Abstract

A new bias method for the optical implementation of cellular neural networks is proposed to reduce electronic precalculation and increase processing speed. A multiple-object joint transform correlator is then used to realize the summation of multiple correlations resulting from the bias method. Compared with other optical systems for cellular neural networks, the proposed method offers the advantages of higher processing speed, easy implementation, and robustness. Computer simulations of the optical cellular neural networks for edge detection and corner and horizontal line extraction are also presented.

© 1999 Optical Society of America

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  1. N. H. Farhat, D. Psaltis, A. Prata, E. Paek, “Optical implementation of the hopfield mode,” Appl. Opt. 24, 1469–1475 (1985).
    [CrossRef]
  2. Y. Owechko, G. J. Dunning, E. Marom, B. H. Soffer, “Holographic associative memory with nonlinearities in the correlation domain,” Appl. Opt. 26, 1900–1910 (1987).
    [CrossRef] [PubMed]
  3. C. C. Guest, R. Tekolste, “Designs and devices for optical bidirectional associative memories,” Appl. Opt. 26, 5055–5060 (1987).
    [CrossRef] [PubMed]
  4. A. P. Ittycheriah, J. F. Walkup, T. F. Krile, S. L. Lim, “Outer product processor using polarization encoding,” Appl. Opt. 29, 275–283 (1990).
    [CrossRef] [PubMed]
  5. A. J. David, B. E. A. Saleh, “Optical implementation of the Hopfield algorithm using correlation,” Appl. Opt. 29, 1063–1064 (1990).
    [CrossRef] [PubMed]
  6. X.-M. Wang, G.-G. Mu, “Optical neural network with bipolar neural states,” Appl. Opt. 31, 4712–4719 (1992).
    [CrossRef] [PubMed]
  7. A. A. Rizvi, M. S. Zubairy, “Implementation of associative memory using grating structures,” Appl. Opt. 33, 3642–3645 (1994).
    [CrossRef] [PubMed]
  8. Y. Hayasaki, I. Tohyama, T. Yatagai, M. Mori, S. Ishihara, “Reversal-input superposing technique for all-optical neural networks,” Appl. Opt. 33, 1477–1484 (1994).
    [CrossRef] [PubMed]
  9. B. Javidi, J. Li, Q. Tang, “Optical implementation of neural networks for face recognition by the use of nonlinear joint transform correlator,” Appl. Opt. 34, 3950–3962 (1995).
    [CrossRef] [PubMed]
  10. L. O. Chua, L. Yang, “Cellular neural networks: theory,” IEEE Trans. Circuits Syst. 35, 1257–1272 (1988).
    [CrossRef]
  11. L. O. Chua, L. Yang, “Cellular neural networks: applications,” IEEE Trans. Circuits Syst. 35, 1273–1290 (1988).
    [CrossRef]
  12. N. Fruehauf, E. Lueder, G. Bader, “Fourier optical realization of cellular neural networks,” IEEE Trans. Circuits Syst. II 40, 156–161 (1993).
    [CrossRef]
  13. N. K. Gupta, H. Ogawa, “Optoelectronic architecture for cellular neural networks based on a new bias method and spatial coding scheme,” Opt. Commun. 138, 11–15 (1997).
    [CrossRef]
  14. C. S. Weaver, J. W. Goodman, “Technique for optically convolving two functions,” Appl. Opt. 5, 1248–1249 (1966).
    [CrossRef] [PubMed]
  15. F. Cheng, P. Andres, F. T. S. Yu, “Removal of intra-class associations in joint transform power spectrum,” Opt. Commun. 99, 7–12 (1993).
    [CrossRef]
  16. M. Deutsch, J. Garcia, D. Mendlovic, “Multichannel single-output color pattern recognition by use of a joint-transform correlator,” Appl. Opt. 35, 6976–6982 (1996).
    [CrossRef] [PubMed]
  17. G. Lu, Z. Zhang, S. Wu, F. T. S. Yu, “Implementation of a non-zero-order joint-transform correlator by use of a phase-shifting technique,” Appl. Opt. 36, 470–483 (1997).
    [CrossRef] [PubMed]
  18. C.-T. Li, S. Yin, F. T. S. Yu, “Nonzero-order joint transform correlator,” Opt. Eng. 37, 58–65 (1998).
    [CrossRef]
  19. J. M. Florence, “Joint-transform correlator systems using deformable-mirror spatial light modulators,” Opt. Lett. 14, 341–343 (1989).
    [CrossRef] [PubMed]
  20. G. S. Pati, K. Singh, “Experimental and simulation studies on performance of binary and gray-valued joint transform correlators under poor illumination conditions and nonoverlapping background noise,” Opt. Eng. 36, 1918–1929 (1997).
    [CrossRef]
  21. F. T. S. Yu, S. Jutamulia, T. W. Lin, D. A. Gregory, “Adaptive real-time pattern recognition using a liquid crystal TV based joint transform correlator,” Appl. Opt. 26, 1370–1372 (1987).
    [CrossRef] [PubMed]
  22. J. S. Kane, M. J. Paquin, “POPART: partial optical implementation of adaptive resonance theory 2,” IEEE Trans. Neural Networks 4, 695–702 (1993).
    [CrossRef]
  23. L. Guibert, Y. Petillot, J.-L. de Bougrenet de la Tocnaye, “Real-time demonstration of an on-board nonlinear joint transform correlator system,” Opt. Eng. 36, 820–824 (1997).
    [CrossRef]
  24. T. J. Grycewicz, “Experimental demonstration of a binary single-lens joint transform correlator using chirp-modulated inputs,” Opt. Eng. 36, 814–819 (1997).
    [CrossRef]
  25. J. Li, J. Hu, Y. Wang, “Experimental investigation of a real-time nonlinear joint transform correlator,” Opt. Eng. 33, 3302–3306 (1994).
    [CrossRef]

1998 (1)

C.-T. Li, S. Yin, F. T. S. Yu, “Nonzero-order joint transform correlator,” Opt. Eng. 37, 58–65 (1998).
[CrossRef]

1997 (5)

G. S. Pati, K. Singh, “Experimental and simulation studies on performance of binary and gray-valued joint transform correlators under poor illumination conditions and nonoverlapping background noise,” Opt. Eng. 36, 1918–1929 (1997).
[CrossRef]

N. K. Gupta, H. Ogawa, “Optoelectronic architecture for cellular neural networks based on a new bias method and spatial coding scheme,” Opt. Commun. 138, 11–15 (1997).
[CrossRef]

L. Guibert, Y. Petillot, J.-L. de Bougrenet de la Tocnaye, “Real-time demonstration of an on-board nonlinear joint transform correlator system,” Opt. Eng. 36, 820–824 (1997).
[CrossRef]

T. J. Grycewicz, “Experimental demonstration of a binary single-lens joint transform correlator using chirp-modulated inputs,” Opt. Eng. 36, 814–819 (1997).
[CrossRef]

G. Lu, Z. Zhang, S. Wu, F. T. S. Yu, “Implementation of a non-zero-order joint-transform correlator by use of a phase-shifting technique,” Appl. Opt. 36, 470–483 (1997).
[CrossRef] [PubMed]

1996 (1)

1995 (1)

1994 (3)

1993 (3)

F. Cheng, P. Andres, F. T. S. Yu, “Removal of intra-class associations in joint transform power spectrum,” Opt. Commun. 99, 7–12 (1993).
[CrossRef]

J. S. Kane, M. J. Paquin, “POPART: partial optical implementation of adaptive resonance theory 2,” IEEE Trans. Neural Networks 4, 695–702 (1993).
[CrossRef]

N. Fruehauf, E. Lueder, G. Bader, “Fourier optical realization of cellular neural networks,” IEEE Trans. Circuits Syst. II 40, 156–161 (1993).
[CrossRef]

1992 (1)

1990 (2)

1989 (1)

1988 (2)

L. O. Chua, L. Yang, “Cellular neural networks: theory,” IEEE Trans. Circuits Syst. 35, 1257–1272 (1988).
[CrossRef]

L. O. Chua, L. Yang, “Cellular neural networks: applications,” IEEE Trans. Circuits Syst. 35, 1273–1290 (1988).
[CrossRef]

1987 (3)

1985 (1)

1966 (1)

Andres, P.

F. Cheng, P. Andres, F. T. S. Yu, “Removal of intra-class associations in joint transform power spectrum,” Opt. Commun. 99, 7–12 (1993).
[CrossRef]

Bader, G.

N. Fruehauf, E. Lueder, G. Bader, “Fourier optical realization of cellular neural networks,” IEEE Trans. Circuits Syst. II 40, 156–161 (1993).
[CrossRef]

Cheng, F.

F. Cheng, P. Andres, F. T. S. Yu, “Removal of intra-class associations in joint transform power spectrum,” Opt. Commun. 99, 7–12 (1993).
[CrossRef]

Chua, L. O.

L. O. Chua, L. Yang, “Cellular neural networks: applications,” IEEE Trans. Circuits Syst. 35, 1273–1290 (1988).
[CrossRef]

L. O. Chua, L. Yang, “Cellular neural networks: theory,” IEEE Trans. Circuits Syst. 35, 1257–1272 (1988).
[CrossRef]

David, A. J.

de Bougrenet de la Tocnaye, J.-L.

L. Guibert, Y. Petillot, J.-L. de Bougrenet de la Tocnaye, “Real-time demonstration of an on-board nonlinear joint transform correlator system,” Opt. Eng. 36, 820–824 (1997).
[CrossRef]

Deutsch, M.

Dunning, G. J.

Farhat, N. H.

Florence, J. M.

Fruehauf, N.

N. Fruehauf, E. Lueder, G. Bader, “Fourier optical realization of cellular neural networks,” IEEE Trans. Circuits Syst. II 40, 156–161 (1993).
[CrossRef]

Garcia, J.

Goodman, J. W.

Gregory, D. A.

Grycewicz, T. J.

T. J. Grycewicz, “Experimental demonstration of a binary single-lens joint transform correlator using chirp-modulated inputs,” Opt. Eng. 36, 814–819 (1997).
[CrossRef]

Guest, C. C.

Guibert, L.

L. Guibert, Y. Petillot, J.-L. de Bougrenet de la Tocnaye, “Real-time demonstration of an on-board nonlinear joint transform correlator system,” Opt. Eng. 36, 820–824 (1997).
[CrossRef]

Gupta, N. K.

N. K. Gupta, H. Ogawa, “Optoelectronic architecture for cellular neural networks based on a new bias method and spatial coding scheme,” Opt. Commun. 138, 11–15 (1997).
[CrossRef]

Hayasaki, Y.

Hu, J.

J. Li, J. Hu, Y. Wang, “Experimental investigation of a real-time nonlinear joint transform correlator,” Opt. Eng. 33, 3302–3306 (1994).
[CrossRef]

Ishihara, S.

Ittycheriah, A. P.

Javidi, B.

Jutamulia, S.

Kane, J. S.

J. S. Kane, M. J. Paquin, “POPART: partial optical implementation of adaptive resonance theory 2,” IEEE Trans. Neural Networks 4, 695–702 (1993).
[CrossRef]

Krile, T. F.

Li, C.-T.

C.-T. Li, S. Yin, F. T. S. Yu, “Nonzero-order joint transform correlator,” Opt. Eng. 37, 58–65 (1998).
[CrossRef]

Li, J.

B. Javidi, J. Li, Q. Tang, “Optical implementation of neural networks for face recognition by the use of nonlinear joint transform correlator,” Appl. Opt. 34, 3950–3962 (1995).
[CrossRef] [PubMed]

J. Li, J. Hu, Y. Wang, “Experimental investigation of a real-time nonlinear joint transform correlator,” Opt. Eng. 33, 3302–3306 (1994).
[CrossRef]

Lim, S. L.

Lin, T. W.

Lu, G.

Lueder, E.

N. Fruehauf, E. Lueder, G. Bader, “Fourier optical realization of cellular neural networks,” IEEE Trans. Circuits Syst. II 40, 156–161 (1993).
[CrossRef]

Marom, E.

Mendlovic, D.

Mori, M.

Mu, G.-G.

Ogawa, H.

N. K. Gupta, H. Ogawa, “Optoelectronic architecture for cellular neural networks based on a new bias method and spatial coding scheme,” Opt. Commun. 138, 11–15 (1997).
[CrossRef]

Owechko, Y.

Paek, E.

Paquin, M. J.

J. S. Kane, M. J. Paquin, “POPART: partial optical implementation of adaptive resonance theory 2,” IEEE Trans. Neural Networks 4, 695–702 (1993).
[CrossRef]

Pati, G. S.

G. S. Pati, K. Singh, “Experimental and simulation studies on performance of binary and gray-valued joint transform correlators under poor illumination conditions and nonoverlapping background noise,” Opt. Eng. 36, 1918–1929 (1997).
[CrossRef]

Petillot, Y.

L. Guibert, Y. Petillot, J.-L. de Bougrenet de la Tocnaye, “Real-time demonstration of an on-board nonlinear joint transform correlator system,” Opt. Eng. 36, 820–824 (1997).
[CrossRef]

Prata, A.

Psaltis, D.

Rizvi, A. A.

Saleh, B. E. A.

Singh, K.

G. S. Pati, K. Singh, “Experimental and simulation studies on performance of binary and gray-valued joint transform correlators under poor illumination conditions and nonoverlapping background noise,” Opt. Eng. 36, 1918–1929 (1997).
[CrossRef]

Soffer, B. H.

Tang, Q.

Tekolste, R.

Tohyama, I.

Walkup, J. F.

Wang, X.-M.

Wang, Y.

J. Li, J. Hu, Y. Wang, “Experimental investigation of a real-time nonlinear joint transform correlator,” Opt. Eng. 33, 3302–3306 (1994).
[CrossRef]

Weaver, C. S.

Wu, S.

Yang, L.

L. O. Chua, L. Yang, “Cellular neural networks: theory,” IEEE Trans. Circuits Syst. 35, 1257–1272 (1988).
[CrossRef]

L. O. Chua, L. Yang, “Cellular neural networks: applications,” IEEE Trans. Circuits Syst. 35, 1273–1290 (1988).
[CrossRef]

Yatagai, T.

Yin, S.

C.-T. Li, S. Yin, F. T. S. Yu, “Nonzero-order joint transform correlator,” Opt. Eng. 37, 58–65 (1998).
[CrossRef]

Yu, F. T. S.

Zhang, Z.

Zubairy, M. S.

Appl. Opt. (13)

N. H. Farhat, D. Psaltis, A. Prata, E. Paek, “Optical implementation of the hopfield mode,” Appl. Opt. 24, 1469–1475 (1985).
[CrossRef]

Y. Owechko, G. J. Dunning, E. Marom, B. H. Soffer, “Holographic associative memory with nonlinearities in the correlation domain,” Appl. Opt. 26, 1900–1910 (1987).
[CrossRef] [PubMed]

C. C. Guest, R. Tekolste, “Designs and devices for optical bidirectional associative memories,” Appl. Opt. 26, 5055–5060 (1987).
[CrossRef] [PubMed]

A. P. Ittycheriah, J. F. Walkup, T. F. Krile, S. L. Lim, “Outer product processor using polarization encoding,” Appl. Opt. 29, 275–283 (1990).
[CrossRef] [PubMed]

A. J. David, B. E. A. Saleh, “Optical implementation of the Hopfield algorithm using correlation,” Appl. Opt. 29, 1063–1064 (1990).
[CrossRef] [PubMed]

X.-M. Wang, G.-G. Mu, “Optical neural network with bipolar neural states,” Appl. Opt. 31, 4712–4719 (1992).
[CrossRef] [PubMed]

A. A. Rizvi, M. S. Zubairy, “Implementation of associative memory using grating structures,” Appl. Opt. 33, 3642–3645 (1994).
[CrossRef] [PubMed]

Y. Hayasaki, I. Tohyama, T. Yatagai, M. Mori, S. Ishihara, “Reversal-input superposing technique for all-optical neural networks,” Appl. Opt. 33, 1477–1484 (1994).
[CrossRef] [PubMed]

B. Javidi, J. Li, Q. Tang, “Optical implementation of neural networks for face recognition by the use of nonlinear joint transform correlator,” Appl. Opt. 34, 3950–3962 (1995).
[CrossRef] [PubMed]

M. Deutsch, J. Garcia, D. Mendlovic, “Multichannel single-output color pattern recognition by use of a joint-transform correlator,” Appl. Opt. 35, 6976–6982 (1996).
[CrossRef] [PubMed]

G. Lu, Z. Zhang, S. Wu, F. T. S. Yu, “Implementation of a non-zero-order joint-transform correlator by use of a phase-shifting technique,” Appl. Opt. 36, 470–483 (1997).
[CrossRef] [PubMed]

F. T. S. Yu, S. Jutamulia, T. W. Lin, D. A. Gregory, “Adaptive real-time pattern recognition using a liquid crystal TV based joint transform correlator,” Appl. Opt. 26, 1370–1372 (1987).
[CrossRef] [PubMed]

C. S. Weaver, J. W. Goodman, “Technique for optically convolving two functions,” Appl. Opt. 5, 1248–1249 (1966).
[CrossRef] [PubMed]

IEEE Trans. Circuits Syst. (2)

L. O. Chua, L. Yang, “Cellular neural networks: theory,” IEEE Trans. Circuits Syst. 35, 1257–1272 (1988).
[CrossRef]

L. O. Chua, L. Yang, “Cellular neural networks: applications,” IEEE Trans. Circuits Syst. 35, 1273–1290 (1988).
[CrossRef]

IEEE Trans. Circuits Syst. II (1)

N. Fruehauf, E. Lueder, G. Bader, “Fourier optical realization of cellular neural networks,” IEEE Trans. Circuits Syst. II 40, 156–161 (1993).
[CrossRef]

IEEE Trans. Neural Networks (1)

J. S. Kane, M. J. Paquin, “POPART: partial optical implementation of adaptive resonance theory 2,” IEEE Trans. Neural Networks 4, 695–702 (1993).
[CrossRef]

Opt. Commun. (2)

N. K. Gupta, H. Ogawa, “Optoelectronic architecture for cellular neural networks based on a new bias method and spatial coding scheme,” Opt. Commun. 138, 11–15 (1997).
[CrossRef]

F. Cheng, P. Andres, F. T. S. Yu, “Removal of intra-class associations in joint transform power spectrum,” Opt. Commun. 99, 7–12 (1993).
[CrossRef]

Opt. Eng. (5)

G. S. Pati, K. Singh, “Experimental and simulation studies on performance of binary and gray-valued joint transform correlators under poor illumination conditions and nonoverlapping background noise,” Opt. Eng. 36, 1918–1929 (1997).
[CrossRef]

L. Guibert, Y. Petillot, J.-L. de Bougrenet de la Tocnaye, “Real-time demonstration of an on-board nonlinear joint transform correlator system,” Opt. Eng. 36, 820–824 (1997).
[CrossRef]

T. J. Grycewicz, “Experimental demonstration of a binary single-lens joint transform correlator using chirp-modulated inputs,” Opt. Eng. 36, 814–819 (1997).
[CrossRef]

J. Li, J. Hu, Y. Wang, “Experimental investigation of a real-time nonlinear joint transform correlator,” Opt. Eng. 33, 3302–3306 (1994).
[CrossRef]

C.-T. Li, S. Yin, F. T. S. Yu, “Nonzero-order joint transform correlator,” Opt. Eng. 37, 58–65 (1998).
[CrossRef]

Opt. Lett. (1)

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Figures (11)

Fig. 1
Fig. 1

Arrangement of the input plane for CNN’s.

Fig. 2
Fig. 2

Output plane characteristics corresponding to the input of Fig. 1.

Fig. 3
Fig. 3

Optical JTC setup for CNN’s.

Fig. 4
Fig. 4

Image to be processed.

Fig. 5
Fig. 5

Templates used in edge and corner detection: (a) template A and (b) template B.

Fig. 6
Fig. 6

Joint input image at the first iteration.

Fig. 7
Fig. 7

Correlation distribution at the output plane corresponding to the joint input image of Fig. 6.

Fig. 8
Fig. 8

Correlation distribution centered at (0, -2b).

Fig. 9
Fig. 9

Thresholded output: (a) the edge and (b) the corner.

Fig. 10
Fig. 10

Templates used in horizontal line detection: (a) template A and (b) template B.

Fig. 11
Fig. 11

Results of the third iteration: (a) the joint input image, (b) the correlation distribution centered at (0, -2b), (c) the thresholded output.

Equations (19)

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

xi,jn+1=k=-rrl=-rr Ak,lyi+k,j+ln+k=-rrl=-rr Bk,lui+k,j+l+I,
yi,jn+1=THxi,jn+1,
|ui,j|1,  |yi,jn|1.
α=|minmink,l Ak,l, 0|,  β=|minmink,l Bk,l, 0|.
ui,j+=ui,j+1,  yi,j+n=yi,jn+1,Ak,l+=Ak,l+α,  Bk,l+=Bk,l+β.
xi,jn+1=k=-rrl=-rrAk,l+-αyi+k,j+l+n-1+k=-rrl=-rrBk,l+-βui+k,j+l+-1+I=k=-rrl=-rr Ak,l+yi+k,j+l+n+k=-rrl=-rr Bk,l+ui+k,j+l++-k=-rrl=-rr αyi+k,j+l+n-k=-rrl=-rr βui+k,j+l++-k=-rrl=-rr Ak,l+-k=-rrl=-rr Bk,l++k=-rrl=-rr α+k=-rrl=-rr β+I=k=-rrl=-rr Ak,l+yi+k,j+l+n+k=-rrl=-rr Bk,l+ui+k,j+l++k=-rrl=-rr α2-yi+k,j+l+n+k=-rrl=-rr β2-ui+k,j+l+-k=-rrl=-rr 2α-k=-rrl=-rr 2β+-k=-rrl=-rr Ak,l+-k=-rrl=-rr Bk,l++k=-rrl=-rr α+k=-rrl=-rr β+I=k=-rrl=-rr Ak,l+yi+k,j+l+n+k=-rrl=-rr Bk,l+ui+k,j+l++k=-rrl=-rr Ck,l+yi+k,j+l+n¯+k=-rrl=-rr Dk,l+ui+k,j+l+¯-I++I,
ui+k,j+l+¯=2-ui+k,j+l+=1-ui+k,j+l,
yi+k,j+l+n¯=2-yi+k,j+l+n=1-yi+k,j+ln,
Ck,l+=α, Dk,l+=β,  k, lNr,
I+=k=-rrl=-rr Ak,l++k=-rrl=-rr Bk,l++k=-rrl=-rr Ck,l++k=-rrl=-rr Dk,l+.
xi,j+n+1=k=-rrl=-rr Ak,l+yi+k,j+l+n+k=-rrl=-rr Bk,l+ui+k,j+l++k=-rrl=-rr Ck,l+yi+k,j+l+n¯+k=-rrl=-rr Dk,l+ui+k,j+l+¯.
yi,jn+1=TH1xi,j+n+1,
TH1x=THx-I++I
fp, q=k=1N tkp-ak, q-bk,
Fu, v=k=1N Tku, vexp-jaku+bkv,
|Fu, v|2=k=1N Tku, vexp-jaku+bkv2=k=1N |Tku, v|2+k=1Nl=1lkN Tku, vTl*u, vexpjual-ak+jvbl-bk,
fp, q=k=1N tkp, qtkp, q+k=1Nl=1lkN tkp, qtl*p, q  δp-al-ak, q-bl-bk,
fp, q=y+p+3a2, q-b+y+¯p+a2, q-b+u+p-a2, q-b+u+¯p-3a2, q-b+A+p+3a2, q+b+C+p+a2, q+b+B+p-a2, q+b+D+p-3a2, q+b.
DpM,  DqN,

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