Abstract

We present a statistical approach to recognize three-dimensional (3D) objects with a small number of photons captured by using integral imaging (II). For 3D recognition of the events, the photon-limited elemental image set of a 3D object is obtained using the II technique. A computational geometrical ray propagation algorithm and the parametric maximum likelihood estimator are applied to the photon-limited elemental image set to reconstruct the irradiance of the original 3D scene voxels. The sampling distributions for the statistical parameters of the reconstructed image are determined. Finally, hypothesis testing for the equality of the statistical parameters between reference and input data sets is performed for statistical classification of populations on the basis of sampling distribution information. It is shown that large data sets of photon-limited 3D images can be converted into sampling distributions with their own statistical parameters, resulting in a substantial data dimensionality reduction for processing.

© 2009 Optical Society of America

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References

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  1. B.Javidi and F.Okano, eds., Three-Dimensional Television, Video, and Display Technologies (Springer, 2002).
  2. G. Lippmann, C. R. Acad. Sci. 146, 446 (1908).
  3. M. Levoy, IEEE Comp. Mag. 39, 46 (2006).
  4. Y. Hwang, S. Hong, and B. Javidi, J. Disp. Technol. 3, 64 (2007).
    [CrossRef]
  5. S. Yeom, B. Javidi, and E. Watson, Opt. Express 15, 1513 (2007).
    [CrossRef] [PubMed]
  6. M. Guillaume, P. Melon, and P. Refregier, J. Opt. Soc. Am. A 15, 2841 (1998).
    [CrossRef]
  7. F. Dubois, Appl. Opt. 32, 4365 (1993).
    [CrossRef] [PubMed]
  8. J. Goodman, Statistical Optics (Wiley, 1985).
  9. M.Hollander and D.Wolfe, eds., Nonparametric Statistical Methods (Wiley, 1999).
  10. N. Mukhopadhyay, Probability and Statistical Inference (Marcel Dekker, 2000).

2007 (2)

Y. Hwang, S. Hong, and B. Javidi, J. Disp. Technol. 3, 64 (2007).
[CrossRef]

S. Yeom, B. Javidi, and E. Watson, Opt. Express 15, 1513 (2007).
[CrossRef] [PubMed]

2006 (1)

M. Levoy, IEEE Comp. Mag. 39, 46 (2006).

1998 (1)

1993 (1)

1908 (1)

G. Lippmann, C. R. Acad. Sci. 146, 446 (1908).

Dubois, F.

Goodman, J.

J. Goodman, Statistical Optics (Wiley, 1985).

Guillaume, M.

Hong, S.

Y. Hwang, S. Hong, and B. Javidi, J. Disp. Technol. 3, 64 (2007).
[CrossRef]

Hwang, Y.

Y. Hwang, S. Hong, and B. Javidi, J. Disp. Technol. 3, 64 (2007).
[CrossRef]

Javidi, B.

Y. Hwang, S. Hong, and B. Javidi, J. Disp. Technol. 3, 64 (2007).
[CrossRef]

S. Yeom, B. Javidi, and E. Watson, Opt. Express 15, 1513 (2007).
[CrossRef] [PubMed]

Levoy, M.

M. Levoy, IEEE Comp. Mag. 39, 46 (2006).

Lippmann, G.

G. Lippmann, C. R. Acad. Sci. 146, 446 (1908).

Melon, P.

Mukhopadhyay, N.

N. Mukhopadhyay, Probability and Statistical Inference (Marcel Dekker, 2000).

Refregier, P.

Watson, E.

Yeom, S.

Appl. Opt. (1)

C. R. Acad. Sci. (1)

G. Lippmann, C. R. Acad. Sci. 146, 446 (1908).

IEEE Comp. Mag. (1)

M. Levoy, IEEE Comp. Mag. 39, 46 (2006).

J. Disp. Technol. (1)

Y. Hwang, S. Hong, and B. Javidi, J. Disp. Technol. 3, 64 (2007).
[CrossRef]

J. Opt. Soc. Am. A (1)

Opt. Express (1)

Other (4)

B.Javidi and F.Okano, eds., Three-Dimensional Television, Video, and Display Technologies (Springer, 2002).

J. Goodman, Statistical Optics (Wiley, 1985).

M.Hollander and D.Wolfe, eds., Nonparametric Statistical Methods (Wiley, 1999).

N. Mukhopadhyay, Probability and Statistical Inference (Marcel Dekker, 2000).

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Figures (5)

Fig. 1
Fig. 1

Schematic setup of II system with camera array for 3D object visualization and recognition. Two toy cars were used in the experiments.

Fig. 2
Fig. 2

Sectional 3D image reconstruction at distance z 0 = 100 cm , where the size of the reconstructed image is 150 × 100   pixels . (a) Car I, (b) car II.

Fig. 3
Fig. 3

Subset of elemental images having an average of single photon per elemental image generated according to a photon counting detection model. (a) Car I, (b) car II.

Fig. 4
Fig. 4

Sectional images of the 3D scenes reconstructed with a small number of photons-counted elemental images. (a) Car I with N ̃ = 1 , (b) car II with N ̃ = 1 , (c) car I with N ̃ = 11 , (d) car II with N ̃ = 11 , (e) car I with N ̃ = 51 , (f) car II with N ̃ = 51 .

Fig. 5
Fig. 5

(a) Experimental results of the K–S test for checking the equality of two histograms of the true class reference car I and unknown input data car II. Cumulative density function plots of the statistical sampling distributions of the reference car I and unknown input data car II for the random variable σ. N ̃ = ( b ) 11 and (c) 51.

Equations (2)

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Pr ( C ρ , T ) = [ ρ T ] C e ρ T C ! ,
F ( u ) = P ( X ( i ) u ) = # { X ( i ) u } n ,

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