Abstract

If striate cells had the receptive-field (RF) shapes classically attributed to them, their preferred spatial frequencies would vary considerably with orientation. Other models of RF shape would predict a greater independence between orientation and spatial-frequency tuning. We have examined this by recording the responses of cat striate-cortex cells to a wide range of different spatial-frequency and orientation combinations. In almost all cells studied, peak orientation did not consistently vary with spatial frequency, but the majority of cells showed some change in peak spatial-frequency tuning with orientation. The amount of change in peak spatial frequency tended to be greater for cells that were narrowly tuned for orientation. However, cells narrowly (and also very broadly) tuned for spatial frequency tended to show considerable independence of spatial-frequency and orientation tuning, and in all but a few cells the degree of change was less than predicted by the classic RF model. Such cells were found to fire only to patterns whose local spatial spectra fell within a compact, restricted, roughly circular two-dimensional spatial-frequency region. We conclude that the two-dimensional RF shape of striate cells more closely approximates that predicted by a two-dimensional Gabor model or by a Gaussian-derivative model than it does the classic shape based on the output of geniculate cells with aligned RF’s.

© 1985 Optical Society of America

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References

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  1. J. G. Daugman, “Two-dimensional spectral analysis of cortical receptive field profiles,” Vision Res. 20, 847–856 (1980).
    [CrossRef] [PubMed]
  2. J. G. Daugman, “Six formal properties of two-dimensional anisotropic visual filters: structural principles and frequency/orientation selectivity,” IEEE Trans. Sys. Man Cybern. SMC-13, 882–887 (1983);J. G. Daugman, “Representational issues and local filter models of two-dimensional spatial visual encoding,” in Models of the Visual Cortex, D. Rose, V. G. Dobson, eds. (Wiley, New York, 1984).
    [CrossRef]
  3. 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).
  4. G. H. Henry, P. O. Bishop, B. Dreher, “Orientation, axis and direction as stimulus parameters for striate cells,” Vision Res. 14, 767–777 (1974);D. Rose, C. Blakemore, “An analysis of orientation selectivity in the cat’s visual cortex,” Exp. Brain Res. 20, 1–17 (1974);H. Ikeda, M. J. Wright, “Spatial and temporal properties of ‘sustained’ and ‘transient’ neurones in area 17 of the cat’s visual cortex,” Exp. Brain Res. 22, 363–383 (1975);R. J. W. Mansfield, “Neural basis of orientation perception in primate vision,” Science 186, 1133–1135 (1974);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);G. F. Poggio, F. H. Baker, R. J. W. Mansfield, A. Sillito, P. Grigg, “Spatial and chromatic properties of neurons subserving foveal and parafoveal vision in rhesus monkey,” Brain Res. 100, 25–59 (1975);R. L. De Valois, E. W. Yund, N. Hepler, “The orientation and direction selectivity of cells in macaque visual cortex,” Vision Res. 22, 531–544 (1982).
    [CrossRef] [PubMed]
  5. F. W. Campbell, G. F. Cooper, C. Enroth-Cugell, “The spatial selectivity of the visual cells of the cat,” J. Physiol. (London) 203, 223–235 (1969);L. Maffei, A. Fiorentini, “The visual cortex as a spatial frequency analyzer,” Vision Res. 13, 1255–1267 (1973);P. H. Schiller, B. L. Finlay, S. F. Volman, “Quantitative studies of single-cell properties in monkey striate cortex. I. Spatiotemporal organization of receptive fields,” J. Neurophysiol. 39, 1288–1319 (1976);J. A. Movshon, I. D. Thompson, D. J. Tolhurst, “Spatial summation in the receptive fields of simple cells in the cat’s striate cortex,” J. Physiol. (London) 283, 53–77 (1978);B. W. Andrews, D. A. Pollen, “Relationship between spatial frequency selectivity and receptive field profile of simple cells,” J. Physiol. (London) 287, 163–176 (1979);J. J. Kulikowski, P. O. Bishop, “Linear analysis of the responses of simple cells in the cat visual cortex,” Exp. Brain Res. 44, 386–400 (1981);R. L. De Valois, D. G. Albrecht, L. G. Thorell, “Spatial frequency selectivity of cells in macaque visual cortex,” Vision Res. 22, 545–559 (1982).
    [CrossRef] [PubMed]
  6. R. L. De Valois, D. G. Albrecht, L. G. Thorell, “Spatial frequency selectivity of cells in macaque visual cortex,” Vision Res. 22, 545–559 (1982).
    [CrossRef] [PubMed]
  7. J. A. Movshon, “Two-dimensional spatial frequency tuning of cat striate cortical neurons,” Soc. Neurosci. 5, 799 (1979).
  8. S. Marcelja, “Mathematical description of the responses of simple cortical cells,” J. Opt. Soc. Am. 70, 1297–1300 (1980).
    [CrossRef] [PubMed]
  9. V. D. Glezer, T. A. Tsherbach, V. E. Gauselman, V. M. Bondarko, “Spatiotemporal organization of receptive fields in the cat striate cortex,” Biol. Cybern. 43, 35–49 (1982).
    [CrossRef]
  10. J. A. Movshon, I. D. Thompson, D. J. Tolhurst, “Spatial and temporal contrast sensitivity of neurones in areas 17 and 18 of the cat’s visual cortex,” J. Physiol. (London) 283, 101–120 (1978).
  11. R. W. Rodieck, “Quantitative analysis of cat retinal ganglion cell response to visual stimuli,” Vision Res. 5, 583–601 (1965).
    [CrossRef] [PubMed]
  12. R. A. Young, R. T. Marrocco, “Gaussian derivative model of receptive field structure,” Computer Science Department, General Motors Research Laboratories, Warren, Michigan 48090-9057 (personal communication).

1983

J. G. Daugman, “Six formal properties of two-dimensional anisotropic visual filters: structural principles and frequency/orientation selectivity,” IEEE Trans. Sys. Man Cybern. SMC-13, 882–887 (1983);J. G. Daugman, “Representational issues and local filter models of two-dimensional spatial visual encoding,” in Models of the Visual Cortex, D. Rose, V. G. Dobson, eds. (Wiley, New York, 1984).
[CrossRef]

1982

R. L. De Valois, D. G. Albrecht, L. G. Thorell, “Spatial frequency selectivity of cells in macaque visual cortex,” Vision Res. 22, 545–559 (1982).
[CrossRef] [PubMed]

V. D. Glezer, T. A. Tsherbach, V. E. Gauselman, V. M. Bondarko, “Spatiotemporal organization of receptive fields in the cat striate cortex,” Biol. Cybern. 43, 35–49 (1982).
[CrossRef]

1980

J. G. Daugman, “Two-dimensional spectral analysis of cortical receptive field profiles,” Vision Res. 20, 847–856 (1980).
[CrossRef] [PubMed]

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

1979

J. A. Movshon, “Two-dimensional spatial frequency tuning of cat striate cortical neurons,” Soc. Neurosci. 5, 799 (1979).

1978

J. A. Movshon, I. D. Thompson, D. J. Tolhurst, “Spatial and temporal contrast sensitivity of neurones in areas 17 and 18 of the cat’s visual cortex,” J. Physiol. (London) 283, 101–120 (1978).

1974

G. H. Henry, P. O. Bishop, B. Dreher, “Orientation, axis and direction as stimulus parameters for striate cells,” Vision Res. 14, 767–777 (1974);D. Rose, C. Blakemore, “An analysis of orientation selectivity in the cat’s visual cortex,” Exp. Brain Res. 20, 1–17 (1974);H. Ikeda, M. J. Wright, “Spatial and temporal properties of ‘sustained’ and ‘transient’ neurones in area 17 of the cat’s visual cortex,” Exp. Brain Res. 22, 363–383 (1975);R. J. W. Mansfield, “Neural basis of orientation perception in primate vision,” Science 186, 1133–1135 (1974);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);G. F. Poggio, F. H. Baker, R. J. W. Mansfield, A. Sillito, P. Grigg, “Spatial and chromatic properties of neurons subserving foveal and parafoveal vision in rhesus monkey,” Brain Res. 100, 25–59 (1975);R. L. De Valois, E. W. Yund, N. Hepler, “The orientation and direction selectivity of cells in macaque visual cortex,” Vision Res. 22, 531–544 (1982).
[CrossRef] [PubMed]

1969

F. W. Campbell, G. F. Cooper, C. Enroth-Cugell, “The spatial selectivity of the visual cells of the cat,” J. Physiol. (London) 203, 223–235 (1969);L. Maffei, A. Fiorentini, “The visual cortex as a spatial frequency analyzer,” Vision Res. 13, 1255–1267 (1973);P. H. Schiller, B. L. Finlay, S. F. Volman, “Quantitative studies of single-cell properties in monkey striate cortex. I. Spatiotemporal organization of receptive fields,” J. Neurophysiol. 39, 1288–1319 (1976);J. A. Movshon, I. D. Thompson, D. J. Tolhurst, “Spatial summation in the receptive fields of simple cells in the cat’s striate cortex,” J. Physiol. (London) 283, 53–77 (1978);B. W. Andrews, D. A. Pollen, “Relationship between spatial frequency selectivity and receptive field profile of simple cells,” J. Physiol. (London) 287, 163–176 (1979);J. J. Kulikowski, P. O. Bishop, “Linear analysis of the responses of simple cells in the cat visual cortex,” Exp. Brain Res. 44, 386–400 (1981);R. L. De Valois, D. G. Albrecht, L. G. Thorell, “Spatial frequency selectivity of cells in macaque visual cortex,” Vision Res. 22, 545–559 (1982).
[CrossRef] [PubMed]

1965

R. W. Rodieck, “Quantitative analysis of cat retinal ganglion cell response to visual stimuli,” Vision Res. 5, 583–601 (1965).
[CrossRef] [PubMed]

1962

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).

Albrecht, D. G.

R. L. De Valois, D. G. Albrecht, L. G. Thorell, “Spatial frequency selectivity of cells in macaque visual cortex,” Vision Res. 22, 545–559 (1982).
[CrossRef] [PubMed]

Bishop, P. O.

G. H. Henry, P. O. Bishop, B. Dreher, “Orientation, axis and direction as stimulus parameters for striate cells,” Vision Res. 14, 767–777 (1974);D. Rose, C. Blakemore, “An analysis of orientation selectivity in the cat’s visual cortex,” Exp. Brain Res. 20, 1–17 (1974);H. Ikeda, M. J. Wright, “Spatial and temporal properties of ‘sustained’ and ‘transient’ neurones in area 17 of the cat’s visual cortex,” Exp. Brain Res. 22, 363–383 (1975);R. J. W. Mansfield, “Neural basis of orientation perception in primate vision,” Science 186, 1133–1135 (1974);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);G. F. Poggio, F. H. Baker, R. J. W. Mansfield, A. Sillito, P. Grigg, “Spatial and chromatic properties of neurons subserving foveal and parafoveal vision in rhesus monkey,” Brain Res. 100, 25–59 (1975);R. L. De Valois, E. W. Yund, N. Hepler, “The orientation and direction selectivity of cells in macaque visual cortex,” Vision Res. 22, 531–544 (1982).
[CrossRef] [PubMed]

Bondarko, V. M.

V. D. Glezer, T. A. Tsherbach, V. E. Gauselman, V. M. Bondarko, “Spatiotemporal organization of receptive fields in the cat striate cortex,” Biol. Cybern. 43, 35–49 (1982).
[CrossRef]

Campbell, F. W.

F. W. Campbell, G. F. Cooper, C. Enroth-Cugell, “The spatial selectivity of the visual cells of the cat,” J. Physiol. (London) 203, 223–235 (1969);L. Maffei, A. Fiorentini, “The visual cortex as a spatial frequency analyzer,” Vision Res. 13, 1255–1267 (1973);P. H. Schiller, B. L. Finlay, S. F. Volman, “Quantitative studies of single-cell properties in monkey striate cortex. I. Spatiotemporal organization of receptive fields,” J. Neurophysiol. 39, 1288–1319 (1976);J. A. Movshon, I. D. Thompson, D. J. Tolhurst, “Spatial summation in the receptive fields of simple cells in the cat’s striate cortex,” J. Physiol. (London) 283, 53–77 (1978);B. W. Andrews, D. A. Pollen, “Relationship between spatial frequency selectivity and receptive field profile of simple cells,” J. Physiol. (London) 287, 163–176 (1979);J. J. Kulikowski, P. O. Bishop, “Linear analysis of the responses of simple cells in the cat visual cortex,” Exp. Brain Res. 44, 386–400 (1981);R. L. De Valois, D. G. Albrecht, L. G. Thorell, “Spatial frequency selectivity of cells in macaque visual cortex,” Vision Res. 22, 545–559 (1982).
[CrossRef] [PubMed]

Cooper, G. F.

F. W. Campbell, G. F. Cooper, C. Enroth-Cugell, “The spatial selectivity of the visual cells of the cat,” J. Physiol. (London) 203, 223–235 (1969);L. Maffei, A. Fiorentini, “The visual cortex as a spatial frequency analyzer,” Vision Res. 13, 1255–1267 (1973);P. H. Schiller, B. L. Finlay, S. F. Volman, “Quantitative studies of single-cell properties in monkey striate cortex. I. Spatiotemporal organization of receptive fields,” J. Neurophysiol. 39, 1288–1319 (1976);J. A. Movshon, I. D. Thompson, D. J. Tolhurst, “Spatial summation in the receptive fields of simple cells in the cat’s striate cortex,” J. Physiol. (London) 283, 53–77 (1978);B. W. Andrews, D. A. Pollen, “Relationship between spatial frequency selectivity and receptive field profile of simple cells,” J. Physiol. (London) 287, 163–176 (1979);J. J. Kulikowski, P. O. Bishop, “Linear analysis of the responses of simple cells in the cat visual cortex,” Exp. Brain Res. 44, 386–400 (1981);R. L. De Valois, D. G. Albrecht, L. G. Thorell, “Spatial frequency selectivity of cells in macaque visual cortex,” Vision Res. 22, 545–559 (1982).
[CrossRef] [PubMed]

Daugman, J. G.

J. G. Daugman, “Six formal properties of two-dimensional anisotropic visual filters: structural principles and frequency/orientation selectivity,” IEEE Trans. Sys. Man Cybern. SMC-13, 882–887 (1983);J. G. Daugman, “Representational issues and local filter models of two-dimensional spatial visual encoding,” in Models of the Visual Cortex, D. Rose, V. G. Dobson, eds. (Wiley, New York, 1984).
[CrossRef]

J. G. Daugman, “Two-dimensional spectral analysis of cortical receptive field profiles,” Vision Res. 20, 847–856 (1980).
[CrossRef] [PubMed]

De Valois, R. L.

R. L. De Valois, D. G. Albrecht, L. G. Thorell, “Spatial frequency selectivity of cells in macaque visual cortex,” Vision Res. 22, 545–559 (1982).
[CrossRef] [PubMed]

Dreher, B.

G. H. Henry, P. O. Bishop, B. Dreher, “Orientation, axis and direction as stimulus parameters for striate cells,” Vision Res. 14, 767–777 (1974);D. Rose, C. Blakemore, “An analysis of orientation selectivity in the cat’s visual cortex,” Exp. Brain Res. 20, 1–17 (1974);H. Ikeda, M. J. Wright, “Spatial and temporal properties of ‘sustained’ and ‘transient’ neurones in area 17 of the cat’s visual cortex,” Exp. Brain Res. 22, 363–383 (1975);R. J. W. Mansfield, “Neural basis of orientation perception in primate vision,” Science 186, 1133–1135 (1974);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);G. F. Poggio, F. H. Baker, R. J. W. Mansfield, A. Sillito, P. Grigg, “Spatial and chromatic properties of neurons subserving foveal and parafoveal vision in rhesus monkey,” Brain Res. 100, 25–59 (1975);R. L. De Valois, E. W. Yund, N. Hepler, “The orientation and direction selectivity of cells in macaque visual cortex,” Vision Res. 22, 531–544 (1982).
[CrossRef] [PubMed]

Enroth-Cugell, C.

F. W. Campbell, G. F. Cooper, C. Enroth-Cugell, “The spatial selectivity of the visual cells of the cat,” J. Physiol. (London) 203, 223–235 (1969);L. Maffei, A. Fiorentini, “The visual cortex as a spatial frequency analyzer,” Vision Res. 13, 1255–1267 (1973);P. H. Schiller, B. L. Finlay, S. F. Volman, “Quantitative studies of single-cell properties in monkey striate cortex. I. Spatiotemporal organization of receptive fields,” J. Neurophysiol. 39, 1288–1319 (1976);J. A. Movshon, I. D. Thompson, D. J. Tolhurst, “Spatial summation in the receptive fields of simple cells in the cat’s striate cortex,” J. Physiol. (London) 283, 53–77 (1978);B. W. Andrews, D. A. Pollen, “Relationship between spatial frequency selectivity and receptive field profile of simple cells,” J. Physiol. (London) 287, 163–176 (1979);J. J. Kulikowski, P. O. Bishop, “Linear analysis of the responses of simple cells in the cat visual cortex,” Exp. Brain Res. 44, 386–400 (1981);R. L. De Valois, D. G. Albrecht, L. G. Thorell, “Spatial frequency selectivity of cells in macaque visual cortex,” Vision Res. 22, 545–559 (1982).
[CrossRef] [PubMed]

Gauselman, V. E.

V. D. Glezer, T. A. Tsherbach, V. E. Gauselman, V. M. Bondarko, “Spatiotemporal organization of receptive fields in the cat striate cortex,” Biol. Cybern. 43, 35–49 (1982).
[CrossRef]

Glezer, V. D.

V. D. Glezer, T. A. Tsherbach, V. E. Gauselman, V. M. Bondarko, “Spatiotemporal organization of receptive fields in the cat striate cortex,” Biol. Cybern. 43, 35–49 (1982).
[CrossRef]

Henry, G. H.

G. H. Henry, P. O. Bishop, B. Dreher, “Orientation, axis and direction as stimulus parameters for striate cells,” Vision Res. 14, 767–777 (1974);D. Rose, C. Blakemore, “An analysis of orientation selectivity in the cat’s visual cortex,” Exp. Brain Res. 20, 1–17 (1974);H. Ikeda, M. J. Wright, “Spatial and temporal properties of ‘sustained’ and ‘transient’ neurones in area 17 of the cat’s visual cortex,” Exp. Brain Res. 22, 363–383 (1975);R. J. W. Mansfield, “Neural basis of orientation perception in primate vision,” Science 186, 1133–1135 (1974);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);G. F. Poggio, F. H. Baker, R. J. W. Mansfield, A. Sillito, P. Grigg, “Spatial and chromatic properties of neurons subserving foveal and parafoveal vision in rhesus monkey,” Brain Res. 100, 25–59 (1975);R. L. De Valois, E. W. Yund, N. Hepler, “The orientation and direction selectivity of cells in macaque visual cortex,” Vision Res. 22, 531–544 (1982).
[CrossRef] [PubMed]

Hubel, D. H.

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).

Marcelja, S.

Marrocco, R. T.

R. A. Young, R. T. Marrocco, “Gaussian derivative model of receptive field structure,” Computer Science Department, General Motors Research Laboratories, Warren, Michigan 48090-9057 (personal communication).

Movshon, J. A.

J. A. Movshon, “Two-dimensional spatial frequency tuning of cat striate cortical neurons,” Soc. Neurosci. 5, 799 (1979).

J. A. Movshon, I. D. Thompson, D. J. Tolhurst, “Spatial and temporal contrast sensitivity of neurones in areas 17 and 18 of the cat’s visual cortex,” J. Physiol. (London) 283, 101–120 (1978).

Rodieck, R. W.

R. W. Rodieck, “Quantitative analysis of cat retinal ganglion cell response to visual stimuli,” Vision Res. 5, 583–601 (1965).
[CrossRef] [PubMed]

Thompson, I. D.

J. A. Movshon, I. D. Thompson, D. J. Tolhurst, “Spatial and temporal contrast sensitivity of neurones in areas 17 and 18 of the cat’s visual cortex,” J. Physiol. (London) 283, 101–120 (1978).

Thorell, L. G.

R. L. De Valois, D. G. Albrecht, L. G. Thorell, “Spatial frequency selectivity of cells in macaque visual cortex,” Vision Res. 22, 545–559 (1982).
[CrossRef] [PubMed]

Tolhurst, D. J.

J. A. Movshon, I. D. Thompson, D. J. Tolhurst, “Spatial and temporal contrast sensitivity of neurones in areas 17 and 18 of the cat’s visual cortex,” J. Physiol. (London) 283, 101–120 (1978).

Tsherbach, T. A.

V. D. Glezer, T. A. Tsherbach, V. E. Gauselman, V. M. Bondarko, “Spatiotemporal organization of receptive fields in the cat striate cortex,” Biol. Cybern. 43, 35–49 (1982).
[CrossRef]

Wiesel, T. N.

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).

Young, R. A.

R. A. Young, R. T. Marrocco, “Gaussian derivative model of receptive field structure,” Computer Science Department, General Motors Research Laboratories, Warren, Michigan 48090-9057 (personal communication).

Biol. Cybern.

V. D. Glezer, T. A. Tsherbach, V. E. Gauselman, V. M. Bondarko, “Spatiotemporal organization of receptive fields in the cat striate cortex,” Biol. Cybern. 43, 35–49 (1982).
[CrossRef]

IEEE Trans. Sys. Man Cybern.

J. G. Daugman, “Six formal properties of two-dimensional anisotropic visual filters: structural principles and frequency/orientation selectivity,” IEEE Trans. Sys. Man Cybern. SMC-13, 882–887 (1983);J. G. Daugman, “Representational issues and local filter models of two-dimensional spatial visual encoding,” in Models of the Visual Cortex, D. Rose, V. G. Dobson, eds. (Wiley, New York, 1984).
[CrossRef]

J. Opt. Soc. Am.

J. Physiol. (London)

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).

F. W. Campbell, G. F. Cooper, C. Enroth-Cugell, “The spatial selectivity of the visual cells of the cat,” J. Physiol. (London) 203, 223–235 (1969);L. Maffei, A. Fiorentini, “The visual cortex as a spatial frequency analyzer,” Vision Res. 13, 1255–1267 (1973);P. H. Schiller, B. L. Finlay, S. F. Volman, “Quantitative studies of single-cell properties in monkey striate cortex. I. Spatiotemporal organization of receptive fields,” J. Neurophysiol. 39, 1288–1319 (1976);J. A. Movshon, I. D. Thompson, D. J. Tolhurst, “Spatial summation in the receptive fields of simple cells in the cat’s striate cortex,” J. Physiol. (London) 283, 53–77 (1978);B. W. Andrews, D. A. Pollen, “Relationship between spatial frequency selectivity and receptive field profile of simple cells,” J. Physiol. (London) 287, 163–176 (1979);J. J. Kulikowski, P. O. Bishop, “Linear analysis of the responses of simple cells in the cat visual cortex,” Exp. Brain Res. 44, 386–400 (1981);R. L. De Valois, D. G. Albrecht, L. G. Thorell, “Spatial frequency selectivity of cells in macaque visual cortex,” Vision Res. 22, 545–559 (1982).
[CrossRef] [PubMed]

J. A. Movshon, I. D. Thompson, D. J. Tolhurst, “Spatial and temporal contrast sensitivity of neurones in areas 17 and 18 of the cat’s visual cortex,” J. Physiol. (London) 283, 101–120 (1978).

Soc. Neurosci.

J. A. Movshon, “Two-dimensional spatial frequency tuning of cat striate cortical neurons,” Soc. Neurosci. 5, 799 (1979).

Vision Res.

J. G. Daugman, “Two-dimensional spectral analysis of cortical receptive field profiles,” Vision Res. 20, 847–856 (1980).
[CrossRef] [PubMed]

R. W. Rodieck, “Quantitative analysis of cat retinal ganglion cell response to visual stimuli,” Vision Res. 5, 583–601 (1965).
[CrossRef] [PubMed]

R. L. De Valois, D. G. Albrecht, L. G. Thorell, “Spatial frequency selectivity of cells in macaque visual cortex,” Vision Res. 22, 545–559 (1982).
[CrossRef] [PubMed]

G. H. Henry, P. O. Bishop, B. Dreher, “Orientation, axis and direction as stimulus parameters for striate cells,” Vision Res. 14, 767–777 (1974);D. Rose, C. Blakemore, “An analysis of orientation selectivity in the cat’s visual cortex,” Exp. Brain Res. 20, 1–17 (1974);H. Ikeda, M. J. Wright, “Spatial and temporal properties of ‘sustained’ and ‘transient’ neurones in area 17 of the cat’s visual cortex,” Exp. Brain Res. 22, 363–383 (1975);R. J. W. Mansfield, “Neural basis of orientation perception in primate vision,” Science 186, 1133–1135 (1974);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);G. F. Poggio, F. H. Baker, R. J. W. Mansfield, A. Sillito, P. Grigg, “Spatial and chromatic properties of neurons subserving foveal and parafoveal vision in rhesus monkey,” Brain Res. 100, 25–59 (1975);R. L. De Valois, E. W. Yund, N. Hepler, “The orientation and direction selectivity of cells in macaque visual cortex,” Vision Res. 22, 531–544 (1982).
[CrossRef] [PubMed]

Other

R. A. Young, R. T. Marrocco, “Gaussian derivative model of receptive field structure,” Computer Science Department, General Motors Research Laboratories, Warren, Michigan 48090-9057 (personal communication).

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Figures (8)

Fig. 1
Fig. 1

A, Responses of a simple cell to gratings of each of various spatial frequencies at each of several different orientations. Note that, whereas the response of course decreases at off orientations, the peak spatial-frequency tuning does not change with orientation. B, Responses of the same cell to various orientations at each of several spatial frequencies. Note the invariance of the orientation tuning with spatial frequency.

Fig. 2
Fig. 2

A, Plots of the peak spatial frequency as a function of orientation and B, peak orientation as a function of spatial frequency for each of four cells. The data from the cell whose detailed data were presented in Fig. 1 (cell 3) are plotted at the top. Note that all cells show orientation peaks that are largely independent of spatial frequency, but some cells (notably cell 16) show considerable change in spatial-frequency tuning at off orientations.

Fig. 3
Fig. 3

Responses of the cell that showed the most extreme shift in spatial-frequency tuning (to lower frequencies) at off orientations.

Fig. 4
Fig. 4

Shift in peak spatial frequency with change in orientation. Data are from all cells tested, grouped by their orientation bandwidths. Also plotted (dashed lines) are the predictions from the classic aligned-LGN model. Note that, with the exception of the cells most narrowly tuned for orientation, the amount of spatial-frequency change is much less than that predicted by this model.

Fig. 5
Fig. 5

Peak spatial frequency as a function of orientation. Data from all cells, grouped by their spatial-frequency bandwidths. Note that the cells most narrowly tuned for spatial frequency show invariant frequency tuning with orientation, as do the most broadly tuned cells.

Fig. 6
Fig. 6

Peak spatial frequency as a function of orientation of cells grouped by their aspect ratios (relative spatial-frequency versus orientation tuning). Note that the cells with small aspect ratios (those relatively more narrowly tuned for spatial frequency than for orientation) show little dependence of frequency on orientation. Also plotted are the predictions for Gabor RF’s. It can be seen that the data in general fit this model quite well.

Fig. 7
Fig. 7

A, Two-dimensional spatial-frequency plot of the responses of cell 3. Note that the cell responds to only a restricted two-dimensional spatial-frequency region. Note also the indication of a surrounding inhibitory region in the frequency domain (at higher spatial frequencies). B, The receptive field in the space domain for this cell, calculated by the inverse Fourier transform. Note the oscillations in the RF for this narrowly tuned (0.94-octave) cell. C and D, Cross sections through the RF of this cell in x and y along with the best-fitting Gabor function (dashed lines).

Fig. 8
Fig. 8

A, Two-dimensional spatial-frequency plot of the responses of cell 5 [a cell broadly tuned (1.94 octaves) for spatial frequency]. Note, nonetheless, that the cell responds only within a restricted two-dimensonal spatial-frequency region. B, The computed RF for this cell. Note the absence of multiple sidebands. C and D, Cross sections through the RF of this cell, with the predictions from the Gabor model in dashed lines.

Equations (2)

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AR = lenght of ellipse’s axis along x axis lenght of ellipse’s axis along y axis .
AR = ( 2 Δ W 1 ) ( 2 Δ W + 1 ) × 1 sin ( Δ O 1 / 2 ) ,

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