Abstract

The minimum speed required for discriminating the direction of drifting gratings was measured at a variety of spatial frequencies, display durations, and contrasts. As was reported previously, speed thresholds were relatively constant for middle and high spatial frequencies, but speed threshold was found to be almost inversely proportional to spatial frequency in the range of 0.25 to 1.0 c/deg. Speed threshold was also found to be inversely proportional to duration between 73 and 400 ms. These results at low frequencies and short durations are shown to be consistent with limits set by the spread of energy in the stimuli, producing velocity uncertainty. A quantitative model of temporal filtering is presented that largely accounts for results at all spatial frequencies and durations by the inclusion of constant positional noise. A discussion includes the possible roles of magnocellular and parvocellular mechanisms in mediating speed thresholds.

© 1997 Optical Society of America

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  28. J. C. Boulton, R. F. Hess, “Luminance contrast and motion detection,” Vision Res. 30, 175–179 (1990).
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    [CrossRef] [PubMed]
  30. J. Yang, X. Qi, W. Makous, “Zero frequency masking and a model of contrast sensitivity,” Vision Res. 35, 1965–1978 (1995).
    [CrossRef] [PubMed]
  31. M. J. Wright, “Spatiotemporal properties of grating motion detection in the center and the periphery of the visual field,” J. Opt. Soc. Am. A 4, 1627–1633 (1987).
    [CrossRef] [PubMed]
  32. P. Thompson, “Perceived rate of movement depends on contrast,” Vision Res. 22, 377–380 (1982).
    [CrossRef] [PubMed]
  33. J. Yang, W. Makous, “Spatiotemporal separability in contrast sensitivity,” Vision Res. 34, 2569–2576 (1994).
    [CrossRef] [PubMed]
  34. W. H. Merigan, C. Byrne, J. H. Maunsell, “Does primate motion perception depend on the magnocellular pathway?” J. Neurosci. 11, 3422–3429 (1991).
    [PubMed]
  35. W. H. Merigan, J. H. R. Maunsell, “How parallel are the primate visual pathways?” Annu. Rev. Neurosci. 16, 369–402 (1993).
    [CrossRef] [PubMed]

1996 (1)

M. Edwards, D. R. Badcock, S. Nishida, “Contrast sensitivity of the motion system,” Vision Res. 36, 2411–2421 (1996).
[CrossRef] [PubMed]

1995 (1)

J. Yang, X. Qi, W. Makous, “Zero frequency masking and a model of contrast sensitivity,” Vision Res. 35, 1965–1978 (1995).
[CrossRef] [PubMed]

1994 (2)

J. Yang, W. Makous, “Spatiotemporal separability in contrast sensitivity,” Vision Res. 34, 2569–2576 (1994).
[CrossRef] [PubMed]

R. Müller, M. W. Greenlee, “Effect of contrast and adaptation on the perception of the direction and speed of drifting gratings,” Vision Res. 34, 2071–2092 (1994).
[CrossRef] [PubMed]

1993 (1)

W. H. Merigan, J. H. R. Maunsell, “How parallel are the primate visual pathways?” Annu. Rev. Neurosci. 16, 369–402 (1993).
[CrossRef] [PubMed]

1991 (1)

W. H. Merigan, C. Byrne, J. H. Maunsell, “Does primate motion perception depend on the magnocellular pathway?” J. Neurosci. 11, 3422–3429 (1991).
[PubMed]

1990 (4)

J. C. Boulton, R. F. Hess, “Luminance contrast and motion detection,” Vision Res. 30, 175–179 (1990).
[CrossRef] [PubMed]

G. Sclar, J. H. R. Maunsell, P. Lennie, “Coding of image contrast in central visual pathways of the macaque monkey,” Vision Res. 30, 1–10 (1990).
[CrossRef] [PubMed]

R. Shapley, “Visual sensitivity and parallel retinocortical channels,” Annu. Rev. Psychol. 41, 635–658 (1990).
[CrossRef] [PubMed]

P. H. Schiller, N. K. Logothetis, E. R. Charles, “Role of the color-opponent and broadband channels in vision,” Visual Neurosci. 5, 321–346 (1990).

1989 (1)

A. M. Derrington, P. A. Goddard, “Failure of motion discrimination at high contrasts: evidence for saturation,” Vision Res. 29, 1767–1776 (1989).
[CrossRef] [PubMed]

1988 (1)

M. Livingstone, D. H. Hubel, “Segregation of form, color, movement, and depth: anatomy, physiology, and perception,” Science 240, 740–749 (1988).
[CrossRef] [PubMed]

1987 (4)

1986 (2)

S. P. McKee, G. H. Silverman, K. Nakayama, “Precise velocity discrimination despite random variations in temporal frequency and contrast,” Vision Res. 26, 609–619 (1986).
[CrossRef] [PubMed]

E. Kaplan, R. Shapley, “The primate retina contains two types of ganglion cells, with high and low contrast sensitivity,” Proc. Natl. Acad. Sci. USA 83, 2755–2757 (1986).
[CrossRef] [PubMed]

1985 (4)

1984 (2)

J. P. H. van Santen, G. Sperling, “Temporal covariance model of human motion perception,” J. Opt. Soc. Am. A 1, 451–473 (1984).
[CrossRef] [PubMed]

M. Green, “Masking by light and the sustained-transient dichotomy,” Percept. Psychophys. 35, 519–535 (1984).
[CrossRef] [PubMed]

1983 (2)

A. Johnston, M. J. Wright, “Visual motion and cortical velocity,” Nature (London) 304, 436–438 (1983).
[CrossRef]

A. B. Watson, D. G. Pelli, “QUEST: a Bayesian adaptive psychometric method,” Percept. Psychophys. 33, 113–120 (1983).
[CrossRef] [PubMed]

1982 (1)

P. Thompson, “Perceived rate of movement depends on contrast,” Vision Res. 22, 377–380 (1982).
[CrossRef] [PubMed]

1981 (1)

M. Green, “Psychophysical relationships among mechanisms sensitive to pattern, motion and flicker,” Vision Res. 21, 971–983 (1981).
[CrossRef] [PubMed]

1978 (1)

1976 (1)

B. G. Breitmeyer, L. Ganz, “Implication of sustained and transient channels for theories of visual pattern masking, saccadic suppression, and information processing,” Psychol. Rev. 83, 1–36 (1976).
[CrossRef] [PubMed]

1973 (2)

D. J. Tolhurst, “Separate channels for the analysis of the shape and the movement of moving visual stimulus,” J. Physiol. (London) 231, 385–402 (1973).

J. J. Kulikowski, D. J. Tolhurst, “Psychophysical evidence for sustained and transient detectors in human vision,” J. Physiol. (London) 232, 149–162 (1973).

1972 (1)

1971 (1)

J. J. Kulikowski, “Effect of eye movements on the contrast sensitivity of spatio-temporal patterns,” Vision Res. 11, 261–273 (1971).
[CrossRef] [PubMed]

Adelson, E. H.

Ahumada, A. J.

Badcock, D. R.

M. Edwards, D. R. Badcock, S. Nishida, “Contrast sensitivity of the motion system,” Vision Res. 36, 2411–2421 (1996).
[CrossRef] [PubMed]

Bergen, J. R.

Boulton, J. C.

J. C. Boulton, R. F. Hess, “Luminance contrast and motion detection,” Vision Res. 30, 175–179 (1990).
[CrossRef] [PubMed]

J. C. Boulton, “Two mechanisms for detection of slow motion,” J. Opt. Soc. Am. A 4, 1634–1642 (1987).
[CrossRef] [PubMed]

Breitmeyer, B. G.

B. G. Breitmeyer, L. Ganz, “Implication of sustained and transient channels for theories of visual pattern masking, saccadic suppression, and information processing,” Psychol. Rev. 83, 1–36 (1976).
[CrossRef] [PubMed]

B. G. Breitmeyer, “Parallel processing in human vision: history, review, and critique,” in Application of Parallel Processing in Vision, J. R. Brannan, ed. (Elsevier, Amsterdam, 1992), pp. 37–77.

Byrne, C.

W. H. Merigan, C. Byrne, J. H. Maunsell, “Does primate motion perception depend on the magnocellular pathway?” J. Neurosci. 11, 3422–3429 (1991).
[PubMed]

Charles, E. R.

P. H. Schiller, N. K. Logothetis, E. R. Charles, “Role of the color-opponent and broadband channels in vision,” Visual Neurosci. 5, 321–346 (1990).

Derrington, A. M.

A. M. Derrington, P. A. Goddard, “Failure of motion discrimination at high contrasts: evidence for saturation,” Vision Res. 29, 1767–1776 (1989).
[CrossRef] [PubMed]

Edwards, M.

M. Edwards, D. R. Badcock, S. Nishida, “Contrast sensitivity of the motion system,” Vision Res. 36, 2411–2421 (1996).
[CrossRef] [PubMed]

Ganz, L.

B. G. Breitmeyer, L. Ganz, “Implication of sustained and transient channels for theories of visual pattern masking, saccadic suppression, and information processing,” Psychol. Rev. 83, 1–36 (1976).
[CrossRef] [PubMed]

Goddard, P. A.

A. M. Derrington, P. A. Goddard, “Failure of motion discrimination at high contrasts: evidence for saturation,” Vision Res. 29, 1767–1776 (1989).
[CrossRef] [PubMed]

Green, M.

M. Green, “Masking by light and the sustained-transient dichotomy,” Percept. Psychophys. 35, 519–535 (1984).
[CrossRef] [PubMed]

M. Green, “Psychophysical relationships among mechanisms sensitive to pattern, motion and flicker,” Vision Res. 21, 971–983 (1981).
[CrossRef] [PubMed]

Greenlee, M. W.

R. Müller, M. W. Greenlee, “Effect of contrast and adaptation on the perception of the direction and speed of drifting gratings,” Vision Res. 34, 2071–2092 (1994).
[CrossRef] [PubMed]

Heeger, D. J.

D. J. Heeger, “Model for the extraction of image flow,” J. Opt. Soc. Am. A 8, 1455–1471 (1987);D. H. Kelly, “Fourier components of moving gratings,” Behav. Res. Methods Instrum. 14, 435–437 (1980).
[CrossRef]

Hess, R. F.

J. C. Boulton, R. F. Hess, “Luminance contrast and motion detection,” Vision Res. 30, 175–179 (1990).
[CrossRef] [PubMed]

Hubel, D. H.

M. Livingstone, D. H. Hubel, “Segregation of form, color, movement, and depth: anatomy, physiology, and perception,” Science 240, 740–749 (1988).
[CrossRef] [PubMed]

Johnston, A.

A. Johnston, M. J. Wright, “Lower thresholds of motion for gratings as function of eccentricity and contrast,” Vision Res. 25, 179–185 (1985).
[CrossRef]

A. Johnston, M. J. Wright, “Visual motion and cortical velocity,” Nature (London) 304, 436–438 (1983).
[CrossRef]

Kaplan, E.

E. Kaplan, R. Shapley, “The primate retina contains two types of ganglion cells, with high and low contrast sensitivity,” Proc. Natl. Acad. Sci. USA 83, 2755–2757 (1986).
[CrossRef] [PubMed]

Keesey, U. T.

Klein, S.

Koenderink, J. J.

Kulikowski, J. J.

J. J. Kulikowski, D. J. Tolhurst, “Psychophysical evidence for sustained and transient detectors in human vision,” J. Physiol. (London) 232, 149–162 (1973).

J. J. Kulikowski, “Effect of eye movements on the contrast sensitivity of spatio-temporal patterns,” Vision Res. 11, 261–273 (1971).
[CrossRef] [PubMed]

Lennie, P.

G. Sclar, J. H. R. Maunsell, P. Lennie, “Coding of image contrast in central visual pathways of the macaque monkey,” Vision Res. 30, 1–10 (1990).
[CrossRef] [PubMed]

Livingstone, M.

M. Livingstone, D. H. Hubel, “Segregation of form, color, movement, and depth: anatomy, physiology, and perception,” Science 240, 740–749 (1988).
[CrossRef] [PubMed]

Logothetis, N. K.

P. H. Schiller, N. K. Logothetis, E. R. Charles, “Role of the color-opponent and broadband channels in vision,” Visual Neurosci. 5, 321–346 (1990).

Madsen, J. C.

Makous, W.

J. Yang, X. Qi, W. Makous, “Zero frequency masking and a model of contrast sensitivity,” Vision Res. 35, 1965–1978 (1995).
[CrossRef] [PubMed]

J. Yang, W. Makous, “Spatiotemporal separability in contrast sensitivity,” Vision Res. 34, 2569–2576 (1994).
[CrossRef] [PubMed]

Maunsell, J. H.

W. H. Merigan, C. Byrne, J. H. Maunsell, “Does primate motion perception depend on the magnocellular pathway?” J. Neurosci. 11, 3422–3429 (1991).
[PubMed]

Maunsell, J. H. R.

W. H. Merigan, J. H. R. Maunsell, “How parallel are the primate visual pathways?” Annu. Rev. Neurosci. 16, 369–402 (1993).
[CrossRef] [PubMed]

G. Sclar, J. H. R. Maunsell, P. Lennie, “Coding of image contrast in central visual pathways of the macaque monkey,” Vision Res. 30, 1–10 (1990).
[CrossRef] [PubMed]

McKee, S. P.

S. P. McKee, G. H. Silverman, K. Nakayama, “Precise velocity discrimination despite random variations in temporal frequency and contrast,” Vision Res. 26, 609–619 (1986).
[CrossRef] [PubMed]

Merigan, W. H.

W. H. Merigan, J. H. R. Maunsell, “How parallel are the primate visual pathways?” Annu. Rev. Neurosci. 16, 369–402 (1993).
[CrossRef] [PubMed]

W. H. Merigan, C. Byrne, J. H. Maunsell, “Does primate motion perception depend on the magnocellular pathway?” J. Neurosci. 11, 3422–3429 (1991).
[PubMed]

Müller, R.

R. Müller, M. W. Greenlee, “Effect of contrast and adaptation on the perception of the direction and speed of drifting gratings,” Vision Res. 34, 2071–2092 (1994).
[CrossRef] [PubMed]

Nakayama, K.

S. P. McKee, G. H. Silverman, K. Nakayama, “Precise velocity discrimination despite random variations in temporal frequency and contrast,” Vision Res. 26, 609–619 (1986).
[CrossRef] [PubMed]

K. Nakayama, G. H. Silverman, “Detection and discrimination of sinusoidal grating displacements,” J. Opt. Soc. Am. A 2, 267–274 (1985).
[CrossRef] [PubMed]

Nishida, S.

M. Edwards, D. R. Badcock, S. Nishida, “Contrast sensitivity of the motion system,” Vision Res. 36, 2411–2421 (1996).
[CrossRef] [PubMed]

Pelli, D. G.

A. B. Watson, D. G. Pelli, “QUEST: a Bayesian adaptive psychometric method,” Percept. Psychophys. 33, 113–120 (1983).
[CrossRef] [PubMed]

Qi, X.

J. Yang, X. Qi, W. Makous, “Zero frequency masking and a model of contrast sensitivity,” Vision Res. 35, 1965–1978 (1995).
[CrossRef] [PubMed]

Schiller, P. H.

P. H. Schiller, N. K. Logothetis, E. R. Charles, “Role of the color-opponent and broadband channels in vision,” Visual Neurosci. 5, 321–346 (1990).

Sclar, G.

G. Sclar, J. H. R. Maunsell, P. Lennie, “Coding of image contrast in central visual pathways of the macaque monkey,” Vision Res. 30, 1–10 (1990).
[CrossRef] [PubMed]

Shapley, R.

R. Shapley, “Visual sensitivity and parallel retinocortical channels,” Annu. Rev. Psychol. 41, 635–658 (1990).
[CrossRef] [PubMed]

E. Kaplan, R. Shapley, “The primate retina contains two types of ganglion cells, with high and low contrast sensitivity,” Proc. Natl. Acad. Sci. USA 83, 2755–2757 (1986).
[CrossRef] [PubMed]

Silverman, G. H.

S. P. McKee, G. H. Silverman, K. Nakayama, “Precise velocity discrimination despite random variations in temporal frequency and contrast,” Vision Res. 26, 609–619 (1986).
[CrossRef] [PubMed]

K. Nakayama, G. H. Silverman, “Detection and discrimination of sinusoidal grating displacements,” J. Opt. Soc. Am. A 2, 267–274 (1985).
[CrossRef] [PubMed]

Sperling, G.

Stromeyer, C. F.

Thompson, P.

P. Thompson, “Perceived rate of movement depends on contrast,” Vision Res. 22, 377–380 (1982).
[CrossRef] [PubMed]

Tolhurst, D. J.

J. J. Kulikowski, D. J. Tolhurst, “Psychophysical evidence for sustained and transient detectors in human vision,” J. Physiol. (London) 232, 149–162 (1973).

D. J. Tolhurst, “Separate channels for the analysis of the shape and the movement of moving visual stimulus,” J. Physiol. (London) 231, 385–402 (1973).

van de Grind, W. A.

Van Doorn, A. J.

van Santen, J. P. H.

Watson, A. B.

A. B. Watson, A. J. Ahumada, “Model of human visual-motion sensing,” J. Opt. Soc. Am. A 2, 322–341 (1985).
[CrossRef] [PubMed]

A. B. Watson, D. G. Pelli, “QUEST: a Bayesian adaptive psychometric method,” Percept. Psychophys. 33, 113–120 (1983).
[CrossRef] [PubMed]

Wright, M. J.

M. J. Wright, “Spatiotemporal properties of grating motion detection in the center and the periphery of the visual field,” J. Opt. Soc. Am. A 4, 1627–1633 (1987).
[CrossRef] [PubMed]

A. Johnston, M. J. Wright, “Lower thresholds of motion for gratings as function of eccentricity and contrast,” Vision Res. 25, 179–185 (1985).
[CrossRef]

A. Johnston, M. J. Wright, “Visual motion and cortical velocity,” Nature (London) 304, 436–438 (1983).
[CrossRef]

Yang, J.

J. Yang, X. Qi, W. Makous, “Zero frequency masking and a model of contrast sensitivity,” Vision Res. 35, 1965–1978 (1995).
[CrossRef] [PubMed]

J. Yang, W. Makous, “Spatiotemporal separability in contrast sensitivity,” Vision Res. 34, 2569–2576 (1994).
[CrossRef] [PubMed]

Zeevi, Y. Y.

Annu. Rev. Neurosci. (1)

W. H. Merigan, J. H. R. Maunsell, “How parallel are the primate visual pathways?” Annu. Rev. Neurosci. 16, 369–402 (1993).
[CrossRef] [PubMed]

Annu. Rev. Psychol. (1)

R. Shapley, “Visual sensitivity and parallel retinocortical channels,” Annu. Rev. Psychol. 41, 635–658 (1990).
[CrossRef] [PubMed]

J. Neurosci. (1)

W. H. Merigan, C. Byrne, J. H. Maunsell, “Does primate motion perception depend on the magnocellular pathway?” J. Neurosci. 11, 3422–3429 (1991).
[PubMed]

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (8)

J. Physiol. (London) (2)

D. J. Tolhurst, “Separate channels for the analysis of the shape and the movement of moving visual stimulus,” J. Physiol. (London) 231, 385–402 (1973).

J. J. Kulikowski, D. J. Tolhurst, “Psychophysical evidence for sustained and transient detectors in human vision,” J. Physiol. (London) 232, 149–162 (1973).

Nature (London) (1)

A. Johnston, M. J. Wright, “Visual motion and cortical velocity,” Nature (London) 304, 436–438 (1983).
[CrossRef]

Percept. Psychophys. (2)

M. Green, “Masking by light and the sustained-transient dichotomy,” Percept. Psychophys. 35, 519–535 (1984).
[CrossRef] [PubMed]

A. B. Watson, D. G. Pelli, “QUEST: a Bayesian adaptive psychometric method,” Percept. Psychophys. 33, 113–120 (1983).
[CrossRef] [PubMed]

Proc. Natl. Acad. Sci. USA (1)

E. Kaplan, R. Shapley, “The primate retina contains two types of ganglion cells, with high and low contrast sensitivity,” Proc. Natl. Acad. Sci. USA 83, 2755–2757 (1986).
[CrossRef] [PubMed]

Psychol. Rev. (1)

B. G. Breitmeyer, L. Ganz, “Implication of sustained and transient channels for theories of visual pattern masking, saccadic suppression, and information processing,” Psychol. Rev. 83, 1–36 (1976).
[CrossRef] [PubMed]

Science (1)

M. Livingstone, D. H. Hubel, “Segregation of form, color, movement, and depth: anatomy, physiology, and perception,” Science 240, 740–749 (1988).
[CrossRef] [PubMed]

Vision Res. (12)

M. Green, “Psychophysical relationships among mechanisms sensitive to pattern, motion and flicker,” Vision Res. 21, 971–983 (1981).
[CrossRef] [PubMed]

A. M. Derrington, P. A. Goddard, “Failure of motion discrimination at high contrasts: evidence for saturation,” Vision Res. 29, 1767–1776 (1989).
[CrossRef] [PubMed]

A. Johnston, M. J. Wright, “Lower thresholds of motion for gratings as function of eccentricity and contrast,” Vision Res. 25, 179–185 (1985).
[CrossRef]

J. J. Kulikowski, “Effect of eye movements on the contrast sensitivity of spatio-temporal patterns,” Vision Res. 11, 261–273 (1971).
[CrossRef] [PubMed]

G. Sclar, J. H. R. Maunsell, P. Lennie, “Coding of image contrast in central visual pathways of the macaque monkey,” Vision Res. 30, 1–10 (1990).
[CrossRef] [PubMed]

R. Müller, M. W. Greenlee, “Effect of contrast and adaptation on the perception of the direction and speed of drifting gratings,” Vision Res. 34, 2071–2092 (1994).
[CrossRef] [PubMed]

M. Edwards, D. R. Badcock, S. Nishida, “Contrast sensitivity of the motion system,” Vision Res. 36, 2411–2421 (1996).
[CrossRef] [PubMed]

S. P. McKee, G. H. Silverman, K. Nakayama, “Precise velocity discrimination despite random variations in temporal frequency and contrast,” Vision Res. 26, 609–619 (1986).
[CrossRef] [PubMed]

J. C. Boulton, R. F. Hess, “Luminance contrast and motion detection,” Vision Res. 30, 175–179 (1990).
[CrossRef] [PubMed]

J. Yang, X. Qi, W. Makous, “Zero frequency masking and a model of contrast sensitivity,” Vision Res. 35, 1965–1978 (1995).
[CrossRef] [PubMed]

P. Thompson, “Perceived rate of movement depends on contrast,” Vision Res. 22, 377–380 (1982).
[CrossRef] [PubMed]

J. Yang, W. Makous, “Spatiotemporal separability in contrast sensitivity,” Vision Res. 34, 2569–2576 (1994).
[CrossRef] [PubMed]

Visual Neurosci. (1)

P. H. Schiller, N. K. Logothetis, E. R. Charles, “Role of the color-opponent and broadband channels in vision,” Visual Neurosci. 5, 321–346 (1990).

Other (1)

B. G. Breitmeyer, “Parallel processing in human vision: history, review, and critique,” in Application of Parallel Processing in Vision, J. R. Brannan, ed. (Elsevier, Amsterdam, 1992), pp. 37–77.

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Figures (10)

Fig. 1
Fig. 1

Simplified diagram of velocity detection. The gray circles represent visual sensors in the spatiotemporal domain, and the two ellipses represent the motion energy of a moving grating. The optimal velocity is estimated by the slope of the line, which is computed with the motion sensors excited by the motion energy.

Fig. 2
Fig. 2

Simplified diagram of speed threshold for motion detection. The gray circles represent visual sensors in the spatiotemporal domain. For a given spatial frequency f1, the energy of a static grating is represented by the three white ellipses centered at -f1, 0, and f1. The height of the ellipses represents the energy spread in temporal frequency, which is inversely proportional to the duration of the test grating. For example, when the duration is doubled, the grating is represented by the two less-elongated concentric ellipses (gray). As the grating moves, the centers of the ellipses would shift away from the f axis, with one, e.g., at f1, moving up and the one at -f1 moving down. If the spread of the stimulus energy in this spatiotemporal-frequency domain determines the discrimination between the set of sensors excited by a moving grating and those excited by a static grating, speed threshold will be proportional to the height of the ellipse (comparing the slopes of the solid and the dashed lines) or inversely proportional to duration τ. Furthermore, by comparing the slope of the dashed line (for f1) and the slope of the dotted line (for f2), one can see that speed threshold will be inversely proportional to spatial frequency.

Fig. 3
Fig. 3

Contrast threshold for detecting static gratings at stimulus durations of 73 to 1600 ms. The smooth curves are the fits of Eq. (3) to data at durations of 73 (thick solid), 200 (dashed lines), 400 (dotted-dashed), 800 (dotted), and 1600 (thin solid) ms. The fits were used to determine contrast values of equal visibility across spatial frequencies to be used in the subsequent experiments.

Fig. 4
Fig. 4

(a) Speed threshold for discriminating motion direction plotted against spatial frequency for subjects QW, JY, and SBS. Contrasts were five times the detection thresholds for static gratings. Stimulus duration was 400 ms. Error bars represent ±2 standard errors. (b) Same data plotted as temporal frequency at threshold, converted by the formula ω=vf.

Fig. 5
Fig. 5

Speed threshold for discriminating motion direction plotted against spatial frequency at stimulus durations of 73 to 800 ms for subjects QW, JY, and SBS. Contrasts were five times the detection threshold for static gratings. The dotted-line slope of -1 in the log–log plot is the predicted slope for a system limited by the velocity spread. Error bars represent ±2 errors.

Fig. 6
Fig. 6

Speed threshold versus stimulus duration, at spatial frequencies of 0.25 to 8 c/deg, for subjects QW, JY, and SBS. Contrast was five times the detection threshold for static gratings. The dotted-line slope of -1 in the log–log plot is the predicted slope for a system limited by the velocity spread. Error bars represent ±2 standard errors.

Fig. 7
Fig. 7

Speed threshold versus ratio of grating contrast to contrast threshold at frequencies of 0.25 to 8 c/deg. Stimulus duration was 400 ms. Error bars represent ±2 standard errors.

Fig. 8
Fig. 8

Speed threshold versus spatial frequency at stimulus durations of 73 to 400 ms. Contrast was 0.2. The dotted-line slope of -1 in the log–log plot is also shown. Error bars represent ±2 standard errors.

Fig. 9
Fig. 9

Relative power distribution in the temporal-frequency domain for a drifting grating with a display duration of 200 ms, a spatial frequency of 0.5 c/deg, and a temporal frequency of 1.25 Hz, which give a speed of 2.5 deg/s.

Fig. 10
Fig. 10

Comparison of the fits (solid curves) and the averaged data across three subjects for the durations shown (milliseconds).

Tables (1)

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Table 1 Estimated Model Parameters for the Three Subjects

Equations (9)

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v=ω/f,
s(x, t)=L{1+C sin[2π(fx-ωt)]},
Ct=exp(αf){N0+βt1/2+η[1-exp(-t/λ)]tσ2/(f2+σ2)}/t,
t=ττ0/(τ+τ0),
A(ω, ω0, τ)=sin[π(ω-ω0)τ]/[π(ω-ω0)],
e(ω, ω0, τ)=[A(ω, ω0, τ)M(ω)]*G(ω),
ER=0+e(ω, ω0, τ)2dω+N,
EL=-0e(ω, ω0, τ)2dω+N,
ρ=ER/EL.

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