. (Springer, 2002), Chap. 4, pp. 101- 123.

Bahn, J.-E.

J.-Y. Son, V. V. Saveljev, Y.-J. Choi, J.-E. Bahn, S.-K. Kim, and H.-H. Choi, " Parameters for designing autostereoscopic imaging systems based on lenticular, parallax barrier and IP plates," Opt. Eng. 42, 3326- 3333 ( 2003).
[CrossRef]

Brewin, M.

M. Brewin, M. Forman, and N. Davis, " Electronic capture and display of full parallax 3D images," in Proc. SPIE 2409, 118- 124 ( 1995).
[CrossRef]

Choi, H.-H.

J.-Y. Son, V. V. Saveljev, Y.-J. Choi, J.-E. Bahn, S.-K. Kim, and H.-H. Choi, " Parameters for designing autostereoscopic imaging systems based on lenticular, parallax barrier and IP plates," Opt. Eng. 42, 3326- 3333 ( 2003).
[CrossRef]

Choi, Y.-J.

J.-Y. Son, V. V. Saveljev, Y.-J. Choi, J.-E. Bahn, S.-K. Kim, and H.-H. Choi, " Parameters for designing autostereoscopic imaging systems based on lenticular, parallax barrier and IP plates," Opt. Eng. 42, 3326- 3333 ( 2003).
[CrossRef]

J.-Y. Son, V. V. Saveljev, Y.-J. Choi, and S.-S. Kim, " Full parallax images with a diamond shaped pixel cell," in Proc. SPIE 5006, 58- 64 ( 2003).
[CrossRef]

J.-Y. Son, V. Saveljev, S.-H. Shin, Y.-J. Choi, and S.-S. Kim, " Moire pattern reduction in full-parallax autostereoscopic imaging systems using two crossed lenticular plates as a viewing zone forming optics," in Proceedings of the Ninth International Display Workshop (IDWOS, 2003), pp. 1401- 1404.

Davis, N.

M. Brewin, M. Forman, and N. Davis, " Electronic capture and display of full parallax 3D images," in Proc. SPIE 2409, 118- 124 ( 1995).
[CrossRef]

Forman, M.

M. Brewin, M. Forman, and N. Davis, " Electronic capture and display of full parallax 3D images," in Proc. SPIE 2409, 118- 124 ( 1995).
[CrossRef]

Hoshino, H.

F. Okano, H. Hoshino, J. Arai, M. Yamada, and I. Yuyama, " Three-dimensional television system based on integral photography," in Three-Dimensional Television, Video, and Display Technology, B.Javidi and F.Okano, eds. (Springer, 2002), Chap. 4, pp. 101- 123.

Jang, J.-S.

J.-S. Jang and B. Javidi, " Improved viewing resolution of three-dimensional integral imaging with nonstationsary micro-optics," Opt. Lett. 28, 324- 326 ( 2003).

Javidi, B.

J.-Y. Son and B. Javidi, " 3-dimensional imaging systems based on multiview images," J. Display Technol. 1, 125- 140 ( 2005).
[CrossRef]

J.-S. Jang and B. Javidi, " Improved viewing resolution of three-dimensional integral imaging with nonstationsary micro-optics," Opt. Lett. 28, 324- 326 ( 2003).

Kim, S.-K.

J.-Y. Son, V. V. Saveljev, Y.-J. Choi, J.-E. Bahn, S.-K. Kim, and H.-H. Choi, " Parameters for designing autostereoscopic imaging systems based on lenticular, parallax barrier and IP plates," Opt. Eng. 42, 3326- 3333 ( 2003).
[CrossRef]

Kim, S.-S.

J.-Y. Son, V. V. Saveljev, Y.-J. Choi, and S.-S. Kim, " Full parallax images with a diamond shaped pixel cell," in Proc. SPIE 5006, 58- 64 ( 2003).
[CrossRef]

J.-Y. Son, V. Saveljev, S.-H. Shin, Y.-J. Choi, and S.-S. Kim, " Moire pattern reduction in full-parallax autostereoscopic imaging systems using two crossed lenticular plates as a viewing zone forming optics," in Proceedings of the Ninth International Display Workshop (IDWOS, 2003), pp. 1401- 1404.

McCormick, M.

J. Ren, A. Aggoun, and M. McCormick, " Computer generation of integral 3D images with maximum effective viewing," in Proc. SPIE 5006, 65- 73 ( 2003).
[CrossRef]

Okano, F.

F. Okano, H. Hoshino, J. Arai, M. Yamada, and I. Yuyama, " Three-dimensional television system based on integral photography," in Three-Dimensional Television, Video, and Display Technology, B.Javidi and F.Okano, eds. (Springer, 2002), Chap. 4, pp. 101- 123.

Ren, J.

J. Ren, A. Aggoun, and M. McCormick, " Computer generation of integral 3D images with maximum effective viewing," in Proc. SPIE 5006, 65- 73 ( 2003).
[CrossRef]

Saveljev, V.

J.-Y. Son, V. Saveljev, S.-H. Shin, Y.-J. Choi, and S.-S. Kim, " Moire pattern reduction in full-parallax autostereoscopic imaging systems using two crossed lenticular plates as a viewing zone forming optics," in Proceedings of the Ninth International Display Workshop (IDWOS, 2003), pp. 1401- 1404.

Saveljev, V. V.

J.-Y. Son, V. V. Saveljev, Y.-J. Choi, and S.-S. Kim, " Full parallax images with a diamond shaped pixel cell," in Proc. SPIE 5006, 58- 64 ( 2003).
[CrossRef]

J.-Y. Son, V. V. Saveljev, Y.-J. Choi, J.-E. Bahn, S.-K. Kim, and H.-H. Choi, " Parameters for designing autostereoscopic imaging systems based on lenticular, parallax barrier and IP plates," Opt. Eng. 42, 3326- 3333 ( 2003).
[CrossRef]

Shin, S.-H.

J.-Y. Son, V. Saveljev, S.-H. Shin, Y.-J. Choi, and S.-S. Kim, " Moire pattern reduction in full-parallax autostereoscopic imaging systems using two crossed lenticular plates as a viewing zone forming optics," in Proceedings of the Ninth International Display Workshop (IDWOS, 2003), pp. 1401- 1404.

Son, J.-Y.

J.-Y. Son and B. Javidi, " 3-dimensional imaging systems based on multiview images," J. Display Technol. 1, 125- 140 ( 2005).
[CrossRef]

J.-Y. Son, V. V. Saveljev, Y.-J. Choi, J.-E. Bahn, S.-K. Kim, and H.-H. Choi, " Parameters for designing autostereoscopic imaging systems based on lenticular, parallax barrier and IP plates," Opt. Eng. 42, 3326- 3333 ( 2003).
[CrossRef]

J.-Y. Son, V. V. Saveljev, Y.-J. Choi, and S.-S. Kim, " Full parallax images with a diamond shaped pixel cell," in Proc. SPIE 5006, 58- 64 ( 2003).
[CrossRef]

J.-Y. Son, V. Saveljev, S.-H. Shin, Y.-J. Choi, and S.-S. Kim, " Moire pattern reduction in full-parallax autostereoscopic imaging systems using two crossed lenticular plates as a viewing zone forming optics," in Proceedings of the Ninth International Display Workshop (IDWOS, 2003), pp. 1401- 1404.

Yamada, M.

F. Okano, H. Hoshino, J. Arai, M. Yamada, and I. Yuyama, " Three-dimensional television system based on integral photography," in Three-Dimensional Television, Video, and Display Technology, B.Javidi and F.Okano, eds. (Springer, 2002), Chap. 4, pp. 101- 123.

Yuyama, I.

F. Okano, H. Hoshino, J. Arai, M. Yamada, and I. Yuyama, " Three-dimensional television system based on integral photography," in Three-Dimensional Television, Video, and Display Technology, B.Javidi and F.Okano, eds. (Springer, 2002), Chap. 4, pp. 101- 123.

J. Display Technol. (1)

Opt. Eng. (1)

J.-Y. Son, V. V. Saveljev, Y.-J. Choi, J.-E. Bahn, S.-K. Kim, and H.-H. Choi, " Parameters for designing autostereoscopic imaging systems based on lenticular, parallax barrier and IP plates," Opt. Eng. 42, 3326- 3333 ( 2003).
[CrossRef]

Opt. Lett. (1)

J.-S. Jang and B. Javidi, " Improved viewing resolution of three-dimensional integral imaging with nonstationsary micro-optics," Opt. Lett. 28, 324- 326 ( 2003).

Proc. SPIE (3)

J. Ren, A. Aggoun, and M. McCormick, " Computer generation of integral 3D images with maximum effective viewing," in Proc. SPIE 5006, 65- 73 ( 2003).
[CrossRef]

J.-Y. Son, V. V. Saveljev, Y.-J. Choi, and S.-S. Kim, " Full parallax images with a diamond shaped pixel cell," in Proc. SPIE 5006, 58- 64 ( 2003).
[CrossRef]

M. Brewin, M. Forman, and N. Davis, " Electronic capture and display of full parallax 3D images," in Proc. SPIE 2409, 118- 124 ( 1995).
[CrossRef]

Other (3)

F. Okano, H. Hoshino, J. Arai, M. Yamada, and I. Yuyama, " Three-dimensional television system based on integral photography," in Three-Dimensional Television, Video, and Display Technology, B.Javidi and F.Okano, eds. (Springer, 2002), Chap. 4, pp. 101- 123.

I. Amidror, The Theory of the Moire Phenomenon (Kluwer Academic, 2000), pp. 42-57, 60-61.
[CrossRef]

J.-Y. Son, V. Saveljev, S.-H. Shin, Y.-J. Choi, and S.-S. Kim, " Moire pattern reduction in full-parallax autostereoscopic imaging systems using two crossed lenticular plates as a viewing zone forming optics," in Proceedings of the Ninth International Display Workshop (IDWOS, 2003), pp. 1401- 1404.

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Figures (10)

Fig. 1
Fig. 1

Basic optical geometry of a full-parallax 3-D imaging system based on VZFO.

Fig. 2
Fig. 2

Rhombic-shaped pixel cells created in square- and rectangular-shaped pixel cells with 4 × 4, 5 × 5, 6 × 4, 4 × 3, 5 × 4, and 6 × 5 pixel arrays.

Fig. 3
Fig. 3

Rhombic cell created by shifting the rhombuses a half-pixel to the right in 6 × 4 pixel arrays.

Fig. 4
Fig. 4

Regular rhomboidal net.

Fig. 5
Fig. 5

Discrete line approximations for parallel lines having slopes of m∕n = 1, 1∕2, 1∕3, 1∕4, 1∕5, 2∕3, 3∕4, 4∕5, and 2∕5 for the case of a = b.

Fig. 6
Fig. 6

Rhombic cells created by discrete lines with slopes of ±(2∕3). (a) Possible ways of crossing discrete lines with slopes ±(2∕3). (b) Rhombic cells created by the different crossings in (a).

Fig. 7
Fig. 7

Various rhombic cells created by changing the distance between parallel lines.

Fig. 8
Fig. 8

Background images on display panels when the panels are composed of (a) square and (b) rhombic pixel cells, respectively. For the case of a square pixel cell, the moiré fringes are apparent. (a) Background image with square pixel cells. (b) Background image with rhombic pixel cells.

Fig. 9
Fig. 9

Pseudoscopic viewing regions in viewing-zone cross sections for two possible rhombic cells created by discrete line slope pairs of ±1, ±(2∕3), and ±(1∕3). (a) Internal structure of viewing-zone cross sections for two rhombic cells of the slope pair of ±1. (b) Internal structure of viewing-zone cross sections for two rhombic cells of the slope pair of ±(2∕3). (c) Internal structure of viewing-zone cross sections for two rhombic cells of the slope pair of ±(1∕3).

Fig. 10
Fig. 10

Full-parallax images displayed on a 24 in. LCD monitor and actual pixel pattern of the full-parallax image. (a) Images seen at left and right, top and bottom, and normal directions. (b) The magnified image of a part of the display panel's pixel pattern for the full-parallax image.

Equations (3)

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tan α = m b n a .
W = 2 l n a , H = 2 l m b .
S = 2 l 2 m n a b .

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