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 photonlimited 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 distortiontolerant 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

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2005 (4)

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).

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]

2004 (3)

2003 (1)

2002 (1)

2001 (5)

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

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).

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 (2)

1999 (1)

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).

1998 (1)

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).

1997 (2)

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).

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).

1996 (1)

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

1995 (1)

1992 (2)

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

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

1990 (1)

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 (1)

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

1984 (2)

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

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

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).

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).

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).

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).

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).

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).

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).

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).

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

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).

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

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

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).

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).

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).

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).

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).

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).

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).

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).

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).

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).

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).

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).

Yang, J.

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

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).

Zhuang, Y.

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

Appl. Opt. (9)

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

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

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).

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

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).

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).

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

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

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. (1)

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Supplementary Material (3)

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