Abstract

We studied the detection of coherent motion in stroboscopically moving random-dot patterns for foveal vision and at eccentricities of 6, 12, 24, and 48 deg in the temporal visual field. Threshold signal-to-noise ratios (SNR’s) were determined as a function of velocity for a range of stimulus sizes. It was found that the motion-detection performance is roughly invariant throughout the temporal visual field, provided that the stimuli are scaled according to the cortical magnification factor to obtain equivalent cortical sizes and velocities at all eccentricities. The maximum field velocity compatible with the percept of coherent motion increased about linearly with the width of the square stimuli. At this high-velocity threshold any pixel crossed the field in five to nine equal steps with a constant total crossing time of 50–90 msec, regardless of stimulus size or eccentricity. The lowest SNR values were reached at the optimal or tuning velocity V0. They approached the amazingly low values of 0.04–0.05 for large stimuli and at all eccentricities. Regardless of stimulus size, the parameter V0 increased about linearly with eccentricity from roughly 1 deg sec−1 at the fovea to some 8 deg sec−1 at 48 deg in the temporal visual field.

© 1983 Optical Society of America

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  1. J. J. Koenderink and A. J. van Doorn, “Invariant features of contrast detection: an explanation in terms of self-similar detector arrays,” J. Opt. Soc. Am. 72, 83–87 (1982).
    [CrossRef] [PubMed]
  2. D. Whitteridge and P. M. Daniel, “The representation of the visual field on the calcarine cortex,” in The Visual System: Neurophysiology and Psychophysics, R. Jung and H. Kornhuber, eds. (Springer-Verlag, Berlin, 1961), pp. 222–228.
  3. P. M. Daniel and D. Whitteridge, “The representation of the visual field on the cerebral cortex in monkeys,” J. Physiol. London 159, 203–221 (1961).
  4. E. T. Rolls and A. Cowey, “Topography of the retina and striate cortex and its relationship to visual acuity in rhesus monkeys and squirrel monkeys,” Exp. Brain Res. 10, 298–310 (1970).
    [CrossRef] [PubMed]
  5. A. Cowey and E. T. Rolls, “Human cortical magnification factor and its relation to visual acuity,” Exp. Brain Res. 21, 447–459 (1974).
    [CrossRef] [PubMed]
  6. N. Drasdo, “The neural representation of visual space,” Nature 266, 554–556 (1977).
    [CrossRef] [PubMed]
  7. J. J. Koenderink, M. A. Bouman, A. E. Bueno de Mesquita, and S. Slappendel, “Perimetry of contrast detection thresholds of moving spatial sine wave patterns. I–IV,” J. Opt. Soc. Am. 68, 845–865 (1978).
    [CrossRef] [PubMed]
  8. V. Virsu and J. Rovamo, “Visual resolution, contrast sensitivity, and the cortical magnification factor,” Exp. Brain Res. 37, 475–494 (1979).
    [CrossRef] [PubMed]
  9. J. J. Koenderink and A. J. van Doorn, “Invariances in human visual spatiotemporal contrast detection,” presented at the ICO-11 Conference, Madrid, Spain, 1978.
  10. V. Virsu, J. Rovamo, P. Laurinen, and R. Näsänen, “Temporal contrast sensitivity and cortical magnification,” Vision Res. 22, 1211–1217 (1982).
    [CrossRef] [PubMed]
  11. C. Noorlander, J. J. Koenderink, R. J. den Ouden, and B. Wigbold Edens, “Sensitivity to spatio-temporal colour contrast in the peripheral visual field,” Vision Res. 23, 1–11 (1983).
    [CrossRef]
  12. G. Westheimer, “The spatial grain of the perifoveal visual field,” Vision Res. 22, 157–162 (1982).
    [CrossRef] [PubMed]
  13. B. M. Dow, A. Z. Snyder, R. G. Vautin, and R. Bauer, “Magnification factor and receptive field size in foveal striate cortex of the monkey,” Exp. Brain Res. 44, 213–228 (1981).
    [CrossRef] [PubMed]
  14. S. M. Zeki, “Functional specialisation in the visual cortex of the rhesus monkey,” Nature 274, 423–428 (1978).
    [CrossRef] [PubMed]
  15. P. Lennie, “Neuroanatomy of visual acuity,” Nature 266, 496 (1977).
    [CrossRef]
  16. W. R. Uttal, A Taxonomy of Visual Processes (Erlbaum, Hillsdale, N.J., 1981).
  17. Y. LeGrand, Form and Space Vision (Indiana U. Press, Bloomington, Ind., 1967); see especially p. 180.
  18. F. W. Campbell and L. Maffei, “The influence of spatial frequency and contrast on the perception of moving patterns,” Vision Res. 21, 713–721 (1981).
    [CrossRef] [PubMed]
  19. P. D. Tynan and R. Sekuler, “Motion processing in peripheral vision: reaction time and perceived velocity,” Vision Res. 22, 61–68 (1982).
    [CrossRef] [PubMed]
  20. B. Julesz, Foundations of Cyclopean Perception (U. Chicago Press, Chicago, Ill., 1971).
  21. A. J. van Doorn and J. J. Koenderink, “Temporal properties of the visual detectability of moving spatial white noise,” Exp. Brain Res. 45, 179–188 (1982).
    [PubMed]
  22. A. J. van Doorn and J. J. Koenderink, “Spatial properties of the visual detectability of moving spatial white noise,” Exp. Brain Res. 45, 189–195 (1982).
    [PubMed]
  23. A. J. van Doorn and J. J. Koenderink, “Visibility of movement gradients,” Biol. Cybern. 44, 167–175 (1982).
    [CrossRef] [PubMed]
  24. A. J. van Doorn and J. J. Koenderink, “The structure of the human motion detection system.” IEEE Trans. Syst. Man Cybern. (to be published).
  25. A. J. van Doorn and J. J. Koenderink, “Spatiotemporal integration in the detection of coherent motion,” Vision Res. (to be published).
  26. F. W. Weymouth, D. C. Hines, L. H. Acres, J. E. Raaf, and M. C. Wheeler, “Visual acuity within the area centralis and its relation to eye movements and fixation,” Am. J. Ophthalmol. 11, 947–960 (1928).
  27. T. Wertheim, “Über die indirekte Sehschäfe,” Z. Psychol. Physiol. Sinnesorg 7, 172–189 (1894).
  28. A. J. van Doorn, J. J. Koenderink, and M. A. Bouman, “The influence of the retinal inhomogeneity on the perception of spatial patterns,” Kybernetik 10, 223–230 (1972).
    [CrossRef] [PubMed]
  29. J. S. Lappin and H. H. Bell, “The detection of coherence in moving random-dot patterns,” Vision Res. 16, 161–168 (1976).
    [CrossRef] [PubMed]
  30. W. Reichardt, “Autocorrelation, a principle for the evaluation of sensory information by the central nervous system,” in Sensory Communication, W. A. Rosenblith, ed. (MIT Press, Cambridge, Mass., 1961), pp. 303–317.
  31. W. Reichardt and T. Poggio, “Visual control of orientation behavior in the fly,” Q. Rev. Biophys. 9, 311–348 (1976).
    [CrossRef]
  32. J. Rovamo and V. Virsu, “An estimation and application of the human cortical magnification factor,” Exp. Brain Res. 37, 495–510 (1979).
    [CrossRef] [PubMed]
  33. C. L. Baker and O. J. Braddick, “The basis of area and dot number effects in random dot motion perception,” Vision Res. 22, 1252–1259 (1982).
    [CrossRef]
  34. D. Finlay, “Motion perception in the peripheral visual field,” Percept. 11, 457–462 (1982).
    [CrossRef]
  35. J. H. R. Maunsell and D. C. van Essen, “Functional properties of neurons in middle temporal visual area of the macaque monkey. I. Selectivity for stimulus direction, speed, and orientation,” J. Neurophysiol. 49, 1127–1147 (1983).
    [PubMed]

1983 (2)

C. Noorlander, J. J. Koenderink, R. J. den Ouden, and B. Wigbold Edens, “Sensitivity to spatio-temporal colour contrast in the peripheral visual field,” Vision Res. 23, 1–11 (1983).
[CrossRef]

J. H. R. Maunsell and D. C. van Essen, “Functional properties of neurons in middle temporal visual area of the macaque monkey. I. Selectivity for stimulus direction, speed, and orientation,” J. Neurophysiol. 49, 1127–1147 (1983).
[PubMed]

1982 (9)

J. J. Koenderink and A. J. van Doorn, “Invariant features of contrast detection: an explanation in terms of self-similar detector arrays,” J. Opt. Soc. Am. 72, 83–87 (1982).
[CrossRef] [PubMed]

G. Westheimer, “The spatial grain of the perifoveal visual field,” Vision Res. 22, 157–162 (1982).
[CrossRef] [PubMed]

P. D. Tynan and R. Sekuler, “Motion processing in peripheral vision: reaction time and perceived velocity,” Vision Res. 22, 61–68 (1982).
[CrossRef] [PubMed]

A. J. van Doorn and J. J. Koenderink, “Temporal properties of the visual detectability of moving spatial white noise,” Exp. Brain Res. 45, 179–188 (1982).
[PubMed]

A. J. van Doorn and J. J. Koenderink, “Spatial properties of the visual detectability of moving spatial white noise,” Exp. Brain Res. 45, 189–195 (1982).
[PubMed]

A. J. van Doorn and J. J. Koenderink, “Visibility of movement gradients,” Biol. Cybern. 44, 167–175 (1982).
[CrossRef] [PubMed]

V. Virsu, J. Rovamo, P. Laurinen, and R. Näsänen, “Temporal contrast sensitivity and cortical magnification,” Vision Res. 22, 1211–1217 (1982).
[CrossRef] [PubMed]

C. L. Baker and O. J. Braddick, “The basis of area and dot number effects in random dot motion perception,” Vision Res. 22, 1252–1259 (1982).
[CrossRef]

D. Finlay, “Motion perception in the peripheral visual field,” Percept. 11, 457–462 (1982).
[CrossRef]

1981 (2)

F. W. Campbell and L. Maffei, “The influence of spatial frequency and contrast on the perception of moving patterns,” Vision Res. 21, 713–721 (1981).
[CrossRef] [PubMed]

B. M. Dow, A. Z. Snyder, R. G. Vautin, and R. Bauer, “Magnification factor and receptive field size in foveal striate cortex of the monkey,” Exp. Brain Res. 44, 213–228 (1981).
[CrossRef] [PubMed]

1979 (2)

V. Virsu and J. Rovamo, “Visual resolution, contrast sensitivity, and the cortical magnification factor,” Exp. Brain Res. 37, 475–494 (1979).
[CrossRef] [PubMed]

J. Rovamo and V. Virsu, “An estimation and application of the human cortical magnification factor,” Exp. Brain Res. 37, 495–510 (1979).
[CrossRef] [PubMed]

1978 (2)

1977 (2)

P. Lennie, “Neuroanatomy of visual acuity,” Nature 266, 496 (1977).
[CrossRef]

N. Drasdo, “The neural representation of visual space,” Nature 266, 554–556 (1977).
[CrossRef] [PubMed]

1976 (2)

J. S. Lappin and H. H. Bell, “The detection of coherence in moving random-dot patterns,” Vision Res. 16, 161–168 (1976).
[CrossRef] [PubMed]

W. Reichardt and T. Poggio, “Visual control of orientation behavior in the fly,” Q. Rev. Biophys. 9, 311–348 (1976).
[CrossRef]

1974 (1)

A. Cowey and E. T. Rolls, “Human cortical magnification factor and its relation to visual acuity,” Exp. Brain Res. 21, 447–459 (1974).
[CrossRef] [PubMed]

1972 (1)

A. J. van Doorn, J. J. Koenderink, and M. A. Bouman, “The influence of the retinal inhomogeneity on the perception of spatial patterns,” Kybernetik 10, 223–230 (1972).
[CrossRef] [PubMed]

1970 (1)

E. T. Rolls and A. Cowey, “Topography of the retina and striate cortex and its relationship to visual acuity in rhesus monkeys and squirrel monkeys,” Exp. Brain Res. 10, 298–310 (1970).
[CrossRef] [PubMed]

1961 (1)

P. M. Daniel and D. Whitteridge, “The representation of the visual field on the cerebral cortex in monkeys,” J. Physiol. London 159, 203–221 (1961).

1928 (1)

F. W. Weymouth, D. C. Hines, L. H. Acres, J. E. Raaf, and M. C. Wheeler, “Visual acuity within the area centralis and its relation to eye movements and fixation,” Am. J. Ophthalmol. 11, 947–960 (1928).

1894 (1)

T. Wertheim, “Über die indirekte Sehschäfe,” Z. Psychol. Physiol. Sinnesorg 7, 172–189 (1894).

Acres, L. H.

F. W. Weymouth, D. C. Hines, L. H. Acres, J. E. Raaf, and M. C. Wheeler, “Visual acuity within the area centralis and its relation to eye movements and fixation,” Am. J. Ophthalmol. 11, 947–960 (1928).

Baker, C. L.

C. L. Baker and O. J. Braddick, “The basis of area and dot number effects in random dot motion perception,” Vision Res. 22, 1252–1259 (1982).
[CrossRef]

Bauer, R.

B. M. Dow, A. Z. Snyder, R. G. Vautin, and R. Bauer, “Magnification factor and receptive field size in foveal striate cortex of the monkey,” Exp. Brain Res. 44, 213–228 (1981).
[CrossRef] [PubMed]

Bell, H. H.

J. S. Lappin and H. H. Bell, “The detection of coherence in moving random-dot patterns,” Vision Res. 16, 161–168 (1976).
[CrossRef] [PubMed]

Bouman, M. A.

J. J. Koenderink, M. A. Bouman, A. E. Bueno de Mesquita, and S. Slappendel, “Perimetry of contrast detection thresholds of moving spatial sine wave patterns. I–IV,” J. Opt. Soc. Am. 68, 845–865 (1978).
[CrossRef] [PubMed]

A. J. van Doorn, J. J. Koenderink, and M. A. Bouman, “The influence of the retinal inhomogeneity on the perception of spatial patterns,” Kybernetik 10, 223–230 (1972).
[CrossRef] [PubMed]

Braddick, O. J.

C. L. Baker and O. J. Braddick, “The basis of area and dot number effects in random dot motion perception,” Vision Res. 22, 1252–1259 (1982).
[CrossRef]

Bueno de Mesquita, A. E.

Campbell, F. W.

F. W. Campbell and L. Maffei, “The influence of spatial frequency and contrast on the perception of moving patterns,” Vision Res. 21, 713–721 (1981).
[CrossRef] [PubMed]

Cowey, A.

A. Cowey and E. T. Rolls, “Human cortical magnification factor and its relation to visual acuity,” Exp. Brain Res. 21, 447–459 (1974).
[CrossRef] [PubMed]

E. T. Rolls and A. Cowey, “Topography of the retina and striate cortex and its relationship to visual acuity in rhesus monkeys and squirrel monkeys,” Exp. Brain Res. 10, 298–310 (1970).
[CrossRef] [PubMed]

Daniel, P. M.

P. M. Daniel and D. Whitteridge, “The representation of the visual field on the cerebral cortex in monkeys,” J. Physiol. London 159, 203–221 (1961).

D. Whitteridge and P. M. Daniel, “The representation of the visual field on the calcarine cortex,” in The Visual System: Neurophysiology and Psychophysics, R. Jung and H. Kornhuber, eds. (Springer-Verlag, Berlin, 1961), pp. 222–228.

den Ouden, R. J.

C. Noorlander, J. J. Koenderink, R. J. den Ouden, and B. Wigbold Edens, “Sensitivity to spatio-temporal colour contrast in the peripheral visual field,” Vision Res. 23, 1–11 (1983).
[CrossRef]

Dow, B. M.

B. M. Dow, A. Z. Snyder, R. G. Vautin, and R. Bauer, “Magnification factor and receptive field size in foveal striate cortex of the monkey,” Exp. Brain Res. 44, 213–228 (1981).
[CrossRef] [PubMed]

Drasdo, N.

N. Drasdo, “The neural representation of visual space,” Nature 266, 554–556 (1977).
[CrossRef] [PubMed]

Finlay, D.

D. Finlay, “Motion perception in the peripheral visual field,” Percept. 11, 457–462 (1982).
[CrossRef]

Hines, D. C.

F. W. Weymouth, D. C. Hines, L. H. Acres, J. E. Raaf, and M. C. Wheeler, “Visual acuity within the area centralis and its relation to eye movements and fixation,” Am. J. Ophthalmol. 11, 947–960 (1928).

Julesz, B.

B. Julesz, Foundations of Cyclopean Perception (U. Chicago Press, Chicago, Ill., 1971).

Koenderink, J. J.

C. Noorlander, J. J. Koenderink, R. J. den Ouden, and B. Wigbold Edens, “Sensitivity to spatio-temporal colour contrast in the peripheral visual field,” Vision Res. 23, 1–11 (1983).
[CrossRef]

A. J. van Doorn and J. J. Koenderink, “Temporal properties of the visual detectability of moving spatial white noise,” Exp. Brain Res. 45, 179–188 (1982).
[PubMed]

J. J. Koenderink and A. J. van Doorn, “Invariant features of contrast detection: an explanation in terms of self-similar detector arrays,” J. Opt. Soc. Am. 72, 83–87 (1982).
[CrossRef] [PubMed]

A. J. van Doorn and J. J. Koenderink, “Visibility of movement gradients,” Biol. Cybern. 44, 167–175 (1982).
[CrossRef] [PubMed]

A. J. van Doorn and J. J. Koenderink, “Spatial properties of the visual detectability of moving spatial white noise,” Exp. Brain Res. 45, 189–195 (1982).
[PubMed]

J. J. Koenderink, M. A. Bouman, A. E. Bueno de Mesquita, and S. Slappendel, “Perimetry of contrast detection thresholds of moving spatial sine wave patterns. I–IV,” J. Opt. Soc. Am. 68, 845–865 (1978).
[CrossRef] [PubMed]

A. J. van Doorn, J. J. Koenderink, and M. A. Bouman, “The influence of the retinal inhomogeneity on the perception of spatial patterns,” Kybernetik 10, 223–230 (1972).
[CrossRef] [PubMed]

A. J. van Doorn and J. J. Koenderink, “The structure of the human motion detection system.” IEEE Trans. Syst. Man Cybern. (to be published).

A. J. van Doorn and J. J. Koenderink, “Spatiotemporal integration in the detection of coherent motion,” Vision Res. (to be published).

J. J. Koenderink and A. J. van Doorn, “Invariances in human visual spatiotemporal contrast detection,” presented at the ICO-11 Conference, Madrid, Spain, 1978.

Lappin, J. S.

J. S. Lappin and H. H. Bell, “The detection of coherence in moving random-dot patterns,” Vision Res. 16, 161–168 (1976).
[CrossRef] [PubMed]

Laurinen, P.

V. Virsu, J. Rovamo, P. Laurinen, and R. Näsänen, “Temporal contrast sensitivity and cortical magnification,” Vision Res. 22, 1211–1217 (1982).
[CrossRef] [PubMed]

LeGrand, Y.

Y. LeGrand, Form and Space Vision (Indiana U. Press, Bloomington, Ind., 1967); see especially p. 180.

Lennie, P.

P. Lennie, “Neuroanatomy of visual acuity,” Nature 266, 496 (1977).
[CrossRef]

Maffei, L.

F. W. Campbell and L. Maffei, “The influence of spatial frequency and contrast on the perception of moving patterns,” Vision Res. 21, 713–721 (1981).
[CrossRef] [PubMed]

Maunsell, J. H. R.

J. H. R. Maunsell and D. C. van Essen, “Functional properties of neurons in middle temporal visual area of the macaque monkey. I. Selectivity for stimulus direction, speed, and orientation,” J. Neurophysiol. 49, 1127–1147 (1983).
[PubMed]

Näsänen, R.

V. Virsu, J. Rovamo, P. Laurinen, and R. Näsänen, “Temporal contrast sensitivity and cortical magnification,” Vision Res. 22, 1211–1217 (1982).
[CrossRef] [PubMed]

Noorlander, C.

C. Noorlander, J. J. Koenderink, R. J. den Ouden, and B. Wigbold Edens, “Sensitivity to spatio-temporal colour contrast in the peripheral visual field,” Vision Res. 23, 1–11 (1983).
[CrossRef]

Poggio, T.

W. Reichardt and T. Poggio, “Visual control of orientation behavior in the fly,” Q. Rev. Biophys. 9, 311–348 (1976).
[CrossRef]

Raaf, J. E.

F. W. Weymouth, D. C. Hines, L. H. Acres, J. E. Raaf, and M. C. Wheeler, “Visual acuity within the area centralis and its relation to eye movements and fixation,” Am. J. Ophthalmol. 11, 947–960 (1928).

Reichardt, W.

W. Reichardt and T. Poggio, “Visual control of orientation behavior in the fly,” Q. Rev. Biophys. 9, 311–348 (1976).
[CrossRef]

W. Reichardt, “Autocorrelation, a principle for the evaluation of sensory information by the central nervous system,” in Sensory Communication, W. A. Rosenblith, ed. (MIT Press, Cambridge, Mass., 1961), pp. 303–317.

Rolls, E. T.

A. Cowey and E. T. Rolls, “Human cortical magnification factor and its relation to visual acuity,” Exp. Brain Res. 21, 447–459 (1974).
[CrossRef] [PubMed]

E. T. Rolls and A. Cowey, “Topography of the retina and striate cortex and its relationship to visual acuity in rhesus monkeys and squirrel monkeys,” Exp. Brain Res. 10, 298–310 (1970).
[CrossRef] [PubMed]

Rovamo, J.

V. Virsu, J. Rovamo, P. Laurinen, and R. Näsänen, “Temporal contrast sensitivity and cortical magnification,” Vision Res. 22, 1211–1217 (1982).
[CrossRef] [PubMed]

V. Virsu and J. Rovamo, “Visual resolution, contrast sensitivity, and the cortical magnification factor,” Exp. Brain Res. 37, 475–494 (1979).
[CrossRef] [PubMed]

J. Rovamo and V. Virsu, “An estimation and application of the human cortical magnification factor,” Exp. Brain Res. 37, 495–510 (1979).
[CrossRef] [PubMed]

Sekuler, R.

P. D. Tynan and R. Sekuler, “Motion processing in peripheral vision: reaction time and perceived velocity,” Vision Res. 22, 61–68 (1982).
[CrossRef] [PubMed]

Slappendel, S.

Snyder, A. Z.

B. M. Dow, A. Z. Snyder, R. G. Vautin, and R. Bauer, “Magnification factor and receptive field size in foveal striate cortex of the monkey,” Exp. Brain Res. 44, 213–228 (1981).
[CrossRef] [PubMed]

Tynan, P. D.

P. D. Tynan and R. Sekuler, “Motion processing in peripheral vision: reaction time and perceived velocity,” Vision Res. 22, 61–68 (1982).
[CrossRef] [PubMed]

Uttal, W. R.

W. R. Uttal, A Taxonomy of Visual Processes (Erlbaum, Hillsdale, N.J., 1981).

van Doorn, A. J.

A. J. van Doorn and J. J. Koenderink, “Temporal properties of the visual detectability of moving spatial white noise,” Exp. Brain Res. 45, 179–188 (1982).
[PubMed]

A. J. van Doorn and J. J. Koenderink, “Visibility of movement gradients,” Biol. Cybern. 44, 167–175 (1982).
[CrossRef] [PubMed]

J. J. Koenderink and A. J. van Doorn, “Invariant features of contrast detection: an explanation in terms of self-similar detector arrays,” J. Opt. Soc. Am. 72, 83–87 (1982).
[CrossRef] [PubMed]

A. J. van Doorn and J. J. Koenderink, “Spatial properties of the visual detectability of moving spatial white noise,” Exp. Brain Res. 45, 189–195 (1982).
[PubMed]

A. J. van Doorn, J. J. Koenderink, and M. A. Bouman, “The influence of the retinal inhomogeneity on the perception of spatial patterns,” Kybernetik 10, 223–230 (1972).
[CrossRef] [PubMed]

A. J. van Doorn and J. J. Koenderink, “The structure of the human motion detection system.” IEEE Trans. Syst. Man Cybern. (to be published).

A. J. van Doorn and J. J. Koenderink, “Spatiotemporal integration in the detection of coherent motion,” Vision Res. (to be published).

J. J. Koenderink and A. J. van Doorn, “Invariances in human visual spatiotemporal contrast detection,” presented at the ICO-11 Conference, Madrid, Spain, 1978.

van Essen, D. C.

J. H. R. Maunsell and D. C. van Essen, “Functional properties of neurons in middle temporal visual area of the macaque monkey. I. Selectivity for stimulus direction, speed, and orientation,” J. Neurophysiol. 49, 1127–1147 (1983).
[PubMed]

Vautin, R. G.

B. M. Dow, A. Z. Snyder, R. G. Vautin, and R. Bauer, “Magnification factor and receptive field size in foveal striate cortex of the monkey,” Exp. Brain Res. 44, 213–228 (1981).
[CrossRef] [PubMed]

Virsu, V.

V. Virsu, J. Rovamo, P. Laurinen, and R. Näsänen, “Temporal contrast sensitivity and cortical magnification,” Vision Res. 22, 1211–1217 (1982).
[CrossRef] [PubMed]

J. Rovamo and V. Virsu, “An estimation and application of the human cortical magnification factor,” Exp. Brain Res. 37, 495–510 (1979).
[CrossRef] [PubMed]

V. Virsu and J. Rovamo, “Visual resolution, contrast sensitivity, and the cortical magnification factor,” Exp. Brain Res. 37, 475–494 (1979).
[CrossRef] [PubMed]

Wertheim, T.

T. Wertheim, “Über die indirekte Sehschäfe,” Z. Psychol. Physiol. Sinnesorg 7, 172–189 (1894).

Westheimer, G.

G. Westheimer, “The spatial grain of the perifoveal visual field,” Vision Res. 22, 157–162 (1982).
[CrossRef] [PubMed]

Weymouth, F. W.

F. W. Weymouth, D. C. Hines, L. H. Acres, J. E. Raaf, and M. C. Wheeler, “Visual acuity within the area centralis and its relation to eye movements and fixation,” Am. J. Ophthalmol. 11, 947–960 (1928).

Wheeler, M. C.

F. W. Weymouth, D. C. Hines, L. H. Acres, J. E. Raaf, and M. C. Wheeler, “Visual acuity within the area centralis and its relation to eye movements and fixation,” Am. J. Ophthalmol. 11, 947–960 (1928).

Whitteridge, D.

P. M. Daniel and D. Whitteridge, “The representation of the visual field on the cerebral cortex in monkeys,” J. Physiol. London 159, 203–221 (1961).

D. Whitteridge and P. M. Daniel, “The representation of the visual field on the calcarine cortex,” in The Visual System: Neurophysiology and Psychophysics, R. Jung and H. Kornhuber, eds. (Springer-Verlag, Berlin, 1961), pp. 222–228.

Wigbold Edens, B.

C. Noorlander, J. J. Koenderink, R. J. den Ouden, and B. Wigbold Edens, “Sensitivity to spatio-temporal colour contrast in the peripheral visual field,” Vision Res. 23, 1–11 (1983).
[CrossRef]

Zeki, S. M.

S. M. Zeki, “Functional specialisation in the visual cortex of the rhesus monkey,” Nature 274, 423–428 (1978).
[CrossRef] [PubMed]

Am. J. Ophthalmol. (1)

F. W. Weymouth, D. C. Hines, L. H. Acres, J. E. Raaf, and M. C. Wheeler, “Visual acuity within the area centralis and its relation to eye movements and fixation,” Am. J. Ophthalmol. 11, 947–960 (1928).

Biol. Cybern. (1)

A. J. van Doorn and J. J. Koenderink, “Visibility of movement gradients,” Biol. Cybern. 44, 167–175 (1982).
[CrossRef] [PubMed]

Exp. Brain Res. (7)

A. J. van Doorn and J. J. Koenderink, “Temporal properties of the visual detectability of moving spatial white noise,” Exp. Brain Res. 45, 179–188 (1982).
[PubMed]

A. J. van Doorn and J. J. Koenderink, “Spatial properties of the visual detectability of moving spatial white noise,” Exp. Brain Res. 45, 189–195 (1982).
[PubMed]

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[CrossRef] [PubMed]

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J. Neurophysiol. (1)

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Kybernetik (1)

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[CrossRef] [PubMed]

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A. J. van Doorn and J. J. Koenderink, “Spatiotemporal integration in the detection of coherent motion,” Vision Res. (to be published).

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J. J. Koenderink and A. J. van Doorn, “Invariances in human visual spatiotemporal contrast detection,” presented at the ICO-11 Conference, Madrid, Spain, 1978.

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Y. LeGrand, Form and Space Vision (Indiana U. Press, Bloomington, Ind., 1967); see especially p. 180.

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D. Whitteridge and P. M. Daniel, “The representation of the visual field on the calcarine cortex,” in The Visual System: Neurophysiology and Psychophysics, R. Jung and H. Kornhuber, eds. (Springer-Verlag, Berlin, 1961), pp. 222–228.

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Figures (4)

Fig. 1
Fig. 1

Double logarithmic representation of the normalized cortical magnification factor N−1 = M/Mo [see formula (1)] and acuity λ−1 as a function of eccentricity E in the visual field. E is expressed in degrees of visual angle; λ, the minimum angle of resolution (inverse acuity), is expressed in minutes of arc; and N−1 is dimensionless. Acuity data are the classical data from Weymouth et al.,26 (squares) and Wertheim27 (circles) taken from Fig. 6 of Ref. 13. Open diamonds represent the inverse of the interpixel distance in minutes of arc as used in our experiments. Also included are data on the resolution of the right eyes of our subjects as measured with a square-wave grating flickering on and off at 2 Hz. They represent the inverse of the spatial period (inverse minutes of arc) of the grating that could just be discriminated from a uniform field. The results were obtained with square stimulus fields of 4 deg × 4 deg (×, subject AD; +, subject WG) and 8 deg × 8 deg (▼, subject AD; ■, subject WG). The foveal acuity of each subject is about 1. The dotted-dashed curve represents N−1 [formula (1)] as a function of E, with Eh = 2 deg [formula (1)]. The dotted curve is the relation between N−1 and E proposed by Rovamo and Virsu29 and referred to in Section 5. The short lines parallel to the abscissa symbolize the positions in the visual field and the width (in degrees) of the stimulus fields used in this study.

Fig. 2
Fig. 2

Main data sets for subject WG. The panels present the threshold SNR S for seeing coherent motion in the stroboscopically moving random-dot arrays as a function of the cortical velocity Vc (in millimeters of the cortex per second). The numbers along the abscissas represent the values of the scaled visual field velocity V′, defined as V′ = V/N, with N a dimensionless scaling factor defined in formula (1). These numbers thus have the dimension of degrees per second, and after multiplication with Mo, the foveal cortical magnification factor (in millimeters of the cortex per degree) the result is Vc in millimeters of the cortex per second. The first five panels present the data sets SVc for the five eccentricities used in this study, viz., 0, 6, 12, 24, and 48 deg (nasal retina). The sixth panel reproduces the data of panel 3 (E = 12 deg) and shows the fit of relation (A1) to these data as obtained with the curve-fitting procedures described in Appendix A. The symbols in all panels refer as follows to cortically equivalent stimulus dimensions; ○, W1; ●, W2 = W1/2; □, W3 = W1/4; ■, W4 = W1/8; ▼, W5 = W1/16. The ordered sets of values (in degrees of arc) used for these widths at the five eccentricities 0, 6, 12, 24, and 48 deg were as follows: W1 =2, 7.7, 13.4, 25, 48}, W2 = {1, 3.85, 6.7, 12.5, 24}, W3 = {0.5, 1.9, 3.4, 6.25, 12}, W4 = {0.25, 0.96, 1.7, 3.1, 6}, and W5 = {0.125, 0.48, 0.84, 1.6, 3}. The standard deviation proved to be roughly equal for all data points and amounted to about 0.1 log unit. The small vertical arrows on the abscissas give the positions of the visual field velocity of 10 deg/sec. One could thus present all results on a single field velocity scale by superimposing all sets from panels 2, 3, etc. on panel 1 in such a way that the arrows all coincide.

Fig. 3
Fig. 3

Main data for subject AD. The first five panels are analogous to those in Fig. 2. The symbols and scales are as explained in the caption of Fig. 2. The sixth panel presents superimposed curve-fitting results (see Appendix A) for the data sets of all eccentricities and the following widths: ○, W1; ●, W2; □, W3; and ■, W4. For the sake of clarity the curves and the corresponding data sets are shifted arbitrary amounts along the direction of the long oblique arrow. The thick vertical arrows indicate the positions of the minima of the curves.

Fig. 4
Fig. 4

High-velocity cutoff values Vm (in degrees per second), as determined by fitting relation (A1) to the data of Figs. 2 and 3, are plotted as a function of the stimulus width W (in degrees). The data points and the regression line for subject AD are shifted upward by a factor of 8 (left-hand ordinate) relative to those for WG (right-hand ordinate). The regression lines are described by formula (3).

Tables (1)

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Table 1 Eccentricities E and Corresponding Viewing Distances L, Maximum Stimulus Widths W1, Interpixel Distances p, and Velocities vp

Equations (9)

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M = M 0 N - 1 = M 0 ( 1 + E / E h ) - 1 ,
λ ( E ) = N λ 0 ,
V m = V m x ( W / W x ) b
V 0 = V 00 ( 1 + E E h 0 )             ( r 2 = 0.95 ) .
S 0 - S 0 * = S 0 x ( W W x ) n ( 1 + E E h ) .
S = k exp [ exp ( c V V m ) + exp ( c V * V ) ] .
c = ln ( 5 - ln k ) .
V 0 2 = V m V *
S 0 = k exp [ 2 exp ( c V 0 / V m ) ] .