Abstract

Some experimental studies of subthreshold summation between sinusoidal grating components have been interpreted as showing very narrow channel bandwidths in human visions. This paper discusses an alternative interpretation of these experiments based on consideration of probability-summation effects among spatially distributed detectors. We conclude that frequency-selective channels must still be hypothesized in order to fit the data, but the channel bandwidth may be much wider than earlier interpretations suggest.

© 1978 Optical Society of America

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  1. F. W. Campbell and J. G. Robson, "Application of Fourier Analysis to the Visibility of Gratings," J. Physiol. (London) 197, 551–556 (1968).
  2. C. Blakemore and F. W. Campbell, "On the Existence of Neurones in the Human Visual System Selectively Sensitive to the Orientation and Size of Retinal Images," J. Physiol. (London) 203, 237–260 (1969).
  3. C. F. Stromeyer III and B. Julesz, "Spatial-Frequency Masking in Vision: Critical Bands and Spread of Masking," J. Opt. Soc. Am. 62, 1221–1232 (1972).
  4. M. B. Sachs, J. Nachmias, and J. G. Robson, "Spatial-Frequency Channels in Human Vision," J. Opt. Soc. Am. 61, 1176–1186 (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. R. F. Quick, Jr. and T. A. Reichert, "Spatial-Frequency Selectivity in Contrast Detection," Vision Res. 15, 637–643 (1975).
  7. R. F. Quick, Jr., "A Vector-Magnitude Model of Contrast Detection," Kybernetik 16, 65–67 (1974).
  8. C. F. Stromeyer III and S. Klein, "Evidence Against Narrow-Band Spatial Frequency Channels in Human Vision: The Detectability of Frequency Modulated Gratings," Vision Res. 15, 899–910 (1975).
  9. H. Mostafavi and D. J. Sakrison, "Structure and Properties of a Single Channel in the Human Visual System," Vision Res. 16, 957–968 (1976).
  10. N. Graham, "Visual Detection of Aperiodic Spatial Stimuli by Probability Summation Among Multiple Channels," Vision Res. (in press).
  11. The components actually used in the experiments were squarewaves; near threshold the harmonics have negligible effect (see Quick and Reichert6), so we have included only the fundamental components in this study.
  12. J. G. Robson, "Regional Variation of Contrast Sensitivity in the Visual Field," presented to the Association for Research in Vision and Ophthalmology, April 1975 (unpublished).
  13. R. F. Quick, Jr., J. R. Hamerly, and T. A. Reichert, "The Absence of a Measurable 'Critical Band' at Low Suprathreshold Contrasts," Vision Res. 16, 351–355 (1976).
  14. Strictly, the limit is the essential supremum of |ƒ(x)|, which ignores pathological points on sets of zero measure. This does not matter if ƒ(x) is continuous and of finite spatial extent.
  15. C. F. Stromeyer III and S. Klein, "Spatial Frequency Channels in Human Vision as Asymmetric (Edge) Mechanisms," Vision Res. 14, 1409–1420 (1974).
  16. We are aware that Dr. Stanley Klein obtained similar results in an earlier unpublished study. Apparently Klein's results were obtained with a model similar to that of Stromeyer and Klein, 8 which includes a spatial "pooling" mechanism in addition to probability summation. On the basis of the present study we do not believe that a pooling mechanism is necessary to explain our data.

1976 (2)

H. Mostafavi and D. J. Sakrison, "Structure and Properties of a Single Channel in the Human Visual System," Vision Res. 16, 957–968 (1976).

R. F. Quick, Jr., J. R. Hamerly, and T. A. Reichert, "The Absence of a Measurable 'Critical Band' at Low Suprathreshold Contrasts," Vision Res. 16, 351–355 (1976).

1975 (2)

R. F. Quick, Jr. and T. A. Reichert, "Spatial-Frequency Selectivity in Contrast Detection," Vision Res. 15, 637–643 (1975).

C. F. Stromeyer III and S. Klein, "Evidence Against Narrow-Band Spatial Frequency Channels in Human Vision: The Detectability of Frequency Modulated Gratings," Vision Res. 15, 899–910 (1975).

1974 (2)

R. F. Quick, Jr., "A Vector-Magnitude Model of Contrast Detection," Kybernetik 16, 65–67 (1974).

C. F. Stromeyer III and S. Klein, "Spatial Frequency Channels in Human Vision as Asymmetric (Edge) Mechanisms," Vision Res. 14, 1409–1420 (1974).

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).

1972 (1)

1971 (1)

1969 (1)

C. Blakemore and F. W. Campbell, "On the Existence of Neurones in the Human Visual System Selectively Sensitive to the Orientation and Size of Retinal Images," J. Physiol. (London) 203, 237–260 (1969).

1968 (1)

F. W. Campbell and J. G. Robson, "Application of Fourier Analysis to the Visibility of Gratings," J. Physiol. (London) 197, 551–556 (1968).

Blakemore, C.

C. Blakemore and F. W. Campbell, "On the Existence of Neurones in the Human Visual System Selectively Sensitive to the Orientation and Size of Retinal Images," J. Physiol. (London) 203, 237–260 (1969).

Campbell, F. W.

C. Blakemore and F. W. Campbell, "On the Existence of Neurones in the Human Visual System Selectively Sensitive to the Orientation and Size of Retinal Images," J. Physiol. (London) 203, 237–260 (1969).

F. W. Campbell and J. G. Robson, "Application of Fourier Analysis to the Visibility of Gratings," J. Physiol. (London) 197, 551–556 (1968).

Graham, N.

N. Graham, "Visual Detection of Aperiodic Spatial Stimuli by Probability Summation Among Multiple Channels," Vision Res. (in press).

Hamerly, J. R.

R. F. Quick, Jr., J. R. Hamerly, and T. A. Reichert, "The Absence of a Measurable 'Critical Band' at Low Suprathreshold Contrasts," Vision Res. 16, 351–355 (1976).

Julesz, B.

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).

Klein, S.

C. F. Stromeyer III and S. Klein, "Evidence Against Narrow-Band Spatial Frequency Channels in Human Vision: The Detectability of Frequency Modulated Gratings," Vision Res. 15, 899–910 (1975).

C. F. Stromeyer III and S. Klein, "Spatial Frequency Channels in Human Vision as Asymmetric (Edge) Mechanisms," Vision Res. 14, 1409–1420 (1974).

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).

Mostafavi, H.

H. Mostafavi and D. J. Sakrison, "Structure and Properties of a Single Channel in the Human Visual System," Vision Res. 16, 957–968 (1976).

Nachmias, J.

Quick, Jr., R. F.

R. F. Quick, Jr., J. R. Hamerly, and T. A. Reichert, "The Absence of a Measurable 'Critical Band' at Low Suprathreshold Contrasts," Vision Res. 16, 351–355 (1976).

R. F. Quick, Jr. and T. A. Reichert, "Spatial-Frequency Selectivity in Contrast Detection," Vision Res. 15, 637–643 (1975).

R. F. Quick, Jr., "A Vector-Magnitude Model of Contrast Detection," Kybernetik 16, 65–67 (1974).

Reichert, T. A.

R. F. Quick, Jr., J. R. Hamerly, and T. A. Reichert, "The Absence of a Measurable 'Critical Band' at Low Suprathreshold Contrasts," Vision Res. 16, 351–355 (1976).

R. F. Quick, Jr. and T. A. Reichert, "Spatial-Frequency Selectivity in Contrast Detection," Vision Res. 15, 637–643 (1975).

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. (London) 197, 551–556 (1968).

J. G. Robson, "Regional Variation of Contrast Sensitivity in the Visual Field," presented to the Association for Research in Vision and Ophthalmology, April 1975 (unpublished).

Sachs, M. B.

Sakrison, D. J.

H. Mostafavi and D. J. Sakrison, "Structure and Properties of a Single Channel in the Human Visual System," Vision Res. 16, 957–968 (1976).

Stromeyer III, C. F.

C. F. Stromeyer III and S. Klein, "Evidence Against Narrow-Band Spatial Frequency Channels in Human Vision: The Detectability of Frequency Modulated Gratings," Vision Res. 15, 899–910 (1975).

C. F. Stromeyer III and S. Klein, "Spatial Frequency Channels in Human Vision as Asymmetric (Edge) Mechanisms," Vision Res. 14, 1409–1420 (1974).

C. F. Stromeyer III and B. Julesz, "Spatial-Frequency Masking in Vision: Critical Bands and Spread of Masking," J. Opt. Soc. Am. 62, 1221–1232 (1972).

J. Opt. Soc. Am. (2)

J. Physiol. (2)

F. W. Campbell and J. G. Robson, "Application of Fourier Analysis to the Visibility of Gratings," J. Physiol. (London) 197, 551–556 (1968).

C. Blakemore and F. W. Campbell, "On the Existence of Neurones in the Human Visual System Selectively Sensitive to the Orientation and Size of Retinal Images," J. Physiol. (London) 203, 237–260 (1969).

Kybernetik (1)

R. F. Quick, Jr., "A Vector-Magnitude Model of Contrast Detection," Kybernetik 16, 65–67 (1974).

Vision Res. (6)

C. F. Stromeyer III and S. Klein, "Evidence Against Narrow-Band Spatial Frequency Channels in Human Vision: The Detectability of Frequency Modulated Gratings," Vision Res. 15, 899–910 (1975).

H. Mostafavi and D. J. Sakrison, "Structure and Properties of a Single Channel in the Human Visual System," Vision Res. 16, 957–968 (1976).

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).

R. F. Quick, Jr. and T. A. Reichert, "Spatial-Frequency Selectivity in Contrast Detection," Vision Res. 15, 637–643 (1975).

R. F. Quick, Jr., J. R. Hamerly, and T. A. Reichert, "The Absence of a Measurable 'Critical Band' at Low Suprathreshold Contrasts," Vision Res. 16, 351–355 (1976).

C. F. Stromeyer III and S. Klein, "Spatial Frequency Channels in Human Vision as Asymmetric (Edge) Mechanisms," Vision Res. 14, 1409–1420 (1974).

Other (5)

We are aware that Dr. Stanley Klein obtained similar results in an earlier unpublished study. Apparently Klein's results were obtained with a model similar to that of Stromeyer and Klein, 8 which includes a spatial "pooling" mechanism in addition to probability summation. On the basis of the present study we do not believe that a pooling mechanism is necessary to explain our data.

Strictly, the limit is the essential supremum of |ƒ(x)|, which ignores pathological points on sets of zero measure. This does not matter if ƒ(x) is continuous and of finite spatial extent.

N. Graham, "Visual Detection of Aperiodic Spatial Stimuli by Probability Summation Among Multiple Channels," Vision Res. (in press).

The components actually used in the experiments were squarewaves; near threshold the harmonics have negligible effect (see Quick and Reichert6), so we have included only the fundamental components in this study.

J. G. Robson, "Regional Variation of Contrast Sensitivity in the Visual Field," presented to the Association for Research in Vision and Ophthalmology, April 1975 (unpublished).

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