Abstract

Under the general assumption that visual contrast detection occurs by a parallel array of linear detectors, either without probability summation or with probability summation of a commonly assumed type, it is shown that the set of functions representing subthreshold stimuli must be convex. Thus, for example, a planar plot of the threshold locus using multiples of any two functions as axes, must be convex (cannot bulge inward). If experimental evidence to the contrary were discovered, it would rule out detection by parallel linear detectors of the above type. One possible kind of such evidence would be an inward cusp of the threshold locus corresponding to one of a special class of stimuli to which the visual system might be specifically sensitive.

© 1978 Optical Society of America

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  1. F. W. Campbell, R. H. S. Carpenter, and J. Z. Levinson, "Visibility of aperiodic patterns compared with that of sinusoidal gratings," J. Physiol. 204, 283–298 (1969).
  2. F. W. Campbell and J. G. Robson, "Application of Fourier analysis to the visibility of gratings," J. Physiol. 197, 551–566 (1968).
  3. M. B. Sachs, J. Nachmias, and J. G. Robson, "Spatial-frequency channels in human vision," J. Opt. Soc. Am. 61, 1176–1186 (1971).
  4. N. Graham and J. Nachmias, "Detection of grating patterns containing two spatial frequencies: a comparison of single-channel and multiple-channel models," Vision Res. 11, 251–259 (1971).
  5. J. J. Kulikowski and P. E. King-Smith, "Spatial arrangement of line, edge and grating detectors revealed by subthreshold summation," Vision Res. 13, 1455–1478 (1973).
  6. A. N. Kolmogorov and S. N. Fomin, Elements of the Theory of Functions and Functional Analysis, Vol. I: Metric and Normed Spaces (Graylock, Rochester, N. Y. 1957).
  7. R. F. Quick, Jr., "A vector-magnitude model of contrast detection," Kybernetik 16, 65–67 (1974).
  8. R. F. Quick, Jr., Spatial frequency selectivity in human vision: the frequency response of contrast detection channels, Thesis, Carnegie-Mellon University, 1973 (unpublished).
  9. H. Mortavi and D. J. Sakrison, "Structure and properties of a single channel in the human visual system," Visition Res. 16, 957–968 (1976).

1976 (1)

H. Mortavi and D. J. Sakrison, "Structure and properties of a single channel in the human visual system," Visition Res. 16, 957–968 (1976).

1973 (1)

J. J. Kulikowski and P. E. King-Smith, "Spatial arrangement of line, edge and grating detectors revealed by subthreshold summation," Vision Res. 13, 1455–1478 (1973).

1971 (2)

N. Graham and J. Nachmias, "Detection of grating patterns containing two spatial frequencies: a comparison of single-channel and multiple-channel models," Vision Res. 11, 251–259 (1971).

M. B. Sachs, J. Nachmias, and J. G. Robson, "Spatial-frequency channels in human vision," J. Opt. Soc. Am. 61, 1176–1186 (1971).

1969 (1)

F. W. Campbell, R. H. S. Carpenter, and J. Z. Levinson, "Visibility of aperiodic patterns compared with that of sinusoidal gratings," J. Physiol. 204, 283–298 (1969).

1968 (1)

F. W. Campbell and J. G. Robson, "Application of Fourier analysis to the visibility of gratings," J. Physiol. 197, 551–566 (1968).

Campbell, F. W.

F. W. Campbell, R. H. S. Carpenter, and J. Z. Levinson, "Visibility of aperiodic patterns compared with that of sinusoidal gratings," J. Physiol. 204, 283–298 (1969).

F. W. Campbell and J. G. Robson, "Application of Fourier analysis to the visibility of gratings," J. Physiol. 197, 551–566 (1968).

Carpenter, R. H. S.

F. W. Campbell, R. H. S. Carpenter, and J. Z. Levinson, "Visibility of aperiodic patterns compared with that of sinusoidal gratings," J. Physiol. 204, 283–298 (1969).

Fomin, S. N.

A. N. Kolmogorov and S. N. Fomin, Elements of the Theory of Functions and Functional Analysis, Vol. I: Metric and Normed Spaces (Graylock, Rochester, N. Y. 1957).

Graham, N.

N. Graham and J. Nachmias, "Detection of grating patterns containing two spatial frequencies: a comparison of single-channel and multiple-channel models," Vision Res. 11, 251–259 (1971).

King-Smith, P. E.

J. J. Kulikowski and P. E. King-Smith, "Spatial arrangement of line, edge and grating detectors revealed by subthreshold summation," Vision Res. 13, 1455–1478 (1973).

Kolmogorov, A. N.

A. N. Kolmogorov and S. N. Fomin, Elements of the Theory of Functions and Functional Analysis, Vol. I: Metric and Normed Spaces (Graylock, Rochester, N. Y. 1957).

Kulikowski, J. J.

J. J. Kulikowski and P. E. King-Smith, "Spatial arrangement of line, edge and grating detectors revealed by subthreshold summation," Vision Res. 13, 1455–1478 (1973).

Levinson, J. Z.

F. W. Campbell, R. H. S. Carpenter, and J. Z. Levinson, "Visibility of aperiodic patterns compared with that of sinusoidal gratings," J. Physiol. 204, 283–298 (1969).

Mortavi, H.

H. Mortavi and D. J. Sakrison, "Structure and properties of a single channel in the human visual system," Visition Res. 16, 957–968 (1976).

Nachmias, J.

M. B. Sachs, J. Nachmias, and J. G. Robson, "Spatial-frequency channels in human vision," J. Opt. Soc. Am. 61, 1176–1186 (1971).

N. Graham and J. Nachmias, "Detection of grating patterns containing two spatial frequencies: a comparison of single-channel and multiple-channel models," Vision Res. 11, 251–259 (1971).

Quick, Jr., R. F.

R. F. Quick, Jr., Spatial frequency selectivity in human vision: the frequency response of contrast detection channels, Thesis, Carnegie-Mellon University, 1973 (unpublished).

R. F. Quick, Jr., "A vector-magnitude model of contrast detection," Kybernetik 16, 65–67 (1974).

Robson, J. G.

M. B. Sachs, J. Nachmias, and J. G. Robson, "Spatial-frequency channels in human vision," J. Opt. Soc. Am. 61, 1176–1186 (1971).

F. W. Campbell and J. G. Robson, "Application of Fourier analysis to the visibility of gratings," J. Physiol. 197, 551–566 (1968).

Sachs, M. B.

Sakrison, D. J.

H. Mortavi and D. J. Sakrison, "Structure and properties of a single channel in the human visual system," Visition Res. 16, 957–968 (1976).

J. Opt. Soc. Am. (1)

J. Physiol. (2)

F. W. Campbell, R. H. S. Carpenter, and J. Z. Levinson, "Visibility of aperiodic patterns compared with that of sinusoidal gratings," J. Physiol. 204, 283–298 (1969).

F. W. Campbell and J. G. Robson, "Application of Fourier analysis to the visibility of gratings," J. Physiol. 197, 551–566 (1968).

Vision Res. (2)

N. Graham and J. Nachmias, "Detection of grating patterns containing two spatial frequencies: a comparison of single-channel and multiple-channel models," Vision Res. 11, 251–259 (1971).

J. J. Kulikowski and P. E. King-Smith, "Spatial arrangement of line, edge and grating detectors revealed by subthreshold summation," Vision Res. 13, 1455–1478 (1973).

Visition Res. (1)

H. Mortavi and D. J. Sakrison, "Structure and properties of a single channel in the human visual system," Visition Res. 16, 957–968 (1976).

Other (3)

A. N. Kolmogorov and S. N. Fomin, Elements of the Theory of Functions and Functional Analysis, Vol. I: Metric and Normed Spaces (Graylock, Rochester, N. Y. 1957).

R. F. Quick, Jr., "A vector-magnitude model of contrast detection," Kybernetik 16, 65–67 (1974).

R. F. Quick, Jr., Spatial frequency selectivity in human vision: the frequency response of contrast detection channels, Thesis, Carnegie-Mellon University, 1973 (unpublished).

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