Abstract

Photon counting techniques have been introduced with integral imaging for three-dimensional (3D) imaging applications. The previous reports in this area assumed a priori knowledge of exact sensor positions for 3D image reconstruction, which may be difficult to satisfy in certain applications. In this paper, we extend the photon counting 3D imaging system to situations where sensor positions are unknown. To estimate sensor positions in photon counting integral imaging, scene details of photon counting images are needed for image correspondences matching. Therefore, an iterative method based on the total variation maximum a posteriori expectation maximization (MAP-EM) algorithm is used to restore photon counting images. Experimental results are presented to show the feasibility of the method. To the best of our knowledge, this is the first report on 3D photon counting integral imaging with unknown sensor positions.

© 2012 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  14. Z. Zhang, “A flexible new technique for camera calibration,” IEEE Trans. Pattern Anal. Machine Intell. 22, 1330–1334 (2000).
    [CrossRef]
  15. M. Pollefeys, R. Koch, M. Vergauwen, B. Deknuydt, and L. Van Gool, “Three-dimensional scene reconstruction from images,” in Proc. SPIE 3958, 215–226 (2000).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  28. C. H. Yeh, “Wavelet-based corner detection using eigenvectors of covariance matrices,” Patt. Recog. Lett. 24, 2797–2806 (2003).
    [CrossRef]
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2011 (2)

2010 (2)

X. Xiao, M. DaneshPanah, M. Cho, and B. Javidi, “3D integral imaging using sparse sensors with unknown positions,” J. Disp. Technol. 6, 614–619 (2010).
[CrossRef]

M. DaneshPanah, B. Javidi, and E. A. Watson, “Three dimensional object recognition with photon counting imagery in the presence of noise,” Opt. Express 18, 26450–26460(2010).
[CrossRef]

2009 (3)

M. Bertero, P. Boccacci, G. Desidera, and G. Vicidomini, “Image deblurring with Poisson data: from cells to galaxies,” Inverse Probl. 25, 123006 (2009).
[CrossRef]

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

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

2008 (2)

2007 (1)

2006 (2)

N. Dey, L. Blanc‐Feraud, C. Zimmer, P. Roux, Z. Kam, J. C. Olivo‐Marin, and J. Zerubia, “Richardson–Lucy algorithm with total variation regularization for 3D confocal microscope deconvolution,” Microsc. Res. Tech. 69, 260–266 (2006).
[CrossRef]

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

2005 (1)

2004 (1)

2003 (2)

M. C. Forman, N. Davies, and M. McCormick, “Continuous parallax in discrete pixelated integral three-dimensional displays,” J. Opt. Soc. Am. A 20, 411–420 (2003).
[CrossRef]

C. H. Yeh, “Wavelet-based corner detection using eigenvectors of covariance matrices,” Patt. Recog. Lett. 24, 2797–2806 (2003).
[CrossRef]

2002 (1)

2000 (2)

Z. Zhang, “A flexible new technique for camera calibration,” IEEE Trans. Pattern Anal. Machine Intell. 22, 1330–1334 (2000).
[CrossRef]

M. Pollefeys, R. Koch, M. Vergauwen, B. Deknuydt, and L. Van Gool, “Three-dimensional scene reconstruction from images,” in Proc. SPIE 3958, 215–226 (2000).

1999 (1)

V. Y. Panin, G. L. Zeng, and G. T. Gullberg, “Total variation regulated EM algorithm,” IEEE Trans. Nucl. Sci. 46, 2202–2210 (1999).
[CrossRef]

1997 (1)

1990 (1)

P. J. Green, “Bayesian reconstructions from emission tomography data using a modified EM algorithm,” IEEE Trans. Med. Imaging 9, 84–93 (1990).
[CrossRef]

1968 (1)

1931 (1)

1908 (1)

G. Lippmann, “La photographie intégrale,” C. R. Acad. Sci. 146, 446–451 (1908).

Aloni, D.

Arai, J.

Bay, H.

H. Bay, T. Tuytelaars, and L. Van Gool, “SURF: speeded-up robust features,” in 9th European Conference on Computer Vision (2008), pp. 346–359.

Bertero, M.

M. Bertero, P. Boccacci, G. Desidera, and G. Vicidomini, “Image deblurring with Poisson data: from cells to galaxies,” Inverse Probl. 25, 123006 (2009).
[CrossRef]

Blanc-Feraud, L.

N. Dey, L. Blanc‐Feraud, C. Zimmer, P. Roux, Z. Kam, J. C. Olivo‐Marin, and J. Zerubia, “Richardson–Lucy algorithm with total variation regularization for 3D confocal microscope deconvolution,” Microsc. Res. Tech. 69, 260–266 (2006).
[CrossRef]

Boccacci, P.

M. Bertero, P. Boccacci, G. Desidera, and G. Vicidomini, “Image deblurring with Poisson data: from cells to galaxies,” Inverse Probl. 25, 123006 (2009).
[CrossRef]

Burckhardt, C. B.

Cho, M.

Y. Zhao, X. Xiao, M. Cho, and B. Javidi, “Tracking of multiple objects in unknown background using Bayesian estimation in 3D space,” J. Opt. Soc. Am. A 28, 1935–1940 (2011).
[CrossRef]

X. Xiao, M. DaneshPanah, M. Cho, and B. Javidi, “3D integral imaging using sparse sensors with unknown positions,” J. Disp. Technol. 6, 614–619 (2010).
[CrossRef]

DaneshPanah, M.

Davies, N.

Deknuydt, B.

M. Pollefeys, R. Koch, M. Vergauwen, B. Deknuydt, and L. Van Gool, “Three-dimensional scene reconstruction from images,” in Proc. SPIE 3958, 215–226 (2000).

Desidera, G.

M. Bertero, P. Boccacci, G. Desidera, and G. Vicidomini, “Image deblurring with Poisson data: from cells to galaxies,” Inverse Probl. 25, 123006 (2009).
[CrossRef]

Dey, N.

N. Dey, L. Blanc‐Feraud, C. Zimmer, P. Roux, Z. Kam, J. C. Olivo‐Marin, and J. Zerubia, “Richardson–Lucy algorithm with total variation regularization for 3D confocal microscope deconvolution,” Microsc. Res. Tech. 69, 260–266 (2006).
[CrossRef]

Forman, M. C.

Goodman, J. W.

J. W. Goodman, Statistical Optics (Wiley-Interscience, 1985).

Green, P. J.

P. J. Green, “Bayesian reconstructions from emission tomography data using a modified EM algorithm,” IEEE Trans. Med. Imaging 9, 84–93 (1990).
[CrossRef]

Gullberg, G. T.

V. Y. Panin, G. L. Zeng, and G. T. Gullberg, “Total variation regulated EM algorithm,” IEEE Trans. Nucl. Sci. 46, 2202–2210 (1999).
[CrossRef]

Harris, C.

C. Harris and M. Stephens, “A combined corner and edge detector,” in Alvey Vision Conference (1988), p. 50.

Hartley, R.

R. Hartley and A. Zisserman, Multiple View Geometry in Computer Vision (Cambridge University, 2000).

Hong, S. H.

Hoshino, H.

Ives, H. E.

Jang, J. S.

Javidi, B.

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

Y. Zhao, X. Xiao, M. Cho, and B. Javidi, “Tracking of multiple objects in unknown background using Bayesian estimation in 3D space,” J. Opt. Soc. Am. A 28, 1935–1940 (2011).
[CrossRef]

X. Xiao, M. DaneshPanah, M. Cho, and B. Javidi, “3D integral imaging using sparse sensors with unknown positions,” J. Disp. Technol. 6, 614–619 (2010).
[CrossRef]

M. DaneshPanah, B. Javidi, and E. A. Watson, “Three dimensional object recognition with photon counting imagery in the presence of noise,” Opt. Express 18, 26450–26460(2010).
[CrossRef]

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

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

M. DaneshPanah, B. Javidi, and E. A. Watson, “Three dimensional imaging with randomly distributed sensors,” Opt. Express 16, 6368–6377 (2008).
[CrossRef]

B. Tavakoli, B. Javidi, and E. Watson, “Three dimensional visualization by photon counting computational Integral Imaging,” Opt. Express 16, 4426–4436 (2008).
[CrossRef]

S. Yeom, B. Javidi, and E. Watson, “Three-dimensional distortion-tolerant object recognition using photon-counting integral imaging,” Opt. Express 15, 1513–1533 (2007).
[CrossRef]

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

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

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

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

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

Kam, Z.

N. Dey, L. Blanc‐Feraud, C. Zimmer, P. Roux, Z. Kam, J. C. Olivo‐Marin, and J. Zerubia, “Richardson–Lucy algorithm with total variation regularization for 3D confocal microscope deconvolution,” Microsc. Res. Tech. 69, 260–266 (2006).
[CrossRef]

Koch, R.

M. Pollefeys, R. Koch, M. Vergauwen, B. Deknuydt, and L. Van Gool, “Three-dimensional scene reconstruction from images,” in Proc. SPIE 3958, 215–226 (2000).

Lippmann, G.

G. Lippmann, “La photographie intégrale,” C. R. 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. IEEE 97, 1067–1077 (2009).
[CrossRef]

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, 1067–1077 (2009).
[CrossRef]

McCormick, M.

Okano, F.

Olivo-Marin, J. C.

N. Dey, L. Blanc‐Feraud, C. Zimmer, P. Roux, Z. Kam, J. C. Olivo‐Marin, and J. Zerubia, “Richardson–Lucy algorithm with total variation regularization for 3D confocal microscope deconvolution,” Microsc. Res. Tech. 69, 260–266 (2006).
[CrossRef]

Panin, V. Y.

V. Y. Panin, G. L. Zeng, and G. T. Gullberg, “Total variation regulated EM algorithm,” IEEE Trans. Nucl. Sci. 46, 2202–2210 (1999).
[CrossRef]

Pollefeys, M.

M. Pollefeys, R. Koch, M. Vergauwen, B. Deknuydt, and L. Van Gool, “Three-dimensional scene reconstruction from images,” in Proc. SPIE 3958, 215–226 (2000).

Roux, P.

N. Dey, L. Blanc‐Feraud, C. Zimmer, P. Roux, Z. Kam, J. C. Olivo‐Marin, and J. Zerubia, “Richardson–Lucy algorithm with total variation regularization for 3D confocal microscope deconvolution,” Microsc. Res. Tech. 69, 260–266 (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. IEEE 97, 1067–1077 (2009).
[CrossRef]

Son, J. Y.

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

Stephens, M.

C. Harris and M. Stephens, “A combined corner and edge detector,” in Alvey Vision Conference (1988), p. 50.

Stern, A.

Tavakoli, B.

Tuytelaars, T.

H. Bay, T. Tuytelaars, and L. Van Gool, “SURF: speeded-up robust features,” in 9th European Conference on Computer Vision (2008), pp. 346–359.

Van Gool, L.

M. Pollefeys, R. Koch, M. Vergauwen, B. Deknuydt, and L. Van Gool, “Three-dimensional scene reconstruction from images,” in Proc. SPIE 3958, 215–226 (2000).

H. Bay, T. Tuytelaars, and L. Van Gool, “SURF: speeded-up robust features,” in 9th European Conference on Computer Vision (2008), pp. 346–359.

Vergauwen, M.

M. Pollefeys, R. Koch, M. Vergauwen, B. Deknuydt, and L. Van Gool, “Three-dimensional scene reconstruction from images,” in Proc. SPIE 3958, 215–226 (2000).

Vicidomini, G.

M. Bertero, P. Boccacci, G. Desidera, and G. Vicidomini, “Image deblurring with Poisson data: from cells to galaxies,” Inverse Probl. 25, 123006 (2009).
[CrossRef]

Watson, E.

Watson, E. A.

Xiao, X.

Y. Zhao, X. Xiao, M. Cho, and B. Javidi, “Tracking of multiple objects in unknown background using Bayesian estimation in 3D space,” J. Opt. Soc. Am. A 28, 1935–1940 (2011).
[CrossRef]

X. Xiao, M. DaneshPanah, M. Cho, and B. Javidi, “3D integral imaging using sparse sensors with unknown positions,” J. Disp. Technol. 6, 614–619 (2010).
[CrossRef]

Yeh, C. H.

C. H. Yeh, “Wavelet-based corner detection using eigenvectors of covariance matrices,” Patt. Recog. Lett. 24, 2797–2806 (2003).
[CrossRef]

Yeom, S.

Yuyama, I.

Zeng, G. L.

V. Y. Panin, G. L. Zeng, and G. T. Gullberg, “Total variation regulated EM algorithm,” IEEE Trans. Nucl. Sci. 46, 2202–2210 (1999).
[CrossRef]

Zerubia, J.

N. Dey, L. Blanc‐Feraud, C. Zimmer, P. Roux, Z. Kam, J. C. Olivo‐Marin, and J. Zerubia, “Richardson–Lucy algorithm with total variation regularization for 3D confocal microscope deconvolution,” Microsc. Res. Tech. 69, 260–266 (2006).
[CrossRef]

Zhang, Z.

Z. Zhang, “A flexible new technique for camera calibration,” IEEE Trans. Pattern Anal. Machine Intell. 22, 1330–1334 (2000).
[CrossRef]

Zhao, Y.

Zimmer, C.

N. Dey, L. Blanc‐Feraud, C. Zimmer, P. Roux, Z. Kam, J. C. Olivo‐Marin, and J. Zerubia, “Richardson–Lucy algorithm with total variation regularization for 3D confocal microscope deconvolution,” Microsc. Res. Tech. 69, 260–266 (2006).
[CrossRef]

Zisserman, A.

R. Hartley and A. Zisserman, Multiple View Geometry in Computer Vision (Cambridge University, 2000).

Appl. Opt. (1)

C. R. Acad. Sci. (1)

G. Lippmann, “La photographie intégrale,” C. R. Acad. Sci. 146, 446–451 (1908).

IEEE Trans. Med. Imaging (1)

P. J. Green, “Bayesian reconstructions from emission tomography data using a modified EM algorithm,” IEEE Trans. Med. Imaging 9, 84–93 (1990).
[CrossRef]

IEEE Trans. Nucl. Sci. (1)

V. Y. Panin, G. L. Zeng, and G. T. Gullberg, “Total variation regulated EM algorithm,” IEEE Trans. Nucl. Sci. 46, 2202–2210 (1999).
[CrossRef]

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

Z. Zhang, “A flexible new technique for camera calibration,” IEEE Trans. Pattern Anal. Machine Intell. 22, 1330–1334 (2000).
[CrossRef]

Inverse Probl. (1)

M. Bertero, P. Boccacci, G. Desidera, and G. Vicidomini, “Image deblurring with Poisson data: from cells to galaxies,” Inverse Probl. 25, 123006 (2009).
[CrossRef]

J. Disp. Technol. (1)

X. Xiao, M. DaneshPanah, M. Cho, and B. Javidi, “3D integral imaging using sparse sensors with unknown positions,” J. Disp. Technol. 6, 614–619 (2010).
[CrossRef]

J. Opt. Soc. Am. (2)

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

Microsc. Res. Tech. (1)

N. Dey, L. Blanc‐Feraud, C. Zimmer, P. Roux, Z. Kam, J. C. Olivo‐Marin, and J. Zerubia, “Richardson–Lucy algorithm with total variation regularization for 3D confocal microscope deconvolution,” Microsc. Res. Tech. 69, 260–266 (2006).
[CrossRef]

Opt. Express (7)

Opt. Lett. (2)

Patt. Recog. Lett. (1)

C. H. Yeh, “Wavelet-based corner detection using eigenvectors of covariance matrices,” Patt. Recog. Lett. 24, 2797–2806 (2003).
[CrossRef]

Proc. IEEE (2)

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

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

Proc. SPIE (1)

M. Pollefeys, R. Koch, M. Vergauwen, B. Deknuydt, and L. Van Gool, “Three-dimensional scene reconstruction from images,” in Proc. SPIE 3958, 215–226 (2000).

Other (5)

R. Hartley and A. Zisserman, Multiple View Geometry in Computer Vision (Cambridge University, 2000).

J. W. Goodman, Statistical Optics (Wiley-Interscience, 1985).

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

C. Harris and M. Stephens, “A combined corner and edge detector,” in Alvey Vision Conference (1988), p. 50.

H. Bay, T. Tuytelaars, and L. Van Gool, “SURF: speeded-up robust features,” in 9th European Conference on Computer Vision (2008), pp. 346–359.

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Figures (6)

Fig. 1.
Fig. 1.

3D photon counting integral imaging pickup process.

Fig. 2.
Fig. 2.

Camera projective model.

Fig. 3.
Fig. 3.

Elemental images. (a) Original 3D scene’ (b–d) cropped photon counting elemental image when Np=5,000 (0.08photon/pixel), Np=10,000 (0.17photon/pixel), and Np=30,000 (0.51photon/pixel), respectively.

Fig. 4.
Fig. 4.

(a) and (c) Cropped binary photon counting elemental images when Np=10,000 and Np=30,000, respectively; (b) and (d) the corresponding image restoration results.

Fig. 5.
Fig. 5.

Estimated sensor position error percentage for the different number of photons.

Fig. 6.
Fig. 6.

3D reconstruction images by using measured sensor positions (a) and (b) and estimated sensor positions (c) and (d) at the different depths (z=300mm and 370 mm, respectively).

Tables (1)

Tables Icon

Table 1. Experimental Results with Different Number of Photons (MSE Being MSE between 3D Reconstructed Images)

Equations (8)

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

P(y|α,W)=(αW)yeαWy!,y=0,1,2,,
yi|IiPoisson(NpIi),
R={R:R(u,v|z)=1NpKLk=0K1l=0L1PCkl(u+SxklγklM,v+SyklγklM),z=[zmin,zmax]},
y=αHx˜=Hxx=αx˜,
p(xj)exp(U(xj)),
U(xs,t)=(xs+1,txs,t)2+(xs,t+1xs,t)2,
xj(n+1)=xj(n)iHij+β(U(x(n))/xj)iHijyikHikxk(n),
Sx=q=1Q(Zq(uqax)fXq)/fQ,Sy=q=1Q(Zq(vqay)fYq)/fQ,

Metrics