Abstract

Three dimensional (3D) imaging systems have been recently suggested for passive sensing and recognition of objects in photon-starved environments where only a few photons are emitted or reflected from the object. In this paradigm, it is important to make optimal use of limited information carried by photons. We present a statistical framework for 3D passive object recognition in presence of noise. Since in quantum-limited regime, detector dark noise is present, our approach takes into account the effect of noise on information bearing photons. The model is tested when background noise and dark noise sources are present for identifying a target in a 3D scene. It is shown that reliable object recognition is possible in photon-counting domain. The results suggest that with proper translation of physical characteristics of the imaging system into the information processing algorithms, photon-counting imagery can be used for object classification.

© 2010 Optical Society of America

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2010

S. R. Narravula, M. M. Hayat, and B. Javidi, "Information theoretic approach for assessing image fidelity in photon-counting arrays," Opt. Express 18, 2449-2466 (2010).
[CrossRef] [PubMed]

2009

I. Moon, and B. Javidi, "Three dimensional imaging and recognition using truncated photon counting model and parametric maximum likelihood estimator," Opt. Express 17, 15709-15715 (2009).
[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, 1067-1077 (2009).
[CrossRef]

2007

S. Yeom, B. Javidi, C. W. Lee, and E. Watson, "Photon-counting passive 3d image sensing for reconstruction and recognition of partially occluded objects," Opt. Express 15, 16189-16195 (2007).
[CrossRef] [PubMed]

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] [PubMed]

2006

H. Kwon, and N. M. Nasrabadi, "Kernel matched subspace detectors for hyperspectral target detection," IEEE Trans. Pattern Anal. Mach. Intell. 28, 178-194 (2006).
[CrossRef] [PubMed]

B. Javidi, R. Ponce-Díaz, and S.-H. Hong, "Three-dimensional recognition of occluded objects by using computational integral imaging," Opt. Lett. 31, 1106-1108 (2006).
[CrossRef] [PubMed]

A. Stern, and B. Javidi, "Three-dimensional image sensing, visualization, and processing using integral imaging," Proc. IEEE 94, 591-607 (2006).
[CrossRef]

F. Okano, J. Arai, K. Mitani, and M. Okui, "Real-time integral imaging based on extremely high resolution video system," Proc. IEEE 94, 490-501 (2006).
[CrossRef]

2005

S. Yeom, B. Javidi, and E. Watson, "Photon counting passive 3d image sensing for automatic target recognition," Opt. Express 13, 9310-9330 (2005).
[CrossRef] [PubMed]

2004

A. Mahalanobis, R. R. Muise, and S. R. Stanfill, "Quadratic correlation filter design methodology for target detection and surveillance applications," Appl. Opt. 43, 5198-5205 (2004).
[CrossRef] [PubMed]

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] [PubMed]

2003

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

2002

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

2001

O. Matoba, E. Tajahuerce, and B. Javidi, "Real-time three-dimensional object recognition with multiple perspectives imaging," Appl. Opt. 40, 3318-3325 (2001).
[CrossRef]

1999

V. Page, F. Goudail, and P. Refregier, "Improved robustness of target location in nonhomogeneous backgrounds by use of the maximum-likelihood ratio test location algorithm," Opt. Lett. 24, 1383-1385 (1999).
[CrossRef]

1993

F. Dubois, "Automatic spatial frequency selection algorithm for pattern recognition by correlation," Appl. Opt. 32, 4365-4371 (1993).
[CrossRef] [PubMed]

B. Javidi, P. Refregier, and P. Willett, "Optimum receiver design for pattern recognition with nonoverlapping target and scene noise," Opt. Lett. 18, 1660 (1993).
[CrossRef] [PubMed]

1992

E. A. Watson, and G. M. Morris, "Imaging thermal objects with photon-counting detectors," Appl. Opt. 31, 4751-4757 (1992).
[CrossRef] [PubMed]

1984

G. M. Morris, "Scene matching using photon-limited images," J. Opt. Soc. Am. A 1, 482-488 (1984).
[CrossRef]

1980

T. Okoshi, "Three-dimensional displays," Proc. IEEE 68, 548-564 (1980).
[CrossRef]

1969

E. A. Richards, "Limitations in optical imaging devices at low light levels," Appl. Opt. 8, 1999-2005 (1969).
[CrossRef] [PubMed]

1968

C. B. Burckhardt, "Optimum parameters and resolution limitation of integral photography," J. Opt. Soc. Am. 58, 71-76 (1968).
[CrossRef]

1908

M. G. Lippmann, "La photographie intégrale," Comptes-rendus de l’Académie des Sciences 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. IEEE 94, 490-501 (2006).
[CrossRef]

Burckhardt, C. B.

C. B. Burckhardt, "Optimum parameters and resolution limitation of integral photography," J. Opt. Soc. Am. 58, 71-76 (1968).
[CrossRef]

Davies, N.

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

Dubois, F.

F. Dubois, "Automatic spatial frequency selection algorithm for pattern recognition by correlation," Appl. Opt. 32, 4365-4371 (1993).
[CrossRef] [PubMed]

Forman, M. C.

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

Goudail, F.

V. Page, F. Goudail, and P. Refregier, "Improved robustness of target location in nonhomogeneous backgrounds by use of the maximum-likelihood ratio test location algorithm," Opt. Lett. 24, 1383-1385 (1999).
[CrossRef]

Hayat, M. M.

S. R. Narravula, M. M. Hayat, and B. Javidi, "Information theoretic approach for assessing image fidelity in photon-counting arrays," Opt. Express 18, 2449-2466 (2010).
[CrossRef] [PubMed]

Hong, S.-H.

B. Javidi, R. Ponce-Díaz, and S.-H. Hong, "Three-dimensional recognition of occluded objects by using computational integral imaging," Opt. Lett. 31, 1106-1108 (2006).
[CrossRef] [PubMed]

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] [PubMed]

Jang, J.-S.

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] [PubMed]

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

Javidi, B.

S. R. Narravula, M. M. Hayat, and B. Javidi, "Information theoretic approach for assessing image fidelity in photon-counting arrays," Opt. Express 18, 2449-2466 (2010).
[CrossRef] [PubMed]

I. Moon, and B. Javidi, "Three dimensional imaging and recognition using truncated photon counting model and parametric maximum likelihood estimator," Opt. Express 17, 15709-15715 (2009).
[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, 1067-1077 (2009).
[CrossRef]

S. Yeom, B. Javidi, C. W. Lee, and E. Watson, "Photon-counting passive 3d image sensing for reconstruction and recognition of partially occluded objects," Opt. Express 15, 16189-16195 (2007).
[CrossRef] [PubMed]

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] [PubMed]

B. Javidi, R. Ponce-Díaz, and S.-H. Hong, "Three-dimensional recognition of occluded objects by using computational integral imaging," Opt. Lett. 31, 1106-1108 (2006).
[CrossRef] [PubMed]

A. Stern, and B. Javidi, "Three-dimensional 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] [PubMed]

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] [PubMed]

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

O. Matoba, E. Tajahuerce, and B. Javidi, "Real-time three-dimensional object recognition with multiple perspectives imaging," Appl. Opt. 40, 3318-3325 (2001).
[CrossRef]

B. Javidi, P. Refregier, and P. Willett, "Optimum receiver design for pattern recognition with nonoverlapping target and scene noise," Opt. Lett. 18, 1660 (1993).
[CrossRef] [PubMed]

Kwon, H.

H. Kwon, and N. M. Nasrabadi, "Kernel matched subspace detectors for hyperspectral target detection," IEEE Trans. Pattern Anal. Mach. Intell. 28, 178-194 (2006).
[CrossRef] [PubMed]

Lee, C. W.

S. Yeom, B. Javidi, C. W. Lee, and E. Watson, "Photon-counting passive 3d image sensing for reconstruction and recognition of partially occluded objects," Opt. Express 15, 16189-16195 (2007).
[CrossRef] [PubMed]

Lippmann, M. G.

M. G. Lippmann, "La photographie intégrale," Comptes-rendus de l’Académie des Sciences 146, 446-451 (1908).

Mahalanobis, A.

A. Mahalanobis, R. R. Muise, and S. R. Stanfill, "Quadratic correlation filter design methodology for target detection and surveillance applications," Appl. Opt. 43, 5198-5205 (2004).
[CrossRef] [PubMed]

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]

Matoba, O.

O. Matoba, E. Tajahuerce, and B. Javidi, "Real-time three-dimensional object recognition with multiple perspectives imaging," Appl. Opt. 40, 3318-3325 (2001).
[CrossRef]

McCormick, M.

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

Mitani, K.

F. Okano, J. Arai, K. Mitani, and M. Okui, "Real-time integral imaging based on extremely high resolution video system," Proc. IEEE 94, 490-501 (2006).
[CrossRef]

Moon, I.

I. Moon, and B. Javidi, "Three dimensional imaging and recognition using truncated photon counting model and parametric maximum likelihood estimator," Opt. Express 17, 15709-15715 (2009).
[CrossRef] [PubMed]

Morris, G. M.

E. A. Watson, and G. M. Morris, "Imaging thermal objects with photon-counting detectors," Appl. Opt. 31, 4751-4757 (1992).
[CrossRef] [PubMed]

G. M. Morris, "Scene matching using photon-limited images," J. Opt. Soc. Am. A 1, 482-488 (1984).
[CrossRef]

Muise, R. R.

A. Mahalanobis, R. R. Muise, and S. R. Stanfill, "Quadratic correlation filter design methodology for target detection and surveillance applications," Appl. Opt. 43, 5198-5205 (2004).
[CrossRef] [PubMed]

Narravula, S. R.

S. R. Narravula, M. M. Hayat, and B. Javidi, "Information theoretic approach for assessing image fidelity in photon-counting arrays," Opt. Express 18, 2449-2466 (2010).
[CrossRef] [PubMed]

Nasrabadi, N. M.

H. Kwon, and N. M. Nasrabadi, "Kernel matched subspace detectors for hyperspectral target detection," IEEE Trans. Pattern Anal. Mach. Intell. 28, 178-194 (2006).
[CrossRef] [PubMed]

Okano, F.

F. Okano, J. Arai, K. Mitani, and M. Okui, "Real-time integral imaging based on extremely high resolution video system," Proc. IEEE 94, 490-501 (2006).
[CrossRef]

Okoshi, T.

T. Okoshi, "Three-dimensional displays," Proc. IEEE 68, 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. IEEE 94, 490-501 (2006).
[CrossRef]

Page, V.

V. Page, F. Goudail, and P. Refregier, "Improved robustness of target location in nonhomogeneous backgrounds by use of the maximum-likelihood ratio test location algorithm," Opt. Lett. 24, 1383-1385 (1999).
[CrossRef]

Ponce-Díaz, R.

B. Javidi, R. Ponce-Díaz, and S.-H. Hong, "Three-dimensional recognition of occluded objects by using computational integral imaging," Opt. Lett. 31, 1106-1108 (2006).
[CrossRef] [PubMed]

Refregier, P.

V. Page, F. Goudail, and P. Refregier, "Improved robustness of target location in nonhomogeneous backgrounds by use of the maximum-likelihood ratio test location algorithm," Opt. Lett. 24, 1383-1385 (1999).
[CrossRef]

B. Javidi, P. Refregier, and P. Willett, "Optimum receiver design for pattern recognition with nonoverlapping target and scene noise," Opt. Lett. 18, 1660 (1993).
[CrossRef] [PubMed]

Richards, E. A.

E. A. Richards, "Limitations in optical imaging devices at low light levels," Appl. Opt. 8, 1999-2005 (1969).
[CrossRef] [PubMed]

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]

Stanfill, S. R.

A. Mahalanobis, R. R. Muise, and S. R. Stanfill, "Quadratic correlation filter design methodology for target detection and surveillance applications," Appl. Opt. 43, 5198-5205 (2004).
[CrossRef] [PubMed]

Stern, A.

A. Stern, and B. Javidi, "Three-dimensional image sensing, visualization, and processing using integral imaging," Proc. IEEE 94, 591-607 (2006).
[CrossRef]

Tajahuerce, E.

O. Matoba, E. Tajahuerce, and B. Javidi, "Real-time three-dimensional object recognition with multiple perspectives imaging," Appl. Opt. 40, 3318-3325 (2001).
[CrossRef]

Watson, E.

S. Yeom, B. Javidi, C. W. Lee, and E. Watson, "Photon-counting passive 3d image sensing for reconstruction and recognition of partially occluded objects," Opt. Express 15, 16189-16195 (2007).
[CrossRef] [PubMed]

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] [PubMed]

S. Yeom, B. Javidi, and E. Watson, "Photon counting passive 3d image sensing for automatic target recognition," Opt. Express 13, 9310-9330 (2005).
[CrossRef] [PubMed]

Watson, E. A.

E. A. Watson, and G. M. Morris, "Imaging thermal objects with photon-counting detectors," Appl. Opt. 31, 4751-4757 (1992).
[CrossRef] [PubMed]

Willett, P.

B. Javidi, P. Refregier, and P. Willett, "Optimum receiver design for pattern recognition with nonoverlapping target and scene noise," Opt. Lett. 18, 1660 (1993).
[CrossRef] [PubMed]

Yeom, S.

S. Yeom, B. Javidi, C. W. Lee, and E. Watson, "Photon-counting passive 3d image sensing for reconstruction and recognition of partially occluded objects," Opt. Express 15, 16189-16195 (2007).
[CrossRef] [PubMed]

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] [PubMed]

S. Yeom, B. Javidi, and E. Watson, "Photon counting passive 3d image sensing for automatic target recognition," Opt. Express 13, 9310-9330 (2005).
[CrossRef] [PubMed]

Appl. Opt.

F. Dubois, "Automatic spatial frequency selection algorithm for pattern recognition by correlation," Appl. Opt. 32, 4365-4371 (1993).
[CrossRef] [PubMed]

A. Mahalanobis, R. R. Muise, and S. R. Stanfill, "Quadratic correlation filter design methodology for target detection and surveillance applications," Appl. Opt. 43, 5198-5205 (2004).
[CrossRef] [PubMed]

O. Matoba, E. Tajahuerce, and B. Javidi, "Real-time three-dimensional object recognition with multiple perspectives imaging," Appl. Opt. 40, 3318-3325 (2001).
[CrossRef]

E. A. Watson, and G. M. Morris, "Imaging thermal objects with photon-counting detectors," Appl. Opt. 31, 4751-4757 (1992).
[CrossRef] [PubMed]

E. A. Richards, "Limitations in optical imaging devices at low light levels," Appl. Opt. 8, 1999-2005 (1969).
[CrossRef] [PubMed]

Comptes-rendus de l’Académie des Sciences

M. G. Lippmann, "La photographie intégrale," Comptes-rendus de l’Académie des Sciences 146, 446-451 (1908).

IEEE Trans. Pattern Anal. Mach. Intell.

H. Kwon, and N. M. Nasrabadi, "Kernel matched subspace detectors for hyperspectral target detection," IEEE Trans. Pattern Anal. Mach. Intell. 28, 178-194 (2006).
[CrossRef] [PubMed]

J. Opt. Soc. Am.

C. B. Burckhardt, "Optimum parameters and resolution limitation of integral photography," J. Opt. Soc. Am. 58, 71-76 (1968).
[CrossRef]

J. Opt. Soc. Am. A

G. M. Morris, "Scene matching using photon-limited images," J. Opt. Soc. Am. A 1, 482-488 (1984).
[CrossRef]

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

Opt. Express

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] [PubMed]

S. Yeom, B. Javidi, and E. Watson, "Photon counting passive 3d image sensing for automatic target recognition," Opt. Express 13, 9310-9330 (2005).
[CrossRef] [PubMed]

I. Moon, and B. Javidi, "Three dimensional imaging and recognition using truncated photon counting model and parametric maximum likelihood estimator," Opt. Express 17, 15709-15715 (2009).
[CrossRef] [PubMed]

S. R. Narravula, M. M. Hayat, and B. Javidi, "Information theoretic approach for assessing image fidelity in photon-counting arrays," Opt. Express 18, 2449-2466 (2010).
[CrossRef] [PubMed]

S. Yeom, B. Javidi, C. W. Lee, and E. Watson, "Photon-counting passive 3d image sensing for reconstruction and recognition of partially occluded objects," Opt. Express 15, 16189-16195 (2007).
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Figures (6)

Fig. 1
Fig. 1

Illustration of multi-view imaging system.

Fig. 2
Fig. 2

Reference objects used in the experiment. (a) True class (blue truck), and (b) false class (white truck). Objects share similar shape and features.

Fig. 3
Fig. 3

4×4 subset of the total 11×11 elemental images captured from true (blue) class.

Fig. 4
Fig. 4

Simulation of photon-counting imagery. Photons are shown in green, dark counts shown in red. (a) Full intensity image of real unknown object, (b) detected 191 photons from intensity distribution of (a) according to Eq. (9), (c) dark frame generated with appx. 5400 counts, and (d) addition of photon image (b) and dark frame (c).

Fig. 5
Fig. 5

(a) Log likelihood ratio for the blue and white truck in a scene with background noise (a) without dark counts, and (b) with dark counts varying linearly with photon-counts. True class is the blue truck.

Fig. 6
Fig. 6

Fisher Ratio increases with number of detected photons. The slope decreases with increasing dark noise.

Tables (1)

Tables Icon

Table 1 Discrimination performance between two classes with and without presence of dark noise. FR is the Fisher Ratio

Equations (13)

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R k z = { r k i k p ˜ : i = 1 M } ,
R = { R z q : q = 1 Q }
r k i = [ α . s k i + n d ] w k i + [ n B k i + n d ] ( 1 w k i ) ,
Pr ( r i = m ) = ( r i ) m e r i m !
s k i = N ph I k i / i k I k i ,
( R ) = ( R | H 1 ) ( R | H 2 ) H 2 H 1 1 ,
( R | H j ; α ) = q = 1 Q P r ( R z q | H j ; α ) = q = 1 Q k = 1 K P r ( R k z q | H j ; α ) = q = 1 Q k = 1 K i = 1 M P r ( r k i k p ˜ | H j ; α )
Pr ( r k i k p ˜ | H j ; α ) = Pr ( r k i k p ˜ | H j ; α ) j w k i k p ˜ × Pr ( r k i k p ˜ | H j ; α ) 1 j w k i k p ˜
r k i | H j , α 𝒫 ( α . j s k i + n d ) for j w k i = 1 ,
log ( R | H j ; α ) = q = 1 Q k = 1 K i = 1 M j w k i ˜ [ α . j ˜ s k i ˜ n d + r k i ˜ log ( α . j s k i ˜ + n d ) log r k i ˜ ! ]
α log ( R | H j ; α ) = 0 q = 1 Q k = 1 K i = 1 M j w k i ˜ ( r k i ˜ . j s k i ˜ α ^ . j s k i ˜ n d k i ˜ j s k i ˜ ) = 0 .
α ^ = Σ q , k , i j w k i ˜ r k i ˜ Σ q , k , i ˜ j w k i ˜ j s k i ˜ ,
log ( R | H 1 ; α ^ ) H 2 H 1 log ( R | H 2 ; α ^ ) .

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