Abstract

The purpose of our experiments was to estimate basic sensitivity to motion gradients and to evaluate the evidence for second-order integration and differentiation of motion signals. We measured sensitivity to spatially sinusoidal contrast modulation between two oppositely moving bandpass-filtered noise images. The motion-contrast sensitivity function, defined as the inverse of threshold modulation amplitude as a function of modulation spatial frequency, was bandpass in shape with declines at both highest and lowest frequencies. The functions for three noise spatial frequencies had approximately the same shape when modulation frequency was expressed as a fraction of noise frequency. We compared the data with a model in which linear motion filters, whose outputs are squared or rectified, are followed by a second stage of excitatory or inhibitory pooling. The data are consistent with a model in which (1) all excitatory pooling occurs at the linear stage and (2) the second stage contains a large inhibitory pooling area, with a radius approximately eight times that of the linear receptive field.

© 1994 Optical Society of America

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  1. A. B. Watson, A. J. Ahumada, “A look at motion in the frequency domain,” in Motion: Perception and Representation, J. K. Tsotsos, ed. (Association for Computing Machinery, New York, 1983).
  2. A. B. Watson, A. J. Ahumada, “Model of human visual-motion sensing,” J. Opt. Soc. Am. A 2, 322–342 (1985).
    [CrossRef] [PubMed]
  3. E. H. Adelson, J. R. Bergen, “Spatiotemporal energy models for the perception of motion,” J. Opt. Soc. Am. A 2, 284–299 (1985).
    [CrossRef] [PubMed]
  4. R. C. Emerson, J. R. Bergen, E. H. Adelson, “Directionally selective complex cells and the computation of motion energy in cat visual cortex,” Vision Res. 32, 203–218 (1992).
    [CrossRef] [PubMed]
  5. 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]
  6. J. P. H. van Santen, G. Sperling, “Elaborated Reichardt detectors,” J. Opt. Soc. Am. A 2, 300–321 (1985).
    [CrossRef] [PubMed]
  7. A. B. Watson, “Optimal displacement in apparent motion and quadrature models of motion sensing,” Vision Res. 30, 1389–1393 (1990).
    [CrossRef] [PubMed]
  8. E. H. Adelson, J. A. Movshon, “Phenomenal coherence of moving visual patterns,” Nature (London) 300, 523–525 (1982).
    [CrossRef]
  9. S. J. Anderson, D. C. Burr, “Spatial and temporal selectivity of the human motion detection system,” Vision Res. 25, 1147–1154 (1985).
    [CrossRef] [PubMed]
  10. G. J. Anderson, “Perception of self-motion: psychophysical and computational approaches,” Psychol. Bull. 99, 52–65 (1986).
    [CrossRef]
  11. 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]
  12. 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]
  13. 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]
  14. J. J. Gibson, The Perception of the Visual World (Houghton Mifflin, Boston, Mass., 1950).
  15. M. L. Braunstein, G. J. Anderson, “Velocity gradients and relative depth perception,” Percept. Psychophys. 29, 145–155 (1981).
    [CrossRef] [PubMed]
  16. A. J. van Doorn, J. J. Koenderink, “Visibility of movement gradients,” Biol. Cybern. 44, 167–175 (1982).
    [CrossRef] [PubMed]
  17. B. Rogers, M. Graham, “Motion parallax as an independent cue for depth perception,” Perception 8, 125–134 (1979).
    [CrossRef] [PubMed]
  18. A. J. van Doorn, J. J. Koenderink, “Spatial properties of the visual detectability of moving spatial white noise,” Exp. Brain Res. 45, 189–195 (1982).
    [PubMed]
  19. K. Nakayama, C. W. Tyler, “Psychophysical isolation of movement sensitivity by removal of familiar position cues,” Vision Res. 21, 427–433 (1981).
    [CrossRef] [PubMed]
  20. K. Nakayama, G. H. Silverman, D. I. A. Macleod, J. Mulligan, “Sensitivity to shearing and compressive motion in random dots,” Perception 14, 225–238 (1985).
    [CrossRef] [PubMed]
  21. A. B. Watson, K. R. K. Nielsen, A. Poirson, A. Fitzhugh, A. Bilson, K. Nguyen, A. J. Ahumada, “Use of a raster framebuffer in vision research,” Behav. Res. Methods Instrum. Comput. 18, 587–594 (1986).
    [CrossRef]
  22. A. B. Watson, D. G. Pelli, “QUEST: a Bayesian adaptive psychometric method,” Percept. Psychophys. 33, 113–120 (1983).
    [CrossRef] [PubMed]
  23. A. B. Watson, “Probability summation over time,” Vision Res. 19, 515–522 (1979).
    [CrossRef] [PubMed]
  24. A. B. Watson, “Temporal sensitivity,” in Handbook of Perception and Human Performance, K. Boff, L. Kaufman, J. Thomas, eds. (Wiley, New York, 1986).
  25. D. J. Heeger, E. P. Simoncelli, “Model of visual motion sensing,” in Spatial Vision in Humans and Robots, L. Harris, M. Jenkin, eds. (Cambridge U. Press, New York, 1992).
  26. F. W. Campbell, J. G. Robson, “Application of Fourier analysis to the visibility of gratings,”J. Physiol. (London) 197, 551–566 (1968).
  27. B. J. Frost, K. Nakayama, “Single visual neurons code opposing motion independent of direction,” Science 220, 744–745 (1983).
    [CrossRef] [PubMed]
  28. J. Allman, F. Meizin, E. McGuinness, “Direction- and velocity-specific responses from beyond the classical receptive field in the middle temporal visual area (MT),” Perception 14, 105–126 (1985).
    [CrossRef] [PubMed]
  29. J. R. Maunsell, D. C. Van Essen, “Functional properties of neurons in middle temporal visual area of the macaque monkey. I. Selectivity for stimulus direction, speed, and orientation,”J. Neurophysiol. 49, 1127–1147 (1983).
    [PubMed]
  30. D. J. Heeger, A. D. Jepson, E. P. Simoncelli, “Recovering observer translation with center-surround operators,” in Proceedings of IEEE Workshop on Visual Motion, Princeton N.J., T. S. Huang, P. J. Burt, eds. (Institute of Electrical and Electronics Engineers, New York, 1991).
    [CrossRef]
  31. K. Nakayama, J. M. Loomis, “Optical velocity patterns, velocity-sensitive neurons, and space perception: a hypothesis,” Perception 3, 63–80 (1974).
    [CrossRef] [PubMed]
  32. T. D. Albright, R. Desimone, “Local precision of visuotopic organization in the middle temporal area (MT) of the macaque,” Exp. Brain Res. 65, 582–592 (1987).
    [CrossRef] [PubMed]
  33. D. W. Williams, R. Sekuler, “Coherent global motion percepts from stochastic local motions,” Vision Res. 24, 55–62 (1984).
    [CrossRef] [PubMed]
  34. S. N. J. Watamaniuk, R. Sekuler, “Temporal and spatial integration in dynamic random-dot stimuli,” Vision Res. 32, 2341–2347 (1992).
    [CrossRef] [PubMed]
  35. A. B. Watson, “Motion pooling areas estimated from motion contrast sensitivity functions,” Invest. Ophthalmol. Vis. Sci. 33, 974 (1992).
  36. A. B. Watson, “Sensitivity to spatial variations in image motion,” in Annual Meeting, Vol. 17 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), p. 217.

1992 (3)

R. C. Emerson, J. R. Bergen, E. H. Adelson, “Directionally selective complex cells and the computation of motion energy in cat visual cortex,” Vision Res. 32, 203–218 (1992).
[CrossRef] [PubMed]

S. N. J. Watamaniuk, R. Sekuler, “Temporal and spatial integration in dynamic random-dot stimuli,” Vision Res. 32, 2341–2347 (1992).
[CrossRef] [PubMed]

A. B. Watson, “Motion pooling areas estimated from motion contrast sensitivity functions,” Invest. Ophthalmol. Vis. Sci. 33, 974 (1992).

1991 (2)

1990 (1)

A. B. Watson, “Optimal displacement in apparent motion and quadrature models of motion sensing,” Vision Res. 30, 1389–1393 (1990).
[CrossRef] [PubMed]

1989 (1)

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]

1987 (1)

T. D. Albright, R. Desimone, “Local precision of visuotopic organization in the middle temporal area (MT) of the macaque,” Exp. Brain Res. 65, 582–592 (1987).
[CrossRef] [PubMed]

1986 (2)

A. B. Watson, K. R. K. Nielsen, A. Poirson, A. Fitzhugh, A. Bilson, K. Nguyen, A. J. Ahumada, “Use of a raster framebuffer in vision research,” Behav. Res. Methods Instrum. Comput. 18, 587–594 (1986).
[CrossRef]

G. J. Anderson, “Perception of self-motion: psychophysical and computational approaches,” Psychol. Bull. 99, 52–65 (1986).
[CrossRef]

1985 (6)

J. P. H. van Santen, G. Sperling, “Elaborated Reichardt detectors,” J. Opt. Soc. Am. A 2, 300–321 (1985).
[CrossRef] [PubMed]

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

A. B. Watson, A. J. Ahumada, “Model of human visual-motion sensing,” J. Opt. Soc. Am. A 2, 322–342 (1985).
[CrossRef] [PubMed]

E. H. Adelson, J. R. Bergen, “Spatiotemporal energy models for the perception of motion,” J. Opt. Soc. Am. A 2, 284–299 (1985).
[CrossRef] [PubMed]

K. Nakayama, G. H. Silverman, D. I. A. Macleod, J. Mulligan, “Sensitivity to shearing and compressive motion in random dots,” Perception 14, 225–238 (1985).
[CrossRef] [PubMed]

J. Allman, F. Meizin, E. McGuinness, “Direction- and velocity-specific responses from beyond the classical receptive field in the middle temporal visual area (MT),” Perception 14, 105–126 (1985).
[CrossRef] [PubMed]

1984 (2)

D. W. Williams, R. Sekuler, “Coherent global motion percepts from stochastic local motions,” Vision Res. 24, 55–62 (1984).
[CrossRef] [PubMed]

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]

1983 (3)

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

B. J. Frost, K. Nakayama, “Single visual neurons code opposing motion independent of direction,” Science 220, 744–745 (1983).
[CrossRef] [PubMed]

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

1982 (3)

E. H. Adelson, J. A. Movshon, “Phenomenal coherence of moving visual patterns,” Nature (London) 300, 523–525 (1982).
[CrossRef]

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

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

1981 (2)

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

M. L. Braunstein, G. J. Anderson, “Velocity gradients and relative depth perception,” Percept. Psychophys. 29, 145–155 (1981).
[CrossRef] [PubMed]

1979 (2)

B. Rogers, M. Graham, “Motion parallax as an independent cue for depth perception,” Perception 8, 125–134 (1979).
[CrossRef] [PubMed]

A. B. Watson, “Probability summation over time,” Vision Res. 19, 515–522 (1979).
[CrossRef] [PubMed]

1974 (1)

K. Nakayama, J. M. Loomis, “Optical velocity patterns, velocity-sensitive neurons, and space perception: a hypothesis,” Perception 3, 63–80 (1974).
[CrossRef] [PubMed]

1968 (1)

F. W. Campbell, J. G. Robson, “Application of Fourier analysis to the visibility of gratings,”J. Physiol. (London) 197, 551–566 (1968).

Adelson, E. H.

R. C. Emerson, J. R. Bergen, E. H. Adelson, “Directionally selective complex cells and the computation of motion energy in cat visual cortex,” Vision Res. 32, 203–218 (1992).
[CrossRef] [PubMed]

E. H. Adelson, J. R. Bergen, “Spatiotemporal energy models for the perception of motion,” J. Opt. Soc. Am. A 2, 284–299 (1985).
[CrossRef] [PubMed]

E. H. Adelson, J. A. Movshon, “Phenomenal coherence of moving visual patterns,” Nature (London) 300, 523–525 (1982).
[CrossRef]

Ahumada, A. J.

A. B. Watson, K. R. K. Nielsen, A. Poirson, A. Fitzhugh, A. Bilson, K. Nguyen, A. J. Ahumada, “Use of a raster framebuffer in vision research,” Behav. Res. Methods Instrum. Comput. 18, 587–594 (1986).
[CrossRef]

A. B. Watson, A. J. Ahumada, “Model of human visual-motion sensing,” J. Opt. Soc. Am. A 2, 322–342 (1985).
[CrossRef] [PubMed]

A. B. Watson, A. J. Ahumada, “A look at motion in the frequency domain,” in Motion: Perception and Representation, J. K. Tsotsos, ed. (Association for Computing Machinery, New York, 1983).

Albright, T. D.

T. D. Albright, R. Desimone, “Local precision of visuotopic organization in the middle temporal area (MT) of the macaque,” Exp. Brain Res. 65, 582–592 (1987).
[CrossRef] [PubMed]

Allman, J.

J. Allman, F. Meizin, E. McGuinness, “Direction- and velocity-specific responses from beyond the classical receptive field in the middle temporal visual area (MT),” Perception 14, 105–126 (1985).
[CrossRef] [PubMed]

Anderson, G. J.

G. J. Anderson, “Perception of self-motion: psychophysical and computational approaches,” Psychol. Bull. 99, 52–65 (1986).
[CrossRef]

M. L. Braunstein, G. J. Anderson, “Velocity gradients and relative depth perception,” Percept. Psychophys. 29, 145–155 (1981).
[CrossRef] [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, 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, “Spatial and temporal selectivity of the human motion detection system,” Vision Res. 25, 1147–1154 (1985).
[CrossRef] [PubMed]

Bergen, J. R.

R. C. Emerson, J. R. Bergen, E. H. Adelson, “Directionally selective complex cells and the computation of motion energy in cat visual cortex,” Vision Res. 32, 203–218 (1992).
[CrossRef] [PubMed]

E. H. Adelson, J. R. Bergen, “Spatiotemporal energy models for the perception of motion,” J. Opt. Soc. Am. A 2, 284–299 (1985).
[CrossRef] [PubMed]

Bilson, A.

A. B. Watson, K. R. K. Nielsen, A. Poirson, A. Fitzhugh, A. Bilson, K. Nguyen, A. J. Ahumada, “Use of a raster framebuffer in vision research,” Behav. Res. Methods Instrum. Comput. 18, 587–594 (1986).
[CrossRef]

Braunstein, M. L.

M. L. Braunstein, G. J. Anderson, “Velocity gradients and relative depth perception,” Percept. Psychophys. 29, 145–155 (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, “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]

Campbell, F. W.

F. W. Campbell, J. G. Robson, “Application of Fourier analysis to the visibility of gratings,”J. Physiol. (London) 197, 551–566 (1968).

Desimone, R.

T. D. Albright, R. Desimone, “Local precision of visuotopic organization in the middle temporal area (MT) of the macaque,” Exp. Brain Res. 65, 582–592 (1987).
[CrossRef] [PubMed]

Emerson, R. C.

R. C. Emerson, J. R. Bergen, E. H. Adelson, “Directionally selective complex cells and the computation of motion energy in cat visual cortex,” Vision Res. 32, 203–218 (1992).
[CrossRef] [PubMed]

Fitzhugh, A.

A. B. Watson, K. R. K. Nielsen, A. Poirson, A. Fitzhugh, A. Bilson, K. Nguyen, A. J. Ahumada, “Use of a raster framebuffer in vision research,” Behav. Res. Methods Instrum. Comput. 18, 587–594 (1986).
[CrossRef]

Frost, B. J.

B. J. Frost, K. Nakayama, “Single visual neurons code opposing motion independent of direction,” Science 220, 744–745 (1983).
[CrossRef] [PubMed]

Gibson, J. J.

J. J. Gibson, The Perception of the Visual World (Houghton Mifflin, Boston, Mass., 1950).

Graham, M.

B. Rogers, M. Graham, “Motion parallax as an independent cue for depth perception,” Perception 8, 125–134 (1979).
[CrossRef] [PubMed]

Heeger, D. J.

D. J. Heeger, E. P. Simoncelli, “Model of visual motion sensing,” in Spatial Vision in Humans and Robots, L. Harris, M. Jenkin, eds. (Cambridge U. Press, New York, 1992).

D. J. Heeger, A. D. Jepson, E. P. Simoncelli, “Recovering observer translation with center-surround operators,” in Proceedings of IEEE Workshop on Visual Motion, Princeton N.J., T. S. Huang, P. J. Burt, eds. (Institute of Electrical and Electronics Engineers, New York, 1991).
[CrossRef]

Jepson, A. D.

D. J. Heeger, A. D. Jepson, E. P. Simoncelli, “Recovering observer translation with center-surround operators,” in Proceedings of IEEE Workshop on Visual Motion, Princeton N.J., T. S. Huang, P. J. Burt, eds. (Institute of Electrical and Electronics Engineers, New York, 1991).
[CrossRef]

Koenderink, J. J.

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

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

Loomis, J. M.

K. Nakayama, J. M. Loomis, “Optical velocity patterns, velocity-sensitive neurons, and space perception: a hypothesis,” Perception 3, 63–80 (1974).
[CrossRef] [PubMed]

Macleod, D. I. A.

K. Nakayama, G. H. Silverman, D. I. A. Macleod, J. Mulligan, “Sensitivity to shearing and compressive motion in random dots,” Perception 14, 225–238 (1985).
[CrossRef] [PubMed]

Maunsell, J. R.

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

McGuinness, E.

J. Allman, F. Meizin, E. McGuinness, “Direction- and velocity-specific responses from beyond the classical receptive field in the middle temporal visual area (MT),” Perception 14, 105–126 (1985).
[CrossRef] [PubMed]

Meizin, F.

J. Allman, F. Meizin, E. McGuinness, “Direction- and velocity-specific responses from beyond the classical receptive field in the middle temporal visual area (MT),” Perception 14, 105–126 (1985).
[CrossRef] [PubMed]

Morrone, M. C.

Movshon, J. A.

E. H. Adelson, J. A. Movshon, “Phenomenal coherence of moving visual patterns,” Nature (London) 300, 523–525 (1982).
[CrossRef]

Mulligan, J.

K. Nakayama, G. H. Silverman, D. I. A. Macleod, J. Mulligan, “Sensitivity to shearing and compressive motion in random dots,” Perception 14, 225–238 (1985).
[CrossRef] [PubMed]

Nakayama, K.

K. Nakayama, G. H. Silverman, D. I. A. Macleod, J. Mulligan, “Sensitivity to shearing and compressive motion in random dots,” Perception 14, 225–238 (1985).
[CrossRef] [PubMed]

B. J. Frost, K. Nakayama, “Single visual neurons code opposing motion independent of direction,” Science 220, 744–745 (1983).
[CrossRef] [PubMed]

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

K. Nakayama, J. M. Loomis, “Optical velocity patterns, velocity-sensitive neurons, and space perception: a hypothesis,” Perception 3, 63–80 (1974).
[CrossRef] [PubMed]

Nguyen, K.

A. B. Watson, K. R. K. Nielsen, A. Poirson, A. Fitzhugh, A. Bilson, K. Nguyen, A. J. Ahumada, “Use of a raster framebuffer in vision research,” Behav. Res. Methods Instrum. Comput. 18, 587–594 (1986).
[CrossRef]

Nielsen, K. R. K.

A. B. Watson, K. R. K. Nielsen, A. Poirson, A. Fitzhugh, A. Bilson, K. Nguyen, A. J. Ahumada, “Use of a raster framebuffer in vision research,” Behav. Res. Methods Instrum. Comput. 18, 587–594 (1986).
[CrossRef]

Pelli, D. G.

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

Poirson, A.

A. B. Watson, K. R. K. Nielsen, A. Poirson, A. Fitzhugh, A. Bilson, K. Nguyen, A. J. Ahumada, “Use of a raster framebuffer in vision research,” Behav. Res. Methods Instrum. Comput. 18, 587–594 (1986).
[CrossRef]

Robson, J. G.

F. W. Campbell, J. G. Robson, “Application of Fourier analysis to the visibility of gratings,”J. Physiol. (London) 197, 551–566 (1968).

Rogers, B.

B. Rogers, M. Graham, “Motion parallax as an independent cue for depth perception,” Perception 8, 125–134 (1979).
[CrossRef] [PubMed]

Sekuler, R.

S. N. J. Watamaniuk, R. Sekuler, “Temporal and spatial integration in dynamic random-dot stimuli,” Vision Res. 32, 2341–2347 (1992).
[CrossRef] [PubMed]

D. W. Williams, R. Sekuler, “Coherent global motion percepts from stochastic local motions,” Vision Res. 24, 55–62 (1984).
[CrossRef] [PubMed]

Silverman, G. H.

K. Nakayama, G. H. Silverman, D. I. A. Macleod, J. Mulligan, “Sensitivity to shearing and compressive motion in random dots,” Perception 14, 225–238 (1985).
[CrossRef] [PubMed]

Simoncelli, E. P.

D. J. Heeger, E. P. Simoncelli, “Model of visual motion sensing,” in Spatial Vision in Humans and Robots, L. Harris, M. Jenkin, eds. (Cambridge U. Press, New York, 1992).

D. J. Heeger, A. D. Jepson, E. P. Simoncelli, “Recovering observer translation with center-surround operators,” in Proceedings of IEEE Workshop on Visual Motion, Princeton N.J., T. S. Huang, P. J. Burt, eds. (Institute of Electrical and Electronics Engineers, New York, 1991).
[CrossRef]

Sperling, G.

Tyler, C. W.

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

van Doorn, A. J.

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

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

Van Essen, D. C.

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

van Santen, J. P. H.

Watamaniuk, S. N. J.

S. N. J. Watamaniuk, R. Sekuler, “Temporal and spatial integration in dynamic random-dot stimuli,” Vision Res. 32, 2341–2347 (1992).
[CrossRef] [PubMed]

Watson, A. B.

A. B. Watson, “Motion pooling areas estimated from motion contrast sensitivity functions,” Invest. Ophthalmol. Vis. Sci. 33, 974 (1992).

A. B. Watson, “Optimal displacement in apparent motion and quadrature models of motion sensing,” Vision Res. 30, 1389–1393 (1990).
[CrossRef] [PubMed]

A. B. Watson, K. R. K. Nielsen, A. Poirson, A. Fitzhugh, A. Bilson, K. Nguyen, A. J. Ahumada, “Use of a raster framebuffer in vision research,” Behav. Res. Methods Instrum. Comput. 18, 587–594 (1986).
[CrossRef]

A. B. Watson, A. J. Ahumada, “Model of human visual-motion sensing,” J. Opt. Soc. Am. A 2, 322–342 (1985).
[CrossRef] [PubMed]

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

A. B. Watson, “Probability summation over time,” Vision Res. 19, 515–522 (1979).
[CrossRef] [PubMed]

A. B. Watson, “Temporal sensitivity,” in Handbook of Perception and Human Performance, K. Boff, L. Kaufman, J. Thomas, eds. (Wiley, New York, 1986).

A. B. Watson, “Sensitivity to spatial variations in image motion,” in Annual Meeting, Vol. 17 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), p. 217.

A. B. Watson, A. J. Ahumada, “A look at motion in the frequency domain,” in Motion: Perception and Representation, J. K. Tsotsos, ed. (Association for Computing Machinery, New York, 1983).

Williams, D. W.

D. W. Williams, R. Sekuler, “Coherent global motion percepts from stochastic local motions,” Vision Res. 24, 55–62 (1984).
[CrossRef] [PubMed]

Behav. Res. Methods Instrum. Comput. (1)

A. B. Watson, K. R. K. Nielsen, A. Poirson, A. Fitzhugh, A. Bilson, K. Nguyen, A. J. Ahumada, “Use of a raster framebuffer in vision research,” Behav. Res. Methods Instrum. Comput. 18, 587–594 (1986).
[CrossRef]

Biol. Cybern. (1)

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

Exp. Brain Res. (2)

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

T. D. Albright, R. Desimone, “Local precision of visuotopic organization in the middle temporal area (MT) of the macaque,” Exp. Brain Res. 65, 582–592 (1987).
[CrossRef] [PubMed]

Invest. Ophthalmol. Vis. Sci. (1)

A. B. Watson, “Motion pooling areas estimated from motion contrast sensitivity functions,” Invest. Ophthalmol. Vis. Sci. 33, 974 (1992).

J. Neurophysiol. (1)

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

J. Opt. Soc. Am. A (6)

J. Physiol. (London) (1)

F. W. Campbell, J. G. Robson, “Application of Fourier analysis to the visibility of gratings,”J. Physiol. (London) 197, 551–566 (1968).

Nature (London) (1)

E. H. Adelson, J. A. Movshon, “Phenomenal coherence of moving visual patterns,” Nature (London) 300, 523–525 (1982).
[CrossRef]

Percept. Psychophys. (2)

M. L. Braunstein, G. J. Anderson, “Velocity gradients and relative depth perception,” Percept. Psychophys. 29, 145–155 (1981).
[CrossRef] [PubMed]

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

Perception (4)

K. Nakayama, G. H. Silverman, D. I. A. Macleod, J. Mulligan, “Sensitivity to shearing and compressive motion in random dots,” Perception 14, 225–238 (1985).
[CrossRef] [PubMed]

J. Allman, F. Meizin, E. McGuinness, “Direction- and velocity-specific responses from beyond the classical receptive field in the middle temporal visual area (MT),” Perception 14, 105–126 (1985).
[CrossRef] [PubMed]

K. Nakayama, J. M. Loomis, “Optical velocity patterns, velocity-sensitive neurons, and space perception: a hypothesis,” Perception 3, 63–80 (1974).
[CrossRef] [PubMed]

B. Rogers, M. Graham, “Motion parallax as an independent cue for depth perception,” Perception 8, 125–134 (1979).
[CrossRef] [PubMed]

Psychol. Bull. (1)

G. J. Anderson, “Perception of self-motion: psychophysical and computational approaches,” Psychol. Bull. 99, 52–65 (1986).
[CrossRef]

Science (1)

B. J. Frost, K. Nakayama, “Single visual neurons code opposing motion independent of direction,” Science 220, 744–745 (1983).
[CrossRef] [PubMed]

Vision Res. (8)

A. B. Watson, “Probability summation over time,” Vision Res. 19, 515–522 (1979).
[CrossRef] [PubMed]

D. W. Williams, R. Sekuler, “Coherent global motion percepts from stochastic local motions,” Vision Res. 24, 55–62 (1984).
[CrossRef] [PubMed]

S. N. J. Watamaniuk, R. Sekuler, “Temporal and spatial integration in dynamic random-dot stimuli,” Vision Res. 32, 2341–2347 (1992).
[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]

A. B. Watson, “Optimal displacement in apparent motion and quadrature models of motion sensing,” Vision Res. 30, 1389–1393 (1990).
[CrossRef] [PubMed]

R. C. Emerson, J. R. Bergen, E. H. Adelson, “Directionally selective complex cells and the computation of motion energy in cat visual cortex,” Vision Res. 32, 203–218 (1992).
[CrossRef] [PubMed]

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

Other (6)

A. B. Watson, A. J. Ahumada, “A look at motion in the frequency domain,” in Motion: Perception and Representation, J. K. Tsotsos, ed. (Association for Computing Machinery, New York, 1983).

J. J. Gibson, The Perception of the Visual World (Houghton Mifflin, Boston, Mass., 1950).

D. J. Heeger, A. D. Jepson, E. P. Simoncelli, “Recovering observer translation with center-surround operators,” in Proceedings of IEEE Workshop on Visual Motion, Princeton N.J., T. S. Huang, P. J. Burt, eds. (Institute of Electrical and Electronics Engineers, New York, 1991).
[CrossRef]

A. B. Watson, “Sensitivity to spatial variations in image motion,” in Annual Meeting, Vol. 17 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), p. 217.

A. B. Watson, “Temporal sensitivity,” in Handbook of Perception and Human Performance, K. Boff, L. Kaufman, J. Thomas, eds. (Wiley, New York, 1986).

D. J. Heeger, E. P. Simoncelli, “Model of visual motion sensing,” in Spatial Vision in Humans and Robots, L. Harris, M. Jenkin, eds. (Cambridge U. Press, New York, 1992).

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Figures (18)

Fig. 1
Fig. 1

Generic motion-contrast grating consisting of alternating strips moving with different velocities v1 and v2. The modulator shown at the right controls the velocity at each point in the stimulus.

Fig. 2
Fig. 2

Two types of pooling of motion signal. Early linear units pool over a small extent; later nonlinear units pool over a larger extent.

Fig. 3
Fig. 3

Modulating functions of m1 (solid curves) and m2 (dashed curves). Motion contrasts of 1 and 0.5 are shown. Modulation frequency is 2 cycles/image. A, constant peak constrast; B, constant variance.

Fig. 4
Fig. 4

Two successive frames from a stimulus sequence. The modulation frequency fm was 2 cycles/image, and the motion was horizontal (shear) at |v1| = 1 pixel/frame. The carrier frequency fc was 32 cycles/image; the image width is 128 pixels.

Fig. 5
Fig. 5

Luminance-contrast sensitivity for noise carriers. Motion was horizontal (filled symbols) or vertical (open symbols). Viewing distance was 48.6 or 97.2 cm, resulting in image sizes of 4 (large symbols) or 2 deg (small symbols). Update interval (dt) was 1, 2, or 4 frames, resulting in speeds of 1.875 (circles), 0.938 (squares), and 0.469 (triangles) deg/s, respectively. The legend notation is direction size dt (for both observers). The error bars are ±1 standard error.

Fig. 6
Fig. 6

Motion-contrast sensitivity functions for compression and shear for observer ABW. The number near each curve indicates the carrier frequency. Data for fm = 0 are plotted at −0.9. The error bars are ±1 standard error.

Fig. 7
Fig. 7

Motion-contrast sensitivity functions for compression and shear for observer MPE. Other details as in Fig. 6.

Fig. 8
Fig. 8

Motion-contrast sensitivity averaged over the two observers. The legend indicates shear (open symbols) or compression (filled symbols) and the carrier frequency.

Fig. 9
Fig. 9

Average motion-contrast sensitivity functions shifted to illustrate scale invariance. Error bars are ±1 standard error.

Fig. 10
Fig. 10

Schematic of the motion-contrast detection model.

Fig. 11
Fig. 11

Output of the model after temporal matching and integration: A, before spatial pooling, B, after spatial pooling with a radius of 3.84 rfu. The input was fc = 16 cycles/image, fm = 2 cycles/image, and m = 1. The image is 15.3 rfu wide.

Fig. 12
Fig. 12

Opponent response (see Fig. 11A) integrated over the horizontal position after pooling by a Gaussian with a radius of 0.24 (line) or 3.84 (dots) rfu.

Fig. 13
Fig. 13

Model predictions for pooling radii of 0.24, 0.48, 0.96, 1.92, and 3.84 rfu (from top to bottom). These are energy predictions for a compression stimulus.

Fig. 14
Fig. 14

Average data compared with model predictions for pooling radii of 0.24, 0.48, 0.96, 1.92, and 3.84 rfu.

Fig. 15
Fig. 15

Motion-contrast sensitivity for square-wave and sine-wave modulators.

Fig. 16
Fig. 16

Motion-contrast sensitivity for moving and stationary square-wave modulators, for observer MPE.

Fig. 17
Fig. 17

Model predictions for an inhibitory surround in the second-order pooling mechanism. The dashed curve shows simulations without inhibition.

Fig. 18
Fig. 18

Comparative widths of first-order linear receptive-field and inhibitory second-order surround. Curve heights are arbitrary. Horizontal scale is in receptive-field units.

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

g ( x ) = J 0 ( 2 π f c x ) exp [ - π x / s ) 2 ] ,
s = f c - 1 2 b + 1 2 b - 1 log ( 2 ) / π ,
w ( t ) = c g exp [ - π ( t / d ) 2 ] ,
m 1 ( y ) = { 1 / 2 [ 1 + m sin ( 2 π f m y ) ] } 1 / 2 ,
m 2 ( y ) = { 1 / 2 [ 1 - m sin ( 2 π f m y ) ] } 1 / 2 = [ 1 - m 1 2 ( y ) ] 1 / 2 ,
L ( x , t ) = L 0 { 1 + w t ( t ) [ m 1 ( y ) c 1 ( x - t v ) + m 2 ( y ) c 2 ( x + t v ) ] } ,

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