Abstract

Vertical sine-wave gratings of varying spatial frequency were stepped instantaneously to the right or to the left at differing phase angles (θ). Separate paradigms measured the contrast threshold for the detection of such a step and for the discrimination of the direction of the same step. By considering the grating before and after its displacement as a rotating phasor, we made the following predictions: (1) Contrast sensitivity for the detection of a displacement should rise as sin(θ). (2) Contrast sensitivity for the discrimination of the direction of the displacement should rise as sin(θ/2). Both predictions were confirmed using a range of spatial frequencies and phase angles. From the results of additional experiments, by measuring the discrimination of the direction thresholds as a function of contrast, we derived a nonlinear contrast response function for the motion system. This function appears to saturate fully at fairly low levels, in the neighborhood of 2 to 3% under the conditions examined. Our results suggest a direct connection among the contrast sensitivity, the contrast response function, and motion-hyperacuity thresholds.

© 1985 Optical Society of America

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References

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  1. O. Braddick, “A short-range process in apparent motion,” Vision Res. 14, 519–527 (1974).
    [CrossRef] [PubMed]
  2. C. L. Baker, O. J. Braddick, “The basis of area and dot number effects in random dot motion perception,” Vision Res. 22, 1253–1260 (1982).
    [CrossRef] [PubMed]
  3. C. L. Baker, O. J. Braddick, “Does segregation of differently moving areas depend on relative or absolute displacement?” Vision Res. 22, 851–856 (1982).
    [CrossRef] [PubMed]
  4. K. Nakayama, G. H. Silverman, “Temporal and spatial properties of the upper displacement limit in random dots,” Vision Res. 24, 293–299 (1984).
    [CrossRef]
  5. J. J. Chang, B. Julesz, “Displacement limits for spatial-frequency filtered random-dot cinematograms in apparent motion,” Vision Res. 23, 1379–1385 (1983).
    [CrossRef]
  6. J. S. Lappin, H. H. Bell, “The detection of coherence in moving random-dot patterns,” Vision Res. 16, 161–168 (1976).
    [CrossRef] [PubMed]
  7. D. C. Burr, J. Ross, “Contrast sensitivity at high velocities,” Vision Res. 22, 479–484 (1982).
    [CrossRef] [PubMed]
  8. A. J. Pantle, “Temporal frequency response characteristics of motion channels measured with three different psychophysical techniques,” Percept. Psychophys. 24, 285–294 (1978).
    [CrossRef] [PubMed]
  9. S. P. McKee, D. Y. Teller, S. Klein, “Statistical properties of forced-choice psychometric function: implication for probit analysis,” Percept. Psychophys. (to be published).
  10. We note some fundamental differences between our comparison of detection and discrimination thresholds and two other studies that might be construed as similar: A. B. Watson, P. G. Thompson, B. G. Murphy, J. Nachmias, “Summation and discrimination of gratings moving in opposite directions,” Vision Res. 20, 341–348 (1980); M. Green, “Contrast detection and direction discrimination of drifting gratings,” Vision Res. 23, 281–289 (1983)]. These studies used drifting gratings rather than stepped gratings. Most important was the difference in task, requiring the observer to detect the presence or absence of a grating rather than the presence or absence of a displacement. Thus the intent and the interpretation of the detection versus the discrimination in these studies are not directly applicable to the experiments reported here.
    [CrossRef] [PubMed]
  11. C. Blakemore, F. W. Campbell, “On the existence of neurons in the human visual system selectively sensitive to the orientation and size of retinal images,”J. Physiol. 203, 237–260 (1967).
  12. I. Ohzawa, G. Schlar, R. E. Freeman, “Contrast gain control in the cat visual cortex,” Nature 298, 266–268 (1982).
    [CrossRef] [PubMed]
  13. K. Nakayama, “Differential motion hyperacuity under conditions of common image motion,” Vision Res. 21, 1475–1482 (1981).
    [CrossRef] [PubMed]
  14. K. Nakayama, C. W. Tyler, “Psychophysical isolation of motion sensitivity by removal of familiar position cues,” Vision Res. 21, 427–433 (1981).
    [CrossRef]
  15. G. Westheimer, “Spatial phase sensitivity for sinusoidal grating targets,” Vision Res. 18, 1073–1074 (1978).
    [CrossRef] [PubMed]
  16. D. G. Watt, M. Morgan, “The recognition and representation of edge blur; evidence for spatial primitives in human vision,” Vision Res. 23, 1465–1477 (1983).
    [CrossRef]
  17. R. Sekuler, A. Pantle, E. Levinson, “Physiological basis of motion perception,” in Handbook of Sensory Physiology, R. Held, H. Liebowitz, H. Terler, eds. (Springer-Verlag, New York, 1978), Vol. III, pp. 67–96.
  18. M. Keck, F. W. Montague, T. P. Burke, “Influence of the spatial periodicity of moving gratings on motion response,” Invest. Ophthalmol. Vis. Sci. 19, 1364–1370 (1980).
    [PubMed]
  19. M. Keck, T. D. Palella, A. Pantle, “Motion aftereffect as a function of the contrast of sinusoidal gratings,” Vision Res. 16, 187 (1976).
    [CrossRef] [PubMed]
  20. G. Legge, “A power law for contrast discrimination,” Vision Res. 21, 457 (1981).
    [CrossRef]
  21. D. Albrecht, D. B. Hamilton, “Striate cortex of monkey and cat: contrast response function,”J. Neurophysiol. 48, 217–237 (1982).
    [PubMed]
  22. K. Nakayama, “Local adaptation in LGN neurons: evidence for a surround antagonism,” Vision Res. 11, 501–509 (1971).
    [CrossRef] [PubMed]
  23. H. B. Barlow, W. R. Levick, “Three factors affecting the reliable detection of light by ganglion cells of the cat,”J. Physiol. (London) 200, 1–24 (1969).
  24. D. J. Tolhurst, J. A. Movshon, A. F. Dean, “The statistical reliability of signals in single neurons in cat and monkey visual cortex,” Vision Res. 23, 775–785 (1983).
    [CrossRef] [PubMed]
  25. H. B. Barlow, R. M. Hill, “Selective sensitivity to direction of motion in ganglion cells in the rabbit’s retina,” Science 139, 412–414 (1963).
    [CrossRef] [PubMed]
  26. E. Kaplan, R. M. Shapley, “X and Y cells in the lateral geniculate nucleus of macaque monkeys,”J. Physiol. 330, 125–143 (1982).
    [PubMed]
  27. J. P. H. Van Santen, G. Sperling, “A temporal covariance model of human motion perception,” J. Opt. Soc. Am. A 2, 300–321 (1985).
    [PubMed]
  28. A. B. Watson, A. J. Ahumada, “A look at motion in the frequency domain,”NASA Tech. Memo. 84352 (1983).
  29. S. Marcelja, “Mathematical description of the responses of simple cortical cells,”J. Opt. Soc. Am. 70, 1297–1300 (1980).
    [CrossRef] [PubMed]
  30. D. A. Pollen, S. F. Ronner, “Phase relationship between adjacent single cells in the visual cortex,” Science 22, 1409–1411 (1981).
    [CrossRef]
  31. M. Green, R. Blake, “Phase effects in monoptic and dichoptic temporal integration: flicker and motion detection,” Vision Res. 21, 365–372 (1981).
    [CrossRef] [PubMed]

1985 (1)

1984 (1)

K. Nakayama, G. H. Silverman, “Temporal and spatial properties of the upper displacement limit in random dots,” Vision Res. 24, 293–299 (1984).
[CrossRef]

1983 (3)

J. J. Chang, B. Julesz, “Displacement limits for spatial-frequency filtered random-dot cinematograms in apparent motion,” Vision Res. 23, 1379–1385 (1983).
[CrossRef]

D. G. Watt, M. Morgan, “The recognition and representation of edge blur; evidence for spatial primitives in human vision,” Vision Res. 23, 1465–1477 (1983).
[CrossRef]

D. J. Tolhurst, J. A. Movshon, A. F. Dean, “The statistical reliability of signals in single neurons in cat and monkey visual cortex,” Vision Res. 23, 775–785 (1983).
[CrossRef] [PubMed]

1982 (6)

D. Albrecht, D. B. Hamilton, “Striate cortex of monkey and cat: contrast response function,”J. Neurophysiol. 48, 217–237 (1982).
[PubMed]

E. Kaplan, R. M. Shapley, “X and Y cells in the lateral geniculate nucleus of macaque monkeys,”J. Physiol. 330, 125–143 (1982).
[PubMed]

I. Ohzawa, G. Schlar, R. E. Freeman, “Contrast gain control in the cat visual cortex,” Nature 298, 266–268 (1982).
[CrossRef] [PubMed]

C. L. Baker, O. J. Braddick, “The basis of area and dot number effects in random dot motion perception,” Vision Res. 22, 1253–1260 (1982).
[CrossRef] [PubMed]

C. L. Baker, O. J. Braddick, “Does segregation of differently moving areas depend on relative or absolute displacement?” Vision Res. 22, 851–856 (1982).
[CrossRef] [PubMed]

D. C. Burr, J. Ross, “Contrast sensitivity at high velocities,” Vision Res. 22, 479–484 (1982).
[CrossRef] [PubMed]

1981 (5)

K. Nakayama, “Differential motion hyperacuity under conditions of common image motion,” Vision Res. 21, 1475–1482 (1981).
[CrossRef] [PubMed]

K. Nakayama, C. W. Tyler, “Psychophysical isolation of motion sensitivity by removal of familiar position cues,” Vision Res. 21, 427–433 (1981).
[CrossRef]

G. Legge, “A power law for contrast discrimination,” Vision Res. 21, 457 (1981).
[CrossRef]

D. A. Pollen, S. F. Ronner, “Phase relationship between adjacent single cells in the visual cortex,” Science 22, 1409–1411 (1981).
[CrossRef]

M. Green, R. Blake, “Phase effects in monoptic and dichoptic temporal integration: flicker and motion detection,” Vision Res. 21, 365–372 (1981).
[CrossRef] [PubMed]

1980 (3)

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

M. Keck, F. W. Montague, T. P. Burke, “Influence of the spatial periodicity of moving gratings on motion response,” Invest. Ophthalmol. Vis. Sci. 19, 1364–1370 (1980).
[PubMed]

We note some fundamental differences between our comparison of detection and discrimination thresholds and two other studies that might be construed as similar: A. B. Watson, P. G. Thompson, B. G. Murphy, J. Nachmias, “Summation and discrimination of gratings moving in opposite directions,” Vision Res. 20, 341–348 (1980); M. Green, “Contrast detection and direction discrimination of drifting gratings,” Vision Res. 23, 281–289 (1983)]. These studies used drifting gratings rather than stepped gratings. Most important was the difference in task, requiring the observer to detect the presence or absence of a grating rather than the presence or absence of a displacement. Thus the intent and the interpretation of the detection versus the discrimination in these studies are not directly applicable to the experiments reported here.
[CrossRef] [PubMed]

1978 (2)

A. J. Pantle, “Temporal frequency response characteristics of motion channels measured with three different psychophysical techniques,” Percept. Psychophys. 24, 285–294 (1978).
[CrossRef] [PubMed]

G. Westheimer, “Spatial phase sensitivity for sinusoidal grating targets,” Vision Res. 18, 1073–1074 (1978).
[CrossRef] [PubMed]

1976 (2)

M. Keck, T. D. Palella, A. Pantle, “Motion aftereffect as a function of the contrast of sinusoidal gratings,” Vision Res. 16, 187 (1976).
[CrossRef] [PubMed]

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

1974 (1)

O. Braddick, “A short-range process in apparent motion,” Vision Res. 14, 519–527 (1974).
[CrossRef] [PubMed]

1971 (1)

K. Nakayama, “Local adaptation in LGN neurons: evidence for a surround antagonism,” Vision Res. 11, 501–509 (1971).
[CrossRef] [PubMed]

1969 (1)

H. B. Barlow, W. R. Levick, “Three factors affecting the reliable detection of light by ganglion cells of the cat,”J. Physiol. (London) 200, 1–24 (1969).

1967 (1)

C. Blakemore, F. W. Campbell, “On the existence of neurons in the human visual system selectively sensitive to the orientation and size of retinal images,”J. Physiol. 203, 237–260 (1967).

1963 (1)

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

Ahumada, A. J.

A. B. Watson, A. J. Ahumada, “A look at motion in the frequency domain,”NASA Tech. Memo. 84352 (1983).

Albrecht, D.

D. Albrecht, D. B. Hamilton, “Striate cortex of monkey and cat: contrast response function,”J. Neurophysiol. 48, 217–237 (1982).
[PubMed]

Baker, C. L.

C. L. Baker, O. J. Braddick, “Does segregation of differently moving areas depend on relative or absolute displacement?” Vision Res. 22, 851–856 (1982).
[CrossRef] [PubMed]

C. L. Baker, O. J. Braddick, “The basis of area and dot number effects in random dot motion perception,” Vision Res. 22, 1253–1260 (1982).
[CrossRef] [PubMed]

Barlow, H. B.

H. B. Barlow, W. R. Levick, “Three factors affecting the reliable detection of light by ganglion cells of the cat,”J. Physiol. (London) 200, 1–24 (1969).

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

Bell, H. H.

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

Blake, R.

M. Green, R. Blake, “Phase effects in monoptic and dichoptic temporal integration: flicker and motion detection,” Vision Res. 21, 365–372 (1981).
[CrossRef] [PubMed]

Blakemore, C.

C. Blakemore, F. W. Campbell, “On the existence of neurons in the human visual system selectively sensitive to the orientation and size of retinal images,”J. Physiol. 203, 237–260 (1967).

Braddick, O.

O. Braddick, “A short-range process in apparent motion,” Vision Res. 14, 519–527 (1974).
[CrossRef] [PubMed]

Braddick, O. J.

C. L. Baker, O. J. Braddick, “The basis of area and dot number effects in random dot motion perception,” Vision Res. 22, 1253–1260 (1982).
[CrossRef] [PubMed]

C. L. Baker, O. J. Braddick, “Does segregation of differently moving areas depend on relative or absolute displacement?” Vision Res. 22, 851–856 (1982).
[CrossRef] [PubMed]

Burke, T. P.

M. Keck, F. W. Montague, T. P. Burke, “Influence of the spatial periodicity of moving gratings on motion response,” Invest. Ophthalmol. Vis. Sci. 19, 1364–1370 (1980).
[PubMed]

Burr, D. C.

D. C. Burr, J. Ross, “Contrast sensitivity at high velocities,” Vision Res. 22, 479–484 (1982).
[CrossRef] [PubMed]

Campbell, F. W.

C. Blakemore, F. W. Campbell, “On the existence of neurons in the human visual system selectively sensitive to the orientation and size of retinal images,”J. Physiol. 203, 237–260 (1967).

Chang, J. J.

J. J. Chang, B. Julesz, “Displacement limits for spatial-frequency filtered random-dot cinematograms in apparent motion,” Vision Res. 23, 1379–1385 (1983).
[CrossRef]

Dean, A. F.

D. J. Tolhurst, J. A. Movshon, A. F. Dean, “The statistical reliability of signals in single neurons in cat and monkey visual cortex,” Vision Res. 23, 775–785 (1983).
[CrossRef] [PubMed]

Freeman, R. E.

I. Ohzawa, G. Schlar, R. E. Freeman, “Contrast gain control in the cat visual cortex,” Nature 298, 266–268 (1982).
[CrossRef] [PubMed]

Green, M.

M. Green, R. Blake, “Phase effects in monoptic and dichoptic temporal integration: flicker and motion detection,” Vision Res. 21, 365–372 (1981).
[CrossRef] [PubMed]

Hamilton, D. B.

D. Albrecht, D. B. Hamilton, “Striate cortex of monkey and cat: contrast response function,”J. Neurophysiol. 48, 217–237 (1982).
[PubMed]

Hill, R. M.

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

Julesz, B.

J. J. Chang, B. Julesz, “Displacement limits for spatial-frequency filtered random-dot cinematograms in apparent motion,” Vision Res. 23, 1379–1385 (1983).
[CrossRef]

Kaplan, E.

E. Kaplan, R. M. Shapley, “X and Y cells in the lateral geniculate nucleus of macaque monkeys,”J. Physiol. 330, 125–143 (1982).
[PubMed]

Keck, M.

M. Keck, F. W. Montague, T. P. Burke, “Influence of the spatial periodicity of moving gratings on motion response,” Invest. Ophthalmol. Vis. Sci. 19, 1364–1370 (1980).
[PubMed]

M. Keck, T. D. Palella, A. Pantle, “Motion aftereffect as a function of the contrast of sinusoidal gratings,” Vision Res. 16, 187 (1976).
[CrossRef] [PubMed]

Klein, S.

S. P. McKee, D. Y. Teller, S. Klein, “Statistical properties of forced-choice psychometric function: implication for probit analysis,” Percept. Psychophys. (to be published).

Lappin, J. S.

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

Legge, G.

G. Legge, “A power law for contrast discrimination,” Vision Res. 21, 457 (1981).
[CrossRef]

Levick, W. R.

H. B. Barlow, W. R. Levick, “Three factors affecting the reliable detection of light by ganglion cells of the cat,”J. Physiol. (London) 200, 1–24 (1969).

Levinson, E.

R. Sekuler, A. Pantle, E. Levinson, “Physiological basis of motion perception,” in Handbook of Sensory Physiology, R. Held, H. Liebowitz, H. Terler, eds. (Springer-Verlag, New York, 1978), Vol. III, pp. 67–96.

Marcelja, S.

McKee, S. P.

S. P. McKee, D. Y. Teller, S. Klein, “Statistical properties of forced-choice psychometric function: implication for probit analysis,” Percept. Psychophys. (to be published).

Montague, F. W.

M. Keck, F. W. Montague, T. P. Burke, “Influence of the spatial periodicity of moving gratings on motion response,” Invest. Ophthalmol. Vis. Sci. 19, 1364–1370 (1980).
[PubMed]

Morgan, M.

D. G. Watt, M. Morgan, “The recognition and representation of edge blur; evidence for spatial primitives in human vision,” Vision Res. 23, 1465–1477 (1983).
[CrossRef]

Movshon, J. A.

D. J. Tolhurst, J. A. Movshon, A. F. Dean, “The statistical reliability of signals in single neurons in cat and monkey visual cortex,” Vision Res. 23, 775–785 (1983).
[CrossRef] [PubMed]

Murphy, B. G.

We note some fundamental differences between our comparison of detection and discrimination thresholds and two other studies that might be construed as similar: A. B. Watson, P. G. Thompson, B. G. Murphy, J. Nachmias, “Summation and discrimination of gratings moving in opposite directions,” Vision Res. 20, 341–348 (1980); M. Green, “Contrast detection and direction discrimination of drifting gratings,” Vision Res. 23, 281–289 (1983)]. These studies used drifting gratings rather than stepped gratings. Most important was the difference in task, requiring the observer to detect the presence or absence of a grating rather than the presence or absence of a displacement. Thus the intent and the interpretation of the detection versus the discrimination in these studies are not directly applicable to the experiments reported here.
[CrossRef] [PubMed]

Nachmias, J.

We note some fundamental differences between our comparison of detection and discrimination thresholds and two other studies that might be construed as similar: A. B. Watson, P. G. Thompson, B. G. Murphy, J. Nachmias, “Summation and discrimination of gratings moving in opposite directions,” Vision Res. 20, 341–348 (1980); M. Green, “Contrast detection and direction discrimination of drifting gratings,” Vision Res. 23, 281–289 (1983)]. These studies used drifting gratings rather than stepped gratings. Most important was the difference in task, requiring the observer to detect the presence or absence of a grating rather than the presence or absence of a displacement. Thus the intent and the interpretation of the detection versus the discrimination in these studies are not directly applicable to the experiments reported here.
[CrossRef] [PubMed]

Nakayama, K.

K. Nakayama, G. H. Silverman, “Temporal and spatial properties of the upper displacement limit in random dots,” Vision Res. 24, 293–299 (1984).
[CrossRef]

K. Nakayama, “Differential motion hyperacuity under conditions of common image motion,” Vision Res. 21, 1475–1482 (1981).
[CrossRef] [PubMed]

K. Nakayama, C. W. Tyler, “Psychophysical isolation of motion sensitivity by removal of familiar position cues,” Vision Res. 21, 427–433 (1981).
[CrossRef]

K. Nakayama, “Local adaptation in LGN neurons: evidence for a surround antagonism,” Vision Res. 11, 501–509 (1971).
[CrossRef] [PubMed]

Ohzawa, I.

I. Ohzawa, G. Schlar, R. E. Freeman, “Contrast gain control in the cat visual cortex,” Nature 298, 266–268 (1982).
[CrossRef] [PubMed]

Palella, T. D.

M. Keck, T. D. Palella, A. Pantle, “Motion aftereffect as a function of the contrast of sinusoidal gratings,” Vision Res. 16, 187 (1976).
[CrossRef] [PubMed]

Pantle, A.

M. Keck, T. D. Palella, A. Pantle, “Motion aftereffect as a function of the contrast of sinusoidal gratings,” Vision Res. 16, 187 (1976).
[CrossRef] [PubMed]

R. Sekuler, A. Pantle, E. Levinson, “Physiological basis of motion perception,” in Handbook of Sensory Physiology, R. Held, H. Liebowitz, H. Terler, eds. (Springer-Verlag, New York, 1978), Vol. III, pp. 67–96.

Pantle, A. J.

A. J. Pantle, “Temporal frequency response characteristics of motion channels measured with three different psychophysical techniques,” Percept. Psychophys. 24, 285–294 (1978).
[CrossRef] [PubMed]

Pollen, D. A.

D. A. Pollen, S. F. Ronner, “Phase relationship between adjacent single cells in the visual cortex,” Science 22, 1409–1411 (1981).
[CrossRef]

Ronner, S. F.

D. A. Pollen, S. F. Ronner, “Phase relationship between adjacent single cells in the visual cortex,” Science 22, 1409–1411 (1981).
[CrossRef]

Ross, J.

D. C. Burr, J. Ross, “Contrast sensitivity at high velocities,” Vision Res. 22, 479–484 (1982).
[CrossRef] [PubMed]

Schlar, G.

I. Ohzawa, G. Schlar, R. E. Freeman, “Contrast gain control in the cat visual cortex,” Nature 298, 266–268 (1982).
[CrossRef] [PubMed]

Sekuler, R.

R. Sekuler, A. Pantle, E. Levinson, “Physiological basis of motion perception,” in Handbook of Sensory Physiology, R. Held, H. Liebowitz, H. Terler, eds. (Springer-Verlag, New York, 1978), Vol. III, pp. 67–96.

Shapley, R. M.

E. Kaplan, R. M. Shapley, “X and Y cells in the lateral geniculate nucleus of macaque monkeys,”J. Physiol. 330, 125–143 (1982).
[PubMed]

Silverman, G. H.

K. Nakayama, G. H. Silverman, “Temporal and spatial properties of the upper displacement limit in random dots,” Vision Res. 24, 293–299 (1984).
[CrossRef]

Sperling, G.

Teller, D. Y.

S. P. McKee, D. Y. Teller, S. Klein, “Statistical properties of forced-choice psychometric function: implication for probit analysis,” Percept. Psychophys. (to be published).

Thompson, P. G.

We note some fundamental differences between our comparison of detection and discrimination thresholds and two other studies that might be construed as similar: A. B. Watson, P. G. Thompson, B. G. Murphy, J. Nachmias, “Summation and discrimination of gratings moving in opposite directions,” Vision Res. 20, 341–348 (1980); M. Green, “Contrast detection and direction discrimination of drifting gratings,” Vision Res. 23, 281–289 (1983)]. These studies used drifting gratings rather than stepped gratings. Most important was the difference in task, requiring the observer to detect the presence or absence of a grating rather than the presence or absence of a displacement. Thus the intent and the interpretation of the detection versus the discrimination in these studies are not directly applicable to the experiments reported here.
[CrossRef] [PubMed]

Tolhurst, D. J.

D. J. Tolhurst, J. A. Movshon, A. F. Dean, “The statistical reliability of signals in single neurons in cat and monkey visual cortex,” Vision Res. 23, 775–785 (1983).
[CrossRef] [PubMed]

Tyler, C. W.

K. Nakayama, C. W. Tyler, “Psychophysical isolation of motion sensitivity by removal of familiar position cues,” Vision Res. 21, 427–433 (1981).
[CrossRef]

Van Santen, J. P. H.

Watson, A. B.

We note some fundamental differences between our comparison of detection and discrimination thresholds and two other studies that might be construed as similar: A. B. Watson, P. G. Thompson, B. G. Murphy, J. Nachmias, “Summation and discrimination of gratings moving in opposite directions,” Vision Res. 20, 341–348 (1980); M. Green, “Contrast detection and direction discrimination of drifting gratings,” Vision Res. 23, 281–289 (1983)]. These studies used drifting gratings rather than stepped gratings. Most important was the difference in task, requiring the observer to detect the presence or absence of a grating rather than the presence or absence of a displacement. Thus the intent and the interpretation of the detection versus the discrimination in these studies are not directly applicable to the experiments reported here.
[CrossRef] [PubMed]

A. B. Watson, A. J. Ahumada, “A look at motion in the frequency domain,”NASA Tech. Memo. 84352 (1983).

Watt, D. G.

D. G. Watt, M. Morgan, “The recognition and representation of edge blur; evidence for spatial primitives in human vision,” Vision Res. 23, 1465–1477 (1983).
[CrossRef]

Westheimer, G.

G. Westheimer, “Spatial phase sensitivity for sinusoidal grating targets,” Vision Res. 18, 1073–1074 (1978).
[CrossRef] [PubMed]

Invest. Ophthalmol. Vis. Sci. (1)

M. Keck, F. W. Montague, T. P. Burke, “Influence of the spatial periodicity of moving gratings on motion response,” Invest. Ophthalmol. Vis. Sci. 19, 1364–1370 (1980).
[PubMed]

J. Neurophysiol. (1)

D. Albrecht, D. B. Hamilton, “Striate cortex of monkey and cat: contrast response function,”J. Neurophysiol. 48, 217–237 (1982).
[PubMed]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

J. Physiol. (2)

E. Kaplan, R. M. Shapley, “X and Y cells in the lateral geniculate nucleus of macaque monkeys,”J. Physiol. 330, 125–143 (1982).
[PubMed]

C. Blakemore, F. W. Campbell, “On the existence of neurons in the human visual system selectively sensitive to the orientation and size of retinal images,”J. Physiol. 203, 237–260 (1967).

J. Physiol. (London) (1)

H. B. Barlow, W. R. Levick, “Three factors affecting the reliable detection of light by ganglion cells of the cat,”J. Physiol. (London) 200, 1–24 (1969).

Nature (1)

I. Ohzawa, G. Schlar, R. E. Freeman, “Contrast gain control in the cat visual cortex,” Nature 298, 266–268 (1982).
[CrossRef] [PubMed]

Percept. Psychophys. (1)

A. J. Pantle, “Temporal frequency response characteristics of motion channels measured with three different psychophysical techniques,” Percept. Psychophys. 24, 285–294 (1978).
[CrossRef] [PubMed]

Science (2)

D. A. Pollen, S. F. Ronner, “Phase relationship between adjacent single cells in the visual cortex,” Science 22, 1409–1411 (1981).
[CrossRef]

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

Vision Res. (17)

We note some fundamental differences between our comparison of detection and discrimination thresholds and two other studies that might be construed as similar: A. B. Watson, P. G. Thompson, B. G. Murphy, J. Nachmias, “Summation and discrimination of gratings moving in opposite directions,” Vision Res. 20, 341–348 (1980); M. Green, “Contrast detection and direction discrimination of drifting gratings,” Vision Res. 23, 281–289 (1983)]. These studies used drifting gratings rather than stepped gratings. Most important was the difference in task, requiring the observer to detect the presence or absence of a grating rather than the presence or absence of a displacement. Thus the intent and the interpretation of the detection versus the discrimination in these studies are not directly applicable to the experiments reported here.
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M. Green, R. Blake, “Phase effects in monoptic and dichoptic temporal integration: flicker and motion detection,” Vision Res. 21, 365–372 (1981).
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M. Keck, T. D. Palella, A. Pantle, “Motion aftereffect as a function of the contrast of sinusoidal gratings,” Vision Res. 16, 187 (1976).
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G. Legge, “A power law for contrast discrimination,” Vision Res. 21, 457 (1981).
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D. J. Tolhurst, J. A. Movshon, A. F. Dean, “The statistical reliability of signals in single neurons in cat and monkey visual cortex,” Vision Res. 23, 775–785 (1983).
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K. Nakayama, “Local adaptation in LGN neurons: evidence for a surround antagonism,” Vision Res. 11, 501–509 (1971).
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K. Nakayama, “Differential motion hyperacuity under conditions of common image motion,” Vision Res. 21, 1475–1482 (1981).
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K. Nakayama, C. W. Tyler, “Psychophysical isolation of motion sensitivity by removal of familiar position cues,” Vision Res. 21, 427–433 (1981).
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D. G. Watt, M. Morgan, “The recognition and representation of edge blur; evidence for spatial primitives in human vision,” Vision Res. 23, 1465–1477 (1983).
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C. L. Baker, O. J. Braddick, “Does segregation of differently moving areas depend on relative or absolute displacement?” Vision Res. 22, 851–856 (1982).
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Other (3)

R. Sekuler, A. Pantle, E. Levinson, “Physiological basis of motion perception,” in Handbook of Sensory Physiology, R. Held, H. Liebowitz, H. Terler, eds. (Springer-Verlag, New York, 1978), Vol. III, pp. 67–96.

S. P. McKee, D. Y. Teller, S. Klein, “Statistical properties of forced-choice psychometric function: implication for probit analysis,” Percept. Psychophys. (to be published).

A. B. Watson, A. J. Ahumada, “A look at motion in the frequency domain,”NASA Tech. Memo. 84352 (1983).

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Figures (10)

Fig. 1
Fig. 1

A, Two-alternative forced-choice paradigm to obtain detection of displacement thresholds. A sinusoidal grating appears twice, defining two temporal intervals. During only one of the inverals is there a phase shift in either direction, denoted by the step in the phase trace (θ). The observer’s only task is to identify the time interval (either #1 or #2) containing the phase shift. B, One-alternative forced-choice paradigm to obtain discrimination thresholds. The observer sees one of two possibilities presented at random. The target grating steps either to the right as in R or to the left as in L. The observer’s task is to identify the direction of motion.

Fig. 2
Fig. 2

Polar or phasor plot representing the amplitude and position of a sinusoidal grating before and after a step displacement. Gi represents the initial grating, arbitrarily defined to be in cosine phase. Gf represents the final grating after it has been jumped by 135° and when it is in its second position. In A, we describe the hypothetical excitation that can be used to detect the existence of step displacement, it being the vector difference between Gi and Gf. In terms of the phase angle jumped, the excitation is proportional to the sine of one half of the angle (see inset equation in A). In B, we show the hypothetical excitation onto a motion-discrimination system. In this case, it is proportional to the projections of Gf onto the sine or y axis, which is labeled by the vector Q.

Fig. 3
Fig. 3

Effect of grating duration Δt (see inset) on contrast sensitivity for experiments in which the observer was required to discriminate direction. Phase shift is 90°. Spatial frequency is 2 cyc/deg. The subject is KN.

Fig. 4
Fig. 4

A, The raw contrast sensitivity for detection as a function of the phase angle for 2 and 8 cyc/deg. B, Contrast sensitivity of the best-fitting theoretical curve has been normalized to one, and both sets of data have been averaged. Note the linear scale for contrast sensitivity. The subject is JS.

Fig. 5
Fig. 5

Contrast sensitivity for the discrimination of motion direction. A, Raw contrast sensitivities as a function of phase angle for 2 cyc/deg (squares), 4 cyc/deg (triangles), and 8 cyc/deg (circles). B, Normalized and averaged contrast sensitivity for 1, 2, 4, 8 cyc/deg. Note linear scale for contrast sensitivity. The subject is JS.

Fig. 6
Fig. 6

Polar coordinate representation of discrimination contrast thresholds taken from Fig. 5A (2 cyc/deg). Distance of the data point from the origin defines a radius vector whose length is proportional to the contrast of the grating and whose angle with respect to the positive X axis defines the phase angle jumped. The radius vector Ci and phase angle θi are illustrated for just one data point by the arrow. Semicircles represent grating contrasts of 1 and 2%, respectively. Note that, with the possible exception of the leftmost point, all data fall on a horizontal line, which by definition has the same projection onto the y axis.

Fig. 7
Fig. 7

Derivation of the effective contrast for motion discrimination. We assume that motion discrimination requires a minimum amount of energy to be projected onto the orthogonal or quadrature axis (TQ). If the coding of effective contrast were linear, then given any input contrast Ci we can predict the displacement threshold (ϕ) [see Eq. (4)]. This can be seen by noting arrow Ci and its associated phase angle (ϕ). If the system had a compressive nonlinearity, then the effective contrast Ce would be smaller than Ci. For Ce to project equally on to the Y axis with a value of TQ, θ would have to be correspondingly larger. As such, a measurement of θ also permits an estimate of Ce. See the equation in the inset, which is the same as Eq. (5). Note that the angles in this figure are not drawn to scale; they have been increased for purposes of clarity.

Fig. 8
Fig. 8

Phase-angle thresholds as a function of grating contrast. Crosses are data from the θ = F(c) experiment. Circles are data from the C = F(θ) experiment. The spatial frequency is 2 cyc/deg. The solid line is the best-fitting sinusoid to account for contrast thresholds in the C = F(θ) experiment (as in Fig. 5).

Fig. 9
Fig. 9

Effective contrast versus contrast input for the motion system. A shows the effective contrast response output versus input derived from the data of Fig. 5B and of Fig. 9 for observer JS. Derivation is based on Eq. (5). B shows similar data taken from observer KN. All data are taken at 2 cyc/deg. Solid lines represent the best-fitting hyperbolic-ratio functions [see Eq. (6)].

Fig. 10
Fig. 10

Two configurations of RF’s feeding a motion sensor that have been proposed by Van Santen and Sperling.28 In A, two symmetric receptive fields are displaced. In B, the receptive fields are centered on the same region of space, one being spatially symmetric, the other being spatially antisymmetric.

Equations (12)

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S = ( Δ x 2 + Δ y 2 ) 0.5 ,
S = 2 A sin ( θ / 2 ) ,
Discrimination sensitivity = A B S A sin ( θ ) .
ϕ = arcsin ( T Q / C i ) ,
C e = T Q / sin ( θ ) ,
R = k C n / ( C n + C 50 n ) ,
S = ( Δ X 2 + Δ Y 2 ) 0.5 ,
S 2 = Δ X 2 + Δ Y 2 ,
S 2 = ( A - A cos θ ) 2 + ( - A sin θ ) 2 ,
S 2 = 2 A 2 ( 1 - cos θ ) ,
S = 2 A [ ( 1 - cos θ ) 2 ] 1 / 2 ,
S = 2 A sin ( θ / 2 ) .

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