Abstract

Our goal in this paper was to measure psychophysically the receptive-field size of motion units in human vision. To this aim, length and width spatial summation functions were measured for drifting (8-Hz) sinusoidal gratings of spatial frequencies 0.1, 1.0, and 10.0 cycles per degree (c/deg) with two threshold criteria: direction discrimination and simple detection. For each spatial frequency, contrast sensitivity for detection of the direction of drift increased with increasing stimulus size (length or width), at first rapidly (slope ≥ 1.0) and then more gradually (slope 0.29). For most stimuli, the detection and direction-discrimination contrast thresholds were nearly the same. However, for stimuli severely curtailed in width, significantly more contrast was required for direction discrimination than for detection. These results were predicted with a summation model, which incorporated three-dimensional (space–space–time) linear input filters, and probability summation over space and among different filter types. The fit of the model gave an estimate of both the receptive-field length and width of motion-detector units in human vision. At each spatial frequency, the estimates of receptive-field width and length were similar, indicating that the receptive fields of motion-detector units are as long as they are wide at all spatial scales. Receptive-field size varied from approximately 0.12 cycle at 0.1 c/deg to 0.52 cycle at 10.0 c/deg.

© 1991 Optical Society of America

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    [CrossRef] [PubMed]
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  44. J. P. Jones, A. Stepmoski, L. A. Palmer, “The two-dimensional spectral structure of simple receptive fields in cat striate cortex,”J. Neurophysiol. 58, 1212–1232 (1987).
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  45. J. P. Jones, L. A. Palmer, “An evaluation of the two-dimensional Gabor filter model of simple receptive fields in cat striate cortex,”J. Neurophysiol. 58, 1233–1258 (1987).
    [PubMed]
  46. S. J. Anderson, R. F. Hess, “Post-receptoral under-sampling in normal human peripheral vision,” Vision Res. 30, 1507–1515 (1990).
    [CrossRef]
  47. M. C. Morrone, D. C. Burr, L. Maffei, “Functional implications of cross-orientation inhibition of cortical visual cells. I. Neurophysiological evidence,” Proc. R. Soc. London Ser. B 216, 335–354 (1982).
    [CrossRef]
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  55. To approximate the functions of sensitivity against stimulus length and width [from expression (A11)], we assumed retinal homogeneity of sensitivity over the region of the stimulus. To help validate this assumption, we measured both length and width summation functions (for a test frequency of 1.0 c/deg) using a more uniform patch of retina (5-deg eccentric fixation; temporal retina). The estimates of receptive-field length and width for central (Fig. 5) and eccentric fixation were comparable.

1991 (1)

1990 (3)

1989 (2)

S. J. Anderson, D. C. Burr, “Receptive field properties of human motion detection units inferred from spatial frequency masking,” Vision Res. 29, 1343–1358 (1989).
[CrossRef]

J. G. Daugman, “Entropy reduction and decorrelation in visual coding by oriented neural receptive fields,”IEEE Trans. Biomed. Eng. 36, 107–114 (1989).
[CrossRef] [PubMed]

1988 (2)

J. G. Daugman, “Complete discrete 2-D Gabor transforms by neural networks for image analysis and compression,”IEEE Trans. Acoust. Speech Signal Process. 36, 1169–1179 (1988).
[CrossRef]

C. L. Baker, M. S. Cynader, “Space-time separability of direction selectivity in cat striate cortex,” Vision Res. 28, 239–246 (1988).
[CrossRef]

1987 (5)

S. J. Anderson, D. C. Burr, “Receptive field size of human motion detector units,” Vision Res. 27, 621–635 (1987).
[CrossRef]

R. C. Emerson, M. C. Citron, W. J. Vaughn, S. A. Klein, “Non-linear directionally selective subunits in complex cells of cat striate cortex,” J. Neurophysiol. 58, 33–65 (1987).
[PubMed]

J. P. Jones, L. A. Palmer, “The two-dimensional spatial structure of simple receptive fields in cat striate cortex,”J. Neurophysiol. 58, 1187–1211 (1987).
[PubMed]

J. P. Jones, A. Stepmoski, L. A. Palmer, “The two-dimensional spectral structure of simple receptive fields in cat striate cortex,”J. Neurophysiol. 58, 1212–1232 (1987).
[PubMed]

J. P. Jones, L. A. Palmer, “An evaluation of the two-dimensional Gabor filter model of simple receptive fields in cat striate cortex,”J. Neurophysiol. 58, 1233–1258 (1987).
[PubMed]

1986 (2)

D. C. Burr, J. Ross, M. C. Morrone, “Seeing objects in motion,” Proc. R. Soc. London Ser. B 227, 249–265 (1986).
[CrossRef]

M. C. Morrone, D. C. Burr, “Evidence for the existence and development of visual inhibition in humans,” Nature (London) 321, 235–237 (1986).
[CrossRef]

1985 (9)

1984 (4)

J. G. Daugman, “Spatial visual channels in the Fourier plane,” Vision Res. 24, 891–910 (1984).
[CrossRef] [PubMed]

R. A. Schumer, J. A. Movshon, “Length summation in simple cells of cat striate cortex,” Vision Res. 6, 565–571 (1984).
[CrossRef]

P. Heggelund, S. Krekling, B. C. Skottun, “Spatial summation in subregions of simple cell receptive fields in cat striate cortex as a function of slit length,”J. Physiol. (London) 352, 327–337 (1984).

G. C. Phillips, R. W. Wilson, “Orientation bandwidths of spatial frequency mechanisms measured by masking,” J. Opt. Soc. Am. A 1, 226–232 (1984).
[CrossRef] [PubMed]

1983 (3)

H. R. Wilson, D. K. McFarlane, G. C. Phillips, “Spatial frequency tuning of orientation selective units estimated by oblique masking,” Vision Res. 23, 873–882 (1983).
[CrossRef] [PubMed]

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

D. C. Burr, “Human vision in space and time,” Proc. Intl. Union Physiolog. Sci. XV, 510.04 (1983).

1982 (3)

R. L. De Valois, D. G. Albrecht, L. G. Thorell, “Spatial frequency selectivity of cells in macaque visual cortex,” Vision Res. 22, 545–559 (1982).
[CrossRef] [PubMed]

R. L. De Valois, E. W. Yund, N. Hepler, “The orientation and direction selectivity of cells in macaque visual cortex,” Vision Res. 22, 531–544 (1982).
[CrossRef] [PubMed]

M. C. Morrone, D. C. Burr, L. Maffei, “Functional implications of cross-orientation inhibition of cortical visual cells. I. Neurophysiological evidence,” Proc. R. Soc. London Ser. B 216, 335–354 (1982).
[CrossRef]

1981 (4)

J. G. Robson, N. Graham, “Probability summation and regional variation in contrast sensitivity across the visual field,” Vision Res. 21, 409–418 (1981).
[CrossRef] [PubMed]

E. T. Davis, N. Graham, “Spatial frequency uncertainty effects in the detection of sinusoidal gratings,” Vision Res. 21, 705–712 (1981).
[CrossRef] [PubMed]

D. C. Burr, “Temporal summation of moving images by the human visual system,” Proc. R. Soc. London Ser. B 211, 321–339 (1981).
[CrossRef]

J. J. Kulikowski, P. O. Bishop, “Linear analysis of the responses of simple cells in the cat visual cortex,” Exp. Brain Res. 44, 386–400 (1981).
[CrossRef] [PubMed]

1980 (1)

J. G. Daugman, “Two-dimensional spectral analysis of cortical receptive field profiles,” Vision Res. 20, 847–856 (1980).
[CrossRef] [PubMed]

1979 (2)

1978 (2)

J. A. Movshon, I. D. Thompson, D. J. Tolhurst, “Spatial and temporal contrast sensitivity of neurones in areas 17 and 18 of the cat’s visual cortex,”J. Physiol. (London) 283, 101–120 (1978).

E. R. Howell, R. F. Hess, “The functional area of summation to threshold for sinusoidal gratings,” Vision Res. 18, 369–374 (1978).
[CrossRef]

1977 (1)

D. Rose, “Responses of single units in the cat visual cortex to moving bars of light as a function of bar length,”J. Physiol. (London) 271, 1–23 (1977).

1975 (1)

E. Levinson, R. Sekuler, “The independence of channels in human vision selective for direction of movement,”J. Physiol. (London) 250, 347–366 (1975).

1974 (1)

R. F. Quick, “A vector-magnitude model of contrast selection,” Kybernetic 16, 65–67 (1974).
[CrossRef]

1971 (1)

H. Levitt, “Transformed up–down methods in psychoacoustics,”J. Acoust. Soc. Am. 49, 467–477 (1971).
[CrossRef]

1970 (1)

J. P. Thomas, “Model of the function of receptive fields in human vision,” Psychol. Rev. 77, 121–134 (1970).
[CrossRef] [PubMed]

1968 (1)

J. P. Thomas, “Linearity of spatial interactions involving inhibitory interactions,” Vision Res. 8, 49–60 (1968).
[CrossRef]

1966 (1)

A. Fiorentini, L. Mazzantini, “Neural inhibition in the human fovea: a study of interactions between two-line stimuli,” Atti Fond. Giorgio Ronchi 21, 738–747 (1966).

1956 (1)

1951 (1)

W. Weibull, “A statistical distribution function of wide applicability,”J. Appl. Mech. 18, 292–297 (1951).

1946 (1)

D. Gabor, “Theory of communication,”J. Inst. Electr. Eng. (London) 93, 429–457 (1946).

Adelson, E. H.

Ahumada, A. J.

Albrecht, D. G.

R. L. De Valois, D. G. Albrecht, L. G. Thorell, “Spatial frequency selectivity of cells in macaque visual cortex,” Vision Res. 22, 545–559 (1982).
[CrossRef] [PubMed]

Anderson, S. J.

S. J. Anderson, D. C. Burr, M. C. Morrone, “Two-dimensional spatial and spatial-frequency selectivity of motion-sensitive mechanisms in human vision,” J. Opt. Soc. Am. A 8, 1340–1351 (1991).
[CrossRef] [PubMed]

S. J. Anderson, R. F. Hess, “Post-receptoral under-sampling in normal human peripheral vision,” Vision Res. 30, 1507–1515 (1990).
[CrossRef]

S. J. Anderson, D. C. Burr, “Receptive field properties of human motion detection units inferred from spatial frequency masking,” Vision Res. 29, 1343–1358 (1989).
[CrossRef]

S. J. Anderson, D. C. Burr, “Receptive field size of human motion detector units,” Vision Res. 27, 621–635 (1987).
[CrossRef]

S. J. Anderson, D. C. Burr, “Spatial and temporal selectivity of the human motion detection system,” Vision Res. 25, 1147–1154 (1985).
[CrossRef] [PubMed]

Baker, C. L.

C. L. Baker, M. S. Cynader, “Space-time separability of direction selectivity in cat striate cortex,” Vision Res. 28, 239–246 (1988).
[CrossRef]

Bergen, J. R.

Bishop, P. O.

J. J. Kulikowski, P. O. Bishop, “Linear analysis of the responses of simple cells in the cat visual cortex,” Exp. Brain Res. 44, 386–400 (1981).
[CrossRef] [PubMed]

Burr, D. C.

S. J. Anderson, D. C. Burr, M. C. Morrone, “Two-dimensional spatial and spatial-frequency selectivity of motion-sensitive mechanisms in human vision,” J. Opt. Soc. Am. A 8, 1340–1351 (1991).
[CrossRef] [PubMed]

S. J. Anderson, D. C. Burr, “Receptive field properties of human motion detection units inferred from spatial frequency masking,” Vision Res. 29, 1343–1358 (1989).
[CrossRef]

S. J. Anderson, D. C. Burr, “Receptive field size of human motion detector units,” Vision Res. 27, 621–635 (1987).
[CrossRef]

D. C. Burr, J. Ross, M. C. Morrone, “Seeing objects in motion,” Proc. R. Soc. London Ser. B 227, 249–265 (1986).
[CrossRef]

M. C. Morrone, D. C. Burr, “Evidence for the existence and development of visual inhibition in humans,” Nature (London) 321, 235–237 (1986).
[CrossRef]

S. J. Anderson, D. C. Burr, “Spatial and temporal selectivity of the human motion detection system,” Vision Res. 25, 1147–1154 (1985).
[CrossRef] [PubMed]

D. C. Burr, “Human vision in space and time,” Proc. Intl. Union Physiolog. Sci. XV, 510.04 (1983).

M. C. Morrone, D. C. Burr, L. Maffei, “Functional implications of cross-orientation inhibition of cortical visual cells. I. Neurophysiological evidence,” Proc. R. Soc. London Ser. B 216, 335–354 (1982).
[CrossRef]

D. C. Burr, “Temporal summation of moving images by the human visual system,” Proc. R. Soc. London Ser. B 211, 321–339 (1981).
[CrossRef]

Citron, M. C.

R. C. Emerson, M. C. Citron, W. J. Vaughn, S. A. Klein, “Non-linear directionally selective subunits in complex cells of cat striate cortex,” J. Neurophysiol. 58, 33–65 (1987).
[PubMed]

Cynader, M. S.

C. L. Baker, M. S. Cynader, “Space-time separability of direction selectivity in cat striate cortex,” Vision Res. 28, 239–246 (1988).
[CrossRef]

Dannemiller, J. L.

Daugman, J. G.

J. G. Daugman, “Entropy reduction and decorrelation in visual coding by oriented neural receptive fields,”IEEE Trans. Biomed. Eng. 36, 107–114 (1989).
[CrossRef] [PubMed]

J. G. Daugman, “Complete discrete 2-D Gabor transforms by neural networks for image analysis and compression,”IEEE Trans. Acoust. Speech Signal Process. 36, 1169–1179 (1988).
[CrossRef]

J. G. Daugman, “Uncertainty relation for resolution in space, spatial frequency, and orientation optimized by two-dimensional visual cortical filters,” J. Opt. Soc. Am. A 2, 1160–1169 (1985).
[CrossRef] [PubMed]

J. G. Daugman, “Spatial visual channels in the Fourier plane,” Vision Res. 24, 891–910 (1984).
[CrossRef] [PubMed]

J. G. Daugman, “Two-dimensional spectral analysis of cortical receptive field profiles,” Vision Res. 20, 847–856 (1980).
[CrossRef] [PubMed]

Davis, E. T.

E. T. Davis, N. Graham, “Spatial frequency uncertainty effects in the detection of sinusoidal gratings,” Vision Res. 21, 705–712 (1981).
[CrossRef] [PubMed]

De Valois, R. L.

M. A. Webster, R. L. De Valois, “Relationship between spatial frequency and orientation tuning of striate-cortex cells,” J. Opt. Soc. Am. A 2, 1124–1132 (1985).
[CrossRef] [PubMed]

R. L. De Valois, D. G. Albrecht, L. G. Thorell, “Spatial frequency selectivity of cells in macaque visual cortex,” Vision Res. 22, 545–559 (1982).
[CrossRef] [PubMed]

R. L. De Valois, E. W. Yund, N. Hepler, “The orientation and direction selectivity of cells in macaque visual cortex,” Vision Res. 22, 531–544 (1982).
[CrossRef] [PubMed]

Doan, V. V.

Emerson, R. C.

R. C. Emerson, M. C. Citron, W. J. Vaughn, S. A. Klein, “Non-linear directionally selective subunits in complex cells of cat striate cortex,” J. Neurophysiol. 58, 33–65 (1987).
[PubMed]

Fiorentini, A.

A. Fiorentini, L. Mazzantini, “Neural inhibition in the human fovea: a study of interactions between two-line stimuli,” Atti Fond. Giorgio Ronchi 21, 738–747 (1966).

Gabor, D.

D. Gabor, “Theory of communication,”J. Inst. Electr. Eng. (London) 93, 429–457 (1946).

Gille, J.

Gorea, A.

A. Gorea, “Spatial integration characteristics in motion detection and direction identification,” Spatial Vis, 1, 85–102 (1985).
[CrossRef]

Graham, N.

E. T. Davis, N. Graham, “Spatial frequency uncertainty effects in the detection of sinusoidal gratings,” Vision Res. 21, 705–712 (1981).
[CrossRef] [PubMed]

J. G. Robson, N. Graham, “Probability summation and regional variation in contrast sensitivity across the visual field,” Vision Res. 21, 409–418 (1981).
[CrossRef] [PubMed]

Harvey, L. O.

Heggelund, P.

P. Heggelund, S. Krekling, B. C. Skottun, “Spatial summation in subregions of simple cell receptive fields in cat striate cortex as a function of slit length,”J. Physiol. (London) 352, 327–337 (1984).

Hepler, N.

R. L. De Valois, E. W. Yund, N. Hepler, “The orientation and direction selectivity of cells in macaque visual cortex,” Vision Res. 22, 531–544 (1982).
[CrossRef] [PubMed]

Hess, R. F.

S. J. Anderson, R. F. Hess, “Post-receptoral under-sampling in normal human peripheral vision,” Vision Res. 30, 1507–1515 (1990).
[CrossRef]

E. R. Howell, R. F. Hess, “The functional area of summation to threshold for sinusoidal gratings,” Vision Res. 18, 369–374 (1978).
[CrossRef]

Howell, E. R.

E. R. Howell, R. F. Hess, “The functional area of summation to threshold for sinusoidal gratings,” Vision Res. 18, 369–374 (1978).
[CrossRef]

Jones, J. P.

J. P. Jones, L. A. Palmer, “An evaluation of the two-dimensional Gabor filter model of simple receptive fields in cat striate cortex,”J. Neurophysiol. 58, 1233–1258 (1987).
[PubMed]

J. P. Jones, L. A. Palmer, “The two-dimensional spatial structure of simple receptive fields in cat striate cortex,”J. Neurophysiol. 58, 1187–1211 (1987).
[PubMed]

J. P. Jones, A. Stepmoski, L. A. Palmer, “The two-dimensional spectral structure of simple receptive fields in cat striate cortex,”J. Neurophysiol. 58, 1212–1232 (1987).
[PubMed]

Klein, S. A.

R. C. Emerson, M. C. Citron, W. J. Vaughn, S. A. Klein, “Non-linear directionally selective subunits in complex cells of cat striate cortex,” J. Neurophysiol. 58, 33–65 (1987).
[PubMed]

Krekling, S.

P. Heggelund, S. Krekling, B. C. Skottun, “Spatial summation in subregions of simple cell receptive fields in cat striate cortex as a function of slit length,”J. Physiol. (London) 352, 327–337 (1984).

Kulikowski, J. J.

J. J. Kulikowski, P. O. Bishop, “Linear analysis of the responses of simple cells in the cat visual cortex,” Exp. Brain Res. 44, 386–400 (1981).
[CrossRef] [PubMed]

Levinson, E.

E. Levinson, R. Sekuler, “The independence of channels in human vision selective for direction of movement,”J. Physiol. (London) 250, 347–366 (1975).

Levitt, H.

H. Levitt, “Transformed up–down methods in psychoacoustics,”J. Acoust. Soc. Am. 49, 467–477 (1971).
[CrossRef]

Maffei, L.

M. C. Morrone, D. C. Burr, L. Maffei, “Functional implications of cross-orientation inhibition of cortical visual cells. I. Neurophysiological evidence,” Proc. R. Soc. London Ser. B 216, 335–354 (1982).
[CrossRef]

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S. J. Anderson, D. C. Burr, M. C. Morrone, “Two-dimensional spatial and spatial-frequency selectivity of motion-sensitive mechanisms in human vision,” J. Opt. Soc. Am. A 8, 1340–1351 (1991).
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R. L. De Valois, E. W. Yund, N. Hepler, “The orientation and direction selectivity of cells in macaque visual cortex,” Vision Res. 22, 531–544 (1982).
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J. A. Movshon, I. D. Thompson, D. J. Tolhurst, “Spatial and temporal contrast sensitivity of neurones in areas 17 and 18 of the cat’s visual cortex,”J. Physiol. (London) 283, 101–120 (1978).

P. Heggelund, S. Krekling, B. C. Skottun, “Spatial summation in subregions of simple cell receptive fields in cat striate cortex as a function of slit length,”J. Physiol. (London) 352, 327–337 (1984).

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S. J. Anderson, D. C. Burr, “Spatial and temporal selectivity of the human motion detection system,” Vision Res. 25, 1147–1154 (1985).
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J. P. Thomas, “Linearity of spatial interactions involving inhibitory interactions,” Vision Res. 8, 49–60 (1968).
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E. R. Howell, R. F. Hess, “The functional area of summation to threshold for sinusoidal gratings,” Vision Res. 18, 369–374 (1978).
[CrossRef]

J. G. Robson, N. Graham, “Probability summation and regional variation in contrast sensitivity across the visual field,” Vision Res. 21, 409–418 (1981).
[CrossRef] [PubMed]

R. A. Schumer, J. A. Movshon, “Length summation in simple cells of cat striate cortex,” Vision Res. 6, 565–571 (1984).
[CrossRef]

H. R. Wilson, D. K. McFarlane, G. C. Phillips, “Spatial frequency tuning of orientation selective units estimated by oblique masking,” Vision Res. 23, 873–882 (1983).
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C. L. Baker, M. S. Cynader, “Space-time separability of direction selectivity in cat striate cortex,” Vision Res. 28, 239–246 (1988).
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S. J. Anderson, D. C. Burr, “Receptive field size of human motion detector units,” Vision Res. 27, 621–635 (1987).
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S. J. Anderson, D. C. Burr, “Receptive field properties of human motion detection units inferred from spatial frequency masking,” Vision Res. 29, 1343–1358 (1989).
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[CrossRef] [PubMed]

R. L. De Valois, E. W. Yund, N. Hepler, “The orientation and direction selectivity of cells in macaque visual cortex,” Vision Res. 22, 531–544 (1982).
[CrossRef] [PubMed]

S. J. Anderson, R. F. Hess, “Post-receptoral under-sampling in normal human peripheral vision,” Vision Res. 30, 1507–1515 (1990).
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Other (2)

To approximate the functions of sensitivity against stimulus length and width [from expression (A11)], we assumed retinal homogeneity of sensitivity over the region of the stimulus. To help validate this assumption, we measured both length and width summation functions (for a test frequency of 1.0 c/deg) using a more uniform patch of retina (5-deg eccentric fixation; temporal retina). The estimates of receptive-field length and width for central (Fig. 5) and eccentric fixation were comparable.

G. A. Orban, Neuronal Operations in the Visual Cortex: Studies of Brain Function II (Springer-Verlag, Berlin, 1984).
[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

Contrast sensitivity to drifting (8-Hz) vertical sine-wave gratings plotted against aperture length for test spatial frequencies of 0.1, 1.0, and 10.0 c/deg for observer S.A. The aperture length, in cycles of sinusoid, equals 2σyfs from Eq. (1). The aperture width (2σxfs) was 1.5 cycles. Each datum is the mean of at least three separate staircase runs, from which a standard error was calculated. The symbol sizes are approximately 1 standard error. The solid curves and the vertical arrow near each curve (indicating receptive-field length) were derived from the summation model described in Appendix A. The method of least mean squares was used to fit the predictions of the model to the data, and the goodness of fit was estimated with the chi-squared test (see text for details). Field length is 0.13 cycle at 0.1 c/deg, 0.2 cycle at 1.0 c/deg, and 0.51 cycle at 10.0 c/deg (see Fig. 5 below for a summary of length estimates and confidence limits).

Fig. 2
Fig. 2

As for Fig. 1 for observer A.P. Psychophysical receptive-field length was determined by a least-mean-squares fit of straight lines of slope 1 (linear summation) and 0.29 (probability summation) to the data. The point of intersection of these gradients (indicated by the vertical arrow near each function) is one possible measure of psychophysical receptive-field length (see text). The arrows indicate a field length of 0.17 cycle at 0.1 c/deg, 0.22 cycle at 1.0 c/deg, and 0.5 cycle at 10.0 c/deg. The summation model described in Appendix A was also used to fit the data in this figure and to estimate receptive-field length: the summation model yields estimates of field length equal to 0.11 cycle at 0.1 c/deg, 0.19 cycle at 1.0 c/deg, and 0.49 cycle at 10.0 c/deg. The model estimates are plotted in Fig. 5 together with the 95% confidence limits for each estimate.

Fig. 3
Fig. 3

Contrast sensitivity to drifting (8-Hz) sine-wave gratings plotted against aperture width for test frequencies of 0.1, 1.0, and 10.0 c/deg for observer S.A. for two criteria. The aperture width, in cycles of sinusoid, equals 2σxfs [from Eq. (1)]. The aperture length (2σyfs) was 1.5 cycles. The symbol sizes are approximately 1 standard error of the mean of three separate staircase runs. The solid and dashed curves are the predictions of the summation model (see Appendix A) for the criteria of direction discrimination and simple detection, respectively. Both sets of data were fitted with the use of a least-mean-squares procedure, and each fit was assessed with the chi-squared test (see text for results). The fit of the model gave an estimate of psychophysical receptive-field width, and this result is indicated by the vertical arrow near each set of curves. Field width is equal to 0.12 cycle at 0.1 c/deg, 0.2 cycle at 1.0 c/deg, and 0.52 cycle at 10.0 c/deg (see Fig. 5 for a summary of results and confidence limits for each width estimate).

Fig. 4
Fig. 4

As for Fig. 3 for observer A.P. The psychophysical receptive-field width (given by vertical arrows) is estimated to be 0.13 cycle at 0.1 c/deg, 0.2 cycle at 1.0 c/deg, and 0.55 cycle at 10.0 c/deg.

Fig. 5
Fig. 5

Summary of results of Figs. 14. The psychophysical receptive-field length and width are plotted against the spatial frequency of the test grating for observers S.A. (top panel) and A.P. (bottom panel) in cycles of sinusoid. All estimates of receptive-field size plotted in this figure are based on the predictions of the summation model described in Appendix A. At each spatial frequency the 95% confidence limits were determined by varying the length parameter or width parameter of the model until the fit was statistically inadequate (chi-squared test; p > 0.05); see the vertical error bars. Note that the estimates of receptive-field length and width are similar at each spatial frequency.

Fig. 6
Fig. 6

Predicted rise in contrast sensitivity with increasing stimulus length [2σyfs, from Eq. (1)] for both detection and direction-discrimination criteria. Stimulus width [2σxfs, from Eq. (1)] was constant and equal to 1.5 cycles. The inverse of Ct [from expression (A11)] is plotted against the length of the input stimulus for psychophysical receptive-field lengths [2σyfs, from Eqs. (A1) and (A2)] equal to 0.1 and 2.0 cycles (see vertical arrows). The receptive-field width [2σxfs, from Eqs. (A1) and (A2)] was 3.0 cycles. Note that both criteria yield identical sensitivity measurements.

Fig. 7
Fig. 7

Predicted rise in contrast sensitivity with increasing stimulus width [2σxfs, from Eq. (1)]. The stimulus length [2σyfs, from Eq. (1)] was constant and equal to 1.5 cycles. The inverse of Ct [from expression (A11)] is plotted against the width of the input stimulus for psychophysical receptive-field widths [2σxfs, from Eqs. (A1) and (A2)] equal to 0.2 and 0.8 cycle (see the vertical arrows), for two criteria. The field length [2σyfs, from Eqs. (A1) and (A2)] was 3.0 cycles. Note that, for small stimulus widths, more contrast is required for direction discrimination than for detection.

Equations (13)

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L t ( x , y , t ) = L o + A sin [ 2 π ( f s x + f t t ) ] exp ( - x 2 / 2 σ x 2 ) × exp ( - y 2 / 2 σ y 2 ) exp ( - t 2 / 2 σ t 2 ) ,
G o ( x , y , t ) = A sin [ 2 π ( f s X + f t t ) ] exp ( - X 2 / 2 σ x 2 ) × exp ( - Y 2 / 2 σ y 2 ) H ( t ) ,
G e ( x , y , t ) = A cos [ 2 π ( f s X + f t t ) ] exp ( - X 2 / 2 σ x 2 ) × exp ( - Y 2 / 2 σ y 2 ) H ( t ) ,
X = x cos ( θ ) - y sin ( θ ) , Y = y cos ( θ ) + x sin ( θ ) ,
R o ( x , y , t ) = I ( x , y , t ) * G o ( x , y , t ) ,
R e ( x , y , t ) = I ( x , y , t ) * G e ( x , y , t ) ,
O right = [ R o ( x , y , t ) 2 + R e ( x , y , t ) 2 ] 1 / 2 .
O ( x , y , t ) = O right - O left .
O ( x , y , t ) = [ ( O right ) β + ( O left ) β ] 1 / β ,
P = 1 - exp [ - C O ( x , y , t ) β ] ,
P = 1 - exp [ - - C O ( x , y , t ) β d x d y d t ] .
C t α [ - O ( x , y , t ) β d x d y d t ] - 1 / β .
C t α [ i j - O i j ( x , y , t ) β d x d y d t ] - 1 / β ,

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