Abstract

In this paper, we propose a novel 3D polarimetric computational integral imaging system by using polarization diversity of objects under natural illumination conditions. In the system, the measured Stokes polarization parameters are utilized to generate degree of polarization images of a 3D scene. Based on degree of polarization images and original 2D images, we utilize a modified computational reconstruction method to perform 3D polarimetric image reconstruction. The system may be used to detect or classify objects with distinct polarization signatures in 3D space. Experimental results also show the proposed system may mitigate the effect of occlusion in 3D reconstruction.

© 2012 OSA

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  1. H. S. Chen and C. Rao, “Polarization of light on reflection by some natural surfaces,” J. Phys. D1(9), 1191–1200 (1968).
    [CrossRef]
  2. T. H. Waterman, “Polarization sensitivity,” Handbook of sensory physiology 7, 281–469 (1981).
  3. L. B. Wolff, “Polarization-based material classification from specular reflection,” IEEE Trans. Pattern Anal. Mach. Intell.12(11), 1059–1071 (1990).
    [CrossRef]
  4. L. B. Wolff, “Polarization vision: a new sensory approach to image understanding,” Image Vision Comput.15, 81–93 (1997).
  5. S. Daly, “Polarimetric imaging,” Rochester Institute of Technology, 2002, (technical report).
  6. M. I. Mishchenko, Y. S. Yatskiv, V. K. Rosenbush, and G. Videen, Polarimetric Detection, Characterization, and Remote Sensing (Springer, 2011).
  7. G. Lippmann, “La photographie integrale,” CR Acad. Sci.146, 446–451 (1908).
  8. H. E. Ives, “Optical properties of a Lippman lenticulated sheet,” J. Opt. Soc. Am. A21(3), 171–176 (1931).
    [CrossRef]
  9. C. B. Burckhardt, “Optimum parameters and resolution limitation of integral photography,” J. Opt. Soc. Am.58(1), 71–74 (1968).
    [CrossRef]
  10. T. Okoshi, “Three-dimensional displays,” Proc. IEEE68(5), 548–564 (1980).
    [CrossRef]
  11. H. Arimoto and B. Javidi, “Integral three-dimensional imaging with digital reconstruction,” Opt. Lett.26(3), 157–159 (2001).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  14. F. Okano, J. Arai, K. Mitani, and M. Okui, “Real-time integral imaging based on extremely high resolution video system,” Proc. IEEE94(3), 490–501 (2006).
    [CrossRef]
  15. A. Stern and B. Javidi, “3D image sensing, visualization, and processing using integral imaging,” Proc. IEEE94, 591–608 (2006).
    [CrossRef]
  16. M. DaneshPanah and B. Javidi, “Profilometry and optical slicing by passive three-dimensional imaging,” Opt. Lett.34(7), 1105–1107 (2009).
    [CrossRef] [PubMed]
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    [CrossRef]
  18. B. Javidi, F. Okano, and J. Y. Son, Three-dimensional Imaging, Visualization, and Display (Springer, 2009).
  19. M. Pollefeys, R. Koch, M. Vergauwen, A. A. Deknuydt, and L. J. Van Gool, “Three-dimensional scene reconstruction from images,” Proc. SPIE3958, 215–226 (2000).
    [CrossRef]
  20. L. Guan, J. S. Franco, E. Boyer, and M. Pollefeys, “Probabilistic 3D occupancy flow with latent silhouette cues,” IEEE Conference on Computer Vision and Pattern Recognition (CVPR) 1379–1386 (2010).
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  23. F. A. Sadjadi, “Passive three-dimensional imaging using polarimetric diversity,” Opt. Lett.32(3), 229–231 (2007).
    [CrossRef] [PubMed]
  24. P. Miché, A. Bensrhair, and D. Lebrun, “Passive 3-D shape recovery of unknown objects using cooperative polarimetric and radiometric stereo vision processes,” Opt. Eng.44(2), 027005 (2005).
    [CrossRef]
  25. K. E. Torrance and E. M. Sparrow, “Theory for off-specular reflection from roughened surfaces,” J. Opt. Soc. Am. A57(9), 1105–1112 (1967).
    [CrossRef]
  26. R. B. Reid, M. E. Oxley, M. T. Eismann, and M. E. Goda, “Quantifying surface normal estimation,” Proc. SPIE6240, 624001, 624001-11 (2006).
    [CrossRef]
  27. E. Collett, Polarized Light: Fundamentals and Applications (Marcel Dekker, 1993).
  28. E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge University Press, 2007).
  29. B. Schaefer, E. Collett, R. Smyth, D. Barrett, and B. Fraher, “Measuring the stokes polarization parameters,” Am. J. Phys.75(2), 163–168 (2007).
    [CrossRef]
  30. J. S. Jang and B. Javidi, “Three-dimensional synthetic aperture integral imaging,” Opt. Lett.27(13), 1144–1146 (2002).
    [CrossRef] [PubMed]

2009 (2)

M. DaneshPanah and B. Javidi, “Profilometry and optical slicing by passive three-dimensional imaging,” Opt. Lett.34(7), 1105–1107 (2009).
[CrossRef] [PubMed]

R. Martinez-Cuenca, G. Saavedra, M. Martinez-Corral, and B. Javidi, “Progress in 3-D multiperspective display by integral imaging,” Proc. IEEE97(6), 1067–1077 (2009).
[CrossRef]

2007 (2)

F. A. Sadjadi, “Passive three-dimensional imaging using polarimetric diversity,” Opt. Lett.32(3), 229–231 (2007).
[CrossRef] [PubMed]

B. Schaefer, E. Collett, R. Smyth, D. Barrett, and B. Fraher, “Measuring the stokes polarization parameters,” Am. J. Phys.75(2), 163–168 (2007).
[CrossRef]

2006 (4)

R. B. Reid, M. E. Oxley, M. T. Eismann, and M. E. Goda, “Quantifying surface normal estimation,” Proc. SPIE6240, 624001, 624001-11 (2006).
[CrossRef]

B. Javidi, S. H. Hong, and O. Matoba, “Multidimensional optical sensor and imaging system,” Appl. Opt.45(13), 2986–2994 (2006).
[CrossRef] [PubMed]

F. Okano, J. Arai, K. Mitani, and M. Okui, “Real-time integral imaging based on extremely high resolution video system,” Proc. IEEE94(3), 490–501 (2006).
[CrossRef]

A. Stern and B. Javidi, “3D image sensing, visualization, and processing using integral imaging,” Proc. IEEE94, 591–608 (2006).
[CrossRef]

2005 (2)

M. Martinez-Corral, B. Javidi, R. Martínez-Cuenca, and G. Saavedra, “Formation of real, orthoscopic integral images by smart pixel mapping,” Opt. Express13(23), 9175–9180 (2005).
[CrossRef] [PubMed]

P. Miché, A. Bensrhair, and D. Lebrun, “Passive 3-D shape recovery of unknown objects using cooperative polarimetric and radiometric stereo vision processes,” Opt. Eng.44(2), 027005 (2005).
[CrossRef]

2004 (2)

2002 (1)

2001 (1)

2000 (1)

M. Pollefeys, R. Koch, M. Vergauwen, A. A. Deknuydt, and L. J. Van Gool, “Three-dimensional scene reconstruction from images,” Proc. SPIE3958, 215–226 (2000).
[CrossRef]

1997 (1)

L. B. Wolff, “Polarization vision: a new sensory approach to image understanding,” Image Vision Comput.15, 81–93 (1997).

1990 (1)

L. B. Wolff, “Polarization-based material classification from specular reflection,” IEEE Trans. Pattern Anal. Mach. Intell.12(11), 1059–1071 (1990).
[CrossRef]

1980 (1)

T. Okoshi, “Three-dimensional displays,” Proc. IEEE68(5), 548–564 (1980).
[CrossRef]

1968 (2)

C. B. Burckhardt, “Optimum parameters and resolution limitation of integral photography,” J. Opt. Soc. Am.58(1), 71–74 (1968).
[CrossRef]

H. S. Chen and C. Rao, “Polarization of light on reflection by some natural surfaces,” J. Phys. D1(9), 1191–1200 (1968).
[CrossRef]

1967 (1)

K. E. Torrance and E. M. Sparrow, “Theory for off-specular reflection from roughened surfaces,” J. Opt. Soc. Am. A57(9), 1105–1112 (1967).
[CrossRef]

1931 (1)

H. E. Ives, “Optical properties of a Lippman lenticulated sheet,” J. Opt. Soc. Am. A21(3), 171–176 (1931).
[CrossRef]

1908 (1)

G. Lippmann, “La photographie integrale,” CR 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. IEEE94(3), 490–501 (2006).
[CrossRef]

Arimoto, H.

Barrett, D.

B. Schaefer, E. Collett, R. Smyth, D. Barrett, and B. Fraher, “Measuring the stokes polarization parameters,” Am. J. Phys.75(2), 163–168 (2007).
[CrossRef]

Bensrhair, A.

P. Miché, A. Bensrhair, and D. Lebrun, “Passive 3-D shape recovery of unknown objects using cooperative polarimetric and radiometric stereo vision processes,” Opt. Eng.44(2), 027005 (2005).
[CrossRef]

Burckhardt, C. B.

Chen, H. S.

H. S. Chen and C. Rao, “Polarization of light on reflection by some natural surfaces,” J. Phys. D1(9), 1191–1200 (1968).
[CrossRef]

Collett, E.

B. Schaefer, E. Collett, R. Smyth, D. Barrett, and B. Fraher, “Measuring the stokes polarization parameters,” Am. J. Phys.75(2), 163–168 (2007).
[CrossRef]

DaneshPanah, M.

Deknuydt, A. A.

M. Pollefeys, R. Koch, M. Vergauwen, A. A. Deknuydt, and L. J. Van Gool, “Three-dimensional scene reconstruction from images,” Proc. SPIE3958, 215–226 (2000).
[CrossRef]

Eismann, M. T.

R. B. Reid, M. E. Oxley, M. T. Eismann, and M. E. Goda, “Quantifying surface normal estimation,” Proc. SPIE6240, 624001, 624001-11 (2006).
[CrossRef]

Fraher, B.

B. Schaefer, E. Collett, R. Smyth, D. Barrett, and B. Fraher, “Measuring the stokes polarization parameters,” Am. J. Phys.75(2), 163–168 (2007).
[CrossRef]

Goda, M. E.

R. B. Reid, M. E. Oxley, M. T. Eismann, and M. E. Goda, “Quantifying surface normal estimation,” Proc. SPIE6240, 624001, 624001-11 (2006).
[CrossRef]

Hong, S. H.

Ives, H. E.

H. E. Ives, “Optical properties of a Lippman lenticulated sheet,” J. Opt. Soc. Am. A21(3), 171–176 (1931).
[CrossRef]

Jang, J. S.

Javidi, B.

Koch, R.

M. Pollefeys, R. Koch, M. Vergauwen, A. A. Deknuydt, and L. J. Van Gool, “Three-dimensional scene reconstruction from images,” Proc. SPIE3958, 215–226 (2000).
[CrossRef]

Lebrun, D.

P. Miché, A. Bensrhair, and D. Lebrun, “Passive 3-D shape recovery of unknown objects using cooperative polarimetric and radiometric stereo vision processes,” Opt. Eng.44(2), 027005 (2005).
[CrossRef]

Lippmann, G.

G. Lippmann, “La photographie integrale,” CR Acad. Sci.146, 446–451 (1908).

Martinez-Corral, M.

R. Martinez-Cuenca, G. Saavedra, M. Martinez-Corral, and B. Javidi, “Progress in 3-D multiperspective display by integral imaging,” Proc. IEEE97(6), 1067–1077 (2009).
[CrossRef]

M. Martinez-Corral, B. Javidi, R. Martínez-Cuenca, and G. Saavedra, “Formation of real, orthoscopic integral images by smart pixel mapping,” Opt. Express13(23), 9175–9180 (2005).
[CrossRef] [PubMed]

Martinez-Cuenca, R.

R. Martinez-Cuenca, G. Saavedra, M. Martinez-Corral, and B. Javidi, “Progress in 3-D multiperspective display by integral imaging,” Proc. IEEE97(6), 1067–1077 (2009).
[CrossRef]

Martínez-Cuenca, R.

Matoba, O.

Miché, P.

P. Miché, A. Bensrhair, and D. Lebrun, “Passive 3-D shape recovery of unknown objects using cooperative polarimetric and radiometric stereo vision processes,” Opt. Eng.44(2), 027005 (2005).
[CrossRef]

Mitani, K.

F. Okano, J. Arai, K. Mitani, and M. Okui, “Real-time integral imaging based on extremely high resolution video system,” Proc. IEEE94(3), 490–501 (2006).
[CrossRef]

Okano, F.

F. Okano, J. Arai, K. Mitani, and M. Okui, “Real-time integral imaging based on extremely high resolution video system,” Proc. IEEE94(3), 490–501 (2006).
[CrossRef]

Okoshi, T.

T. Okoshi, “Three-dimensional displays,” Proc. IEEE68(5), 548–564 (1980).
[CrossRef]

Okui, M.

F. Okano, J. Arai, K. Mitani, and M. Okui, “Real-time integral imaging based on extremely high resolution video system,” Proc. IEEE94(3), 490–501 (2006).
[CrossRef]

Oxley, M. E.

R. B. Reid, M. E. Oxley, M. T. Eismann, and M. E. Goda, “Quantifying surface normal estimation,” Proc. SPIE6240, 624001, 624001-11 (2006).
[CrossRef]

Pollefeys, M.

M. Pollefeys, R. Koch, M. Vergauwen, A. A. Deknuydt, and L. J. Van Gool, “Three-dimensional scene reconstruction from images,” Proc. SPIE3958, 215–226 (2000).
[CrossRef]

Rao, C.

H. S. Chen and C. Rao, “Polarization of light on reflection by some natural surfaces,” J. Phys. D1(9), 1191–1200 (1968).
[CrossRef]

Reid, R. B.

R. B. Reid, M. E. Oxley, M. T. Eismann, and M. E. Goda, “Quantifying surface normal estimation,” Proc. SPIE6240, 624001, 624001-11 (2006).
[CrossRef]

Saavedra, G.

R. Martinez-Cuenca, G. Saavedra, M. Martinez-Corral, and B. Javidi, “Progress in 3-D multiperspective display by integral imaging,” Proc. IEEE97(6), 1067–1077 (2009).
[CrossRef]

M. Martinez-Corral, B. Javidi, R. Martínez-Cuenca, and G. Saavedra, “Formation of real, orthoscopic integral images by smart pixel mapping,” Opt. Express13(23), 9175–9180 (2005).
[CrossRef] [PubMed]

Sadjadi, F. A.

Schaefer, B.

B. Schaefer, E. Collett, R. Smyth, D. Barrett, and B. Fraher, “Measuring the stokes polarization parameters,” Am. J. Phys.75(2), 163–168 (2007).
[CrossRef]

Smyth, R.

B. Schaefer, E. Collett, R. Smyth, D. Barrett, and B. Fraher, “Measuring the stokes polarization parameters,” Am. J. Phys.75(2), 163–168 (2007).
[CrossRef]

Sparrow, E. M.

K. E. Torrance and E. M. Sparrow, “Theory for off-specular reflection from roughened surfaces,” J. Opt. Soc. Am. A57(9), 1105–1112 (1967).
[CrossRef]

Stern, A.

A. Stern and B. Javidi, “3D image sensing, visualization, and processing using integral imaging,” Proc. IEEE94, 591–608 (2006).
[CrossRef]

Torrance, K. E.

K. E. Torrance and E. M. Sparrow, “Theory for off-specular reflection from roughened surfaces,” J. Opt. Soc. Am. A57(9), 1105–1112 (1967).
[CrossRef]

Van Gool, L. J.

M. Pollefeys, R. Koch, M. Vergauwen, A. A. Deknuydt, and L. J. Van Gool, “Three-dimensional scene reconstruction from images,” Proc. SPIE3958, 215–226 (2000).
[CrossRef]

Vergauwen, M.

M. Pollefeys, R. Koch, M. Vergauwen, A. A. Deknuydt, and L. J. Van Gool, “Three-dimensional scene reconstruction from images,” Proc. SPIE3958, 215–226 (2000).
[CrossRef]

Wolff, L. B.

L. B. Wolff, “Polarization vision: a new sensory approach to image understanding,” Image Vision Comput.15, 81–93 (1997).

L. B. Wolff, “Polarization-based material classification from specular reflection,” IEEE Trans. Pattern Anal. Mach. Intell.12(11), 1059–1071 (1990).
[CrossRef]

Am. J. Phys. (1)

B. Schaefer, E. Collett, R. Smyth, D. Barrett, and B. Fraher, “Measuring the stokes polarization parameters,” Am. J. Phys.75(2), 163–168 (2007).
[CrossRef]

Appl. Opt. (1)

CR Acad. Sci. (1)

G. Lippmann, “La photographie integrale,” CR Acad. Sci.146, 446–451 (1908).

IEEE Trans. Pattern Anal. Mach. Intell. (1)

L. B. Wolff, “Polarization-based material classification from specular reflection,” IEEE Trans. Pattern Anal. Mach. Intell.12(11), 1059–1071 (1990).
[CrossRef]

Image Vision Comput. (1)

L. B. Wolff, “Polarization vision: a new sensory approach to image understanding,” Image Vision Comput.15, 81–93 (1997).

J. Opt. Soc. Am. (1)

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

H. E. Ives, “Optical properties of a Lippman lenticulated sheet,” J. Opt. Soc. Am. A21(3), 171–176 (1931).
[CrossRef]

K. E. Torrance and E. M. Sparrow, “Theory for off-specular reflection from roughened surfaces,” J. Opt. Soc. Am. A57(9), 1105–1112 (1967).
[CrossRef]

J. Phys. D (1)

H. S. Chen and C. Rao, “Polarization of light on reflection by some natural surfaces,” J. Phys. D1(9), 1191–1200 (1968).
[CrossRef]

Opt. Eng. (1)

P. Miché, A. Bensrhair, and D. Lebrun, “Passive 3-D shape recovery of unknown objects using cooperative polarimetric and radiometric stereo vision processes,” Opt. Eng.44(2), 027005 (2005).
[CrossRef]

Opt. Express (2)

Opt. Lett. (5)

Proc. IEEE (4)

R. Martinez-Cuenca, G. Saavedra, M. Martinez-Corral, and B. Javidi, “Progress in 3-D multiperspective display by integral imaging,” Proc. IEEE97(6), 1067–1077 (2009).
[CrossRef]

T. Okoshi, “Three-dimensional displays,” Proc. IEEE68(5), 548–564 (1980).
[CrossRef]

F. Okano, J. Arai, K. Mitani, and M. Okui, “Real-time integral imaging based on extremely high resolution video system,” Proc. IEEE94(3), 490–501 (2006).
[CrossRef]

A. Stern and B. Javidi, “3D image sensing, visualization, and processing using integral imaging,” Proc. IEEE94, 591–608 (2006).
[CrossRef]

Proc. SPIE (2)

M. Pollefeys, R. Koch, M. Vergauwen, A. A. Deknuydt, and L. J. Van Gool, “Three-dimensional scene reconstruction from images,” Proc. SPIE3958, 215–226 (2000).
[CrossRef]

R. B. Reid, M. E. Oxley, M. T. Eismann, and M. E. Goda, “Quantifying surface normal estimation,” Proc. SPIE6240, 624001, 624001-11 (2006).
[CrossRef]

Other (7)

E. Collett, Polarized Light: Fundamentals and Applications (Marcel Dekker, 1993).

E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge University Press, 2007).

L. Guan, J. S. Franco, E. Boyer, and M. Pollefeys, “Probabilistic 3D occupancy flow with latent silhouette cues,” IEEE Conference on Computer Vision and Pattern Recognition (CVPR) 1379–1386 (2010).

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

T. H. Waterman, “Polarization sensitivity,” Handbook of sensory physiology 7, 281–469 (1981).

S. Daly, “Polarimetric imaging,” Rochester Institute of Technology, 2002, (technical report).

M. I. Mishchenko, Y. S. Yatskiv, V. K. Rosenbush, and G. Videen, Polarimetric Detection, Characterization, and Remote Sensing (Springer, 2011).

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Figures (6)

Fig. 1
Fig. 1

(a) Measurement configuration of Stokes parameters. (b) Illustration of alignment experiment for LP and QWP.

Fig. 2
Fig. 2

(a) Pickup process of integral imaging. (b) Pickup process of polarimetric integral imaging.

Fig. 3
Fig. 3

Experimental setup of a polarimetric integral imaging system.

Fig. 4
Fig. 4

Four examples of elemental images in our experiment

Fig. 5
Fig. 5

DoLP, DoCP, DoP images of elemental images shown in Fig. 4. (a) DoLP images. (b) DoCP images. (c) DoP images.

Fig. 6
Fig. 6

Reconstruction results at 450mm, 530mm, and 720mm. (a) Reconstruction results of conventional integral imaging. (b) Reconstruction results of the proposed polarimetric integral imaging with p = 0.2. (c) Reconstruction results of the proposed polarimetric integral imaging with p = 0.4.

Equations (5)

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

S=( S 0 S 1 S 2 S 3 ) = ( E x 2 + E y 2 E x 2 E y 2 2 E x E y cosδ 2 E x E y sinδ )
DoLP= S 1 2 + S 2 2 S 0 ;DoCP= S 3 2 S 0 ;DoP= DoLP 2 + DoCP 2
S 0 = I 1 + I 2 S 1 = I 1 I 2 S 2 = I 3 I 4 S 3 =2 I 5 S 0
R(x,y;z)={ 1 T k=1 N ( E I k ( x+ c x k r k M ,y+ c y k r k M ) )*I( A DoP k ( x+ c x k r k M ,y+ c y k r k M )>p )whenT N t 0(black)otherwise
T= k=1 N I( A DoP k ( x+ c x k r k M ,y+ c y k r k M )>p )

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