Abstract

Thresholds for detecting the direction of motion of drifting (8-Hz) vertical gratings [of spatial frequencies 0.1, 1.0, and 10.0 cycles per degree (c/deg)] were measured in the presence of masks that varied in both spatial frequency and orientation. Masks with different temporal properties were used. The specificity of masking was also measured for a stationary test grating of spatial frequency 3.0 c/deg. After suitable scaling and transformation, the masking data gave an estimate of the two-dimensional spatial-frequency tuning surface of cortical detector units in human vision. With the assumption of small-signal linearity and zero phase, the tuning surfaces were inverse Fourier transformed to give an indication of the size and structure of the psychophysical receptive fields of detector units. The results obtained with drifting test gratings and jittering (random phase) mask gratings indicate that motion-detector receptive fields increase in size (in cycles) with increasing spatial frequency but, at all spatial scales, have a length–width ratio of 1. These results are in close agreement with the summation results reported in J. Opt. Soc. Am. A 8, 1330 ( 1991). Using the same jittering mask stimuli and stationary test gratings, we confirm reports by Daugman [ Vision Res. 24, 891 ( 1984)] and Harvey and Doan [ J. Opt. Soc. Am. A 7, 116 ( 1990)] that motion-independent units have elongated receptive fields with a length–width ratio near 1.8. We conclude that the receptive fields of motion-dependent and -independent mechanisms in human vision are fundamentally different. The possibility that the orientation selectivity of a motion unit is sharpened by its selectivity for direction of motion is discussed.

© 1991 Optical Society of America

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    [Crossref] [PubMed]
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  22. The unidirectional mask was drifted at a temporal frequency of 4 Hz. A difference in temporal frequency between the test and the drifting mask aided observers in detecting the direction of drift of the test when the orientation of the test and the mask was similar. A mask drift of 4 Hz was chosen, as this is the most disparate temporal frequency from that of the test to still be within the temporal bandwidth of motion units presumably responding to the test (see Ref. 23).
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  24. As this mask has a single drift direction, it is possible to measure masking through 360 deg of orientation such that, when the test and the mask are coincident in orientation (at 90 deg and again at 270 deg), their directions of motion are either the same (at 90 deg) or opposed (at 270 deg). We attempted this but could obtain reliable results only for mask rotations from 0 to 180 deg. For mask rotations from 180 to 360 deg it was too difficult for observers to maintain a constant criterion (direction discrimination of the test) because of stimulus artifacts created by beating between the test and the mask and spurious contrast changes.
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [PubMed]
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1991 (1)

1990 (2)

1989 (4)

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]

W. S. Geisler, “Sequential ideal-observer analysis of visual discriminations,” Psychol. Rev. 96, 267–314 (1989).
[Crossref] [PubMed]

A. Borst, M. Egelhaaf, “Principles of visual motion detection,” Trends Neurosci. 12, 297–306 (1989).
[Crossref] [PubMed]

D. C. Burr, M. C. Morrone, D. Spinelli, “Evidence for edge and bar detectors in human vision,” Vision Res. 29, 419–432 (1989).
[Crossref] [PubMed]

1987 (5)

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]

P. J. Bennett, M. S. Banks, “Sensitivity loss in odd-symmetric mechanisms and phase anomalies in peripheral vision,” Nature (London) 326, 873–876 (1987).
[Crossref]

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. Stepnoski, 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]

D. J. Field, D. J. Tolhurst, “The structure and symmetry of simple-cell receptive field profiles in the cat’s visual cortex,” Proc. R. Soc. London Ser. B 228, 379–400 (1986).
[Crossref]

1985 (8)

1984 (3)

T. D. Albright, “Direction and orientation selectivity of neurones in visual area MT of the macaque,”J. Neurophysiol. 52, 1106–1130 (1984).
[PubMed]

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

D. J. Field, J. Nachmias, “Phase reversal discrimination,” Vision Res. 24, 333–340 (1984).
[Crossref] [PubMed]

1983 (1)

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

1982 (1)

D. C. Burr, J. Ross, “Contrast sensitivity at high velocities,” Vision Res. 23, 3567–3569 (1982).

1981 (1)

D. A. Pollen, S. F. Ronner, “Phase relationships between adjacent simple cells in the visual cortex,” Science 212, 1409–1411 (1981).
[Crossref] [PubMed]

1980 (4)

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

G. E. Legge, J. M. Foley, “Contrast masking in human vision,”J. Opt. Soc. Am. 70, 1458–1471 (1980).
[Crossref] [PubMed]

S. M. Anstis, “The perception of apparent movement,” Philos. Trans. R. Soc. London Ser. B 290, 153–168 (1980).
[Crossref]

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

1975 (1)

G. Johannson, “Visual motion detection,” Sci. Am. 232, 76–88 (1975).
[Crossref]

1974 (1)

B. M. Dow, “Functional classes of cells and their laminar distribution in monkey visual cortex,”J. Neurophysiol. 37, 927–946 (1974).
[PubMed]

1970 (2)

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

S. M. Anstis, “Phi movement as a subtractive process,” Vision Res. 10, 1411–1430 (1970).
[Crossref] [PubMed]

1968 (1)

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

1956 (1)

Adelson, E. H.

Ahumada, A. J.

Albright, T. D.

T. D. Albright, “Direction and orientation selectivity of neurones in visual area MT of the macaque,”J. Neurophysiol. 52, 1106–1130 (1984).
[PubMed]

Anderson, S. J.

S. J. Anderson, D. C. Burr, “Spatial summation properties of directionally selective mechanisms in human vision,” J. Opt. Soc. Am. A 8, 1330–1339 (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, “Spatial and temporal selectivity of the human motion detection system,” Vision Res. 25, 1147–1154 (1985).
[Crossref] [PubMed]

Anstis, S. M.

S. M. Anstis, “The perception of apparent movement,” Philos. Trans. R. Soc. London Ser. B 290, 153–168 (1980).
[Crossref]

S. M. Anstis, “Phi movement as a subtractive process,” Vision Res. 10, 1411–1430 (1970).
[Crossref] [PubMed]

Banks, M. S.

P. J. Bennett, M. S. Banks, “Sensitivity loss in odd-symmetric mechanisms and phase anomalies in peripheral vision,” Nature (London) 326, 873–876 (1987).
[Crossref]

Bennett, P. J.

P. J. Bennett, M. S. Banks, “Sensitivity loss in odd-symmetric mechanisms and phase anomalies in peripheral vision,” Nature (London) 326, 873–876 (1987).
[Crossref]

Bergen, J. R.

Borst, A.

A. Borst, M. Egelhaaf, “Principles of visual motion detection,” Trends Neurosci. 12, 297–306 (1989).
[Crossref] [PubMed]

Bracewell, R.

R. Bracewell, The Fourier Transform and Its Applications (McGraw-Hill, New York, 1965).

Burr, D. C.

S. J. Anderson, D. C. Burr, “Spatial summation properties of directionally selective mechanisms in human vision,” J. Opt. Soc. Am. A 8, 1330–1339 (1991).
[Crossref] [PubMed]

D. C. Burr, M. C. Morrone, D. Spinelli, “Evidence for edge and bar detectors in human vision,” Vision Res. 29, 419–432 (1989).
[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]

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

D. C. Burr, J. Ross, “Contrast sensitivity at high velocities,” Vision Res. 23, 3567–3569 (1982).

Dannemiller, J. L.

Daugman, J. G.

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]

De Valois, R. L.

Doan, V. V.

Dow, B. M.

B. M. Dow, “Functional classes of cells and their laminar distribution in monkey visual cortex,”J. Neurophysiol. 37, 927–946 (1974).
[PubMed]

Egelhaaf, M.

A. Borst, M. Egelhaaf, “Principles of visual motion detection,” Trends Neurosci. 12, 297–306 (1989).
[Crossref] [PubMed]

Field, D. J.

D. J. Field, D. J. Tolhurst, “The structure and symmetry of simple-cell receptive field profiles in the cat’s visual cortex,” Proc. R. Soc. London Ser. B 228, 379–400 (1986).
[Crossref]

D. J. Field, J. Nachmias, “Phase reversal discrimination,” Vision Res. 24, 333–340 (1984).
[Crossref] [PubMed]

Foley, J. M.

Geisler, W. S.

W. S. Geisler, “Sequential ideal-observer analysis of visual discriminations,” Psychol. Rev. 96, 267–314 (1989).
[Crossref] [PubMed]

Harvey, L. O.

Johannson, G.

G. Johannson, “Visual motion detection,” Sci. Am. 232, 76–88 (1975).
[Crossref]

Jones, J. P.

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. Stepnoski, 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]

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]

Kolers, P. A.

P. A. Kolers, Aspects of Motion Perception (Pergamon, New York, 1972).

Legge, G. E.

Marcelja, S.

Morrone, M. C.

D. C. Burr, M. C. Morrone, D. Spinelli, “Evidence for edge and bar detectors in human vision,” Vision Res. 29, 419–432 (1989).
[Crossref] [PubMed]

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

Nachmias, J.

D. J. Field, J. Nachmias, “Phase reversal discrimination,” Vision Res. 24, 333–340 (1984).
[Crossref] [PubMed]

Nakayama, K.

K. Nakayama, “Biological image motion processing,” Vision Res. 25, 625–660 (1985).
[Crossref]

Palmer, L. A.

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

Pollen, D. A.

D. A. Pollen, S. F. Ronner, “Phase relationships between adjacent simple cells in the visual cortex,” Science 212, 1409–1411 (1981).
[Crossref] [PubMed]

Reichardt, W.

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

Ronner, S. F.

D. A. Pollen, S. F. Ronner, “Phase relationships between adjacent simple cells in the visual cortex,” Science 212, 1409–1411 (1981).
[Crossref] [PubMed]

Ross, J.

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

D. C. Burr, J. Ross, “Contrast sensitivity at high velocities,” Vision Res. 23, 3567–3569 (1982).

Schade, O. H.

Sperling, G.

Spinelli, D.

D. C. Burr, M. C. Morrone, D. Spinelli, “Evidence for edge and bar detectors in human vision,” Vision Res. 29, 419–432 (1989).
[Crossref] [PubMed]

Stepnoski, A.

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

Thomas, J. P.

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

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

Tolhurst, D. J.

D. J. Field, D. J. Tolhurst, “The structure and symmetry of simple-cell receptive field profiles in the cat’s visual cortex,” Proc. R. Soc. London Ser. B 228, 379–400 (1986).
[Crossref]

Ullman, S.

S. Ullman, The Interpretation of Visual Motion (MIT, Cambridge, Mass., 1979).

van Santen, J. P. H.

Ver Hoeve, J. N.

Watson, A. B.

Webster, M. A.

Wilson, H. R.

H. R. Wilson, “A model for direction selectivity in threshold motion perception,” Biol. Cybern. 51, 213–222 (1985).
[Crossref] [PubMed]

Biol. Cybern. (1)

H. R. Wilson, “A model for direction selectivity in threshold motion perception,” Biol. Cybern. 51, 213–222 (1985).
[Crossref] [PubMed]

J. Neurophysiol. (6)

B. M. Dow, “Functional classes of cells and their laminar distribution in monkey visual cortex,”J. Neurophysiol. 37, 927–946 (1974).
[PubMed]

T. D. Albright, “Direction and orientation selectivity of neurones in visual area MT of the macaque,”J. Neurophysiol. 52, 1106–1130 (1984).
[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. Stepnoski, 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]

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. Opt. Soc. Am. (3)

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

Nature (London) (1)

P. J. Bennett, M. S. Banks, “Sensitivity loss in odd-symmetric mechanisms and phase anomalies in peripheral vision,” Nature (London) 326, 873–876 (1987).
[Crossref]

Philos. Trans. R. Soc. London Ser. B (1)

S. M. Anstis, “The perception of apparent movement,” Philos. Trans. R. Soc. London Ser. B 290, 153–168 (1980).
[Crossref]

Proc. Intl. Union Physiolog. Sci. (1)

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

Proc. R. Soc. London Ser. B (1)

D. J. Field, D. J. Tolhurst, “The structure and symmetry of simple-cell receptive field profiles in the cat’s visual cortex,” Proc. R. Soc. London Ser. B 228, 379–400 (1986).
[Crossref]

Proc. R. Soc. London Ser. B. (1)

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

Psychol. Rev. (2)

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

W. S. Geisler, “Sequential ideal-observer analysis of visual discriminations,” Psychol. Rev. 96, 267–314 (1989).
[Crossref] [PubMed]

Sci. Am. (1)

G. Johannson, “Visual motion detection,” Sci. Am. 232, 76–88 (1975).
[Crossref]

Science (1)

D. A. Pollen, S. F. Ronner, “Phase relationships between adjacent simple cells in the visual cortex,” Science 212, 1409–1411 (1981).
[Crossref] [PubMed]

Trends Neurosci. (1)

A. Borst, M. Egelhaaf, “Principles of visual motion detection,” Trends Neurosci. 12, 297–306 (1989).
[Crossref] [PubMed]

Vision Res. (10)

D. J. Field, J. Nachmias, “Phase reversal discrimination,” Vision Res. 24, 333–340 (1984).
[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]

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

S. M. Anstis, “Phi movement as a subtractive process,” Vision Res. 10, 1411–1430 (1970).
[Crossref] [PubMed]

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

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

K. Nakayama, “Biological image motion processing,” Vision Res. 25, 625–660 (1985).
[Crossref]

D. C. Burr, M. C. Morrone, D. Spinelli, “Evidence for edge and bar detectors in human vision,” Vision Res. 29, 419–432 (1989).
[Crossref] [PubMed]

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Other (6)

S. Ullman, The Interpretation of Visual Motion (MIT, Cambridge, Mass., 1979).

P. A. Kolers, Aspects of Motion Perception (Pergamon, New York, 1972).

As this mask has a single drift direction, it is possible to measure masking through 360 deg of orientation such that, when the test and the mask are coincident in orientation (at 90 deg and again at 270 deg), their directions of motion are either the same (at 90 deg) or opposed (at 270 deg). We attempted this but could obtain reliable results only for mask rotations from 0 to 180 deg. For mask rotations from 180 to 360 deg it was too difficult for observers to maintain a constant criterion (direction discrimination of the test) because of stimulus artifacts created by beating between the test and the mask and spurious contrast changes.

The unidirectional mask was drifted at a temporal frequency of 4 Hz. A difference in temporal frequency between the test and the drifting mask aided observers in detecting the direction of drift of the test when the orientation of the test and the mask was similar. A mask drift of 4 Hz was chosen, as this is the most disparate temporal frequency from that of the test to still be within the temporal bandwidth of motion units presumably responding to the test (see Ref. 23).

R. Bracewell, The Fourier Transform and Its Applications (McGraw-Hill, New York, 1965).

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

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Figures (12)

Fig. 1
Fig. 1

Reduction in sensitivity (ratio of masked to unmasked thresholds) of drifting test gratings as a function of mask contrast (range 0.075 to 0.42) for observer S. A. The test was always vertical. The various symbols refer to the degree of angular separation between the test and the mask (□, 0; ●,15; △, 30; ▲, 60; ○, 90 deg). The spatial frequency of both the test and the mask was 1.0 c/deg. In the top panel the test drifted either leftward or rightward (randomized between trials) at 8 Hz, and the mask was jittering (random phase). In the bottom panel the test drifted at 8 Hz and the mask at 4 Hz: When the test and mask had the same orientation (vertical), their direction of drift was the same (right to left). A power-law function (not plotted for clarity) was fitted to each data set with the method of least mean squares: Averaged over all conditions, the slope was 0.73.

Fig. 2
Fig. 2

Reduction in sensitivity of drifting (8-Hz) vertical test gratings (of spatial frequency 0.1, 1.0, and 10.0 c/deg) as a function of mask spatial frequency (indicated on abscissa) and orientation (reported alongside each function as the angular separation between the test and the mask: negative values indicate a mask rotation to the left). The results are for observer S. A. The mask contrast was 0.25. Jittering masks were used (see Methods for details). The symbol size represents 1 standard error of the mean. For clarity, each curve was successively displaced upward by half a log unit from the bottom curve.

Fig. 3
Fig. 3

Same data as Fig. 2, replotted as orientation masking functions at each of several mask spatial frequencies. The spatial frequency of the mask is shown alongside each function. The abscissa shows the angular separation between the test and the mask; 0 deg indicates that the test and mask were parallel (and vertical). The curves were successively displaced upward by half a log unit for clarity.

Fig. 4
Fig. 4

Reduction in sensitivity of stationary test gratings of spatial frequency 3.0 c/deg as a function of mask spatial frequency (indicated by the abscissa) and orientation (reported alongside each function as angular separation between test and mask) for observers S. A. and H. S. Jittering masks were used, and the mask contrast was 0.25. The symbol size is approximately 1 standard error of the mean of five trials. For clarity each masking function was shifted vertically by 0.75 log unit.

Fig. 5
Fig. 5

Same data as Fig. 4 replotted as orientation masking tuning functions at each of several mask spatial frequencies. The spatial frequency of the mask is shown to the right of each function. Angular separation (in degrees) between the test and mask is plotted on the abscissa as mask orientation. For clarity, each curve was successively shifted upward by 0.75 log unit.

Fig. 6
Fig. 6

2D spatial-frequency tuning surfaces produced with jittering mask gratings and a drifting (8-Hz) grating of (a) 0.1, (b) 1.0, and (c) 10.0 c/deg and a stationary (0-Hz) test grating of (d) 3.0 c/deg. Each tuning surface was calculated from the 2D spatial-frequency masking data for observer S, A; The masking data were raised to the power 1.37 (see text for explanation), smoothed over the 2D spectral domain with a second-order smoothing function to form a continuous surface, and plotted as contour maps on linear Cartesian projection coordinates (the center of the abscissa is the origin of coordinates). Each surface was normalized to a maximum gain of 1 in order to facilitate comparison of their structure. The separation between contour lines is 0.25 log unit; the half-amplitude contour is labeled 0.5 in each plot.

Fig. 7
Fig. 7

Like Fig. 6 for observer H. S. The 2D spatial-frequency tuning surfaces were produced with jittering mask gratings and (a) a 3.0-c/deg drifting (8-Hz) test grating, (b) a 3.0-c/deg stationary (0-Hz) test grating.

Fig. 8
Fig. 8

2D spatial-frequency tuning surfaces produced with drifting (4-Hz) mask gratings and 3.0-c/deg drifting (8-Hz) test gratings for observers (a) S. A., (b) H. S. The surfaces were constructed following the procedure outlined in the caption of Fig. 6. Contour lines are separated by 0.25 log unit; the half-amplitude contour is shown as 0.5.

Fig. 9
Fig. 9

3D perspective plots of the psychophysical receptive fields calculated by inverse Fourier transform of the spectral tuning surfaces shown in Fig. 6 (observer S. A.) produced with jittering mask gratings and (a) 0.1-c/deg, (b) 1.0-c/deg, and (c) 10.0-c/deg drifting (8-Hz) test gratings and (d) a stationary (0-Hz) 3.0-c/deg test grating. Zero phase was assumed for each transform (see text). The x and y axes are linear dimensions of space, and the center of the plot is the origin of coordinates. Each plot was normalized to a maximum height of 1.

Fig. 10
Fig. 10

Contour maps of the psychophysical receptive fields calculated by the inverse Fourier transform of the spectral tuning surfaces shown in Fig. 7 (observer H. S.) produced with jittering masks and (a) a 3.0-c/deg drifting (8-Hz) test grating, (b) a 3.0-c/deg stationary (0-Hz) test grating. Zero phase was assumed for each transform; each map has a maximum height of 1, and the contour lines are separated by octave units. The half-amplitude contour of the central positive zone is labeled 0.5.

Fig. 11
Fig. 11

Receptive fields calculated by the inverse Fourier transform of the 2D spatial-frequency tuning surfaces shown in Fig. 8 produced with drifting (4-Hz) mask gratings and a 3.0-c/deg drifting (8-Hz) test grating. Zero phase was assumed for each transform. The transform is shown as (a) a contour map for observer H. S., (b) a 3D perspective plot for observer S. A.

Fig. 12
Fig. 12

Summation and masking estimates (in both degrees and cycles of sinusoid) of the spatial extent [defined as 2ΔS, from Eq. (3)] of the psychophysical receptive-field width and length of motion-dependent units in human vision as a function of spatial frequency. The results are for observer S. A. The masking estimates show the width and the length of the receptive-field profiles depicted in Figs. 9(a)–9(c) (obtained with drifting test gratings and jittering mask gratings). The summation estimates show the width and the length of even-symmetric 2D Gabor signals (σx and σy of each signal were taken from the summation estimates of receptive-field width and length reported in Ref. 11, the companion paper).

Equations (3)

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TE Mc 0.73 .
Mc TE 1.37 .
( Δ S ) 2 = s 2 g g d s g g d s ,

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