Abstract

A three-dimensional (3D) structure designed by our proposed algorithm can simultaneously exhibit multiple two-dimensional patterns. The 3D structure provides multiple patterns having directional characteristics by distributing the effects of the artefacts. In this study, we proposed an iterative algorithm to improve the image quality of the exhibited patterns and have verified the effectiveness of the proposed algorithm using numerical simulations. Moreover, we fabricated different 3D glass structures (an octagonal prism, a cube and a sphere) using the proposed algorithm. All 3D structures exhibit four patterns, and different patterns can be observed depending on the viewing direction.

© 2016 Optical Society of America

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References

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  1. B. G. Blundell, A. J. Schwarz, and D. K. Horrell, “Volumetric three-dimensional display system: their past, present and future,” Eng. Sci. Ed. J. 2, 196–200 (1993).
    [Crossref]
  2. D. L. MacFarlane, “Volumetric three-dimensional display,” Appl. Opt. 33, 7453–7457 (1994).
    [Crossref] [PubMed]
  3. M. Parker, “Lumarca,” ACM SIGGRAPH ASIA 2009 (ACM, 2009) 77.
  4. A. Yagi, M. Imura, Y. Kuroda, and O. Oshiro, “360-degree fog projection interactive display,” ACM SIGGRAPH ASIA 2011 (ACM, 2011), pp. 19.
  5. A. Sand and I. Rakkolainen, “A hand-held immaterial volumetric display,” Proc. SPIE 9011, 90110Q (2014).
    [Crossref]
  6. P. C. Barnum, S. G. Narasimhan, and T. Kanade, “A multi-layered display with water drops,” Proc. ACM SIGGRAPH 2010 29, 76, Los Angeles, CA, USA. (2010, Jul. 26).
    [Crossref]
  7. D. R. Hofstadter, Godel, Escher, Bach: an Eternal Golden Braid, (Basic Books, New York, 1979).
  8. N. J. Mitra and M. Pauly, “Shadow Art,” ACM T. Graphic 28, 156 (2009).
    [Crossref]
  9. H. Nakayama, A. Shiraki, R. Hirayama, N. Masuda, T. Shimobaba, and T. Ito, “Three-dimensional volume containing multiple two-dimensional information patterns,” Sci. Rep. 3, 1931 (2013).
    [PubMed]
  10. R. Hirayama, M. Naruse, H. Nakayama, N. Tate, A. Shiraki, T. Kakue, T. Shimobaba, and T. Ito, “Design, Implementation and characterization of a quantum-dot-based volumetric display,” Sci. Rep. 5, 8472 (2015).
    [Crossref] [PubMed]
  11. A. Wang, A. C. Bovik, H. R. Sheikh, and H. R. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans. Image Process. 13, 600–612 (2004).
    [Crossref] [PubMed]
  12. S. K. Nayar and N. A. Vijay, “Projection volumetric display using passive optical scatters,” Computer 40(7), 54–63 (2007).
    [Crossref]

2015 (1)

R. Hirayama, M. Naruse, H. Nakayama, N. Tate, A. Shiraki, T. Kakue, T. Shimobaba, and T. Ito, “Design, Implementation and characterization of a quantum-dot-based volumetric display,” Sci. Rep. 5, 8472 (2015).
[Crossref] [PubMed]

2014 (1)

A. Sand and I. Rakkolainen, “A hand-held immaterial volumetric display,” Proc. SPIE 9011, 90110Q (2014).
[Crossref]

2013 (1)

H. Nakayama, A. Shiraki, R. Hirayama, N. Masuda, T. Shimobaba, and T. Ito, “Three-dimensional volume containing multiple two-dimensional information patterns,” Sci. Rep. 3, 1931 (2013).
[PubMed]

2009 (1)

N. J. Mitra and M. Pauly, “Shadow Art,” ACM T. Graphic 28, 156 (2009).
[Crossref]

2007 (1)

S. K. Nayar and N. A. Vijay, “Projection volumetric display using passive optical scatters,” Computer 40(7), 54–63 (2007).
[Crossref]

2004 (1)

A. Wang, A. C. Bovik, H. R. Sheikh, and H. R. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans. Image Process. 13, 600–612 (2004).
[Crossref] [PubMed]

1994 (1)

1993 (1)

B. G. Blundell, A. J. Schwarz, and D. K. Horrell, “Volumetric three-dimensional display system: their past, present and future,” Eng. Sci. Ed. J. 2, 196–200 (1993).
[Crossref]

Barnum, P. C.

P. C. Barnum, S. G. Narasimhan, and T. Kanade, “A multi-layered display with water drops,” Proc. ACM SIGGRAPH 2010 29, 76, Los Angeles, CA, USA. (2010, Jul. 26).
[Crossref]

Blundell, B. G.

B. G. Blundell, A. J. Schwarz, and D. K. Horrell, “Volumetric three-dimensional display system: their past, present and future,” Eng. Sci. Ed. J. 2, 196–200 (1993).
[Crossref]

Bovik, A. C.

A. Wang, A. C. Bovik, H. R. Sheikh, and H. R. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans. Image Process. 13, 600–612 (2004).
[Crossref] [PubMed]

Hirayama, R.

R. Hirayama, M. Naruse, H. Nakayama, N. Tate, A. Shiraki, T. Kakue, T. Shimobaba, and T. Ito, “Design, Implementation and characterization of a quantum-dot-based volumetric display,” Sci. Rep. 5, 8472 (2015).
[Crossref] [PubMed]

H. Nakayama, A. Shiraki, R. Hirayama, N. Masuda, T. Shimobaba, and T. Ito, “Three-dimensional volume containing multiple two-dimensional information patterns,” Sci. Rep. 3, 1931 (2013).
[PubMed]

Hofstadter, D. R.

D. R. Hofstadter, Godel, Escher, Bach: an Eternal Golden Braid, (Basic Books, New York, 1979).

Horrell, D. K.

B. G. Blundell, A. J. Schwarz, and D. K. Horrell, “Volumetric three-dimensional display system: their past, present and future,” Eng. Sci. Ed. J. 2, 196–200 (1993).
[Crossref]

Imura, M.

A. Yagi, M. Imura, Y. Kuroda, and O. Oshiro, “360-degree fog projection interactive display,” ACM SIGGRAPH ASIA 2011 (ACM, 2011), pp. 19.

Ito, T.

R. Hirayama, M. Naruse, H. Nakayama, N. Tate, A. Shiraki, T. Kakue, T. Shimobaba, and T. Ito, “Design, Implementation and characterization of a quantum-dot-based volumetric display,” Sci. Rep. 5, 8472 (2015).
[Crossref] [PubMed]

H. Nakayama, A. Shiraki, R. Hirayama, N. Masuda, T. Shimobaba, and T. Ito, “Three-dimensional volume containing multiple two-dimensional information patterns,” Sci. Rep. 3, 1931 (2013).
[PubMed]

Kakue, T.

R. Hirayama, M. Naruse, H. Nakayama, N. Tate, A. Shiraki, T. Kakue, T. Shimobaba, and T. Ito, “Design, Implementation and characterization of a quantum-dot-based volumetric display,” Sci. Rep. 5, 8472 (2015).
[Crossref] [PubMed]

Kanade, T.

P. C. Barnum, S. G. Narasimhan, and T. Kanade, “A multi-layered display with water drops,” Proc. ACM SIGGRAPH 2010 29, 76, Los Angeles, CA, USA. (2010, Jul. 26).
[Crossref]

Kuroda, Y.

A. Yagi, M. Imura, Y. Kuroda, and O. Oshiro, “360-degree fog projection interactive display,” ACM SIGGRAPH ASIA 2011 (ACM, 2011), pp. 19.

MacFarlane, D. L.

Masuda, N.

H. Nakayama, A. Shiraki, R. Hirayama, N. Masuda, T. Shimobaba, and T. Ito, “Three-dimensional volume containing multiple two-dimensional information patterns,” Sci. Rep. 3, 1931 (2013).
[PubMed]

Mitra, N. J.

N. J. Mitra and M. Pauly, “Shadow Art,” ACM T. Graphic 28, 156 (2009).
[Crossref]

Nakayama, H.

R. Hirayama, M. Naruse, H. Nakayama, N. Tate, A. Shiraki, T. Kakue, T. Shimobaba, and T. Ito, “Design, Implementation and characterization of a quantum-dot-based volumetric display,” Sci. Rep. 5, 8472 (2015).
[Crossref] [PubMed]

H. Nakayama, A. Shiraki, R. Hirayama, N. Masuda, T. Shimobaba, and T. Ito, “Three-dimensional volume containing multiple two-dimensional information patterns,” Sci. Rep. 3, 1931 (2013).
[PubMed]

Narasimhan, S. G.

P. C. Barnum, S. G. Narasimhan, and T. Kanade, “A multi-layered display with water drops,” Proc. ACM SIGGRAPH 2010 29, 76, Los Angeles, CA, USA. (2010, Jul. 26).
[Crossref]

Naruse, M.

R. Hirayama, M. Naruse, H. Nakayama, N. Tate, A. Shiraki, T. Kakue, T. Shimobaba, and T. Ito, “Design, Implementation and characterization of a quantum-dot-based volumetric display,” Sci. Rep. 5, 8472 (2015).
[Crossref] [PubMed]

Nayar, S. K.

S. K. Nayar and N. A. Vijay, “Projection volumetric display using passive optical scatters,” Computer 40(7), 54–63 (2007).
[Crossref]

Oshiro, O.

A. Yagi, M. Imura, Y. Kuroda, and O. Oshiro, “360-degree fog projection interactive display,” ACM SIGGRAPH ASIA 2011 (ACM, 2011), pp. 19.

Parker, M.

M. Parker, “Lumarca,” ACM SIGGRAPH ASIA 2009 (ACM, 2009) 77.

Pauly, M.

N. J. Mitra and M. Pauly, “Shadow Art,” ACM T. Graphic 28, 156 (2009).
[Crossref]

Rakkolainen, I.

A. Sand and I. Rakkolainen, “A hand-held immaterial volumetric display,” Proc. SPIE 9011, 90110Q (2014).
[Crossref]

Sand, A.

A. Sand and I. Rakkolainen, “A hand-held immaterial volumetric display,” Proc. SPIE 9011, 90110Q (2014).
[Crossref]

Schwarz, A. J.

B. G. Blundell, A. J. Schwarz, and D. K. Horrell, “Volumetric three-dimensional display system: their past, present and future,” Eng. Sci. Ed. J. 2, 196–200 (1993).
[Crossref]

Sheikh, H. R.

A. Wang, A. C. Bovik, H. R. Sheikh, and H. R. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans. Image Process. 13, 600–612 (2004).
[Crossref] [PubMed]

Shimobaba, T.

R. Hirayama, M. Naruse, H. Nakayama, N. Tate, A. Shiraki, T. Kakue, T. Shimobaba, and T. Ito, “Design, Implementation and characterization of a quantum-dot-based volumetric display,” Sci. Rep. 5, 8472 (2015).
[Crossref] [PubMed]

H. Nakayama, A. Shiraki, R. Hirayama, N. Masuda, T. Shimobaba, and T. Ito, “Three-dimensional volume containing multiple two-dimensional information patterns,” Sci. Rep. 3, 1931 (2013).
[PubMed]

Shiraki, A.

R. Hirayama, M. Naruse, H. Nakayama, N. Tate, A. Shiraki, T. Kakue, T. Shimobaba, and T. Ito, “Design, Implementation and characterization of a quantum-dot-based volumetric display,” Sci. Rep. 5, 8472 (2015).
[Crossref] [PubMed]

H. Nakayama, A. Shiraki, R. Hirayama, N. Masuda, T. Shimobaba, and T. Ito, “Three-dimensional volume containing multiple two-dimensional information patterns,” Sci. Rep. 3, 1931 (2013).
[PubMed]

Simoncelli, H. R.

A. Wang, A. C. Bovik, H. R. Sheikh, and H. R. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans. Image Process. 13, 600–612 (2004).
[Crossref] [PubMed]

Tate, N.

R. Hirayama, M. Naruse, H. Nakayama, N. Tate, A. Shiraki, T. Kakue, T. Shimobaba, and T. Ito, “Design, Implementation and characterization of a quantum-dot-based volumetric display,” Sci. Rep. 5, 8472 (2015).
[Crossref] [PubMed]

Vijay, N. A.

S. K. Nayar and N. A. Vijay, “Projection volumetric display using passive optical scatters,” Computer 40(7), 54–63 (2007).
[Crossref]

Wang, A.

A. Wang, A. C. Bovik, H. R. Sheikh, and H. R. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans. Image Process. 13, 600–612 (2004).
[Crossref] [PubMed]

Yagi, A.

A. Yagi, M. Imura, Y. Kuroda, and O. Oshiro, “360-degree fog projection interactive display,” ACM SIGGRAPH ASIA 2011 (ACM, 2011), pp. 19.

ACM T. Graphic (1)

N. J. Mitra and M. Pauly, “Shadow Art,” ACM T. Graphic 28, 156 (2009).
[Crossref]

Appl. Opt. (1)

Computer (1)

S. K. Nayar and N. A. Vijay, “Projection volumetric display using passive optical scatters,” Computer 40(7), 54–63 (2007).
[Crossref]

Eng. Sci. Ed. J. (1)

B. G. Blundell, A. J. Schwarz, and D. K. Horrell, “Volumetric three-dimensional display system: their past, present and future,” Eng. Sci. Ed. J. 2, 196–200 (1993).
[Crossref]

IEEE Trans. Image Process. (1)

A. Wang, A. C. Bovik, H. R. Sheikh, and H. R. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans. Image Process. 13, 600–612 (2004).
[Crossref] [PubMed]

Proc. SPIE (1)

A. Sand and I. Rakkolainen, “A hand-held immaterial volumetric display,” Proc. SPIE 9011, 90110Q (2014).
[Crossref]

Sci. Rep. (2)

H. Nakayama, A. Shiraki, R. Hirayama, N. Masuda, T. Shimobaba, and T. Ito, “Three-dimensional volume containing multiple two-dimensional information patterns,” Sci. Rep. 3, 1931 (2013).
[PubMed]

R. Hirayama, M. Naruse, H. Nakayama, N. Tate, A. Shiraki, T. Kakue, T. Shimobaba, and T. Ito, “Design, Implementation and characterization of a quantum-dot-based volumetric display,” Sci. Rep. 5, 8472 (2015).
[Crossref] [PubMed]

Other (4)

P. C. Barnum, S. G. Narasimhan, and T. Kanade, “A multi-layered display with water drops,” Proc. ACM SIGGRAPH 2010 29, 76, Los Angeles, CA, USA. (2010, Jul. 26).
[Crossref]

D. R. Hofstadter, Godel, Escher, Bach: an Eternal Golden Braid, (Basic Books, New York, 1979).

M. Parker, “Lumarca,” ACM SIGGRAPH ASIA 2009 (ACM, 2009) 77.

A. Yagi, M. Imura, Y. Kuroda, and O. Oshiro, “360-degree fog projection interactive display,” ACM SIGGRAPH ASIA 2011 (ACM, 2011), pp. 19.

Supplementary Material (3)

NameDescription
» Visualization 1: MOV (9328 KB)      3D structure exhibiting four patterns implemented on a glass octagonal prism.
» Visualization 2: MOV (9171 KB)      3D structure exhibiting four patterns implemented in a glass cube.
» Visualization 3: MOV (9900 KB)      3D structure exhibiting four patterns implemented in a glass sphere.

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Figures (9)

Fig. 1
Fig. 1

3D structure exhibiting three patterns implemented on a glass cube.

Fig. 2
Fig. 2

Original input images (all images have 64 × 64 pixels and are 8-bit grayscale).

Fig. 3
Fig. 3

Schematic of the algorithms: (a) determination of voxel values and (b) description of the iterative computation in the proposed algorithm.

Fig. 4
Fig. 4

Numerical simulation of the 3D octagonal prism structures exhibiting four patterns: (a) Relationship between the exhibiting directions, (b) patterns obtained using the original algorithm and (c) patterns obtained using the proposed algorithm.

Fig. 5
Fig. 5

Numerical simulation of the 3D dodecahedron structures exhibiting six patterns: (a) Relationship between the exhibiting directions, (b) patterns obtained using the original algorithm, (c) patterns obtained using the proposed algorithm.

Fig. 6
Fig. 6

Results of quantitative evaluations. (a) Average SSIM values obtained with three, four and six patterns. (b) The changes of MSE with respect of the iteration number in the case when the four patterns are exhibited.

Fig. 7
Fig. 7

3D structure exhibiting four patterns implemented on a glass octagonal prism (see Visualization 1): (a) 3D structure and (b) images obtained from the exhibiting directions.

Fig. 8
Fig. 8

3D structure exhibiting four patterns implemented in a glass cube (see Visualization 2): (a) 3D structure and (b) images obtained from the exhibiting directions.

Fig. 9
Fig. 9

3D structure exhibiting four patterns implemented in a glass sphere (see Visualization 3): (a) 3D structure and (b) images taken from the exhibiting directions.

Tables (2)

Tables Icon

Table 1 SSIM values of the four exhibited patterns from the 3D octagonal prism structures.

Tables Icon

Table 2 SSIM values of the six exhibited patterns from the 3D dodecahedron structures.

Equations (10)

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

P ( u , v ) = w V ( x , y , z ) .
I i ( u i , v i ) = P i ( u i , v i ) = w i V ( x , y , z ) .
V ( x , y , z ) = i = 1 N I i ( u i , v i ) .
V ( x , y , z ) = I 1 ( x , y ) I 2 ( z , y ) I 3 ( x , z ) .
P 1 ( u 1 , v 1 ) = w 1 V ( x , y , z ) = I 1 ( u 1 , v 1 ) z [ I 2 ( z , y ) = I 3 ( x , z ) ] .
P 2 ( u 2 , v 2 ) = w 2 V ( x , y , z ) = I 2 ( u 2 , v 2 ) x [ I 1 ( x , y ) = I 3 ( x , z ) ] .
P 3 ( u 3 , v 3 ) = w 3 V ( x , y , z ) = I 3 ( u 3 , v 3 ) y [ I 1 ( x , y ) = I 2 ( z , y ) ] .
V ( x , y , z ) ( k ) = i = 1 N I i ( u i , v i ) ( k ) N .
P i ( u i , v i ) ( k ) = w i V ( x , y , z ) ( k ) .
I i ( u i , v i ) ( k + 1 ) = I i ( u i , v i ) ( k ) I i ( u i , v i ) ( 0 ) P i ( u i , v i ) ( k ) .

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