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 OSA

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References

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  1. J. W. Goodman, Statistical Optics (Wiley-Interscience, 1985), Wiley classics ed.
  2. J. R. Janesick, Scientific Charge-Coupled Devices (SPIE Press Monograph Vol. PM83) (SPIE Publications, 2001), 1st ed.
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    [CrossRef]
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    [CrossRef] [PubMed]
  7. 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]
  8. 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]
  9. O. Matoba, E. Tajahuerce, and B. Javidi, “Real-time three-dimensional object recognition with multiple perspectives imaging,” Appl. Opt. 40, 3318–3325 (2001).
    [CrossRef]
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    [CrossRef] [PubMed]
  13. 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]
  14. 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]
  15. 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]
  16. S. Yeom, B. Javidi, C. wook 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]
  17. M. G. Lippmann, “La photographie intégrale,,” Comptes-rendus de l’Académie des Sciences 146, 446–451 (1908).
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    [CrossRef]
  19. T. Okoshi, “Three-dimensional displays,” Proceedings of the IEEE 68, 548–564 (1980).
    [CrossRef]
  20. M. C. Forman, N. Davies, and M. McCormick, “Continuous parallax in discrete pixelated integral three-dimensional displays.” J Opt Soc Am A Opt Image Sci Vis 20, 411–420 (2003).
    [CrossRef] [PubMed]
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    [CrossRef]
  22. F. Okano, J. Arai, K. Mitani, and M. Okui, “Real-time integral imaging based on extremely high resolution video system,” Proceedings of the IEEE 94, 490–501 (2006).
    [CrossRef]
  23. B. Javidi, F. Okano, and J.-Y. Son, eds., Three-Dimensional Imaging, Visualization, and Display (Signals and Communication Technology) (Springer, 2008), 1st ed.
  24. R. Martinez-Cuenca, G. Saavedra, M. Martinez-Corral, and B. Javidi, “Progress in 3-d multiperspective display by integral imaging,” Proceedings of the IEEE 97, 1067–1077 (2009).
    [CrossRef]
  25. J.-S. Jang and B. Javidi, “Three-dimensional synthetic aperture integral imaging,” Opt. Lett. 27, 1144–1146 (2002).
    [CrossRef]
  26. 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]
  27. 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]
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  29. P. Rfrgier, Noise Theory and Application to Physics (Springer, 2004), 1st ed.
  30. A. Papoulis and S. Pillai, Probability, Random Variables and Stochastic Processes (McGraw Hill Higher Education, 2002), 4th ed.
  31. R. J. Schalkoff, Pattern Recognition: Statistical, Structural and Neural Approaches (Wiley, 1991), 1st ed.

2010 (1)

2009 (2)

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,” Proceedings of the IEEE 97, 1067–1077 (2009).
[CrossRef]

2007 (2)

2006 (4)

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,” Proceedings of the 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,” Proceedings of the IEEE 94, 490–501 (2006).
[CrossRef]

2005 (1)

2004 (2)

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 (1)

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

2002 (1)

2001 (1)

1999 (1)

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 (2)

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 (1)

1984 (1)

1980 (1)

T. Okoshi, “Three-dimensional displays,” Proceedings of the IEEE 68, 548–564 (1980).
[CrossRef]

1969 (1)

1968 (1)

C. B. Burckhardt, “Optimum parameters and resolution limitation of integral photography,” J. Opt. Soc. Amer 58, 71–76 (1968).
[CrossRef]

1908 (1)

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,” Proceedings of the IEEE 94, 490–501 (2006).
[CrossRef]

Burckhardt, C. B.

C. B. Burckhardt, “Optimum parameters and resolution limitation of integral photography,” J. Opt. Soc. Amer 58, 71–76 (1968).
[CrossRef]

Davies, N.

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

Dubois, F.

Forman, M. C.

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

Goodman, J. W.

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

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.

Hong, S.-H.

Janesick, J. R.

J. R. Janesick, Scientific Charge-Coupled Devices (SPIE Press Monograph Vol. PM83) (SPIE Publications, 2001), 1st ed.
[CrossRef]

Jang, J.-S.

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,” Proceedings of the IEEE 97, 1067–1077 (2009).
[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] [PubMed]

S. Yeom, B. Javidi, C. wook 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]

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,” Proceedings of the 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]

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,” Proceedings of the 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,” Proceedings of the IEEE 97, 1067–1077 (2009).
[CrossRef]

Matoba, O.

McCormick, M.

M. C. Forman, N. Davies, and M. McCormick, “Continuous parallax in discrete pixelated integral three-dimensional displays.” J Opt Soc Am A Opt Image Sci Vis 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,” Proceedings of the 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.

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.

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,” Proceedings of the IEEE 94, 490–501 (2006).
[CrossRef]

Okoshi, T.

T. Okoshi, “Three-dimensional displays,” Proceedings of the 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,” Proceedings of the 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]

Papoulis, A.

A. Papoulis and S. Pillai, Probability, Random Variables and Stochastic Processes (McGraw Hill Higher Education, 2002), 4th ed.

Pillai, S.

A. Papoulis and S. Pillai, Probability, Random Variables and Stochastic Processes (McGraw Hill Higher Education, 2002), 4th ed.

Ponce-Díaz, R.

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]

Rfrgier, P.

P. Rfrgier, Noise Theory and Application to Physics (Springer, 2004), 1st ed.

Richards, E. A.

Saavedra, G.

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

Schalkoff, R. J.

R. J. Schalkoff, Pattern Recognition: Statistical, Structural and Neural Approaches (Wiley, 1991), 1st ed.

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,” Proceedings of the IEEE 94, 591–607 (2006).
[CrossRef]

Tajahuerce, E.

Watson, E.

Watson, E. A.

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]

wook Lee, C.

Yeom, S.

Appl Opt (1)

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]

Appl. Opt. (4)

Comptes-rendus de l’Académie des Sciences (1)

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

IEEE Trans Pattern Anal Mach Intell (1)

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 A Opt Image Sci Vis (1)

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

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

J. Opt. Soc. Amer (1)

C. B. Burckhardt, “Optimum parameters and resolution limitation of integral photography,” J. Opt. Soc. Amer 58, 71–76 (1968).
[CrossRef]

Opt Express (1)

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]

Opt Lett (2)

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]

Opt. Express (5)

Opt. Lett. (2)

Proceedings of the IEEE (4)

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

T. Okoshi, “Three-dimensional displays,” Proceedings of the IEEE 68, 548–564 (1980).
[CrossRef]

A. Stern and B. Javidi, “Three-dimensional image sensing, visualization, and processing using integral imaging,” Proceedings of the 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,” Proceedings of the IEEE 94, 490–501 (2006).
[CrossRef]

Other (7)

B. Javidi, F. Okano, and J.-Y. Son, eds., Three-Dimensional Imaging, Visualization, and Display (Signals and Communication Technology) (Springer, 2008), 1st ed.

F. Sadjadi, ed., Selected Papers on Automatic Target Recognition (SPIE-CDROM, 1999).

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

J. R. Janesick, Scientific Charge-Coupled Devices (SPIE Press Monograph Vol. PM83) (SPIE Publications, 2001), 1st ed.
[CrossRef]

P. Rfrgier, Noise Theory and Application to Physics (Springer, 2004), 1st ed.

A. Papoulis and S. Pillai, Probability, Random Variables and Stochastic Processes (McGraw Hill Higher Education, 2002), 4th ed.

R. J. Schalkoff, Pattern Recognition: Statistical, Structural and Neural Approaches (Wiley, 1991), 1st ed.

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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)

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

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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