Abstract

We present a two-layer neural network for processing of three-dimensional (3D) images that are obtained by digital holography. The network is trained with a real 3D object to compute the weights of the layers. Experiments are presented to illustrate the system performance. The system is designed to detect a 3D object in the presence of various distortions. As an example, experiments are presented to illustrate how the system is able to recognize a 3D object with 360° out-of-plane rotation.

© 2001 Optical Society of America

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References

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  1. A. B. VanderLugt, Optical Signal Processing (Wiley, New York, 1992).
  2. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).
  3. A. Pu, R. Denkewalter, and D. Psaltis, Opt. Eng. 36, 2737 (1997).
    [CrossRef]
  4. J. Rosen, Opt. Lett. 22, 964 (1997).
    [CrossRef] [PubMed]
  5. B. Javidi and E. Tajahuerce, Opt. Lett. 25, 610 (2000).
    [CrossRef]
  6. H. J. Caulfield, Handbook of Optical Holography (Academic, London, 1979).
  7. A. Mahalanobis, in Optoelectronic Devices and Systems Processing, B. Javidi and K. M. Johnson, eds., Vol. 65 of SPIE Critical Review Series (SPIE, Bellingham, Wash., 1996), p. 240.
  8. B. Javidi and D. Painchaud, Appl. Opt. 35, 318 (1996).
    [CrossRef] [PubMed]
  9. P. Refregier, V. Lauder, and B. Javidi, Opt. Lett. 19, 405 (1994).
    [PubMed]
  10. B. Javidi, J. Li, and Q. Tang, Appl. Opt. 34, 3950 (1995).
    [CrossRef] [PubMed]
  11. A. Khotanzad and C. Chung, Neural Comput. Appl. 7, 249 (1998).
    [CrossRef]
  12. Y. Xiong and G. Zhang, Proc. SPIE 3390, 572 (1998).
    [CrossRef]
  13. A. Massad, B. Mertsching, and S. Schmalz, in Proceedings of the 24th Annual Conference of the IEEE Industrial Electronics Society (IECON ’98) (European Center for Mechatronics, Aachen, Germany, 1998), p. 2074.
  14. G. Coppini, R. Poli, M. Rucci, and G. Valli, Comput. Biomed. Res. 25, 569 (1992).
    [CrossRef] [PubMed]
  15. H. Zha, H. Nanamegi, and T. Nagata, Pattern Recogn. 31, 727 (1998).
    [CrossRef]
  16. Y. K. Ham and R. H. Park, Pattern Recogn. 32, 729 (1999).
    [CrossRef]
  17. A. McAulay, Optical Computer Architectures (Wiley, New York, 1991).
  18. J. H. Bruning, D. R. Herriott, J. E. Gallagher, D. P. Rosenfeld, A. D. White, and D. J. Brangaccio, Appl. Opt. 13, 2693 (1974).
    [CrossRef] [PubMed]
  19. I. Yamaguchi and T. Zhang, Opt. Lett. 22, 1268 (1997).
    [CrossRef] [PubMed]
  20. Y. Frauel, E. Tajahuerce, M. Castro, and B. Javidi, Appl. Opt. 40, 3887 (2001).
    [CrossRef]

2001 (1)

2000 (1)

1999 (1)

Y. K. Ham and R. H. Park, Pattern Recogn. 32, 729 (1999).
[CrossRef]

1998 (3)

A. Khotanzad and C. Chung, Neural Comput. Appl. 7, 249 (1998).
[CrossRef]

Y. Xiong and G. Zhang, Proc. SPIE 3390, 572 (1998).
[CrossRef]

H. Zha, H. Nanamegi, and T. Nagata, Pattern Recogn. 31, 727 (1998).
[CrossRef]

1997 (3)

1996 (1)

1995 (1)

1994 (1)

1992 (1)

G. Coppini, R. Poli, M. Rucci, and G. Valli, Comput. Biomed. Res. 25, 569 (1992).
[CrossRef] [PubMed]

1974 (1)

Brangaccio, D. J.

Bruning, J. H.

Castro, M.

Caulfield, H. J.

H. J. Caulfield, Handbook of Optical Holography (Academic, London, 1979).

Chung, C.

A. Khotanzad and C. Chung, Neural Comput. Appl. 7, 249 (1998).
[CrossRef]

Coppini, G.

G. Coppini, R. Poli, M. Rucci, and G. Valli, Comput. Biomed. Res. 25, 569 (1992).
[CrossRef] [PubMed]

Denkewalter, R.

A. Pu, R. Denkewalter, and D. Psaltis, Opt. Eng. 36, 2737 (1997).
[CrossRef]

Frauel, Y.

Gallagher, J. E.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

Ham, Y. K.

Y. K. Ham and R. H. Park, Pattern Recogn. 32, 729 (1999).
[CrossRef]

Herriott, D. R.

Javidi, B.

Khotanzad, A.

A. Khotanzad and C. Chung, Neural Comput. Appl. 7, 249 (1998).
[CrossRef]

Lauder, V.

Li, J.

Mahalanobis, A.

A. Mahalanobis, in Optoelectronic Devices and Systems Processing, B. Javidi and K. M. Johnson, eds., Vol. 65 of SPIE Critical Review Series (SPIE, Bellingham, Wash., 1996), p. 240.

Massad, A.

A. Massad, B. Mertsching, and S. Schmalz, in Proceedings of the 24th Annual Conference of the IEEE Industrial Electronics Society (IECON ’98) (European Center for Mechatronics, Aachen, Germany, 1998), p. 2074.

McAulay, A.

A. McAulay, Optical Computer Architectures (Wiley, New York, 1991).

Mertsching, B.

A. Massad, B. Mertsching, and S. Schmalz, in Proceedings of the 24th Annual Conference of the IEEE Industrial Electronics Society (IECON ’98) (European Center for Mechatronics, Aachen, Germany, 1998), p. 2074.

Nagata, T.

H. Zha, H. Nanamegi, and T. Nagata, Pattern Recogn. 31, 727 (1998).
[CrossRef]

Nanamegi, H.

H. Zha, H. Nanamegi, and T. Nagata, Pattern Recogn. 31, 727 (1998).
[CrossRef]

Painchaud, D.

Park, R. H.

Y. K. Ham and R. H. Park, Pattern Recogn. 32, 729 (1999).
[CrossRef]

Poli, R.

G. Coppini, R. Poli, M. Rucci, and G. Valli, Comput. Biomed. Res. 25, 569 (1992).
[CrossRef] [PubMed]

Psaltis, D.

A. Pu, R. Denkewalter, and D. Psaltis, Opt. Eng. 36, 2737 (1997).
[CrossRef]

Pu, A.

A. Pu, R. Denkewalter, and D. Psaltis, Opt. Eng. 36, 2737 (1997).
[CrossRef]

Refregier, P.

Rosen, J.

Rosenfeld, D. P.

Rucci, M.

G. Coppini, R. Poli, M. Rucci, and G. Valli, Comput. Biomed. Res. 25, 569 (1992).
[CrossRef] [PubMed]

Schmalz, S.

A. Massad, B. Mertsching, and S. Schmalz, in Proceedings of the 24th Annual Conference of the IEEE Industrial Electronics Society (IECON ’98) (European Center for Mechatronics, Aachen, Germany, 1998), p. 2074.

Tajahuerce, E.

Tang, Q.

Valli, G.

G. Coppini, R. Poli, M. Rucci, and G. Valli, Comput. Biomed. Res. 25, 569 (1992).
[CrossRef] [PubMed]

VanderLugt, A. B.

A. B. VanderLugt, Optical Signal Processing (Wiley, New York, 1992).

White, A. D.

Xiong, Y.

Y. Xiong and G. Zhang, Proc. SPIE 3390, 572 (1998).
[CrossRef]

Yamaguchi, I.

Zha, H.

H. Zha, H. Nanamegi, and T. Nagata, Pattern Recogn. 31, 727 (1998).
[CrossRef]

Zhang, G.

Y. Xiong and G. Zhang, Proc. SPIE 3390, 572 (1998).
[CrossRef]

Zhang, T.

Appl. Opt. (4)

Comput. Biomed. Res. (1)

G. Coppini, R. Poli, M. Rucci, and G. Valli, Comput. Biomed. Res. 25, 569 (1992).
[CrossRef] [PubMed]

Neural Comput. Appl. (1)

A. Khotanzad and C. Chung, Neural Comput. Appl. 7, 249 (1998).
[CrossRef]

Opt. Eng. (1)

A. Pu, R. Denkewalter, and D. Psaltis, Opt. Eng. 36, 2737 (1997).
[CrossRef]

Opt. Lett. (4)

Pattern Recogn. (2)

H. Zha, H. Nanamegi, and T. Nagata, Pattern Recogn. 31, 727 (1998).
[CrossRef]

Y. K. Ham and R. H. Park, Pattern Recogn. 32, 729 (1999).
[CrossRef]

Proc. SPIE (1)

Y. Xiong and G. Zhang, Proc. SPIE 3390, 572 (1998).
[CrossRef]

Other (6)

A. Massad, B. Mertsching, and S. Schmalz, in Proceedings of the 24th Annual Conference of the IEEE Industrial Electronics Society (IECON ’98) (European Center for Mechatronics, Aachen, Germany, 1998), p. 2074.

A. McAulay, Optical Computer Architectures (Wiley, New York, 1991).

H. J. Caulfield, Handbook of Optical Holography (Academic, London, 1979).

A. Mahalanobis, in Optoelectronic Devices and Systems Processing, B. Javidi and K. M. Johnson, eds., Vol. 65 of SPIE Critical Review Series (SPIE, Bellingham, Wash., 1996), p. 240.

A. B. VanderLugt, Optical Signal Processing (Wiley, New York, 1992).

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

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Figures (6)

Fig. 1
Fig. 1

(a) Experimental setup: M1M4, mirrors; BSs, beam splitters; SFs, spatial filters; Ls, lenses; RP1RP2, retardation plates. (b) 3D object reconstructed by digital holography.

Fig. 2
Fig. 2

Shifting the reconstruction window inside the hologram results in a change in the angle of view of the 3D object.

Fig. 3
Fig. 3

Values of the correlation peaks for all the filters when presented with the die in the orientations corresponding to filter 15.

Fig. 4
Fig. 4

Error rates for the classification obtained by use of a one-layer network only.

Fig. 5
Fig. 5

Two-layer neural network used in the experiments. b denotes bias.

Fig. 6
Fig. 6

Error rates for the classification of the 3D object obtained by the two-layer neural network.

Metrics