Abstract

The incoherent optical neuron model uses two different device responses, an inhibitory response and a nonlinear output response, to realize a complete neuron unit that has both inhibitory and excitatory inputs. We describe its use to implement a model of simple cells of the visual cortex. Such simple cells perform the operations of edge detection, orientation selection, and in the case of moving objects, direction and speed selection. Experiments are described that utilize two Hughes liquid-crystal light valves to perform the functions of input transduction and optical neuron unit-array implementation. A multiplexed dichromated gelatin hologram serves as a holographic optical element that forms space-invariant (but otherwise arbitrary) point-spread functions for the network interconnections. Changing the holographic interconnection pattern permits implementation of different simple cells performing, e.g., transient response, edge detection, orientation preference, and direction and speed preference. Experimental results of these operations are presented.

© 1993 Optical Society of America

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  1. See, e.g., feature issue on neural networks, Appl. Opt. 26(23) (1987); Proc. IEEE Int. Conf. Neural Net. III (San Diego, Calif., 1987); Proc. IEEE Int. Conf. Neural Net. II (San Diego, Calif., 1988); and Proc. Int. Joint Conf. Neural Net. II (Washington, D.C., 1989).
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  2. C. Mead, Analog VLSI and Neural Systems (Addison-Wesley, New York, 1989).
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  3. S. P. Deweerth, C. A. Mead, “A two-dimensional visual tracking array,” in Advanced Research in VLSI, J. Elen, F. Thompson, X. Leighton, eds., Proceedings of the Fifth MIT Conference (MIT, Cambridge, Mass., 1988).
  4. M. A. C. Maher, S. P. Deweerth, M. A. Mahowald, C. A. Mead, “Implementing neural architectures using analog VLSI circuits,” IEEE Trans. Circuits Syst. 36, 643–652 (1989).
    [CrossRef]
  5. C. H. Wang, B. K. Jenkins, “Subtracting incoherent optical neuron model: analysis, experiment, and applications,” Appl. Opt. 29, 2171–2186 (1990).
    [CrossRef] [PubMed]
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    [CrossRef]
  7. M. D. Levine, Vision in Man and Machine (McGraw-Hill, New York, 1985), Chaps. 3 and 5.
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  11. K. Toyama, K. Maekawa, T. Takeda, “A analysis of neuronal circuitry for two types of visual cortical neurons classified on the basis of their photic stimuli,” Brain Res. 61, 395–399 (1973).
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  12. T. Nagano, K. Kurata, “A model of complex cell based on recent neurophysiological finding,” Biol. Cybernet. 38, 103–105 (1980).
    [CrossRef]
  13. T. Nagano, K. Kurata, “A self-organizing neural network model for the development of complex cells,” Biol. Cybernet. 40, 195–200 (1981).
    [CrossRef]
  14. M. Wang, A. Freeman, Neural Function (Little, Brown, Boston, Mass., 1987).
  15. C. F. Stevens, “The neuron,” Sci. Am.55–65 (August1979).
  16. G. M. Shepherd, “Microcircuits in the nervous system,” Sci. Am.93–103 (February1978).
    [PubMed]
  17. B. K. Jenkins, C. H. Wang, “Requirements for an incoherent optical neuron that subtracts,” J. Opt. Soc. Am A 4, 127 (1987).
  18. C. H. Wang, B. K. Jenkins, “Implementation considerations of a subtracting incoherent optical neuron,” Proc. IEEE Int. Conf. Neural Net.II, 403–410 (1988).
    [CrossRef]
  19. C. H. Wang, B. K. Jenkins, “Implementation of a subtracting incoherent optical neuron,” presented at the Third Annual Parallel Processing Symposium of the Institute of Electrical and Electronics Engineers, Fullerton, Calif., 27–31 March 1989.
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    [PubMed]
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    [PubMed]
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    [CrossRef] [PubMed]
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    [PubMed]
  24. C. E. Heil, D. F. Walnut, “Continuous and discrete wavelet transforms,” SIAM Rev. 31, 628–666 (1989).
    [CrossRef]
  25. D. H. Hubel, T. N. Wiesel, “Receptive fields of single neurons in the cat’s striate cortex,” J. Physiol. London 148, 574–591 (1959).
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    [PubMed]
  27. H. B. Barlow, R. M. Hill, “Selective sensitivity to direction of movement in ganglion cells of the rabbit retina,” Science 139, 412–414 (1963).
    [CrossRef] [PubMed]
  28. N. E. J. Berman, M. E. Wilkes, B. R. Payne, “Organization of orientation and direction selectivity in areas 17 and 18 of cat cerebral cortex,” J. Neurophysiol. 58, 676–699 (1987).
    [PubMed]
  29. C. L. Baker, “Spatial and temporal determinants of directional selective velocity preference in cat striate cortex neurons,” J. Neurophysiol. 59, 1557–1574 (1988).
    [PubMed]
  30. A. Sillto, “Inhibitory processes underlying the directional specificity of simple, complex and hypercomplex cells in the cat’s visual cortex,” J. Physiol. London 271, 699–720 (1977).
  31. P. I. Ruff, J. P. Rauschecker, G. Palm, “A model of direction-selective simple cells in the visual cortex based on inhibition asymmetry,” Biol. Cybernet. 57, 147–157 (1987).
    [CrossRef]
  32. B. K. Jenkins, C. H. Wang, “Model for an incoherent optical neuron that subtracts,” Opt. Lett. 13, 892–894 (1988).
    [CrossRef] [PubMed]
  33. B. K. Jenkins, P. Chavel, R. Forchheimer, A. A. Sawchuk, T. C. Strand, “Architectural implications of a digital optical processor,” Appl. Opt. 23, 3465–3474 (1984).
    [CrossRef] [PubMed]
  34. J. N. Latta, “Analysis of multiple hologram optical elements with low dispersion and low aberrations,” Appl. Opt. 11, 1686–1696 (1972).
    [CrossRef] [PubMed]
  35. N. Nishida, M. Sakaguchi, “Improvement of nonuniformity of the reconstructed beam intensity from a multiple-exposure hologram,” Appl. Opt. 10, 439–440 (1971).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]

1990 (1)

1989 (2)

M. A. C. Maher, S. P. Deweerth, M. A. Mahowald, C. A. Mead, “Implementing neural architectures using analog VLSI circuits,” IEEE Trans. Circuits Syst. 36, 643–652 (1989).
[CrossRef]

C. E. Heil, D. F. Walnut, “Continuous and discrete wavelet transforms,” SIAM Rev. 31, 628–666 (1989).
[CrossRef]

1988 (2)

B. K. Jenkins, C. H. Wang, “Model for an incoherent optical neuron that subtracts,” Opt. Lett. 13, 892–894 (1988).
[CrossRef] [PubMed]

C. L. Baker, “Spatial and temporal determinants of directional selective velocity preference in cat striate cortex neurons,” J. Neurophysiol. 59, 1557–1574 (1988).
[PubMed]

1987 (7)

P. I. Ruff, J. P. Rauschecker, G. Palm, “A model of direction-selective simple cells in the visual cortex based on inhibition asymmetry,” Biol. Cybernet. 57, 147–157 (1987).
[CrossRef]

See, e.g., feature issue on neural networks, Appl. Opt. 26(23) (1987); Proc. IEEE Int. Conf. Neural Net. III (San Diego, Calif., 1987); Proc. IEEE Int. Conf. Neural Net. II (San Diego, Calif., 1988); and Proc. Int. Joint Conf. Neural Net. II (Washington, D.C., 1989).
[PubMed]

N. E. J. Berman, M. E. Wilkes, B. R. Payne, “Organization of orientation and direction selectivity in areas 17 and 18 of cat cerebral cortex,” J. Neurophysiol. 58, 676–699 (1987).
[PubMed]

B. K. Jenkins, C. H. Wang, “Requirements for an incoherent optical neuron that subtracts,” J. Opt. Soc. Am A 4, 127 (1987).

J. P. Jones, L. A. Palmer, “The two-dimensional spatial structure of simple receptive fields in cat striate cortex,” J. Neurophysiol. 58, 1187–1211 (1987).
[PubMed]

J. P. Jones, L. A. Palmer, “An evaluation of the two-dimensional Gabor filter model of simple receptive fields in cat striate cortex,” J. Neurophysiol. 58, 1233–1258 (1987).
[PubMed]

J. P. Jones, L. A. Palmer, “An evaluation of the two-dimensional Gabor filter model of simple receptive fields in cat striate cortex,” J. Neurophysiol. 58, 1233–1258 (1987).
[PubMed]

1984 (2)

1981 (1)

T. Nagano, K. Kurata, “A self-organizing neural network model for the development of complex cells,” Biol. Cybernet. 40, 195–200 (1981).
[CrossRef]

1980 (2)

T. Nagano, K. Kurata, “A model of complex cell based on recent neurophysiological finding,” Biol. Cybernet. 38, 103–105 (1980).
[CrossRef]

S. Marcelja, “Mathematical description of the responses of simple cortical cells,” J. Opt. Soc. Am. 70, 1297–1300 (1980).
[CrossRef] [PubMed]

1979 (2)

C. F. Stevens, “The neuron,” Sci. Am.55–65 (August1979).

J. Stone, B. Dreher, A. Leventhal, “Hierarchical and parallel mechanisms in the organization of visual cortex,” Brain Res. Rev. 1, 345–394 (1979).
[CrossRef]

1978 (1)

G. M. Shepherd, “Microcircuits in the nervous system,” Sci. Am.93–103 (February1978).
[PubMed]

1977 (2)

R. C. Emerson, G. L. Gerstein, “Simple striate neurons in the cat. II. Mechanisms underlying directional asymmetry and directional selectivity,” J. Neurophysiol. 40, 136–155 (1977).
[PubMed]

A. Sillto, “Inhibitory processes underlying the directional specificity of simple, complex and hypercomplex cells in the cat’s visual cortex,” J. Physiol. London 271, 699–720 (1977).

1976 (1)

P. H. Schiller, B. L. Finlay, S. F. Volman, “Quantitative studies of single cell properties in monkey striate cortex II: orientation specificity and ocular dominance,” J. Neurophysiol. 39, 1320–1333 (1976).
[PubMed]

1973 (1)

K. Toyama, K. Maekawa, T. Takeda, “A analysis of neuronal circuitry for two types of visual cortical neurons classified on the basis of their photic stimuli,” Brain Res. 61, 395–399 (1973).
[CrossRef] [PubMed]

1972 (1)

1971 (1)

1965 (1)

D. H. Hubel, T. N. Wiesel, “Receptive fields and functional architecture in two nonstriate visual areas (18 and 19) of the cat,” J. Neurophysiol. 28, 229–289 (1965).
[PubMed]

1963 (1)

H. B. Barlow, R. M. Hill, “Selective sensitivity to direction of movement in ganglion cells of the rabbit retina,” Science 139, 412–414 (1963).
[CrossRef] [PubMed]

1962 (1)

D. H. Hubel, T. N. Wiesel, “Receptive fields, binocular interaction and functional architecture in the cat’s visual cortex,” J. Physiol. London 160, 106–154 (1962).

1959 (1)

D. H. Hubel, T. N. Wiesel, “Receptive fields of single neurons in the cat’s striate cortex,” J. Physiol. London 148, 574–591 (1959).

Baker, C. L.

C. L. Baker, “Spatial and temporal determinants of directional selective velocity preference in cat striate cortex neurons,” J. Neurophysiol. 59, 1557–1574 (1988).
[PubMed]

Barlow, H. B.

H. B. Barlow, R. M. Hill, “Selective sensitivity to direction of movement in ganglion cells of the rabbit retina,” Science 139, 412–414 (1963).
[CrossRef] [PubMed]

Berman, N. E. J.

N. E. J. Berman, M. E. Wilkes, B. R. Payne, “Organization of orientation and direction selectivity in areas 17 and 18 of cat cerebral cortex,” J. Neurophysiol. 58, 676–699 (1987).
[PubMed]

Chavel, P.

Deweerth, S. P.

M. A. C. Maher, S. P. Deweerth, M. A. Mahowald, C. A. Mead, “Implementing neural architectures using analog VLSI circuits,” IEEE Trans. Circuits Syst. 36, 643–652 (1989).
[CrossRef]

S. P. Deweerth, C. A. Mead, “A two-dimensional visual tracking array,” in Advanced Research in VLSI, J. Elen, F. Thompson, X. Leighton, eds., Proceedings of the Fifth MIT Conference (MIT, Cambridge, Mass., 1988).

Dreher, B.

J. Stone, B. Dreher, A. Leventhal, “Hierarchical and parallel mechanisms in the organization of visual cortex,” Brain Res. Rev. 1, 345–394 (1979).
[CrossRef]

Emerson, R. C.

R. C. Emerson, G. L. Gerstein, “Simple striate neurons in the cat. II. Mechanisms underlying directional asymmetry and directional selectivity,” J. Neurophysiol. 40, 136–155 (1977).
[PubMed]

Finlay, B. L.

P. H. Schiller, B. L. Finlay, S. F. Volman, “Quantitative studies of single cell properties in monkey striate cortex II: orientation specificity and ocular dominance,” J. Neurophysiol. 39, 1320–1333 (1976).
[PubMed]

Forchheimer, R.

Freeman, A.

M. Wang, A. Freeman, Neural Function (Little, Brown, Boston, Mass., 1987).

Gerstein, G. L.

R. C. Emerson, G. L. Gerstein, “Simple striate neurons in the cat. II. Mechanisms underlying directional asymmetry and directional selectivity,” J. Neurophysiol. 40, 136–155 (1977).
[PubMed]

Goodman, J. W.

Heil, C. E.

C. E. Heil, D. F. Walnut, “Continuous and discrete wavelet transforms,” SIAM Rev. 31, 628–666 (1989).
[CrossRef]

Hesselink, L.

Hill, R. M.

H. B. Barlow, R. M. Hill, “Selective sensitivity to direction of movement in ganglion cells of the rabbit retina,” Science 139, 412–414 (1963).
[CrossRef] [PubMed]

Hubel, D. H.

D. H. Hubel, T. N. Wiesel, “Receptive fields and functional architecture in two nonstriate visual areas (18 and 19) of the cat,” J. Neurophysiol. 28, 229–289 (1965).
[PubMed]

D. H. Hubel, T. N. Wiesel, “Receptive fields, binocular interaction and functional architecture in the cat’s visual cortex,” J. Physiol. London 160, 106–154 (1962).

D. H. Hubel, T. N. Wiesel, “Receptive fields of single neurons in the cat’s striate cortex,” J. Physiol. London 148, 574–591 (1959).

Jenkins, B. K.

C. H. Wang, B. K. Jenkins, “Subtracting incoherent optical neuron model: analysis, experiment, and applications,” Appl. Opt. 29, 2171–2186 (1990).
[CrossRef] [PubMed]

B. K. Jenkins, C. H. Wang, “Model for an incoherent optical neuron that subtracts,” Opt. Lett. 13, 892–894 (1988).
[CrossRef] [PubMed]

B. K. Jenkins, C. H. Wang, “Requirements for an incoherent optical neuron that subtracts,” J. Opt. Soc. Am A 4, 127 (1987).

B. K. Jenkins, P. Chavel, R. Forchheimer, A. A. Sawchuk, T. C. Strand, “Architectural implications of a digital optical processor,” Appl. Opt. 23, 3465–3474 (1984).
[CrossRef] [PubMed]

C. H. Wang, B. K. Jenkins, “Implementation considerations of a subtracting incoherent optical neuron,” Proc. IEEE Int. Conf. Neural Net.II, 403–410 (1988).
[CrossRef]

C. H. Wang, B. K. Jenkins, “Implementation of a subtracting incoherent optical neuron,” presented at the Third Annual Parallel Processing Symposium of the Institute of Electrical and Electronics Engineers, Fullerton, Calif., 27–31 March 1989.

Johnson, K. M.

Jones, J. P.

J. P. Jones, L. A. Palmer, “An evaluation of the two-dimensional Gabor filter model of simple receptive fields in cat striate cortex,” J. Neurophysiol. 58, 1233–1258 (1987).
[PubMed]

J. P. Jones, L. A. Palmer, “The two-dimensional spatial structure of simple receptive fields in cat striate cortex,” J. Neurophysiol. 58, 1187–1211 (1987).
[PubMed]

J. P. Jones, L. A. Palmer, “An evaluation of the two-dimensional Gabor filter model of simple receptive fields in cat striate cortex,” J. Neurophysiol. 58, 1233–1258 (1987).
[PubMed]

Kurata, K.

T. Nagano, K. Kurata, “A self-organizing neural network model for the development of complex cells,” Biol. Cybernet. 40, 195–200 (1981).
[CrossRef]

T. Nagano, K. Kurata, “A model of complex cell based on recent neurophysiological finding,” Biol. Cybernet. 38, 103–105 (1980).
[CrossRef]

Latta, J. N.

Leventhal, A.

J. Stone, B. Dreher, A. Leventhal, “Hierarchical and parallel mechanisms in the organization of visual cortex,” Brain Res. Rev. 1, 345–394 (1979).
[CrossRef]

Levine, M. D.

M. D. Levine, Vision in Man and Machine (McGraw-Hill, New York, 1985), Chaps. 3 and 5.

Maekawa, K.

K. Toyama, K. Maekawa, T. Takeda, “A analysis of neuronal circuitry for two types of visual cortical neurons classified on the basis of their photic stimuli,” Brain Res. 61, 395–399 (1973).
[CrossRef] [PubMed]

Maher, M. A. C.

M. A. C. Maher, S. P. Deweerth, M. A. Mahowald, C. A. Mead, “Implementing neural architectures using analog VLSI circuits,” IEEE Trans. Circuits Syst. 36, 643–652 (1989).
[CrossRef]

Mahowald, M. A.

M. A. C. Maher, S. P. Deweerth, M. A. Mahowald, C. A. Mead, “Implementing neural architectures using analog VLSI circuits,” IEEE Trans. Circuits Syst. 36, 643–652 (1989).
[CrossRef]

Marcelja, S.

Mead, C.

C. Mead, Analog VLSI and Neural Systems (Addison-Wesley, New York, 1989).
[CrossRef]

Mead, C. A.

M. A. C. Maher, S. P. Deweerth, M. A. Mahowald, C. A. Mead, “Implementing neural architectures using analog VLSI circuits,” IEEE Trans. Circuits Syst. 36, 643–652 (1989).
[CrossRef]

S. P. Deweerth, C. A. Mead, “A two-dimensional visual tracking array,” in Advanced Research in VLSI, J. Elen, F. Thompson, X. Leighton, eds., Proceedings of the Fifth MIT Conference (MIT, Cambridge, Mass., 1988).

Nagano, T.

T. Nagano, K. Kurata, “A self-organizing neural network model for the development of complex cells,” Biol. Cybernet. 40, 195–200 (1981).
[CrossRef]

T. Nagano, K. Kurata, “A model of complex cell based on recent neurophysiological finding,” Biol. Cybernet. 38, 103–105 (1980).
[CrossRef]

Nishida, N.

Palm, G.

P. I. Ruff, J. P. Rauschecker, G. Palm, “A model of direction-selective simple cells in the visual cortex based on inhibition asymmetry,” Biol. Cybernet. 57, 147–157 (1987).
[CrossRef]

Palmer, L. A.

J. P. Jones, L. A. Palmer, “The two-dimensional spatial structure of simple receptive fields in cat striate cortex,” J. Neurophysiol. 58, 1187–1211 (1987).
[PubMed]

J. P. Jones, L. A. Palmer, “An evaluation of the two-dimensional Gabor filter model of simple receptive fields in cat striate cortex,” J. Neurophysiol. 58, 1233–1258 (1987).
[PubMed]

J. P. Jones, L. A. Palmer, “An evaluation of the two-dimensional Gabor filter model of simple receptive fields in cat striate cortex,” J. Neurophysiol. 58, 1233–1258 (1987).
[PubMed]

Payne, B. R.

N. E. J. Berman, M. E. Wilkes, B. R. Payne, “Organization of orientation and direction selectivity in areas 17 and 18 of cat cerebral cortex,” J. Neurophysiol. 58, 676–699 (1987).
[PubMed]

Rauschecker, J. P.

P. I. Ruff, J. P. Rauschecker, G. Palm, “A model of direction-selective simple cells in the visual cortex based on inhibition asymmetry,” Biol. Cybernet. 57, 147–157 (1987).
[CrossRef]

Ruff, P. I.

P. I. Ruff, J. P. Rauschecker, G. Palm, “A model of direction-selective simple cells in the visual cortex based on inhibition asymmetry,” Biol. Cybernet. 57, 147–157 (1987).
[CrossRef]

Sakaguchi, M.

Sawchuk, A. A.

Schiller, P. H.

P. H. Schiller, B. L. Finlay, S. F. Volman, “Quantitative studies of single cell properties in monkey striate cortex II: orientation specificity and ocular dominance,” J. Neurophysiol. 39, 1320–1333 (1976).
[PubMed]

Shepherd, G. M.

G. M. Shepherd, “Microcircuits in the nervous system,” Sci. Am.93–103 (February1978).
[PubMed]

Sillto, A.

A. Sillto, “Inhibitory processes underlying the directional specificity of simple, complex and hypercomplex cells in the cat’s visual cortex,” J. Physiol. London 271, 699–720 (1977).

Stevens, C. F.

C. F. Stevens, “The neuron,” Sci. Am.55–65 (August1979).

Stone, J.

J. Stone, B. Dreher, A. Leventhal, “Hierarchical and parallel mechanisms in the organization of visual cortex,” Brain Res. Rev. 1, 345–394 (1979).
[CrossRef]

Strand, T. C.

Takeda, T.

K. Toyama, K. Maekawa, T. Takeda, “A analysis of neuronal circuitry for two types of visual cortical neurons classified on the basis of their photic stimuli,” Brain Res. 61, 395–399 (1973).
[CrossRef] [PubMed]

Toyama, K.

K. Toyama, K. Maekawa, T. Takeda, “A analysis of neuronal circuitry for two types of visual cortical neurons classified on the basis of their photic stimuli,” Brain Res. 61, 395–399 (1973).
[CrossRef] [PubMed]

Volman, S. F.

P. H. Schiller, B. L. Finlay, S. F. Volman, “Quantitative studies of single cell properties in monkey striate cortex II: orientation specificity and ocular dominance,” J. Neurophysiol. 39, 1320–1333 (1976).
[PubMed]

Walnut, D. F.

C. E. Heil, D. F. Walnut, “Continuous and discrete wavelet transforms,” SIAM Rev. 31, 628–666 (1989).
[CrossRef]

Wang, C. H.

C. H. Wang, B. K. Jenkins, “Subtracting incoherent optical neuron model: analysis, experiment, and applications,” Appl. Opt. 29, 2171–2186 (1990).
[CrossRef] [PubMed]

B. K. Jenkins, C. H. Wang, “Model for an incoherent optical neuron that subtracts,” Opt. Lett. 13, 892–894 (1988).
[CrossRef] [PubMed]

B. K. Jenkins, C. H. Wang, “Requirements for an incoherent optical neuron that subtracts,” J. Opt. Soc. Am A 4, 127 (1987).

C. H. Wang, B. K. Jenkins, “Implementation of a subtracting incoherent optical neuron,” presented at the Third Annual Parallel Processing Symposium of the Institute of Electrical and Electronics Engineers, Fullerton, Calif., 27–31 March 1989.

C. H. Wang, B. K. Jenkins, “Implementation considerations of a subtracting incoherent optical neuron,” Proc. IEEE Int. Conf. Neural Net.II, 403–410 (1988).
[CrossRef]

Wang, M.

M. Wang, A. Freeman, Neural Function (Little, Brown, Boston, Mass., 1987).

Wiesel, T. N.

D. H. Hubel, T. N. Wiesel, “Receptive fields and functional architecture in two nonstriate visual areas (18 and 19) of the cat,” J. Neurophysiol. 28, 229–289 (1965).
[PubMed]

D. H. Hubel, T. N. Wiesel, “Receptive fields, binocular interaction and functional architecture in the cat’s visual cortex,” J. Physiol. London 160, 106–154 (1962).

D. H. Hubel, T. N. Wiesel, “Receptive fields of single neurons in the cat’s striate cortex,” J. Physiol. London 148, 574–591 (1959).

Wilkes, M. E.

N. E. J. Berman, M. E. Wilkes, B. R. Payne, “Organization of orientation and direction selectivity in areas 17 and 18 of cat cerebral cortex,” J. Neurophysiol. 58, 676–699 (1987).
[PubMed]

Appl. Opt. (6)

Biol. Cybernet. (3)

P. I. Ruff, J. P. Rauschecker, G. Palm, “A model of direction-selective simple cells in the visual cortex based on inhibition asymmetry,” Biol. Cybernet. 57, 147–157 (1987).
[CrossRef]

T. Nagano, K. Kurata, “A model of complex cell based on recent neurophysiological finding,” Biol. Cybernet. 38, 103–105 (1980).
[CrossRef]

T. Nagano, K. Kurata, “A self-organizing neural network model for the development of complex cells,” Biol. Cybernet. 40, 195–200 (1981).
[CrossRef]

Brain Res. (1)

K. Toyama, K. Maekawa, T. Takeda, “A analysis of neuronal circuitry for two types of visual cortical neurons classified on the basis of their photic stimuli,” Brain Res. 61, 395–399 (1973).
[CrossRef] [PubMed]

Brain Res. Rev. (1)

J. Stone, B. Dreher, A. Leventhal, “Hierarchical and parallel mechanisms in the organization of visual cortex,” Brain Res. Rev. 1, 345–394 (1979).
[CrossRef]

IEEE Trans. Circuits Syst. (1)

M. A. C. Maher, S. P. Deweerth, M. A. Mahowald, C. A. Mead, “Implementing neural architectures using analog VLSI circuits,” IEEE Trans. Circuits Syst. 36, 643–652 (1989).
[CrossRef]

J. Neurophysiol. (8)

R. C. Emerson, G. L. Gerstein, “Simple striate neurons in the cat. II. Mechanisms underlying directional asymmetry and directional selectivity,” J. Neurophysiol. 40, 136–155 (1977).
[PubMed]

N. E. J. Berman, M. E. Wilkes, B. R. Payne, “Organization of orientation and direction selectivity in areas 17 and 18 of cat cerebral cortex,” J. Neurophysiol. 58, 676–699 (1987).
[PubMed]

C. L. Baker, “Spatial and temporal determinants of directional selective velocity preference in cat striate cortex neurons,” J. Neurophysiol. 59, 1557–1574 (1988).
[PubMed]

P. H. Schiller, B. L. Finlay, S. F. Volman, “Quantitative studies of single cell properties in monkey striate cortex II: orientation specificity and ocular dominance,” J. Neurophysiol. 39, 1320–1333 (1976).
[PubMed]

D. H. Hubel, T. N. Wiesel, “Receptive fields and functional architecture in two nonstriate visual areas (18 and 19) of the cat,” J. Neurophysiol. 28, 229–289 (1965).
[PubMed]

J. P. Jones, L. A. Palmer, “The two-dimensional spatial structure of simple receptive fields in cat striate cortex,” J. Neurophysiol. 58, 1187–1211 (1987).
[PubMed]

J. P. Jones, L. A. Palmer, “An evaluation of the two-dimensional Gabor filter model of simple receptive fields in cat striate cortex,” J. Neurophysiol. 58, 1233–1258 (1987).
[PubMed]

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Figures (18)

Fig. 1
Fig. 1

The ION model comprises two device responses: I (inhibitory) and N (nonlinear output) elements. The N-element response has an offset, which provides for the required subtraction and the neuron-unit threshold.

Fig. 2
Fig. 2

Typical characteristic of a Hughes-twisted nematic LCLV biased to serve as both I and N elements. Regions A and C are used for the I and N element, respectively. Region B serves to separate the I element from the N element. A self-feedback to the N element was necessary in our case to achieve the N-element input sensitivity and nonlinearity (relative to the I element) shown above. Also shown are Ir, the maximum residual output of the device, α, the nominal offset of the N-element response that corresponds to an output of Ir; and Ibias, the optical bias intensity that is input to the N element.

Fig. 3
Fig. 3

Model for optical implementation of the orientation-sensitive cells showing (a) receptive field, (b) space-invariant neural interconnection pattern, (c) ION implementation (two LCLV’s are required: one for input transduction and the other for implementing the neuron units), and (d) physical layout and interconnection point-spread function.

Fig. 4
Fig. 4

Model for optical implementation of edge-sensitive cells showing (a) receptive field, (b) space-invariant interconnection pattern, and (c) physical layout and interconnection point-spread function. The ION circuit is the same as in Fig. 3(c).

Fig. 5
Fig. 5

Implementation of transient cells and their temporal responses. The shown waveforms are for the binary case: (a) on-transient cell, (b) off-transient cell, and (c) another implentation of off-transient cell. The temporal responses shown assume each N element has one time unit of delay and each I element has negligible time delay. A, B, interneuron outputs.

Fig. 6
Fig. 6

A neural network for direction-sensitive and speed-sensitive motion cells based on lateral inhibition: (a) one-dimensional example in which one fan-out pattern is shown in boldface for clarity and (b) examples of two-dimensional interconnection patterns (projective fields) to the interneurons for various speed preferences. The degree of directional selectivity can be changed by altering the width of the noninhibitory regions.

Fig. 7
Fig. 7

Optical implementation of direction- and speed-sensitive cells based on lateral inhibition, showing (a) ION implementation and (b) physical layout and interconnection point-spread function. The N1 region serves as delay interneurons, and the other regions (I and N2) serve as complete neuron units. This implementation suppresses downward and horizontal movement.

Fig. 8
Fig. 8

Optical setup for the implementation of visual cortex operations: CRT, cathode-ray tube; ND, neutral-density filter; P1, P2, polarizers; O/P, output; SF1, spatial filter.

Fig. 9
Fig. 9

Experimental results of orientation-sensitive cells that prefer vertical line inputs, showing (a) interconnection pattern of the input layer and (b)–(d) output responses corresponding to different input patterns. The input is shown spatially inverted relative to the outputs.

Fig. 10
Fig. 10

Experimental results of orientation-sensitive cells: (a)–(d) output responses corresponding to different input patterns.

Fig. 11
Fig. 11

Experimental results of edge-sensitive cells, showing (a) interconnection pattern and (b)–(f) output responses corresponding to different input patterns.

Fig. 12
Fig. 12

Experimental result of off-transient cells responding to a horizontal moving line input. Successive frames represent samples taken every 66 ms.

Fig. 13
Fig. 13

Time sequences of frames showing responses of off-transient cells corresponding to (a) on-transient inputs and (b) off-transient inputs in the fourth row (of the output). Successive frames represent samples taken every 66 ms.

Fig. 14
Fig. 14

A single time sequence showing responses of off-transient cells to a Chinese character input during and after (a) ON transient and (b) OFF transient. Successive frames represent samples taken every 66 ms.

Fig. 15
Fig. 15

Time sequences showing responses of direction-sensitive cells to (a) an upward-moving bar and (b) a downward-moving bar. (The input is shown spatially inverted relative to the outputs.) Elapsed time (h:min:s) is shown.

Fig. 16
Fig. 16

Time sequences showing responses of direction-sensitive cells to a diagonal line moving (a) up and right and (b) down and left. (The input is shown spatially inverted relative to the outputs.) Elapsed time (h:min:s) is shown.

Fig. 17
Fig. 17

Pyramid structures for a massively connected visual cortex implementation: (a) space-variant connections and (b) space-invariant connections for the neurons in the same layer.

Fig. 18
Fig. 18

Nonuniformity plot of total diffraction efficiency of the hololens used in the implementation of (a) orientation-sensitive cells and (b) direction-sensitive motion cells. The nominal total diffraction efficiency of (a) and (b) are 6.8% and 6.4%, respectively. An open circle represents a positive value and the filled circle represents a negative value, expressed as a percentage deviation from the diffraction efficiency obtained at the center of the hololens.

Equations (3)

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I out = Ψ ( I exc - I inh ) ,
f ( x , y ) = K 0 cos [ - 2 π ( U 0 x + V 0 y ) - Θ ] × exp [ - 1 / 2 ( x r 2 / a 2 + y r 2 / b 2 ) ] ,
DI = 1 - n p / p ,

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