Abstract

An optical network is described that is capable of recognizing at standard video rates the identity of faces for which it has been trained. The faces are presented under a wide variety of conditions to the system and the classification performance is measured. The system is trained by gradually adapting photorefractive holograms.

© 1993 Optical Society of America

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  1. K. Wagner, D. Psaltis, “Multilayer optical learning networks,” Appl. Opt. 26, 5061–5076 (1987).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  3. D. Psaltis, D. Brady, K. Wagner, “Adaptive optical networks using photorefractive crystals,” Appl. Opt. 27, 1752–1759 (1988).
    [CrossRef]
  4. Y. Qiao, D. Psaltis, “Local learning algorithm for optical neural networks,” Appl. Opt. 31, 3285–3288 (1992).
    [CrossRef] [PubMed]
  5. D. Psaltis, D. Brady, X.-G. Gu, S. Lin, “Holography in artificial neural networks,” Nature 343: 325–330 (1990).
    [CrossRef] [PubMed]
  6. H. Yoshinaga, K. Kitayama, T. Hara, “All-optical error-signal generation for backpropagation learning in optical multilayer neural networks,” Opt. Lett. 14, 202–204 (1989).
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  8. M. A. Neifeld, D. Psaltis, “Optical implementation of radial basis classifiers,” Appl. Opt. 32, 1370–1379 (1993).
    [CrossRef] [PubMed]
  9. D. Brady, K. Hsu, D. Psaltis, “Periodically refreshed multiply exposed photorefractive holograms,” Opt. Lett. 15, 817–819 (1990).
    [CrossRef] [PubMed]
  10. Y. Qiao, D. Psaltis, C. Gu, J. Hong, P. Yeh, “Phase-locked sustainment of photorefractive holograms using phase conjugation,” J. Appl. Phys. 70, 4646–4648 (1991).
    [CrossRef]
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    [CrossRef]
  14. J. Yu, F. Mok, D. Psaltis, “Capacity of optical correlators,” in Spatial Light Modulators and Applications II, U. Efron, ed., Proc. Soc. Photo-Opt. Instrum. Eng.825, 114–120 (1987).
  15. C. Gu, J. Hong, S. Cambell, “2-D shift-invariant volume holographic,” Opt. Comm. 88, 309–314 (1992).
    [CrossRef]
  16. M. A. Neifeld, D. Psaltis, “Optical implementations of radial basis classifiers,” Appl. Opt. 32, 1370–1379 (1993).
    [CrossRef] [PubMed]
  17. C. L. Giles, T. Maxwell, “Learning, invariance, and generalization in high-order neural networks,” Appl. Opt. 26, 4972–4978 (1987).
    [CrossRef] [PubMed]
  18. D. Psaltis, C. H. Park, J. Hong, “Higher-order associative memories and their optical implementations,” Neural Net. 1, 149–163 (1988).
    [CrossRef]
  19. M. Mezard, J. P. Nadal, “Learning in feedforward layered networks—the tiling algorithm,” J. Phys. A 22, 2191–2203 (1989).
    [CrossRef]
  20. K. BløtekJaer, “Limitations on holographic storage capacity of photochromic and photorefractive media,” Appl. Opt. 18, 57–67 (1979).
    [CrossRef] [PubMed]
  21. Y. Taketomi, J. E. Ford, H. Sasaki, J. Ma, Y. Fainman, S. H. Lee, “Incremental recording for photorefractive hologram multiplexing,” Opt. Lett. 16, 1774–1776 (1991).
    [CrossRef] [PubMed]
  22. F. Mok, “Applications of holographic storage in lithium niobate,” in Annual Meeting, Vol. 23 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), p. 102.
  23. D. L. Staebler, W. J. Burke, W. Phillips, J. J. Amodei, “Multiple storage and erasure of fixed holograms in Fe-doped LiNbO3,” Appl. Phys. Lett. 26, 182–184 (1975).
    [CrossRef]

1993 (2)

1992 (3)

1991 (3)

1990 (2)

D. Brady, K. Hsu, D. Psaltis, “Periodically refreshed multiply exposed photorefractive holograms,” Opt. Lett. 15, 817–819 (1990).
[CrossRef] [PubMed]

D. Psaltis, D. Brady, X.-G. Gu, S. Lin, “Holography in artificial neural networks,” Nature 343: 325–330 (1990).
[CrossRef] [PubMed]

1989 (2)

1988 (2)

D. Psaltis, D. Brady, K. Wagner, “Adaptive optical networks using photorefractive crystals,” Appl. Opt. 27, 1752–1759 (1988).
[CrossRef]

D. Psaltis, C. H. Park, J. Hong, “Higher-order associative memories and their optical implementations,” Neural Net. 1, 149–163 (1988).
[CrossRef]

1987 (3)

1979 (1)

1975 (1)

D. L. Staebler, W. J. Burke, W. Phillips, J. J. Amodei, “Multiple storage and erasure of fixed holograms in Fe-doped LiNbO3,” Appl. Phys. Lett. 26, 182–184 (1975).
[CrossRef]

1964 (1)

A.B. VanderLugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory IT-10, 139–145 (1964).
[CrossRef]

Amodei, J. J.

D. L. Staebler, W. J. Burke, W. Phillips, J. J. Amodei, “Multiple storage and erasure of fixed holograms in Fe-doped LiNbO3,” Appl. Phys. Lett. 26, 182–184 (1975).
[CrossRef]

BløtekJaer, K.

Boj, S.

Brady, D.

Burke, W. J.

D. L. Staebler, W. J. Burke, W. Phillips, J. J. Amodei, “Multiple storage and erasure of fixed holograms in Fe-doped LiNbO3,” Appl. Phys. Lett. 26, 182–184 (1975).
[CrossRef]

Cambell, S.

C. Gu, J. Hong, S. Cambell, “2-D shift-invariant volume holographic,” Opt. Comm. 88, 309–314 (1992).
[CrossRef]

Dunning, G. J.

Fainman, Y.

Ford, J. E.

Giles, C. L.

Gu, C.

C. Gu, J. Hong, S. Cambell, “2-D shift-invariant volume holographic,” Opt. Comm. 88, 309–314 (1992).
[CrossRef]

Y. Qiao, D. Psaltis, C. Gu, J. Hong, P. Yeh, “Phase-locked sustainment of photorefractive holograms using phase conjugation,” J. Appl. Phys. 70, 4646–4648 (1991).
[CrossRef]

Gu, X.-G.

D. Psaltis, D. Brady, X.-G. Gu, S. Lin, “Holography in artificial neural networks,” Nature 343: 325–330 (1990).
[CrossRef] [PubMed]

Hara, T.

Hinton, G. E.

D. E. Rumelhart, G. E. Hinton, R. J. Williams, “Learning internal representations by error propagation,” in Parallel Distributed Processing, D. E. Rumelhart, J. L. McClelland eds. (MIT, Cambridge, Mass., 1986), Vol. 1, Chap. 8.

Hong, J.

C. Gu, J. Hong, S. Cambell, “2-D shift-invariant volume holographic,” Opt. Comm. 88, 309–314 (1992).
[CrossRef]

Y. Qiao, D. Psaltis, C. Gu, J. Hong, P. Yeh, “Phase-locked sustainment of photorefractive holograms using phase conjugation,” J. Appl. Phys. 70, 4646–4648 (1991).
[CrossRef]

D. Psaltis, C. H. Park, J. Hong, “Higher-order associative memories and their optical implementations,” Neural Net. 1, 149–163 (1988).
[CrossRef]

Hsu, K.

Kitayama, K.

Lee, S. H.

Lin, S.

D. Psaltis, D. Brady, X.-G. Gu, S. Lin, “Holography in artificial neural networks,” Nature 343: 325–330 (1990).
[CrossRef] [PubMed]

Ma, J.

Marom, E.

Maxwell, T.

Mezard, M.

M. Mezard, J. P. Nadal, “Learning in feedforward layered networks—the tiling algorithm,” J. Phys. A 22, 2191–2203 (1989).
[CrossRef]

Mok, F.

J. Yu, F. Mok, D. Psaltis, “Capacity of optical correlators,” in Spatial Light Modulators and Applications II, U. Efron, ed., Proc. Soc. Photo-Opt. Instrum. Eng.825, 114–120 (1987).

F. Mok, “Applications of holographic storage in lithium niobate,” in Annual Meeting, Vol. 23 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), p. 102.

Nadal, J. P.

M. Mezard, J. P. Nadal, “Learning in feedforward layered networks—the tiling algorithm,” J. Phys. A 22, 2191–2203 (1989).
[CrossRef]

Neifeld, M. A.

Owechko, Y.

Park, C. H.

D. Psaltis, C. H. Park, J. Hong, “Higher-order associative memories and their optical implementations,” Neural Net. 1, 149–163 (1988).
[CrossRef]

Pauliat, G.

Phillips, W.

D. L. Staebler, W. J. Burke, W. Phillips, J. J. Amodei, “Multiple storage and erasure of fixed holograms in Fe-doped LiNbO3,” Appl. Phys. Lett. 26, 182–184 (1975).
[CrossRef]

Psaltis, D.

M. A. Neifeld, D. Psaltis, “Optical implementations of radial basis classifiers,” Appl. Opt. 32, 1370–1379 (1993).
[CrossRef] [PubMed]

M. A. Neifeld, D. Psaltis, “Optical implementation of radial basis classifiers,” Appl. Opt. 32, 1370–1379 (1993).
[CrossRef] [PubMed]

Y. Qiao, D. Psaltis, “Local learning algorithm for optical neural networks,” Appl. Opt. 31, 3285–3288 (1992).
[CrossRef] [PubMed]

Y. Qiao, D. Psaltis, C. Gu, J. Hong, P. Yeh, “Phase-locked sustainment of photorefractive holograms using phase conjugation,” J. Appl. Phys. 70, 4646–4648 (1991).
[CrossRef]

D. Brady, K. Hsu, D. Psaltis, “Periodically refreshed multiply exposed photorefractive holograms,” Opt. Lett. 15, 817–819 (1990).
[CrossRef] [PubMed]

D. Psaltis, D. Brady, X.-G. Gu, S. Lin, “Holography in artificial neural networks,” Nature 343: 325–330 (1990).
[CrossRef] [PubMed]

D. Psaltis, D. Brady, K. Wagner, “Adaptive optical networks using photorefractive crystals,” Appl. Opt. 27, 1752–1759 (1988).
[CrossRef]

D. Psaltis, C. H. Park, J. Hong, “Higher-order associative memories and their optical implementations,” Neural Net. 1, 149–163 (1988).
[CrossRef]

K. Wagner, D. Psaltis, “Multilayer optical learning networks,” Appl. Opt. 26, 5061–5076 (1987).
[CrossRef] [PubMed]

J. Yu, F. Mok, D. Psaltis, “Capacity of optical correlators,” in Spatial Light Modulators and Applications II, U. Efron, ed., Proc. Soc. Photo-Opt. Instrum. Eng.825, 114–120 (1987).

Qiao, Y.

Y. Qiao, D. Psaltis, “Local learning algorithm for optical neural networks,” Appl. Opt. 31, 3285–3288 (1992).
[CrossRef] [PubMed]

Y. Qiao, D. Psaltis, C. Gu, J. Hong, P. Yeh, “Phase-locked sustainment of photorefractive holograms using phase conjugation,” J. Appl. Phys. 70, 4646–4648 (1991).
[CrossRef]

Rossen, G.

Rumelhart, D. E.

D. E. Rumelhart, G. E. Hinton, R. J. Williams, “Learning internal representations by error propagation,” in Parallel Distributed Processing, D. E. Rumelhart, J. L. McClelland eds. (MIT, Cambridge, Mass., 1986), Vol. 1, Chap. 8.

Sasaki, H.

Soffer, B. H.

Staebler, D. L.

D. L. Staebler, W. J. Burke, W. Phillips, J. J. Amodei, “Multiple storage and erasure of fixed holograms in Fe-doped LiNbO3,” Appl. Phys. Lett. 26, 182–184 (1975).
[CrossRef]

Taketomi, Y.

VanderLugt, A.B.

A.B. VanderLugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory IT-10, 139–145 (1964).
[CrossRef]

Wagner, K.

Williams, R. J.

D. E. Rumelhart, G. E. Hinton, R. J. Williams, “Learning internal representations by error propagation,” in Parallel Distributed Processing, D. E. Rumelhart, J. L. McClelland eds. (MIT, Cambridge, Mass., 1986), Vol. 1, Chap. 8.

Yeh, P.

Y. Qiao, D. Psaltis, C. Gu, J. Hong, P. Yeh, “Phase-locked sustainment of photorefractive holograms using phase conjugation,” J. Appl. Phys. 70, 4646–4648 (1991).
[CrossRef]

Yoshinaga, H.

Yu, J.

J. Yu, F. Mok, D. Psaltis, “Capacity of optical correlators,” in Spatial Light Modulators and Applications II, U. Efron, ed., Proc. Soc. Photo-Opt. Instrum. Eng.825, 114–120 (1987).

Appl. Opt. (8)

Appl. Phys. Lett. (1)

D. L. Staebler, W. J. Burke, W. Phillips, J. J. Amodei, “Multiple storage and erasure of fixed holograms in Fe-doped LiNbO3,” Appl. Phys. Lett. 26, 182–184 (1975).
[CrossRef]

IEEE Trans. Inf. Theory (1)

A.B. VanderLugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory IT-10, 139–145 (1964).
[CrossRef]

J. Appl. Phys. (1)

Y. Qiao, D. Psaltis, C. Gu, J. Hong, P. Yeh, “Phase-locked sustainment of photorefractive holograms using phase conjugation,” J. Appl. Phys. 70, 4646–4648 (1991).
[CrossRef]

J. Phys. A (1)

M. Mezard, J. P. Nadal, “Learning in feedforward layered networks—the tiling algorithm,” J. Phys. A 22, 2191–2203 (1989).
[CrossRef]

Nature (1)

D. Psaltis, D. Brady, X.-G. Gu, S. Lin, “Holography in artificial neural networks,” Nature 343: 325–330 (1990).
[CrossRef] [PubMed]

Neural Net. (1)

D. Psaltis, C. H. Park, J. Hong, “Higher-order associative memories and their optical implementations,” Neural Net. 1, 149–163 (1988).
[CrossRef]

Opt. Comm. (1)

C. Gu, J. Hong, S. Cambell, “2-D shift-invariant volume holographic,” Opt. Comm. 88, 309–314 (1992).
[CrossRef]

Opt. Lett. (5)

Other (3)

D. E. Rumelhart, G. E. Hinton, R. J. Williams, “Learning internal representations by error propagation,” in Parallel Distributed Processing, D. E. Rumelhart, J. L. McClelland eds. (MIT, Cambridge, Mass., 1986), Vol. 1, Chap. 8.

F. Mok, “Applications of holographic storage in lithium niobate,” in Annual Meeting, Vol. 23 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), p. 102.

J. Yu, F. Mok, D. Psaltis, “Capacity of optical correlators,” in Spatial Light Modulators and Applications II, U. Efron, ed., Proc. Soc. Photo-Opt. Instrum. Eng.825, 114–120 (1987).

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Figures (11)

Fig. 1
Fig. 1

Optical setup of the face-recognition system; PR, photorefractive.

Fig. 2
Fig. 2

Spatial filter used in plane P1 of Fig. 1.

Fig. 3
Fig. 3

Edge-enhanced image and original face.

Fig. 4
Fig. 4

Experiment showing the position of the correlation peak to be proportional to the size of the input face.

Fig. 5
Fig. 5

Schematic diagram of overall system.

Fig. 6
Fig. 6

Flow chart for the algorithm used to train the network; HU, hidden unit.

Fig. 7
Fig. 7

Photographs showing part of the training session.

Fig. 8
Fig. 8

System response before thresholding.

Fig. 9
Fig. 9

Probability of error as a function of the output threshold level.

Fig. 10
Fig. 10

Probability of error as a function of the output threshold level when the output is observed for 6 s to perform the classification.

Fig. 11
Fig. 11

Examples demonstrating the generalization capabilities of the system. A bright dot in the circle at the lower right-hand corner of each photograph indicates that the system classifies the input image as the person it was trained to recognize.

Equations (4)

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g ( x , y ) = f ( x , y ) h ( x - x , y - y ) d x d y sinc ( α x ) ,
α = L sin θ 2 λ F .
τ d w i j d t + w i j = β m i j ,
Δ w i j - Δ t τ w i j + Δ t τ β m i j .

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