Abstract

We develop a method for obtaining 3D polarimetric integral images from elemental images recorded in low light illumination conditions. Since photon-counting images are very sparse, calculation of the Stokes parameters and the degree of polarization should be handled carefully. In our approach, polarimetric 3D integral images are generated using the Maximum Likelihood Estimation and subsequently reconstructed by means of a Total Variation Denoising filter. In this way, polarimetric results are comparable to those obtained in conventional illumination conditions. We also show that polarimetric information retrieved from photon starved images can be used in 3D object recognition problems. To the best of our knowledge, this is the first report on 3D polarimetric photon counting integral imaging.

© 2015 Optical Society of America

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References

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2014 (2)

N. J. Brock, C. Crandall, and J. E. Millerd, “Snap-shot imaging polarimeter: performance and applications,” Proc. SPIE 9099, 909903 (2014).
[Crossref]

S. van der Walt, J. L. Schönberger, J. Nunez-Iglesias, F. Boulogne, J. D. Warner, N. Yager, E. Gouillart, T. Yu, and scikit-image contributors, “scikit-image: image processing in Python,” PeerJ 2, e453 (2014).
[Crossref] [PubMed]

2013 (1)

2012 (4)

A. Stern, A. Doroni, and B. Javidi, “Experiments with three-dimensional integral imaging under low light levels,” IEEE Phot. J. 4(4), 1188–1195 (2012).
[Crossref]

F. Yang, Y. M. Lu, L. Sbaiz, and M. Vetterli, “Bits from Photons: Oversampled Image Acquisition Using Binary Poisson Statistics,” IEEE Trans. Image Process. 21(4), 1421–1436 (2012).
[Crossref] [PubMed]

X. Xiao, B. Javidi, G. Saavedra, M. Eismann, and M. Martinez-Corral, “Three-dimensional polarimetric computational integral imaging,” Opt. Express 20(14), 15481–15488 (2012).
[Crossref] [PubMed]

W. Sparks, T. A. Germer, J. W. MacKenty, and F. Snik, “Compact and robust method for full Stokes spectropolarimetry,” Appl. Opt. 51(22), 5495–5511 (2012).
[Crossref] [PubMed]

2011 (2)

2010 (1)

2009 (2)

R. Martinez-Cuenca, G. Saavedra, M. Martinez-Corral, and B. Javidi, “Progress in 3-D multiperspective display by integral imaging,” Proc. IEEE 97(6), 1067–1077 (2009).
[Crossref]

K. Fujita, Y. Itoh, and T. Mukai, “Development of simultaneous imaging polarimeter for asteroids,” Adv. Space Res. 43(2), 325–327 (2009).
[Crossref]

2008 (2)

2007 (1)

2006 (3)

2005 (1)

2004 (4)

A. Chambolle, “An algorithm for total variation minimization and applications,” J. Math. Imaging Vis. 20(1/2), 89–97 (2004).
[Crossref]

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans. Image Process. 13(4), 600–612 (2004).
[Crossref] [PubMed]

O. Matoba and B. Javidi, “Three-dimensional polarimetric integral imaging,” Opt. Lett. 29(20), 2375–2377 (2004).
[Crossref] [PubMed]

S. H. Hong, J. S. Jang, and B. Javidi, “Three-dimensional volumetric object reconstruction using computational integral imaging,” Opt. Express 12(3), 483–491 (2004).
[Crossref] [PubMed]

2002 (1)

2001 (1)

1999 (1)

T. F. Chan, G. H. Golub, and P. Mulet, “A nonlinear primal-dual method for total variation-based image restoration,” SIAM J. Sci. Comput. 20(6), 1964–1977 (1999).
[Crossref]

1998 (1)

1997 (1)

L. B. Wolff, “Polarization vision: a new sensory approach to image understanding,” Image Vis. Comput. 15(2), 81–93 (1997).
[Crossref]

1992 (1)

L. I. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Physica D 60(1-4), 259–268 (1992).
[Crossref]

1989 (1)

1985 (1)

1982 (1)

R. M. A. Azzam, “Division-of-amplitude photopolarimeter (DOAP) for the simultaneous measurement of all four Stokes parameters of light,” Opt. Acta (Lond.) 29(5), 685–689 (1982).
[Crossref]

1980 (1)

T. Okoshi, “Three-dimensional displays,” Proc. IEEE 68(5), 548–564 (1980).
[Crossref]

1968 (1)

1931 (1)

1908 (1)

G. Lippmann, “Epreuves reversibles donnant la sensation du relief,” J. Phys. Theor. Appl. 7(1), 821–825 (1908).
[Crossref]

Aloni, D.

Arimoto, H.

Azzam, R. M. A.

R. M. A. Azzam, “Arrangement of four photodetectors for measuring the state of polarization of light,” Opt. Lett. 10(7), 309–311 (1985).
[Crossref] [PubMed]

R. M. A. Azzam, “Division-of-amplitude photopolarimeter (DOAP) for the simultaneous measurement of all four Stokes parameters of light,” Opt. Acta (Lond.) 29(5), 685–689 (1982).
[Crossref]

Boulogne, F.

S. van der Walt, J. L. Schönberger, J. Nunez-Iglesias, F. Boulogne, J. D. Warner, N. Yager, E. Gouillart, T. Yu, and scikit-image contributors, “scikit-image: image processing in Python,” PeerJ 2, e453 (2014).
[Crossref] [PubMed]

Bovik, A. C.

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans. Image Process. 13(4), 600–612 (2004).
[Crossref] [PubMed]

Brock, N. J.

N. J. Brock, C. Crandall, and J. E. Millerd, “Snap-shot imaging polarimeter: performance and applications,” Proc. SPIE 9099, 909903 (2014).
[Crossref]

Burckhardt, C. B.

Chambolle, A.

A. Chambolle, “An algorithm for total variation minimization and applications,” J. Math. Imaging Vis. 20(1/2), 89–97 (2004).
[Crossref]

Chan, T. F.

T. F. Chan, G. H. Golub, and P. Mulet, “A nonlinear primal-dual method for total variation-based image restoration,” SIAM J. Sci. Comput. 20(6), 1964–1977 (1999).
[Crossref]

Cho, M.

Crandall, C.

N. J. Brock, C. Crandall, and J. E. Millerd, “Snap-shot imaging polarimeter: performance and applications,” Proc. SPIE 9099, 909903 (2014).
[Crossref]

DeHoog, E.

Dereniak, E. L.

Dey, D. K.

Doroni, A.

A. Stern, A. Doroni, and B. Javidi, “Experiments with three-dimensional integral imaging under low light levels,” IEEE Phot. J. 4(4), 1188–1195 (2012).
[Crossref]

Eismann, M.

Fatemi, E.

L. I. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Physica D 60(1-4), 259–268 (1992).
[Crossref]

Fujita, K.

K. Fujita, Y. Itoh, and T. Mukai, “Development of simultaneous imaging polarimeter for asteroids,” Adv. Space Res. 43(2), 325–327 (2009).
[Crossref]

Germer, T. A.

Golub, G. H.

T. F. Chan, G. H. Golub, and P. Mulet, “A nonlinear primal-dual method for total variation-based image restoration,” SIAM J. Sci. Comput. 20(6), 1964–1977 (1999).
[Crossref]

Gouillart, E.

S. van der Walt, J. L. Schönberger, J. Nunez-Iglesias, F. Boulogne, J. D. Warner, N. Yager, E. Gouillart, T. Yu, and scikit-image contributors, “scikit-image: image processing in Python,” PeerJ 2, e453 (2014).
[Crossref] [PubMed]

Hong, S. H.

Hoshino, H.

Ikeuchi, K.

D. Miyazaki and K. Ikeuchi, “Inverse polarization raytracing: estimating surface shapes of transparent objects,” in IEEE Computer Society Conference on Computer Vision and Pattern Recognition (IEEE, 2005), pp. 910–917.
[Crossref]

Isono, H.

Itoh, Y.

K. Fujita, Y. Itoh, and T. Mukai, “Development of simultaneous imaging polarimeter for asteroids,” Adv. Space Res. 43(2), 325–327 (2009).
[Crossref]

Ives, H. E.

Jang, J. S.

Javidi, B.

X. Xiao, B. Javidi, M. Martinez-Corral, and A. Stern, “Advances in three-dimensional integral imaging: sensing, display, and applications [Invited],” Appl. Opt. 52(4), 546–560 (2013).
[PubMed]

X. Xiao, B. Javidi, G. Saavedra, M. Eismann, and M. Martinez-Corral, “Three-dimensional polarimetric computational integral imaging,” Opt. Express 20(14), 15481–15488 (2012).
[Crossref] [PubMed]

A. Stern, A. Doroni, and B. Javidi, “Experiments with three-dimensional integral imaging under low light levels,” IEEE Phot. J. 4(4), 1188–1195 (2012).
[Crossref]

M. Cho, A. Mahalanobis, and B. Javidi, “3D passive photon counting automatic target recognition using advanced correlation filters,” Opt. Lett. 36(6), 861–863 (2011).
[Crossref] [PubMed]

D. Aloni, A. Stern, and B. Javidi, “Three-dimensional photon counting integral imaging reconstruction using penalized maximum likelihood expectation maximization,” Opt. Express 19(20), 19681–19687 (2011).
[Crossref] [PubMed]

J. Jung, M. Cho, D. K. Dey, and B. Javidi, “Three-dimensional photon counting integral imaging using Bayesian estimation,” Opt. Lett. 35(11), 1825–1827 (2010).
[Crossref] [PubMed]

R. Martinez-Cuenca, G. Saavedra, M. Martinez-Corral, and B. Javidi, “Progress in 3-D multiperspective display by integral imaging,” Proc. IEEE 97(6), 1067–1077 (2009).
[Crossref]

B. Tavakoli, B. Javidi, and E. Watson, “Three dimensional visualization by photon counting computational integral imaging,” Opt. Express 16(7), 4426–4436 (2008).
[Crossref] [PubMed]

A. Stern and B. Javidi, “Three-dimensional image sensing, visualization, and processing using integral imaging,” Proc. IEEE 94(3), 591–607 (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]

S. Yeom, B. Javidi, and E. Watson, “Photon counting passive 3D image sensing for automatic target recognition,” Opt. Express 13(23), 9310–9330 (2005).
[Crossref] [PubMed]

O. Matoba and B. Javidi, “Three-dimensional polarimetric integral imaging,” Opt. Lett. 29(20), 2375–2377 (2004).
[Crossref] [PubMed]

S. H. Hong, J. S. Jang, and B. Javidi, “Three-dimensional volumetric object reconstruction using computational integral imaging,” Opt. Express 12(3), 483–491 (2004).
[Crossref] [PubMed]

J. S. Jang and B. Javidi, “Three-dimensional synthetic aperture integral imaging,” Opt. Lett. 27(13), 1144–1146 (2002).
[Crossref] [PubMed]

H. Arimoto and B. Javidi, “Integral three-dimensional imaging with digital reconstruction,” Opt. Lett. 26(3), 157–159 (2001).
[Crossref] [PubMed]

B. Javidi, “Nonlinear joint power spectrum based optical correlation,” Appl. Opt. 28(12), 2358–2367 (1989).
[Crossref] [PubMed]

Jung, J.

Kudenov, M.

Lippmann, G.

G. Lippmann, “Epreuves reversibles donnant la sensation du relief,” J. Phys. Theor. Appl. 7(1), 821–825 (1908).
[Crossref]

Lu, Y. M.

F. Yang, Y. M. Lu, L. Sbaiz, and M. Vetterli, “Bits from Photons: Oversampled Image Acquisition Using Binary Poisson Statistics,” IEEE Trans. Image Process. 21(4), 1421–1436 (2012).
[Crossref] [PubMed]

Luo, H.

MacKenty, J. W.

Mahalanobis, A.

Martinez-Corral, M.

Martinez-Cuenca, R.

R. Martinez-Cuenca, G. Saavedra, M. Martinez-Corral, and B. Javidi, “Progress in 3-D multiperspective display by integral imaging,” Proc. IEEE 97(6), 1067–1077 (2009).
[Crossref]

Matoba, O.

Millerd, J. E.

N. J. Brock, C. Crandall, and J. E. Millerd, “Snap-shot imaging polarimeter: performance and applications,” Proc. SPIE 9099, 909903 (2014).
[Crossref]

Miyazaki, D.

D. Miyazaki and K. Ikeuchi, “Inverse polarization raytracing: estimating surface shapes of transparent objects,” in IEEE Computer Society Conference on Computer Vision and Pattern Recognition (IEEE, 2005), pp. 910–917.
[Crossref]

Mukai, T.

K. Fujita, Y. Itoh, and T. Mukai, “Development of simultaneous imaging polarimeter for asteroids,” Adv. Space Res. 43(2), 325–327 (2009).
[Crossref]

Mulet, P.

T. F. Chan, G. H. Golub, and P. Mulet, “A nonlinear primal-dual method for total variation-based image restoration,” SIAM J. Sci. Comput. 20(6), 1964–1977 (1999).
[Crossref]

Nunez-Iglesias, J.

S. van der Walt, J. L. Schönberger, J. Nunez-Iglesias, F. Boulogne, J. D. Warner, N. Yager, E. Gouillart, T. Yu, and scikit-image contributors, “scikit-image: image processing in Python,” PeerJ 2, e453 (2014).
[Crossref] [PubMed]

Oka, K.

Okano, F.

Okoshi, T.

T. Okoshi, “Three-dimensional displays,” Proc. IEEE 68(5), 548–564 (1980).
[Crossref]

Osher, S.

L. I. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Physica D 60(1-4), 259–268 (1992).
[Crossref]

Rudin, L. I.

L. I. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Physica D 60(1-4), 259–268 (1992).
[Crossref]

Saavedra, G.

X. Xiao, B. Javidi, G. Saavedra, M. Eismann, and M. Martinez-Corral, “Three-dimensional polarimetric computational integral imaging,” Opt. Express 20(14), 15481–15488 (2012).
[Crossref] [PubMed]

R. Martinez-Cuenca, G. Saavedra, M. Martinez-Corral, and B. Javidi, “Progress in 3-D multiperspective display by integral imaging,” Proc. IEEE 97(6), 1067–1077 (2009).
[Crossref]

Sadjadi, F. A.

Sbaiz, L.

F. Yang, Y. M. Lu, L. Sbaiz, and M. Vetterli, “Bits from Photons: Oversampled Image Acquisition Using Binary Poisson Statistics,” IEEE Trans. Image Process. 21(4), 1421–1436 (2012).
[Crossref] [PubMed]

Schiewgerling, J.

Schönberger, J. L.

S. van der Walt, J. L. Schönberger, J. Nunez-Iglesias, F. Boulogne, J. D. Warner, N. Yager, E. Gouillart, T. Yu, and scikit-image contributors, “scikit-image: image processing in Python,” PeerJ 2, e453 (2014).
[Crossref] [PubMed]

Sheikh, H. R.

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans. Image Process. 13(4), 600–612 (2004).
[Crossref] [PubMed]

Simoncelli, E. P.

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans. Image Process. 13(4), 600–612 (2004).
[Crossref] [PubMed]

Snik, F.

Sparks, W.

Stern, A.

X. Xiao, B. Javidi, M. Martinez-Corral, and A. Stern, “Advances in three-dimensional integral imaging: sensing, display, and applications [Invited],” Appl. Opt. 52(4), 546–560 (2013).
[PubMed]

A. Stern, A. Doroni, and B. Javidi, “Experiments with three-dimensional integral imaging under low light levels,” IEEE Phot. J. 4(4), 1188–1195 (2012).
[Crossref]

D. Aloni, A. Stern, and B. Javidi, “Three-dimensional photon counting integral imaging reconstruction using penalized maximum likelihood expectation maximization,” Opt. Express 19(20), 19681–19687 (2011).
[Crossref] [PubMed]

A. Stern and B. Javidi, “Three-dimensional image sensing, visualization, and processing using integral imaging,” Proc. IEEE 94(3), 591–607 (2006).
[Crossref]

Tavakoli, B.

van der Walt, S.

S. van der Walt, J. L. Schönberger, J. Nunez-Iglesias, F. Boulogne, J. D. Warner, N. Yager, E. Gouillart, T. Yu, and scikit-image contributors, “scikit-image: image processing in Python,” PeerJ 2, e453 (2014).
[Crossref] [PubMed]

Vetterli, M.

F. Yang, Y. M. Lu, L. Sbaiz, and M. Vetterli, “Bits from Photons: Oversampled Image Acquisition Using Binary Poisson Statistics,” IEEE Trans. Image Process. 21(4), 1421–1436 (2012).
[Crossref] [PubMed]

Wang, Z.

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans. Image Process. 13(4), 600–612 (2004).
[Crossref] [PubMed]

Warner, J. D.

S. van der Walt, J. L. Schönberger, J. Nunez-Iglesias, F. Boulogne, J. D. Warner, N. Yager, E. Gouillart, T. Yu, and scikit-image contributors, “scikit-image: image processing in Python,” PeerJ 2, e453 (2014).
[Crossref] [PubMed]

Watson, E.

Wolff, L. B.

L. B. Wolff, “Polarization vision: a new sensory approach to image understanding,” Image Vis. Comput. 15(2), 81–93 (1997).
[Crossref]

Xiao, X.

Yager, N.

S. van der Walt, J. L. Schönberger, J. Nunez-Iglesias, F. Boulogne, J. D. Warner, N. Yager, E. Gouillart, T. Yu, and scikit-image contributors, “scikit-image: image processing in Python,” PeerJ 2, e453 (2014).
[Crossref] [PubMed]

Yang, F.

F. Yang, Y. M. Lu, L. Sbaiz, and M. Vetterli, “Bits from Photons: Oversampled Image Acquisition Using Binary Poisson Statistics,” IEEE Trans. Image Process. 21(4), 1421–1436 (2012).
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Figures (8)

Fig. 1
Fig. 1 Sketch of the polarimetric 3D pick-up system. The 3D scene consists of two vehicles, occlusion, and background.
Fig. 2
Fig. 2 (a) 3D conventional integral imaging, that is, without photon counting and without polarization. The reconstructed image is at z = 530 mm for the green channel of the camera; (b) polarimetric integral imaging results with the DoP at z = 530 mm.
Fig. 3
Fig. 3 Photon-counting 3D integral imaging maximum likelihood estimation reconstruction at z = 530 mm: (a) 0.01 photons/pixel, and (b) 0.05 photons/pixel.
Fig. 4
Fig. 4 DoP for photon-counting 3D integral imaging with maximum likelihood estimation reconstruction at z = 530 mm: (a) 0.01 photons/pixel, and (b) 0.05 photons/pixel.
Fig. 5
Fig. 5 Photon-counting 3D integral imaging reconstruction at z = 530 mm. The resulting image is subsequently processed using total variation minimization with (a) 0.01 photons/pixel, and (b) 0.05 photons/pixel.
Fig. 6
Fig. 6 DoP for photon-counting 3D integral imaging using maximum likelihood reconstruction at z = 530 mm. The resulting polarimetric images are subsequently processed using total variation minimization with (a) 0.01 photons/pixel, and (b) 0.05 photons/pixel.
Fig. 7
Fig. 7 Reference R used in the correlation test
Fig. 8
Fig. 8 Correlations results using DoP of the 3D integral imaging scenes in Fig. (6). The target is shown in Fig. (7). (a) Correlation output plane with 0.01 photons/pixel using MLE reconstruction, (b) 3D correlation plot of the area marked, (c) Correlation output plane with 0.01 photons/pixel using maximum likelihood reconstruction and total variation denosing, and (d) 3D correlation plot of the area marked.

Tables (3)

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Table 1 Integral imaging variables

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Table 2 MSSIM values for integral imaging reconstruction using maximum likelihood estimation and DoP in Fig. (3) and Fig. (4)

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Table 3 MSSIM values for integral imaging reconstruction using maximum likelihood reconstruction and total variation minimization denosing

Equations (12)

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E=( E x ( r,t ), E y ( r,t ),0 ).
S 0 = E x * E x + E y * E y S 1 = E x * E x E y * E y S 2 = E x * E y + E y * E x S 3 =i[ E y * E x E x * E y ]
E i * E j = 1 T T E i * E j dt.
S 0 = I 0°,0 + I 90°,0 S 1 = I 0°,0 I 90°,0 S 2 = I 45°,0 I 135°,0 S 3 = I 45°,π/2 I 135°,π/2 DoP= 1 S 0 S 1 2 + S 2 2 + S 3 2 ,
I α,β ( x,y,z )= k=0 N x 1 l=0 N y 1 i k,l α,β ( xk N x pf c x z ,yl N y pf c y z ) .
P( m;x,y )= [ n k,l α,β ( x,y ) ] m exp( n k,l α,β ( x,y ) ) m! ,
n k,l α,β ( x,y )= N p i k,l α,β ( x,y ) x,y i k,l α,β ( x,y ) ,
I ^ α,β ( x,y,z ) k=0 N x 1 l=0 N y 1 i ^ k,l α,β ( xk N x pf c x z ,yl N y pf c y z ) .
SSIM( x j , y j )= ( 2 μ xj μ yj + c 1j )( 2 σ xyj + c 2j ) ( μ xj 2 + μ yj 2 + c 1j )( σ xj 2 + σ yj 2 + c 2j ) ,
MSSIM( X,Y )= 1 M j=1 M SSIM( x j , y j ) .
min u [ | u 0 u | 2 dxdy+γ ( u x ) 2 + ( u y ) 2 dxdy ]
RD= FT 1 [ FT[ R ]FT [ D ] * | FT[ R ] | 1r | FT[ D ] | 1d ].

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