Abstract

This paper addresses three-dimensional distortion-tolerant object recognition using photon-counting integral imaging (II). A photon-counting linear discriminant analysis (LDA) is proposed for classification photon-limited images. In the photon-counting LDA, classical irradiance images are used to train the classifier. The unknown objects used to test the classifier are labeled by the number of photons detected. The optimal solution of the Fisher’s LDA for photon-limited images is found to be different from the case when irradiance values are used. This difference results in one of the merits of a photon-counting LDA, namely that the high dimensionality of the image can be handled without preprocessing. Thus, the singularity problem of the Fisher’s LDA encountered in the use of irradiance images can be avoided. By using photon-counting II, we build a compact distortion tolerant recognition system that makes use of the multiple-perspective imaging of II to enhance the recognition performance. Experimental and simulation results are presented to classify out-of-plane rotated objects. The performance is analyzed in terms of mean-squared distance (MSD) between the irradiance images. It is shown that a low level of photons is sufficient in the proposed technique.

© 2007 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. A. Mahalanobis and F. Goudail, "Methods for automatic target recognition by use of electro-optic sensors: introduction to the feature issue," Appl. Opt. 43, 207-209 (2004).
    [CrossRef]
  2. P. Refregier, Noise Theory and Applications to Physics (Springer, 2004).
  3. F. A. Sadjadi, ed., Selected Papers on Automatic Target Recognition (SPIE-CDROM, 1999).
  4. B. Javidi, ed., Image Recognition and Classification: Algorithms, Systems, and Applications (Marcel Dekker, New York, 2002).
    [CrossRef]
  5. H. Kwon and N. M. Nasrabadi, "Kernel RX-algorithm: a nonlinear anomaly detector for hyperspectral imagery," IEEE Trans. Geosci. Remote Sens. 43, 388-397 (2005).
    [CrossRef]
  6. B. Javidi, ed., Optical Imaging Sensors and Systems for Homeland Security Applications (Springer, NewYork, 2005).
  7. R. O. Duda, P. E. Hart, and D. G. Stork, Pattern Classification 2nd ed. (Wiley Interscience, New York, 2001).
    [PubMed]
  8. K. Fukunaga, Introduction to Statistical Pattern Recognition 2nd ed. (Academic Press, Boston, 1990).
    [PubMed]
  9. C. M. Bishop, Neural Networks for Pattern Recognition (Oxford University Press, New York, 1995).
  10. D. L. Swets and J. Weng, "Using discriminant eigenfeatures for image retrieval," IEEE Trans. Pattern. Anal. Mach. Intell. 18, 831-836 (1996).
    [CrossRef]
  11. P. N. Belhumer, J. P. Hespanha, and D. J. Kriegman, "Eigenfaces vs. Fisherfaces: recognition using class specific linear projection," IEEE Trans. Pattern. Anal. Mach. Intell. 19, 711-720 (1997).
    [CrossRef]
  12. O. Matoba, E. Tajahuerce, and B. Javidi, "Real-time three-dimensional object recognition with multiple perspectives imaging," Appl. Opt. 40, 3318-3325 (2001).
    [CrossRef]
  13. Y. Frauel and B. Javidi, "Digital three-dimensional image correlation by use of computer-reconstructed integral imaging," Appl. Opt. 41, 5488-5496 (2002).
    [CrossRef] [PubMed]
  14. S. Kishk and B. Javidi, "Improved resolution 3D object sensing and recognition using time multiplexed computational integral imaging," Opt. Express 11, 3528-3541 (2003).
    [CrossRef] [PubMed]
  15. S. Yeom and B. Javidi, "Three-dimensional distortion tolerant object recognition using integral imaging," Opt. Express 12, 5795-5809 (2004).
    [CrossRef] [PubMed]
  16. 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]
  17. B. Javidi and F. Okano, eds., Three-dimensional Television, Video, and Display Technologies (Springer, New York, 2002).
  18. J.-S. Jang and B. Javidi, "Time-multiplexed integral imaging for 3D sensing and display," Optics and Photonics News 15, 36-43 (2004). http://www.osa-opn.org/abstract.cfm?URI=OPN-15-4-36.
  19. F. Okano, H. Hoshino, J. Arai, and I. Yuyama, "Real-time pickup method for a three-dimensional image based on integral photography," Appl. Opt. 36, 1598-1603 (1997).
    [CrossRef] [PubMed]
  20. M. Martínez-Corral, B. Javidi, R. Martínez-Cuenca, and G. Saavedra, "Multifacet structure of observed reconstructed integral images," J. Opt. Soc. Am. A. 22, 597-603 (2005).
    [CrossRef]
  21. E. Hecht, Optics 4th ed. (Addison Wesley, 2001).
    [PubMed]
  22. J. W. Goodman, Statistical Optics (Jonh Wiley & Sons Inc., 1985), Chap 9.
  23. G. M. Morris, "Scene matching using photon-limited images," J. Opt. Soc. Am. A. 1, 482-488 (1984).
    [CrossRef]
  24. G. M. Morris, "Image correlation at low light levels: a computer simulation," Appl. Opt. 23, 3152-3159 (1984).
    [CrossRef] [PubMed]
  25. E. A. Watson and G. M. Morris, "Comparison of infrared upconversion methods for photon-limited imaging," J. Appl. Phys. 67, 6075-6084 (1990).
    [CrossRef]
  26. E. A. Watson and G. M. Morris, "Imaging thermal objects with photon-counting detector," Appl. Opt. 31, 4751-4757 (1992).
    [CrossRef] [PubMed]
  27. M. N. Wernick and G. M. Morris, "Image classification at low light levels" J. Opt. Soc. Am. A. 3, 2179-2187 (1986).
    [CrossRef]
  28. L. A. Saaf and G. M. Morris, "Photon-limited image classification with a feedforward neural network," Appl. Opt. 34, 3963-3970 (1995).
    [CrossRef] [PubMed]
  29. D. Stucki, G. Ribordy, A. Stefanov, H. Zbinden, J. G. Rarity, and T. Wall, "Photon counting for quantum key distribution with Peltier cooled InGaAs/InP APDs," J. Mod. Opt. 48, 1967-1981 (2001).
    [CrossRef]
  30. P. A. Hiskett, G. S. Buller, A. Y. Loudon, J. M. Smith, I Gontijo, A. C. Walker, P. D. Townsend, and M. J. Robertson, "Performance and design of InGaAs/InP photodiodes for single-photon counting at 1.55 um," Appl. Opt. 39, 6818-6829 (2000).
    [CrossRef]
  31. L. Duraffourg, J.-M. Merolla, J.-P. Goedgebuer, N. Butterlin, and W. Rhods, "Photon counting in the 1540-nm wavelength region with a Germanium avalanche photodiode," IEEE J. Quantum Electron. 37, 75-79 (2001).
    [CrossRef]
  32. J. G. Rarity, T. E. Wall, K. D. Ridley, P. C. M. Owens, and P. R. Tapster, "Single-photon counting for the 1300-1600-nm range by use of Peltier-cooled and passively quenched InGaAs avalanche photodiodes," Appl. Opt. 39, 6746-6753 (2000).
    [CrossRef]
  33. M. Guillaume, P. Melon, and P. Refregier, "Maximum-likelihood estimation of an astronomical image from a sequence at low photon levels," J. Opt. Soc. Am. A. 15, 2841-2848 (1998).
    [CrossRef]
  34. K. E. Timmermann and R. D. Nowak, "Multiscale modeling and estimation of Poisson processes with application to photon-limited imaging," IEEE Trans. Infor. Theor. 45, 846-862 (1999).
    [CrossRef]
  35. Ph. Refregier, F. Goudail, and G. Delyon, "Photon noise effect on detection in coherent active images," Opt. Lett. 29, 162-164 (2004).
    [CrossRef] [PubMed]
  36. K-R. Muller, S. Mika, G. Ratsch, K. Tsuda, and B. Scholkopf, "An introduction to kernel-based learning algorithms," IEEE Trans. Neural Networks 12, 181-201 (2001).
    [CrossRef]
  37. A. Ruiz and P. E. Lopez-de-Teruel, "Nonlinear kernel-based statistical pattern analysis," IEEE Trans. Neural Networks 12, 16-32 (2001).
    [CrossRef]
  38. A. Papoulis, Probability, Random Variables, and Stochastic Processes 3rd ed. (McGraw-Hill, Inc. 1991).
    [PubMed]
  39. Y. Cheng, Y. Zhuang, and J. Yang, "Optimal Fisher discriminant analysis using the rank decomposition," Patt.Recog. 25, 101-111 (1992).
    [CrossRef]
  40. J. Schäfer and K. Strimmer, "A shrinkage approach to large-scale covariance matrix estimation and implications for functional genomics," Statistical applications in genetics and molecular biology,  4, 32.1-30 (2005).
    [CrossRef]
  41. S. M. Kay, Fundamentals of Statistical Signal Processing (Prentice Hall, New Jersey, 1993).
  42. N. Mukhopadhyay, Probability and Statistical Inference (Marcel Dekker, Inc. New York, 2000).
  43. N. Ravishanker and D. K. Dey, A First Course in Linear Model Theory (Chapman & Hall/CRC, 2002).

2005

H. Kwon and N. M. Nasrabadi, "Kernel RX-algorithm: a nonlinear anomaly detector for hyperspectral imagery," IEEE Trans. Geosci. Remote Sens. 43, 388-397 (2005).
[CrossRef]

M. Martínez-Corral, B. Javidi, R. Martínez-Cuenca, and G. Saavedra, "Multifacet structure of observed reconstructed integral images," J. Opt. Soc. Am. A. 22, 597-603 (2005).
[CrossRef]

J. Schäfer and K. Strimmer, "A shrinkage approach to large-scale covariance matrix estimation and implications for functional genomics," Statistical applications in genetics and molecular biology,  4, 32.1-30 (2005).
[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]

2004

2003

2002

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]

D. Stucki, G. Ribordy, A. Stefanov, H. Zbinden, J. G. Rarity, and T. Wall, "Photon counting for quantum key distribution with Peltier cooled InGaAs/InP APDs," J. Mod. Opt. 48, 1967-1981 (2001).
[CrossRef]

L. Duraffourg, J.-M. Merolla, J.-P. Goedgebuer, N. Butterlin, and W. Rhods, "Photon counting in the 1540-nm wavelength region with a Germanium avalanche photodiode," IEEE J. Quantum Electron. 37, 75-79 (2001).
[CrossRef]

K-R. Muller, S. Mika, G. Ratsch, K. Tsuda, and B. Scholkopf, "An introduction to kernel-based learning algorithms," IEEE Trans. Neural Networks 12, 181-201 (2001).
[CrossRef]

A. Ruiz and P. E. Lopez-de-Teruel, "Nonlinear kernel-based statistical pattern analysis," IEEE Trans. Neural Networks 12, 16-32 (2001).
[CrossRef]

2000

1999

K. E. Timmermann and R. D. Nowak, "Multiscale modeling and estimation of Poisson processes with application to photon-limited imaging," IEEE Trans. Infor. Theor. 45, 846-862 (1999).
[CrossRef]

1998

M. Guillaume, P. Melon, and P. Refregier, "Maximum-likelihood estimation of an astronomical image from a sequence at low photon levels," J. Opt. Soc. Am. A. 15, 2841-2848 (1998).
[CrossRef]

1997

P. N. Belhumer, J. P. Hespanha, and D. J. Kriegman, "Eigenfaces vs. Fisherfaces: recognition using class specific linear projection," IEEE Trans. Pattern. Anal. Mach. Intell. 19, 711-720 (1997).
[CrossRef]

F. Okano, H. Hoshino, J. Arai, and I. Yuyama, "Real-time pickup method for a three-dimensional image based on integral photography," Appl. Opt. 36, 1598-1603 (1997).
[CrossRef] [PubMed]

1996

D. L. Swets and J. Weng, "Using discriminant eigenfeatures for image retrieval," IEEE Trans. Pattern. Anal. Mach. Intell. 18, 831-836 (1996).
[CrossRef]

1995

1992

Y. Cheng, Y. Zhuang, and J. Yang, "Optimal Fisher discriminant analysis using the rank decomposition," Patt.Recog. 25, 101-111 (1992).
[CrossRef]

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

1990

E. A. Watson and G. M. Morris, "Comparison of infrared upconversion methods for photon-limited imaging," J. Appl. Phys. 67, 6075-6084 (1990).
[CrossRef]

1986

M. N. Wernick and G. M. Morris, "Image classification at low light levels" J. Opt. Soc. Am. A. 3, 2179-2187 (1986).
[CrossRef]

1984

G. M. Morris, "Image correlation at low light levels: a computer simulation," Appl. Opt. 23, 3152-3159 (1984).
[CrossRef] [PubMed]

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

Arai, J.

Belhumer, P. N.

P. N. Belhumer, J. P. Hespanha, and D. J. Kriegman, "Eigenfaces vs. Fisherfaces: recognition using class specific linear projection," IEEE Trans. Pattern. Anal. Mach. Intell. 19, 711-720 (1997).
[CrossRef]

Buller, G. S.

Butterlin, N.

L. Duraffourg, J.-M. Merolla, J.-P. Goedgebuer, N. Butterlin, and W. Rhods, "Photon counting in the 1540-nm wavelength region with a Germanium avalanche photodiode," IEEE J. Quantum Electron. 37, 75-79 (2001).
[CrossRef]

Cheng, Y.

Y. Cheng, Y. Zhuang, and J. Yang, "Optimal Fisher discriminant analysis using the rank decomposition," Patt.Recog. 25, 101-111 (1992).
[CrossRef]

Delyon, G.

Duraffourg, L.

L. Duraffourg, J.-M. Merolla, J.-P. Goedgebuer, N. Butterlin, and W. Rhods, "Photon counting in the 1540-nm wavelength region with a Germanium avalanche photodiode," IEEE J. Quantum Electron. 37, 75-79 (2001).
[CrossRef]

Frauel, Y.

Goedgebuer, J.-P.

L. Duraffourg, J.-M. Merolla, J.-P. Goedgebuer, N. Butterlin, and W. Rhods, "Photon counting in the 1540-nm wavelength region with a Germanium avalanche photodiode," IEEE J. Quantum Electron. 37, 75-79 (2001).
[CrossRef]

Gontijo, I

Goudail, F.

Guillaume, M.

M. Guillaume, P. Melon, and P. Refregier, "Maximum-likelihood estimation of an astronomical image from a sequence at low photon levels," J. Opt. Soc. Am. A. 15, 2841-2848 (1998).
[CrossRef]

Hespanha, J. P.

P. N. Belhumer, J. P. Hespanha, and D. J. Kriegman, "Eigenfaces vs. Fisherfaces: recognition using class specific linear projection," IEEE Trans. Pattern. Anal. Mach. Intell. 19, 711-720 (1997).
[CrossRef]

Hiskett, P. A.

Hoshino, H.

Javidi, B.

Kishk, S.

Kriegman, D. J.

P. N. Belhumer, J. P. Hespanha, and D. J. Kriegman, "Eigenfaces vs. Fisherfaces: recognition using class specific linear projection," IEEE Trans. Pattern. Anal. Mach. Intell. 19, 711-720 (1997).
[CrossRef]

Kwon, H.

H. Kwon and N. M. Nasrabadi, "Kernel RX-algorithm: a nonlinear anomaly detector for hyperspectral imagery," IEEE Trans. Geosci. Remote Sens. 43, 388-397 (2005).
[CrossRef]

Lopez-de-Teruel, P. E.

A. Ruiz and P. E. Lopez-de-Teruel, "Nonlinear kernel-based statistical pattern analysis," IEEE Trans. Neural Networks 12, 16-32 (2001).
[CrossRef]

Loudon, A. Y.

Mahalanobis, A.

Martínez-Corral, M.

M. Martínez-Corral, B. Javidi, R. Martínez-Cuenca, and G. Saavedra, "Multifacet structure of observed reconstructed integral images," J. Opt. Soc. Am. A. 22, 597-603 (2005).
[CrossRef]

Martínez-Cuenca, R.

M. Martínez-Corral, B. Javidi, R. Martínez-Cuenca, and G. Saavedra, "Multifacet structure of observed reconstructed integral images," J. Opt. Soc. Am. A. 22, 597-603 (2005).
[CrossRef]

Matoba, O.

Melon, P.

M. Guillaume, P. Melon, and P. Refregier, "Maximum-likelihood estimation of an astronomical image from a sequence at low photon levels," J. Opt. Soc. Am. A. 15, 2841-2848 (1998).
[CrossRef]

Merolla, J.-M.

L. Duraffourg, J.-M. Merolla, J.-P. Goedgebuer, N. Butterlin, and W. Rhods, "Photon counting in the 1540-nm wavelength region with a Germanium avalanche photodiode," IEEE J. Quantum Electron. 37, 75-79 (2001).
[CrossRef]

Mika, S.

K-R. Muller, S. Mika, G. Ratsch, K. Tsuda, and B. Scholkopf, "An introduction to kernel-based learning algorithms," IEEE Trans. Neural Networks 12, 181-201 (2001).
[CrossRef]

Morris, G. M.

L. A. Saaf and G. M. Morris, "Photon-limited image classification with a feedforward neural network," Appl. Opt. 34, 3963-3970 (1995).
[CrossRef] [PubMed]

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

E. A. Watson and G. M. Morris, "Comparison of infrared upconversion methods for photon-limited imaging," J. Appl. Phys. 67, 6075-6084 (1990).
[CrossRef]

M. N. Wernick and G. M. Morris, "Image classification at low light levels" J. Opt. Soc. Am. A. 3, 2179-2187 (1986).
[CrossRef]

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

G. M. Morris, "Image correlation at low light levels: a computer simulation," Appl. Opt. 23, 3152-3159 (1984).
[CrossRef] [PubMed]

Muller, K-R.

K-R. Muller, S. Mika, G. Ratsch, K. Tsuda, and B. Scholkopf, "An introduction to kernel-based learning algorithms," IEEE Trans. Neural Networks 12, 181-201 (2001).
[CrossRef]

Nasrabadi, N. M.

H. Kwon and N. M. Nasrabadi, "Kernel RX-algorithm: a nonlinear anomaly detector for hyperspectral imagery," IEEE Trans. Geosci. Remote Sens. 43, 388-397 (2005).
[CrossRef]

Nowak, R. D.

K. E. Timmermann and R. D. Nowak, "Multiscale modeling and estimation of Poisson processes with application to photon-limited imaging," IEEE Trans. Infor. Theor. 45, 846-862 (1999).
[CrossRef]

Okano, F.

Owens, P. C. M.

Rarity, J. G.

D. Stucki, G. Ribordy, A. Stefanov, H. Zbinden, J. G. Rarity, and T. Wall, "Photon counting for quantum key distribution with Peltier cooled InGaAs/InP APDs," J. Mod. Opt. 48, 1967-1981 (2001).
[CrossRef]

J. G. Rarity, T. E. Wall, K. D. Ridley, P. C. M. Owens, and P. R. Tapster, "Single-photon counting for the 1300-1600-nm range by use of Peltier-cooled and passively quenched InGaAs avalanche photodiodes," Appl. Opt. 39, 6746-6753 (2000).
[CrossRef]

Ratsch, G.

K-R. Muller, S. Mika, G. Ratsch, K. Tsuda, and B. Scholkopf, "An introduction to kernel-based learning algorithms," IEEE Trans. Neural Networks 12, 181-201 (2001).
[CrossRef]

Refregier, P.

M. Guillaume, P. Melon, and P. Refregier, "Maximum-likelihood estimation of an astronomical image from a sequence at low photon levels," J. Opt. Soc. Am. A. 15, 2841-2848 (1998).
[CrossRef]

Refregier, Ph.

Rhods, W.

L. Duraffourg, J.-M. Merolla, J.-P. Goedgebuer, N. Butterlin, and W. Rhods, "Photon counting in the 1540-nm wavelength region with a Germanium avalanche photodiode," IEEE J. Quantum Electron. 37, 75-79 (2001).
[CrossRef]

Ribordy, G.

D. Stucki, G. Ribordy, A. Stefanov, H. Zbinden, J. G. Rarity, and T. Wall, "Photon counting for quantum key distribution with Peltier cooled InGaAs/InP APDs," J. Mod. Opt. 48, 1967-1981 (2001).
[CrossRef]

Ridley, K. D.

Robertson, M. J.

Ruiz, A.

A. Ruiz and P. E. Lopez-de-Teruel, "Nonlinear kernel-based statistical pattern analysis," IEEE Trans. Neural Networks 12, 16-32 (2001).
[CrossRef]

Saaf, L. A.

Saavedra, G.

M. Martínez-Corral, B. Javidi, R. Martínez-Cuenca, and G. Saavedra, "Multifacet structure of observed reconstructed integral images," J. Opt. Soc. Am. A. 22, 597-603 (2005).
[CrossRef]

Schäfer, J.

J. Schäfer and K. Strimmer, "A shrinkage approach to large-scale covariance matrix estimation and implications for functional genomics," Statistical applications in genetics and molecular biology,  4, 32.1-30 (2005).
[CrossRef]

Scholkopf, B.

K-R. Muller, S. Mika, G. Ratsch, K. Tsuda, and B. Scholkopf, "An introduction to kernel-based learning algorithms," IEEE Trans. Neural Networks 12, 181-201 (2001).
[CrossRef]

Smith, J. M.

Stefanov, A.

D. Stucki, G. Ribordy, A. Stefanov, H. Zbinden, J. G. Rarity, and T. Wall, "Photon counting for quantum key distribution with Peltier cooled InGaAs/InP APDs," J. Mod. Opt. 48, 1967-1981 (2001).
[CrossRef]

Strimmer, K.

J. Schäfer and K. Strimmer, "A shrinkage approach to large-scale covariance matrix estimation and implications for functional genomics," Statistical applications in genetics and molecular biology,  4, 32.1-30 (2005).
[CrossRef]

Stucki, D.

D. Stucki, G. Ribordy, A. Stefanov, H. Zbinden, J. G. Rarity, and T. Wall, "Photon counting for quantum key distribution with Peltier cooled InGaAs/InP APDs," J. Mod. Opt. 48, 1967-1981 (2001).
[CrossRef]

Swets, D. L.

D. L. Swets and J. Weng, "Using discriminant eigenfeatures for image retrieval," IEEE Trans. Pattern. Anal. Mach. Intell. 18, 831-836 (1996).
[CrossRef]

Tajahuerce, E.

Tapster, P. R.

Timmermann, K. E.

K. E. Timmermann and R. D. Nowak, "Multiscale modeling and estimation of Poisson processes with application to photon-limited imaging," IEEE Trans. Infor. Theor. 45, 846-862 (1999).
[CrossRef]

Townsend, P. D.

Tsuda, K.

K-R. Muller, S. Mika, G. Ratsch, K. Tsuda, and B. Scholkopf, "An introduction to kernel-based learning algorithms," IEEE Trans. Neural Networks 12, 181-201 (2001).
[CrossRef]

Walker, A. C.

Wall, T.

D. Stucki, G. Ribordy, A. Stefanov, H. Zbinden, J. G. Rarity, and T. Wall, "Photon counting for quantum key distribution with Peltier cooled InGaAs/InP APDs," J. Mod. Opt. 48, 1967-1981 (2001).
[CrossRef]

Wall, T. E.

Watson, E.

Watson, E. A.

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

E. A. Watson and G. M. Morris, "Comparison of infrared upconversion methods for photon-limited imaging," J. Appl. Phys. 67, 6075-6084 (1990).
[CrossRef]

Weng, J.

D. L. Swets and J. Weng, "Using discriminant eigenfeatures for image retrieval," IEEE Trans. Pattern. Anal. Mach. Intell. 18, 831-836 (1996).
[CrossRef]

Wernick, M. N.

M. N. Wernick and G. M. Morris, "Image classification at low light levels" J. Opt. Soc. Am. A. 3, 2179-2187 (1986).
[CrossRef]

Yang, J.

Y. Cheng, Y. Zhuang, and J. Yang, "Optimal Fisher discriminant analysis using the rank decomposition," Patt.Recog. 25, 101-111 (1992).
[CrossRef]

Yeom, S.

Yuyama, I.

Zbinden, H.

D. Stucki, G. Ribordy, A. Stefanov, H. Zbinden, J. G. Rarity, and T. Wall, "Photon counting for quantum key distribution with Peltier cooled InGaAs/InP APDs," J. Mod. Opt. 48, 1967-1981 (2001).
[CrossRef]

Zhuang, Y.

Y. Cheng, Y. Zhuang, and J. Yang, "Optimal Fisher discriminant analysis using the rank decomposition," Patt.Recog. 25, 101-111 (1992).
[CrossRef]

Appl. Opt.

G. M. Morris, "Image correlation at low light levels: a computer simulation," Appl. Opt. 23, 3152-3159 (1984).
[CrossRef] [PubMed]

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

F. Okano, H. Hoshino, J. Arai, and I. Yuyama, "Real-time pickup method for a three-dimensional image based on integral photography," Appl. Opt. 36, 1598-1603 (1997).
[CrossRef] [PubMed]

L. A. Saaf and G. M. Morris, "Photon-limited image classification with a feedforward neural network," Appl. Opt. 34, 3963-3970 (1995).
[CrossRef] [PubMed]

J. G. Rarity, T. E. Wall, K. D. Ridley, P. C. M. Owens, and P. R. Tapster, "Single-photon counting for the 1300-1600-nm range by use of Peltier-cooled and passively quenched InGaAs avalanche photodiodes," Appl. Opt. 39, 6746-6753 (2000).
[CrossRef]

P. A. Hiskett, G. S. Buller, A. Y. Loudon, J. M. Smith, I Gontijo, A. C. Walker, P. D. Townsend, and M. J. Robertson, "Performance and design of InGaAs/InP photodiodes for single-photon counting at 1.55 um," Appl. Opt. 39, 6818-6829 (2000).
[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]

Y. Frauel and B. Javidi, "Digital three-dimensional image correlation by use of computer-reconstructed integral imaging," Appl. Opt. 41, 5488-5496 (2002).
[CrossRef] [PubMed]

A. Mahalanobis and F. Goudail, "Methods for automatic target recognition by use of electro-optic sensors: introduction to the feature issue," Appl. Opt. 43, 207-209 (2004).
[CrossRef]

IEEE J. Quantum Electron.

L. Duraffourg, J.-M. Merolla, J.-P. Goedgebuer, N. Butterlin, and W. Rhods, "Photon counting in the 1540-nm wavelength region with a Germanium avalanche photodiode," IEEE J. Quantum Electron. 37, 75-79 (2001).
[CrossRef]

IEEE Trans. Geosci. Remote Sens.

H. Kwon and N. M. Nasrabadi, "Kernel RX-algorithm: a nonlinear anomaly detector for hyperspectral imagery," IEEE Trans. Geosci. Remote Sens. 43, 388-397 (2005).
[CrossRef]

IEEE Trans. Infor. Theor.

K. E. Timmermann and R. D. Nowak, "Multiscale modeling and estimation of Poisson processes with application to photon-limited imaging," IEEE Trans. Infor. Theor. 45, 846-862 (1999).
[CrossRef]

IEEE Trans. Neural Networks

K-R. Muller, S. Mika, G. Ratsch, K. Tsuda, and B. Scholkopf, "An introduction to kernel-based learning algorithms," IEEE Trans. Neural Networks 12, 181-201 (2001).
[CrossRef]

A. Ruiz and P. E. Lopez-de-Teruel, "Nonlinear kernel-based statistical pattern analysis," IEEE Trans. Neural Networks 12, 16-32 (2001).
[CrossRef]

IEEE Trans. Pattern. Anal. Mach. Intell.

D. L. Swets and J. Weng, "Using discriminant eigenfeatures for image retrieval," IEEE Trans. Pattern. Anal. Mach. Intell. 18, 831-836 (1996).
[CrossRef]

P. N. Belhumer, J. P. Hespanha, and D. J. Kriegman, "Eigenfaces vs. Fisherfaces: recognition using class specific linear projection," IEEE Trans. Pattern. Anal. Mach. Intell. 19, 711-720 (1997).
[CrossRef]

J. Appl. Phys.

E. A. Watson and G. M. Morris, "Comparison of infrared upconversion methods for photon-limited imaging," J. Appl. Phys. 67, 6075-6084 (1990).
[CrossRef]

J. Mod. Opt.

D. Stucki, G. Ribordy, A. Stefanov, H. Zbinden, J. G. Rarity, and T. Wall, "Photon counting for quantum key distribution with Peltier cooled InGaAs/InP APDs," J. Mod. Opt. 48, 1967-1981 (2001).
[CrossRef]

J. Opt. Soc. Am. A.

M. N. Wernick and G. M. Morris, "Image classification at low light levels" J. Opt. Soc. Am. A. 3, 2179-2187 (1986).
[CrossRef]

M. Guillaume, P. Melon, and P. Refregier, "Maximum-likelihood estimation of an astronomical image from a sequence at low photon levels," J. Opt. Soc. Am. A. 15, 2841-2848 (1998).
[CrossRef]

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

M. Martínez-Corral, B. Javidi, R. Martínez-Cuenca, and G. Saavedra, "Multifacet structure of observed reconstructed integral images," J. Opt. Soc. Am. A. 22, 597-603 (2005).
[CrossRef]

Opt. Express

Opt. Lett.

Recog.

Y. Cheng, Y. Zhuang, and J. Yang, "Optimal Fisher discriminant analysis using the rank decomposition," Patt.Recog. 25, 101-111 (1992).
[CrossRef]

Statistical applications in genetics and molecular biology

J. Schäfer and K. Strimmer, "A shrinkage approach to large-scale covariance matrix estimation and implications for functional genomics," Statistical applications in genetics and molecular biology,  4, 32.1-30 (2005).
[CrossRef]

Other

S. M. Kay, Fundamentals of Statistical Signal Processing (Prentice Hall, New Jersey, 1993).

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

N. Ravishanker and D. K. Dey, A First Course in Linear Model Theory (Chapman & Hall/CRC, 2002).

A. Papoulis, Probability, Random Variables, and Stochastic Processes 3rd ed. (McGraw-Hill, Inc. 1991).
[PubMed]

E. Hecht, Optics 4th ed. (Addison Wesley, 2001).
[PubMed]

J. W. Goodman, Statistical Optics (Jonh Wiley & Sons Inc., 1985), Chap 9.

B. Javidi, ed., Optical Imaging Sensors and Systems for Homeland Security Applications (Springer, NewYork, 2005).

R. O. Duda, P. E. Hart, and D. G. Stork, Pattern Classification 2nd ed. (Wiley Interscience, New York, 2001).
[PubMed]

K. Fukunaga, Introduction to Statistical Pattern Recognition 2nd ed. (Academic Press, Boston, 1990).
[PubMed]

C. M. Bishop, Neural Networks for Pattern Recognition (Oxford University Press, New York, 1995).

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

J.-S. Jang and B. Javidi, "Time-multiplexed integral imaging for 3D sensing and display," Optics and Photonics News 15, 36-43 (2004). http://www.osa-opn.org/abstract.cfm?URI=OPN-15-4-36.

P. Refregier, Noise Theory and Applications to Physics (Springer, 2004).

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

B. Javidi, ed., Image Recognition and Classification: Algorithms, Systems, and Applications (Marcel Dekker, New York, 2002).
[CrossRef]

Supplementary Material (3)

» Media 1: AVI (3678 KB)     
» Media 2: AVI (3678 KB)     
» Media 3: AVI (3678 KB)     

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (16)

Fig. 1.
Fig. 1.

A schematic diagram of the photon-counting II system for the distortion-tolerant object recognition.

Fig. 2.
Fig. 2.

(a) II sensing process, (b) II display process

Fig. 3.
Fig. 3.

Multiple perspective imaging in ray optics: each elemental image records the point A at the pixels which are located differently to its own optical axes (O1~O3) by rays 2,3,4, however, the same directional (parallel) information (rays 1,3,5) is recorded at the pixels of the same relative location.

Fig. 4.
Fig. 4.

Three toy cars used in the experiments; they represent class 1, 2 and 3 from right to left.

Fig. 5.
Fig. 5.

Movies of integral images of three objects with the out-of-plane rotation, (a) (the movie file size: 3.64 MB) class 1, [Media 1] (b) (the movie file size: 3.64 MB) class 2, [Media 2] (c) (the movie file size: 3.64 MB) class 3. [Media 3]

Fig. 6.
Fig. 6.

Classification results when the mean photon number in the test scene is 90. (a) averaged correct classification rate for each class over 1000 runs, (b) averaged false classification rate for each class over 1000 runs. ‘Avg’ denotes the average value of 6 rotation angles.

Fig. 7.
Fig. 7.

Classification results when the mean photon number in the test scene is 150. (a) averaged correct classification rate for each class over 1000 runs, (b) averaged false classification rate for each class over 1000 runs. ‘Avg’ denotes the average value of 6 rotation angles.

Fig. 8.
Fig. 8.

Classification results when the mean photon number in the test scene is 300. (a) averaged correct classification rate for each class over 1000 runs, (b) averaged false classification rate for each class over 1000 runs. ‘Avg’ denotes the average value of 6 rotation angles.

Fig. 9.
Fig. 9.

An example of the test input scene corresponding to class 1 with the rotation angle 30°, the mean photon number in the test scene is 300, and the actual number of photon-counts in this scene is 289.

Fig. 10.
Fig. 10.

MSD in Eq. (36) when (a) j = 1, (b) j = 2, (c) j = 3.

Fig. 11.
Fig. 11.

Classification results when the mean photon number in the test scene is 150, Eq. (28) is used for the within-class covariance estimation, (a) averaged correct classification rate for each class over 1000 runs, (b) averaged false classification rate for each class over 1000 runs, ‘Avg’ denotes the average value of 6 rotation angles.

Fig. 12.
Fig. 12.

Classification results when the mean photon number in the test scene is 300, (a) averaged correct classification rate for each class over 1000 runs, (b) averaged false classification rate for each class over 1000 runs, ‘Avg’ denotes the average value of 6 rotation angles.

Fig. 13.
Fig. 13.

MSD in Eq. (36) when (a) j = 1, (b) j = 2, (c) j = 3.

Fig. 14.
Fig. 14.

Classification results when the mean photon number in the test scene is 300, Eq. (28) is used for the within-class covariance estimation, (a) averaged correct classification rate for each class over 1000 runs, (b) averaged false classification rate for each class over 1000 runs, ‘Avg’ denotes the average value of 6 rotation angles.

Fig. 15.
Fig. 15.

Classification results when the average irradiance is increased by 50 only for the test images, (a) averaged correct classification rates versus the mean photon numbers, (b) averaged false classification rates versus the mean photon numbers.

Fig. 16.
Fig. 16.

Classification results when the average irradiance is increased by 50 only for the test images, Eq. (28) is used for the within-class covariance estimation, (a) averaged correct classification rates versus the mean photon numbers, (b) averaged false classification rates versus the mean photon numbers.

Equations (71)

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

P d ( y ) = [ ] y e y ! , y = 0,1,2 , . . . ,
a = η P o h ν ˉ ,
n p = E y ( y ) = = η P o h ν ˉ τ ,
P d ( y i ; n p ( i ) ) = n p ( i ) y i e n p ( i ) y i ! , y i = 0,1,2 , . . . ,
n p ( i ) = N P x i ,
y = [ y 1 y N T ] t ,
μ y x = E y x ( y x ) = N p x = N p [ x 1 x N T ] t ,
Σ y y x = E y x [ ( y μ y x ) ( y μ y x ) t | x ] = diag ( μ y x ) = N p diag ( x ) ,
Σ xx W = E w j { E x w j [ ( x μ x w j ) ( x μ x w j ) t w j ] } ,
μ x | w j = E x | w j ( x | w j ) .
xx B = E w j [ ( μ x | w j μ x ) ( μ x w j μ x ) t ] ,
μ x = E x ( x ) .
xx = E x [ ( x μ x ) ( x μ x ) t ] .
z = W F t x ,
W F = arg max W R d × r W t xx B W W t xx W W .
μ y = N p μ x ,
yy = N p diag ( μ x ) + N p 2 xx .
yy W = N p diag ( μ x ) + N p 2 xx W ,
yy B = N p 2 xx B .
z = W p t y ,
W p = arg max W R d × r W t yy B W W t yy W W
= arg max W R d × r W t xx B W W t [ diag ( μ x ) N p + xx W ] W .
̂ xx W = 1 n t j = 1 n c n = 1 n j ( x j ( n ) μ ̂ x w j ) ( x j ( n ) μ ̂ x w j ) t ,
μ ̂ x w j = 1 n j n = 1 n j x j ( n ) .
̂ xx B = 1 n t j = 1 n c n j ( μ ̂ x w j μ ̂ x ) ( μ ̂ x w j μ ̂ x ) t ,
μ ̂ x = 1 n t j = 1 n c n = 1 n j x j ( n ) .
̂ yy B = N p 2 ̂ xx B ,
̂ yy W = N p diag ( μ ̂ x ) + N p 2 xx W .
̂ yy W N p diag ( μ ̂ x ) + N p 2 diag ( [ σ ̂ W , 1 2 σ ̂ W , d 2 ] t ) ,
σ ̂ W , i 2 = 1 n t j = 1 n c n = 1 n j x j , i ( n ) μ ̂ x | w j , i 2 ,
z test = W p t n = 1 n test y test ( n ) ,
j ̂ = arg min j = 1 , , n c z test μ ̂ z w j ,
μ ̂ z w j = n test W p t μ ̂ y w j
= n test N p W p t μ ̂ x w j .
r c ( j ) = Number of decision for class j Number of test images in class j ,
r f ( j ) = Number of decision for class j , but are not in class j Number of test images in all classes except for class j .
MSD ( j ; s , i s ) = E x j x test ( s , i s ) 2 ,
M S ̂ D ( j ; s , i s ) = 1 n j n test n = 1 n j m = 1 n test x j ( n ) x test ( m ; s , i s ) 2 ,
μ y = E x [ E y x ( y x ) ]
= E x ( N p x )
= N p μ x ,
μ y | w j = N p μ x | w j .
Σ yy = E y [ ( y μ y ) ( y μ y ) t ]
= E x { E y x [ ( y μ y ) ( y μ y ) t x ] }
= E x { E y x [ yy t μ y μ y t x ] }
= E x [ E y x ( yy t x ) ] N p 2 μ x μ x t
= N p diag ( μ x ) + N p 2 E x ( xx t ) N p 2 μ x μ x t
= N p diag ( μ x ) + N p 2 Σ xx .
Σ yy w j = E y w j [ ( y μ y w j ) ( y μ y w j ) t w j ]
= N p diag ( μ x w j ) + N p 2 Σ xx w j .
Σ yy W = E w j ( E y w j [ ( y μ y w j ) ( y μ y w j ) t | w j ] )
= E w j [ N p diag ( μ x w j ) + N p 2 Σ xx w j ]
= N p diag ( μ x ) + N p 2 Σ xx W ,
Σ yy B = E w j [ ( μ y w j μ y ) ( μ y w j μ y ) t ] ,
= N p 2 E w j [ ( μ x w j μ x ) ( μ x w j μ x ) t ]
= N p 2 Σ xx B ,
μ ̂ x w j = 1 n j n = 1 n j x j ( n ) ,
Σ ̂ xx w j = 1 n j n = 1 n j ( x j ( n ) μ ̂ x w j ) ( x j ( n ) μ ̂ x w j ) t .
xx W = W w j { E x w j [ ( x μ x w j ) ( x μ x w j ) t w j ] }
= j = 1 n c π j Σ xx w j ,
π j = n j n t .
Σ ̂ xx W = j = 1 n c π j Σ ̂ xx | w j
= 1 n t j = 1 n c n = 1 n j ( x j ( n ) μ ̂ x | w j ) ( x j ( n ) μ ̂ x | w j ) t .
μ x = E w j [ E x | w j ( x w j ) ]
= j = 1 n c π j μ x | w j ,
Σ xx B = E w j [ ( μ x w j μ x ) ( μ x w j μ x ) t ]
= j = 1 n c π j ( μ x w j μ x ) ( μ x w j μ x ) t .
μ ̂ x = j = 1 w j π j μ ̂ x w j
= 1 n t j = 1 n c n n j x j ( n ) ,
Σ ̂ xx B = j = 1 n c π j ( μ ̂ x w j μ ̂ x ) ( μ ̂ x w j μ ̂ x ) t
= 1 n t j = 1 n c n j ( μ ̂ x w j μ ̂ x ) ( μ ̂ x w j μ ̂ x ) t .

Metrics