Abstract

Occlusion handling in computer-generated holography is of vast importance as it enhances depth information by presenting correct motion parallax of the 3D scene within the viewing angle. In this paper, we propose a computationally efficient occlusion handling technique based on a fully analytic mesh based computer generated holography. The proposed technique uses angular spectrum convolution that renders exact occlusion while preserving all other aspects of the fully analytic mesh based computer generated holography. The proposed method is computationally efficient as only a single convolution operation is required for each mesh without numerical propagation between the meshes. The proposed method is also exact as it performs the occlusion processing in the tilted mesh plane, being free from artifacts coming from orthographic spatial masking. The proposed method can be applied to the self and the mutual occlusions between the objects in the 3D scene. The computer simulated results show the feasibility of the proposed method.

© 2017 Optical Society of America

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References

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  1. M. Lucente, “Interactive computation of holograms using a look-up table,” J. Electron. Imaging 2(1), 28–34 (1993).
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    [PubMed]
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    [PubMed]
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    [PubMed]
  7. H. Zhang, N. Collings, J. Chen, B. Crossland, D. Chu, and J. Xie, “Full parallax three-dimensional display with occlusion effect using computer generated hologram,” Opt. Eng. 50(7), 074003 (2011).
  8. H. Zhang, Q. Tan, and G. Jin, “Full parallax three-dimensional computer generated hologram with occlusion effect using ray casting technique,” J. Phys. Conf. Ser. 415, 012048 (2013).
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    [PubMed]
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    [PubMed]
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    [PubMed]
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    [PubMed]
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    [PubMed]
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    [PubMed]
  18. Y. Zhao, L. Cao, H. Zhang, D. Kong, and G. Jin, “Accurate calculation of computer-generated holograms using angular-spectrum layer-oriented method,” Opt. Express 23(20), 25440–25449 (2015).
    [PubMed]
  19. L. Ahrenberg, P. Benzie, M. Magnor, and J. Watson, “Computer generated holograms from three dimensional meshes using an analytic light transport model,” Appl. Opt. 47(10), 1567–1574 (2008).
    [PubMed]
  20. Y.-M. Ji, H. Yeom, and J.-H. Park, “Efficient texture mapping by adaptive mesh division in mesh-based computer generated hologram,” Opt. Express 24(24), 28154–28169 (2016).
    [PubMed]
  21. H.-J. Yeom and J.-H. Park, “Calculation of reflectance distribution using angular spectrum convolution in mesh-based computer generated hologram,” Opt. Express 24(17), 19801–19813 (2016).
    [PubMed]
  22. H. Kim, J. Hahn, and B. Lee, “Mathematical modeling of triangle-mesh-modeled three-dimensional surface objects for digital holography,” Appl. Opt. 47(19), D117–D127 (2008).
    [PubMed]
  23. J.-H. Park, H.-J. Yeom, H.-J. Kim, H. Zhang, B. Li, Y.-M. Ji, and S.-H. Kim, “Removal of line artifacts on mesh boundary in computer generated hologram by mesh phase matching,” Opt. Express 23(6), 8006–8013 (2015).
    [PubMed]
  24. J.-H. Park, S.-B. Kim, H.-J. Yeom, H.-J. Kim, H. Zhang, B. Li, Y.-M. Ji, S.-H. Kim, and S.-B. Ko, “Continuous shading and its fast update in fully analytic triangular-mesh-based computer generated hologram,” Opt. Express 23(26), 33893–33901 (2015).
    [PubMed]
  25. K. Matsushima, “Exact hidden-surface removal in digitally synthetic full-parallax holograms,” Proc. SPIE 5742, 25–32 (2005).
  26. K. Matsushima and S. Nakahara, “Extremely high-definition full-parallax computer-generated hologram created by the polygon-based method,” Appl. Opt. 48(34), H54–H63 (2009).
    [PubMed]
  27. K. Matsushima, M. Nakamura, and S. Nakahara, “Silhouette method for hidden surface removal in computer holography and its acceleration using the switch-back technique,” Opt. Express 22(20), 24450–24465 (2014).
    [PubMed]

2017 (1)

2016 (2)

2015 (4)

2014 (1)

2013 (3)

2012 (1)

H. Zhang, Q. Tan, and G. Jin, “Holographic display system of a three- dimensional image with distortion-free magnification and zero-order elimination,” Opt. Eng. 51(7), 075801 (2012).

2011 (2)

H. Zhang, N. Collings, J. Chen, B. Crossland, D. Chu, and J. Xie, “Full parallax three-dimensional display with occlusion effect using computer generated hologram,” Opt. Eng. 50(7), 074003 (2011).

K. Wakunami and M. Yamaguchi, “Calculation for computer generated hologram using ray-sampling plane,” Opt. Express 19(10), 9086–9101 (2011).
[PubMed]

2010 (1)

I. Hanák, M. Janda, and V. Skala, “Detail-driven digital hologram generation,” Vis. Comput. J. 26(2), 83–96 (2010).

2009 (4)

2008 (2)

2005 (1)

K. Matsushima, “Exact hidden-surface removal in digitally synthetic full-parallax holograms,” Proc. SPIE 5742, 25–32 (2005).

1997 (1)

J. S. Underkoffler, “Occlusion processing and smooth surface shading for fully computed synthetic holography,” Proc. SPIE 3011, 19–30 (1997).

1993 (2)

M. Lucente, “Interactive computation of holograms using a look-up table,” J. Electron. Imaging 2(1), 28–34 (1993).

M. Yamaguchi, H. Hoshino, T. Honda, and N. Ohyama, “Phase-added stereogram: calculation of hologram using computer graphics technique,” Proc. SPIE 1914, 25–33 (1993).

1976 (1)

1966 (1)

Ahrenberg, L.

Baradas, J.

Q. Y. J. Smithwick, J. Baradas, D. E. Smalley, and V. M. Bove, “Real-time shader rendering of holographic stereograms,” Proc. SPIE 7233, 723302 (2009).

Benzie, P.

Bove, V. M.

Q. Y. J. Smithwick, J. Baradas, D. E. Smalley, and V. M. Bove, “Real-time shader rendering of holographic stereograms,” Proc. SPIE 7233, 723302 (2009).

Brown, B. R.

Cao, L.

Chen, J.

H. Zhang, N. Collings, J. Chen, B. Crossland, D. Chu, and J. Xie, “Full parallax three-dimensional display with occlusion effect using computer generated hologram,” Opt. Eng. 50(7), 074003 (2011).

Chen, R. H.-Y.

Chu, D.

H. Zhang, N. Collings, J. Chen, B. Crossland, D. Chu, and J. Xie, “Full parallax three-dimensional display with occlusion effect using computer generated hologram,” Opt. Eng. 50(7), 074003 (2011).

Collings, N.

H. Zhang, N. Collings, J. Chen, B. Crossland, D. Chu, and J. Xie, “Full parallax three-dimensional display with occlusion effect using computer generated hologram,” Opt. Eng. 50(7), 074003 (2011).

Crossland, B.

H. Zhang, N. Collings, J. Chen, B. Crossland, D. Chu, and J. Xie, “Full parallax three-dimensional display with occlusion effect using computer generated hologram,” Opt. Eng. 50(7), 074003 (2011).

Hahn, J.

Hanák, I.

I. Hanák, M. Janda, and V. Skala, “Detail-driven digital hologram generation,” Vis. Comput. J. 26(2), 83–96 (2010).

Honda, T.

M. Yamaguchi, H. Hoshino, T. Honda, and N. Ohyama, “Phase-added stereogram: calculation of hologram using computer graphics technique,” Proc. SPIE 1914, 25–33 (1993).

Hoshino, H.

M. Yamaguchi, H. Hoshino, T. Honda, and N. Ohyama, “Phase-added stereogram: calculation of hologram using computer graphics technique,” Proc. SPIE 1914, 25–33 (1993).

Ichihashi, Y.

Ito, T.

Janda, M.

I. Hanák, M. Janda, and V. Skala, “Detail-driven digital hologram generation,” Vis. Comput. J. 26(2), 83–96 (2010).

Ji, Y.-M.

Jin, G.

H. Zhang, L. Cao, and G. Jin, “Computer-generated hologram with occlusion effect using layer-based processing,” Appl. Opt. 56(13), F138–F143 (2017).
[PubMed]

Y. Zhao, L. Cao, H. Zhang, D. Kong, and G. Jin, “Accurate calculation of computer-generated holograms using angular-spectrum layer-oriented method,” Opt. Express 23(20), 25440–25449 (2015).
[PubMed]

H. Zhang, Q. Tan, and G. Jin, “Full parallax three-dimensional computer generated hologram with occlusion effect using ray casting technique,” J. Phys. Conf. Ser. 415, 012048 (2013).

H. Zhang, Q. Tan, and G. Jin, “Holographic display system of a three- dimensional image with distortion-free magnification and zero-order elimination,” Opt. Eng. 51(7), 075801 (2012).

Kakue, T.

Kim, H.

Kim, H.-J.

Kim, S.-B.

Kim, S.-H.

Ko, S.-B.

Kong, D.

Lee, B.

Li, B.

Lohmann, A. W.

Lucente, M.

M. Lucente, “Interactive computation of holograms using a look-up table,” J. Electron. Imaging 2(1), 28–34 (1993).

Magnor, M.

Masuda, N.

Matsushima, K.

Nakahara, S.

Nakamura, M.

Ogihara, Y.

Ohyama, N.

M. Yamaguchi, H. Hoshino, T. Honda, and N. Ohyama, “Phase-added stereogram: calculation of hologram using computer graphics technique,” Proc. SPIE 1914, 25–33 (1993).

Oi, R.

Oikawa, M.

Okada, N.

Park, J.-H.

Sakamoto, Y.

Shimobaba, T.

Skala, V.

I. Hanák, M. Janda, and V. Skala, “Detail-driven digital hologram generation,” Vis. Comput. J. 26(2), 83–96 (2010).

Smalley, D. E.

Q. Y. J. Smithwick, J. Baradas, D. E. Smalley, and V. M. Bove, “Real-time shader rendering of holographic stereograms,” Proc. SPIE 7233, 723302 (2009).

Smithwick, Q. Y. J.

Q. Y. J. Smithwick, J. Baradas, D. E. Smalley, and V. M. Bove, “Real-time shader rendering of holographic stereograms,” Proc. SPIE 7233, 723302 (2009).

Tan, Q.

H. Zhang, Q. Tan, and G. Jin, “Full parallax three-dimensional computer generated hologram with occlusion effect using ray casting technique,” J. Phys. Conf. Ser. 415, 012048 (2013).

H. Zhang, Q. Tan, and G. Jin, “Holographic display system of a three- dimensional image with distortion-free magnification and zero-order elimination,” Opt. Eng. 51(7), 075801 (2012).

Underkoffler, J. S.

J. S. Underkoffler, “Occlusion processing and smooth surface shading for fully computed synthetic holography,” Proc. SPIE 3011, 19–30 (1997).

Wakunami, K.

Watson, J.

Wilkinson, T. D.

Xie, J.

H. Zhang, N. Collings, J. Chen, B. Crossland, D. Chu, and J. Xie, “Full parallax three-dimensional display with occlusion effect using computer generated hologram,” Opt. Eng. 50(7), 074003 (2011).

Yamaguchi, M.

Yamamoto, K.

Yamashita, H.

Yatagai, T.

Yeom, H.

Yeom, H.-J.

Zhang, H.

H. Zhang, L. Cao, and G. Jin, “Computer-generated hologram with occlusion effect using layer-based processing,” Appl. Opt. 56(13), F138–F143 (2017).
[PubMed]

J.-H. Park, S.-B. Kim, H.-J. Yeom, H.-J. Kim, H. Zhang, B. Li, Y.-M. Ji, S.-H. Kim, and S.-B. Ko, “Continuous shading and its fast update in fully analytic triangular-mesh-based computer generated hologram,” Opt. Express 23(26), 33893–33901 (2015).
[PubMed]

Y. Zhao, L. Cao, H. Zhang, D. Kong, and G. Jin, “Accurate calculation of computer-generated holograms using angular-spectrum layer-oriented method,” Opt. Express 23(20), 25440–25449 (2015).
[PubMed]

J.-H. Park, H.-J. Yeom, H.-J. Kim, H. Zhang, B. Li, Y.-M. Ji, and S.-H. Kim, “Removal of line artifacts on mesh boundary in computer generated hologram by mesh phase matching,” Opt. Express 23(6), 8006–8013 (2015).
[PubMed]

H. Zhang, Q. Tan, and G. Jin, “Full parallax three-dimensional computer generated hologram with occlusion effect using ray casting technique,” J. Phys. Conf. Ser. 415, 012048 (2013).

H. Zhang, Q. Tan, and G. Jin, “Holographic display system of a three- dimensional image with distortion-free magnification and zero-order elimination,” Opt. Eng. 51(7), 075801 (2012).

H. Zhang, N. Collings, J. Chen, B. Crossland, D. Chu, and J. Xie, “Full parallax three-dimensional display with occlusion effect using computer generated hologram,” Opt. Eng. 50(7), 074003 (2011).

Zhao, Y.

Appl. Opt. (9)

B. R. Brown and A. W. Lohmann, “Complex spatial filtering with binary masks,” Appl. Opt. 5(6), 967–969 (1966).
[PubMed]

T. Yatagai, “Stereoscopic approach to 3-D display using computer-generated holograms,” Appl. Opt. 15(11), 2722–2729 (1976).
[PubMed]

L. Ahrenberg, P. Benzie, M. Magnor, and J. Watson, “Computer generated holograms from three dimensional meshes using an analytic light transport model,” Appl. Opt. 47(10), 1567–1574 (2008).
[PubMed]

H. Kim, J. Hahn, and B. Lee, “Mathematical modeling of triangle-mesh-modeled three-dimensional surface objects for digital holography,” Appl. Opt. 47(19), D117–D127 (2008).
[PubMed]

R. H.-Y. Chen and T. D. Wilkinson, “Computer generated hologram with geometric occlusion using GPU-accelerated depth buffer rasterization for three-dimensional display,” Appl. Opt. 48(21), 4246–4255 (2009).
[PubMed]

K. Matsushima and S. Nakahara, “Extremely high-definition full-parallax computer-generated hologram created by the polygon-based method,” Appl. Opt. 48(34), H54–H63 (2009).
[PubMed]

R. H.-Y. Chen and T. D. Wilkinson, “Computer generated hologram from point cloud using graphics processor,” Appl. Opt. 48(36), 6841–6850 (2009).
[PubMed]

Y. Ogihara and Y. Sakamoto, “Fast calculation method of a CGH for a patch model using a point-based method,” Appl. Opt. 54(1), A76–A83 (2015).
[PubMed]

H. Zhang, L. Cao, and G. Jin, “Computer-generated hologram with occlusion effect using layer-based processing,” Appl. Opt. 56(13), F138–F143 (2017).
[PubMed]

J. Electron. Imaging (1)

M. Lucente, “Interactive computation of holograms using a look-up table,” J. Electron. Imaging 2(1), 28–34 (1993).

J. Phys. Conf. Ser. (1)

H. Zhang, Q. Tan, and G. Jin, “Full parallax three-dimensional computer generated hologram with occlusion effect using ray casting technique,” J. Phys. Conf. Ser. 415, 012048 (2013).

Opt. Eng. (2)

H. Zhang, Q. Tan, and G. Jin, “Holographic display system of a three- dimensional image with distortion-free magnification and zero-order elimination,” Opt. Eng. 51(7), 075801 (2012).

H. Zhang, N. Collings, J. Chen, B. Crossland, D. Chu, and J. Xie, “Full parallax three-dimensional display with occlusion effect using computer generated hologram,” Opt. Eng. 50(7), 074003 (2011).

Opt. Express (9)

K. Wakunami and M. Yamaguchi, “Calculation for computer generated hologram using ray-sampling plane,” Opt. Express 19(10), 9086–9101 (2011).
[PubMed]

N. Okada, T. Shimobaba, Y. Ichihashi, R. Oi, K. Yamamoto, M. Oikawa, T. Kakue, N. Masuda, and T. Ito, “Band-limited double-step Fresnel diffraction and its application to computer-generated holograms,” Opt. Express 21(7), 9192–9197 (2013).
[PubMed]

K. Wakunami, H. Yamashita, and M. Yamaguchi, “Occlusion culling for computer generated hologram based on ray-wavefront conversion,” Opt. Express 21(19), 21811–21822 (2013).
[PubMed]

K. Matsushima, M. Nakamura, and S. Nakahara, “Silhouette method for hidden surface removal in computer holography and its acceleration using the switch-back technique,” Opt. Express 22(20), 24450–24465 (2014).
[PubMed]

J.-H. Park, H.-J. Yeom, H.-J. Kim, H. Zhang, B. Li, Y.-M. Ji, and S.-H. Kim, “Removal of line artifacts on mesh boundary in computer generated hologram by mesh phase matching,” Opt. Express 23(6), 8006–8013 (2015).
[PubMed]

Y. Zhao, L. Cao, H. Zhang, D. Kong, and G. Jin, “Accurate calculation of computer-generated holograms using angular-spectrum layer-oriented method,” Opt. Express 23(20), 25440–25449 (2015).
[PubMed]

J.-H. Park, S.-B. Kim, H.-J. Yeom, H.-J. Kim, H. Zhang, B. Li, Y.-M. Ji, S.-H. Kim, and S.-B. Ko, “Continuous shading and its fast update in fully analytic triangular-mesh-based computer generated hologram,” Opt. Express 23(26), 33893–33901 (2015).
[PubMed]

H.-J. Yeom and J.-H. Park, “Calculation of reflectance distribution using angular spectrum convolution in mesh-based computer generated hologram,” Opt. Express 24(17), 19801–19813 (2016).
[PubMed]

Y.-M. Ji, H. Yeom, and J.-H. Park, “Efficient texture mapping by adaptive mesh division in mesh-based computer generated hologram,” Opt. Express 24(24), 28154–28169 (2016).
[PubMed]

Proc. SPIE (4)

K. Matsushima, “Exact hidden-surface removal in digitally synthetic full-parallax holograms,” Proc. SPIE 5742, 25–32 (2005).

J. S. Underkoffler, “Occlusion processing and smooth surface shading for fully computed synthetic holography,” Proc. SPIE 3011, 19–30 (1997).

M. Yamaguchi, H. Hoshino, T. Honda, and N. Ohyama, “Phase-added stereogram: calculation of hologram using computer graphics technique,” Proc. SPIE 1914, 25–33 (1993).

Q. Y. J. Smithwick, J. Baradas, D. E. Smalley, and V. M. Bove, “Real-time shader rendering of holographic stereograms,” Proc. SPIE 7233, 723302 (2009).

Vis. Comput. J. (1)

I. Hanák, M. Janda, and V. Skala, “Detail-driven digital hologram generation,” Vis. Comput. J. 26(2), 83–96 (2010).

Supplementary Material (3)

NameDescription
» Visualization 1       Numerical observation of conventional mesh based computer generated hologram from different directions which shows overlapping artifacts due to lack of proper occlusion processing
» Visualization 2       Numerical observation of the proposed mesh based computer generated hologram from different directions which shows proper occlusion of rear triangle within the viewing angle of the hologram
» Visualization 3       Numerical observation of the proposed mesh based computer generated hologram from different directions which shows continuous motion parallax of a complex torus object with proper occlusion.

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Figures (8)

Fig. 1
Fig. 1

Simple illustration of the fully-analytic triangular mesh based CGH

Fig. 2
Fig. 2

Proposed occlusion handling method

Fig. 3
Fig. 3

Angular spectrums and their numerical reconstructions in the front triangle plane (a) AS1(fx,y) (b) AS1,2(fx,y) (c) AS1(fx,y)- AS1,2(fx,y) (d) AS2(fx,y) (e) proposed method, AS1(fx,y) - AS1,2(fx,y) + - AS2(fx,y) (f) conventional method, AS1(fx,y) + AS2(fx,y)

Fig. 4
Fig. 4

Numerical reconstructions of a mug object with multiple carrier wave (a) conventional method without occlusion processing (b) proposed method

Fig. 5
Fig. 5

Numerical observations from different directions of the two-triangle hologram (a) conventional method without occlusion processing (see Visualization 1) (b) proposed method (see Visualization 2)

Fig. 6
Fig. 6

Numerical observation comparison between conventional orthographic spatial masking technique and the proposed method. (a) Overlapping and (b) dark line artifacts are corrected in the proposed method

Fig. 7
Fig. 7

Numerical reconstructions of the complex torus object with a single carrier wave (a) conventional method without occlusion processing, (b) proposed method

Fig. 8
Fig. 8

Numerical observations from different directions of the complex torus object with multiple carrier waves in the proposed method (see Visualization 3)

Tables (1)

Tables Icon

Table 1 Computation cost for occlusion handling using the proposed method.

Equations (13)

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AS( f x,y ; ν x,y ;a )=B( f x,y ; ν x,y )aexp[ j2π ν x,y,z T r x,y,z o ] exp[ j2π f xl,yl,zl T c ] det( A ) f zl f z .
B( f x,y ; ν x,y )=A S r ( A T [ 1 0 0 0 1 0 ]R( f x,y,z ν x,y,z ) ),
AS( f x,y )= AS( f x,y ; ν x,y ;a( ν x,y ) ) d ν x,y ,
B( f x,y ; ν x,y )B( f x,y ν x,y ;[ 0 0 ] ).
AS( f x,y ){ D( f x,y )B( f x,y ;[ 0 0 ] ) } exp[ j2π f xl,yl,zl T c ] det( A ) f zl f z ,
D( f x,y )=a( f x,y )exp[ j2π f x,y,z T r x,y,z o ],
H( r x,y )= A S allmeshes ( f x,y )exp[ j2π f x,y T r x,y ] d f x,y ,
A S 1:n+1 ( f x,y )=A S 1:n ( f x,y )A S 1:n,n+1 ( f x,y )+A S n+1 ( f x,y ),
A S 1:n,n+1 ( f x,y )= A S n+1 ( f x,y ; ν x,y ;A S 1:n ( ν x,y ) ) d ν x,y ,
A S 1:n,n+1 ( f x,y ){ D 1:n ( f x,y ) B n+1 ( f x,y ;[ 0 0 ] ) } E n+1 ( f x,y ),
D 1:n ( f x,y )=A S 1:n ( f x,y )exp[ j2π f x,y,z T r x,y,z o,n+1 ],
E n+1 ( f x,y )= exp[ j2π f xl,yl,zl T c ] det( A ) f zl f z .
A S n+1 ( f x,y )A S 1:n,n+1 ( f x,y ){ ( D n+1 ( f x,y ) D 1:n ( f x,y ) ) B n+1 ( f x,y ;[ 0 0 ] ) } E n+1 ( f x,y ),

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