Abstract

A novel technique, the visual-area coding technique (VACT), for the optical implementation of fuzzy logic with the capability of visualization of the results is presented. This technique is based on the microfont method and is considered to be an instance of digitized analog optical computing. Huge amounts of data can be processed in fuzzy logic with the VACT. In addition, real-time visualization of the processed result can be accomplished.

© 1995 Optical Society of America

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References

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1994

P. Thiran, V. Peiris, P. Heim, B. Hochet, “Quantization effects in digitally behaving circuit implementations of Kohonen networks,” IEEE Trans. Neural Networks 5, 450–458 (1994).
[CrossRef]

T. Konishi, J. Tanida, Y. Ichioka, “Pure optical parallel array logic system: an optical parallel computing architecture,” Inst. Electron. Info. Commun. Eng. Trans. Electron. E77-C, 30–34 (1994).

1993

1992

1991

R. G. A. Craig, B. S. Wherrett, A. C. Walker, F. A. P. Tooley, S. D. Smith, “Optical cellular logic image processor: implementation and programming of a single channel digital optical circuit,” Appl. Opt. 30, 2297–2308 (1991).
[CrossRef] [PubMed]

M. Takahashi, M. Oita, S. Tai, K. Kojima, K. Kyuma, “A quantized backpropagation learning rule and its application to optical neural networks,” Opt. Comput. Process. 1, 175–182 (1991).

1990

J. Jahns, “Optical implementation of the Banyan network,” Opt. Commun. 76, 321–324 (1990).
[CrossRef]

1989

1988

1986

1985

F. Ono, “Binary rendition of continuous-tone pictures using binary patterns having similar Fourier spectra,” Trans. Inst. Electron. Commun. Eng. Jpn. Part D J68D, 686–693 (1985).

1983

1979

Akirakawa, H.

H. Akirakawa, K. Hirota, “Fuzzy inference engine by address-look-up and paging method,” in Proceedings of the International Workshop on Fuzzy System Applications (International Fuzzy Systems Association, Amsterdam, North-Holland, 1988), pp. 45–56.

Allebach, J. P.

Brenner, K.-H.

Chavel, P.

Chen, C.

S. Zhang, S. Lin, C. Chen, “Optical implementation of a fuzzy associative memory,” Opt. Commun. 100, 48–52 (1993).
[CrossRef]

Craig, R. G. A.

Fukui, M.

Glaser, I.

Hang, C. C.

Y.-M. Pok, J.-X. Xu, C. C. Hang, “Visualization of fuzzy control dynamics using vector space,” Asia-Pac. Eng. J. A 3, 105–127 (1993).

Heim, P.

P. Thiran, V. Peiris, P. Heim, B. Hochet, “Quantization effects in digitally behaving circuit implementations of Kohonen networks,” IEEE Trans. Neural Networks 5, 450–458 (1994).
[CrossRef]

Hirota, K.

H. Akirakawa, K. Hirota, “Fuzzy inference engine by address-look-up and paging method,” in Proceedings of the International Workshop on Fuzzy System Applications (International Fuzzy Systems Association, Amsterdam, North-Holland, 1988), pp. 45–56.

Hochet, B.

P. Thiran, V. Peiris, P. Heim, B. Hochet, “Quantization effects in digitally behaving circuit implementations of Kohonen networks,” IEEE Trans. Neural Networks 5, 450–458 (1994).
[CrossRef]

Huang, A.

Huang, K.-S.

Ichioka, Y.

T. Konishi, J. Tanida, Y. Ichioka, “Pure optical parallel array logic system: an optical parallel computing architecture,” Inst. Electron. Info. Commun. Eng. Trans. Electron. E77-C, 30–34 (1994).

J. Tanida, Y. Ichioka, “Optical logic array processor using shadowgrams,” J. Opt. Soc. Am. 73, 800–809 (1983).
[CrossRef]

Jahns, J.

Jenkins, B. K.

Kitayama, K.

Kojima, K.

M. Takahashi, M. Oita, S. Tai, K. Kojima, K. Kyuma, “A quantized backpropagation learning rule and its application to optical neural networks,” Opt. Comput. Process. 1, 175–182 (1991).

Konishi, T.

T. Konishi, J. Tanida, Y. Ichioka, “Pure optical parallel array logic system: an optical parallel computing architecture,” Inst. Electron. Info. Commun. Eng. Trans. Electron. E77-C, 30–34 (1994).

Kyuma, K.

M. Takahashi, M. Oita, S. Tai, K. Kojima, K. Kyuma, “A quantized backpropagation learning rule and its application to optical neural networks,” Opt. Comput. Process. 1, 175–182 (1991).

Lin, S.

S. Zhang, S. Lin, C. Chen, “Optical implementation of a fuzzy associative memory,” Opt. Commun. 100, 48–52 (1993).
[CrossRef]

Liu, L.

Murdocca, M. J.

Oita, M.

M. Takahashi, M. Oita, S. Tai, K. Kojima, K. Kyuma, “A quantized backpropagation learning rule and its application to optical neural networks,” Opt. Comput. Process. 1, 175–182 (1991).

Ono, F.

F. Ono, “Binary rendition of continuous-tone pictures using binary patterns having similar Fourier spectra,” Trans. Inst. Electron. Commun. Eng. Jpn. Part D J68D, 686–693 (1985).

Peiris, V.

P. Thiran, V. Peiris, P. Heim, B. Hochet, “Quantization effects in digitally behaving circuit implementations of Kohonen networks,” IEEE Trans. Neural Networks 5, 450–458 (1994).
[CrossRef]

Pok, Y.-M.

Y.-M. Pok, J.-X. Xu, C. C. Hang, “Visualization of fuzzy control dynamics using vector space,” Asia-Pac. Eng. J. A 3, 105–127 (1993).

Sawchuk, A. A.

Smith, S. D.

Streibl, N.

Tai, S.

M. Takahashi, M. Oita, S. Tai, K. Kojima, K. Kyuma, “A quantized backpropagation learning rule and its application to optical neural networks,” Opt. Comput. Process. 1, 175–182 (1991).

Takahashi, M.

M. Takahashi, M. Oita, S. Tai, K. Kojima, K. Kyuma, “A quantized backpropagation learning rule and its application to optical neural networks,” Opt. Comput. Process. 1, 175–182 (1991).

Tanida, J.

T. Konishi, J. Tanida, Y. Ichioka, “Pure optical parallel array logic system: an optical parallel computing architecture,” Inst. Electron. Info. Commun. Eng. Trans. Electron. E77-C, 30–34 (1994).

J. Tanida, Y. Ichioka, “Optical logic array processor using shadowgrams,” J. Opt. Soc. Am. 73, 800–809 (1983).
[CrossRef]

Thiran, P.

P. Thiran, V. Peiris, P. Heim, B. Hochet, “Quantization effects in digitally behaving circuit implementations of Kohonen networks,” IEEE Trans. Neural Networks 5, 450–458 (1994).
[CrossRef]

Tooley, F. A. P.

Ulichney, R.

R. Ulichney, Digital Halftoning (MIT, Cambridge, Mass., 1987), pp. 1–14.

Walker, A. C.

Wang, C.-H.

Wang, J.-M.

Weber, A. G.

Wherrett, B. S.

Xu, J.-X.

Y.-M. Pok, J.-X. Xu, C. C. Hang, “Visualization of fuzzy control dynamics using vector space,” Asia-Pac. Eng. J. A 3, 105–127 (1993).

Zhang, S.

S. Zhang, S. Lin, C. Chen, “Optical implementation of a fuzzy associative memory,” Opt. Commun. 100, 48–52 (1993).
[CrossRef]

Zhu, Z.

Zimmermann, H.-J.

H.-J. Zimmermann, Fuzzy Set Theory and Its Applications (Kluwer-Nijhoff, Boston, Mass., 1985), pp. 121–177.

Appl. Opt.

Asia-Pac. Eng. J. A

Y.-M. Pok, J.-X. Xu, C. C. Hang, “Visualization of fuzzy control dynamics using vector space,” Asia-Pac. Eng. J. A 3, 105–127 (1993).

IEEE Trans. Neural Networks

P. Thiran, V. Peiris, P. Heim, B. Hochet, “Quantization effects in digitally behaving circuit implementations of Kohonen networks,” IEEE Trans. Neural Networks 5, 450–458 (1994).
[CrossRef]

Inst. Electron. Info. Commun. Eng. Trans. Electron.

T. Konishi, J. Tanida, Y. Ichioka, “Pure optical parallel array logic system: an optical parallel computing architecture,” Inst. Electron. Info. Commun. Eng. Trans. Electron. E77-C, 30–34 (1994).

J. Opt. Soc. Am.

Opt. Commun.

S. Zhang, S. Lin, C. Chen, “Optical implementation of a fuzzy associative memory,” Opt. Commun. 100, 48–52 (1993).
[CrossRef]

L. Liu, “Optical implementation of parallel fuzzy logic,” Opt. Commun. 73, 183–187 (1989).
[CrossRef]

J. Jahns, “Optical implementation of the Banyan network,” Opt. Commun. 76, 321–324 (1990).
[CrossRef]

Opt. Comput. Process.

M. Takahashi, M. Oita, S. Tai, K. Kojima, K. Kyuma, “A quantized backpropagation learning rule and its application to optical neural networks,” Opt. Comput. Process. 1, 175–182 (1991).

Trans. Inst. Electron. Commun. Eng. Jpn. Part D

F. Ono, “Binary rendition of continuous-tone pictures using binary patterns having similar Fourier spectra,” Trans. Inst. Electron. Commun. Eng. Jpn. Part D J68D, 686–693 (1985).

Other

H. Akirakawa, K. Hirota, “Fuzzy inference engine by address-look-up and paging method,” in Proceedings of the International Workshop on Fuzzy System Applications (International Fuzzy Systems Association, Amsterdam, North-Holland, 1988), pp. 45–56.

H.-J. Zimmermann, Fuzzy Set Theory and Its Applications (Kluwer-Nijhoff, Boston, Mass., 1985), pp. 121–177.

R. Ulichney, Digital Halftoning (MIT, Cambridge, Mass., 1987), pp. 1–14.

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Figures (9)

Fig. 1
Fig. 1

Representation of the gray value X with the ACT.

Fig. 2
Fig. 2

Bayer font set of the MFM with 17 gray tones.

Fig. 3
Fig. 3

Rendering process of the MFM.

Fig. 4
Fig. 4

Processing procedure for optical parallel implementation of fuzzy logic with the VACT.

Fig. 5
Fig. 5

Processing procedure of the negation operation with the VACT.

Fig. 6
Fig. 6

Optical setup for parallel implementation of the negation operation.

Fig. 7
Fig. 7

Experimental elements for fuzzy sets A and B: (a) vector A, (b) vector B, (c) fuzzy relation matrix W, (d) coded pattern of W, (e) input vector A′, and (f) expansion of the coded pattern of A′.

Fig. 8
Fig. 8

Experimental setup for the (a) min { a i , w i j } operation, and (b) max [ min { a i , w i j } ] operation.

Fig. 9
Fig. 9

Theoretical results of (a) min { a i , w i j } and (b) max [ min { a i , w i j } ] and experimental results of (c) min { a i , w i j } and (d) max [ min { a i , w i j } ].

Equations (7)

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

μ ( A ) μ ( B ) = max [ μ ( A ) , μ ( B ) ] ,
μ ( A ) μ ( B ) = min [ μ ( A ) , μ ( B ) ] ,
¬ μ ( A ) = 1 μ ( A ) ,
P k , l = P k , ( m l + 1 ) , 1 k m , 1 1 m ,
W = A × B ,
w i j = min [ a i , b j ] , 1 I n , 1 j m ,
b j = max { min [ a i , w i j ] } , 1 i n , 1 j m .

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