Abstract

A motion sequence may be represented as a single pattern in x–y–t space; a velocity of motion corresponds to a three-dimensional orientation in this space. Motion sinformation can be extracted by a system that responds to the oriented spatiotemporal energy. We discuss a class of models for human motion mechanisms in which the first stage consists of linear filters that are oriented in space-time and tuned in spatial frequency. The outputs of quadrature pairs of such filters are squared and summed to give a measure of motion energy. These responses are then fed into an opponent stage. Energy models can be built from elements that are consistent with known physiology and psychophysics, and they permit a qualitative understanding of a variety of motion phenomena.

© 1985 Optical Society of America

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References

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  1. S. Ullman, The Interpretation of Visual Motion (MIT U. Press, Cambridge, Mass., 1979).
  2. S. M. Anstis, “The perception of apparent movement,” Phil. Trans. R. Soc. London Ser. B 290, 153–168 (1980).
    [Crossref]
  3. S. M. Anstis, “Apparent Movement,” in Handbook of Sensory Physiology, Vol. VIII, Perception, R. Held, H. W. Leibowitz, and H.-L. Teuber, eds. (Springer-Verlag, New York, 1977).
  4. J. S. Lappin and H. H. Bell, “Perceptual differentiation of sequential visual patterns,” Percept. Psychophys. 12, 129–134 (1972).
    [Crossref]
  5. D. Marr and S. Ullman, “Direction selectivity and its use in early visual processing,” Proc. R. Soc. London Ser. B 211, 151–180 (1981).
    [Crossref]
  6. J. P. H. van Santen and G. Sperling, “Temporal covariance model of human motion perception,” J. Opt. Soc. Am. A 1, 451–473 (1984).
    [Crossref] [PubMed]
  7. 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).
  8. A. B. Watson and A. J. Ahumada, “A look at motion in the frequency domain,”NASA Tech. Memo. TM-84352 (1983).
  9. J. Ross and D. Burr, “The psychophysics of motion,” in Proceedings of the Workshop of Vision, Brain, and Cooperative Computation, M. A. Arbib and A. R. Hanson eds. (U. Massachusetts Press, Amherst, Mass., 1983); Vision, Brain, and Cooperative Computation (Bradford, Amherst, Mass., to be published).
  10. M. J. Morgan, “Perception of continuity in stroboscopic motion: a temporal frequency analysis.” Vision Res 19, 491–500 (1979); “Analogue models of motion perception,” Phil. Trans. R. Soc. London Ser. B 290, 117–135 (1980).
    [Crossref] [PubMed]
  11. E. H. Adelson, “Some new illusions, and some old ones, analyzed in terms of their Fourier components,” Invest. Opthalmol. Vis. Sci. Suppl. 22, 144 (1982).
  12. E. H. Adelson and J. R. Bergen, “Spatio-temporal energy models for the Perception of Motion,”J. Opt. Soc. Am. 73, 1861 (1983).
  13. C. Enroth-Cugell and J. G. Robson, “The contrast sensitivity of retinal ganglion cells of the cat,”J. Physiol. London 187, 517–552 (1966).
    [PubMed]
  14. J. A. Movshon, I. D. Thompson, and D. J. Tolhurst, “Spatial summation in the receptive fields of simple cells in the cat’s striate cortex.”J. Physiol. (London) 283, 79–99 (1978).
  15. F. W. Campbell and J. G. Robson, “Application of Fourier analysis to the visibility of gratings,”J. Physiol. (London) 197, 551–566 (1968).
  16. H. R. Wilson and J. R. Bergen, “A four mechanism model for threshold spatial vision,” Vision Res. 19, 19–33 (1979).
    [Crossref] [PubMed]
  17. O. Braddick, “A short-range process in apparent motion,” Vision Res. 14, 519–529, (1974); “Low-level and high-level processes in apparent motion,” Phil. Trans. R. Soc. London B 290, 137–151 (1980).
    [Crossref] [PubMed]
  18. J. Hochberg and V. Brooks, “The perception of motion pictures,” in Handbook of Perception, E. C. Carterette and M. Friedmen, eds. (Academic, New York, 1978), Vol. 10.
  19. G. Sperling, “Movement perception in computer-driven visual displays,” Behav. Res. Methods Instrum. 8, 144–151 (1976).
    [Crossref]
  20. P. Burt and G. Sperling, “Time, distance, and feature trade-offs in visual apparent motion,” Psych. Rev. 88, 171–195 (1981).
    [Crossref]
  21. A. J. Pantle and L. Picciano, “A multi-stable movement display: Evidence for two separate motion systems in humans,” Science 193, 500–502 (1976).
    [Crossref] [PubMed]
  22. D. E. Pearson, Transmission and Display of Pictorial Information (Wiley, New York, 1975).
  23. A. B. Watson, A. Ahumada, and J. E. Farrell, “The window of visibility: a psychophysical theory of fidelity in time-sampled visual motion displays,”NASA Tech. Paper TP-2211 (1983).
  24. D. H. Hubel and T. N. Wiesel, “Receptive fields of single neurones in the cat’s striate cortex,”J. Physiol. (London) 148, 574–591 (1959).
  25. D. H. Tolhurst and J. A. Movshon, “Spatial and temporal contrast sensitivity of striate cortical neurons,” Nature 257, 674–675 (1975).
    [Crossref] [PubMed]
  26. J. A. Movshon, I. D. Thompson, and D. J. Tolhurst, “Spatial and temporal contrast sensitivity of neurons in areas 17 and 18 of the cat’s visual contex,”J. Physiol. (London) 283, 101–120 (1978).
  27. A. B. Watson and A. J. Ahumada, “A model of how humans sense image motion,” Invest. Opthalmol. Vis. Sci. Suppl. 25, 14 (1984).
  28. A. Pantle and R. Sekuler, “Contrast response of human visual mechanisms sensitive to orientation and motion.” Vision Res. 9, 397–406 (1969).
    [Crossref] [PubMed]
  29. J. R. Bergen and H. R. Wilson, “Prediction of flicker sensitivities from temporal three pulse data,” Vision Res. (to be published).
  30. J. G. Robson, “Spatial and temporal contrast sensitivity functions of the visual system,”J. Opt. Soc. Am. 56, 1141–1142 (1966).
    [Crossref]
  31. D. H. Kelly, “Motion and vision, II. Stabilized spatio-temporal threshold surface,”J. Opt. Soc. Am. 69, 1340–349 (1979).
    [Crossref] [PubMed]
  32. T. J. Long, “Why not compatible high-definition television?”IBA Tech. Rev. 21, 4–12 (1983); T. S. Robson, “Extended-definition television service,” Proc. IEE 129, 485–489 (1982).
  33. A. B. Watson and J. G. Robson, “Discrimination at threshold: labelled detectors in human vision,” Vision Res. 21, 1115–1122 (1981).
    [Crossref] [PubMed]
  34. P. Thompson, “The coding of velocity of movement in the human visual system,” Vision Res. 24, 41–45 (1984).
    [Crossref] [PubMed]
  35. D. J. Tolhurst, “Sustained and transient channels in human vision,” Vision Res. 15, 1151–1155 (1975).
    [Crossref] [PubMed]
  36. E. Levinson and R. Sekuler, “The independence of channels in human vision selective for direction of movement,”J. Physiol. London 250, 347–366 (1975).
    [PubMed]
  37. A. B. Watson, P. G. Thompson, B. J. Murphy, and J. Nachmias, “Summation and discrimination of gratings moving in opposite directions,” Vision Res. 20, 341–347 (1980).
    [Crossref] [PubMed]
  38. C. F. Stromeyer, R. E. Kronauer, J. C. Madsen, and S. A. Klein, “Opponent mechanisms in human vision,” J. Opt. Soc. Am. A 1, 876–884 (1984).
    [Crossref] [PubMed]
  39. P. Thompson, “Perceived rate of movement depends on contrast,” Vision Res. 22, 377–380 (1982).
    [Crossref] [PubMed]
  40. S. M. Anstis and B. J. Rogers, “Illusory reversal of visual depth and movement during changes of contrast,” Vision Res. 15, 957–961 (1975).
    [Crossref] [PubMed]
  41. S. M. Anstis, Department of Psychology, York University, Toronto, Ontario, Canada (personal communication, 1981).
  42. E. H. Adelson and J. A. Movshon “Phenomenal coherence of moving gratings,” Nature 200, 523–525 (1982).
    [Crossref]
  43. M. Fahle and T. Poggio, “Visual hyperacuity: spatio-temporal interpolation in human vision,” Proc. R. Soc. London Ser. B 213, 451–477 (1981).
    [Crossref]

1984 (4)

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

A. B. Watson and A. J. Ahumada, “A model of how humans sense image motion,” Invest. Opthalmol. Vis. Sci. Suppl. 25, 14 (1984).

P. Thompson, “The coding of velocity of movement in the human visual system,” Vision Res. 24, 41–45 (1984).
[Crossref] [PubMed]

C. F. Stromeyer, R. E. Kronauer, J. C. Madsen, and S. A. Klein, “Opponent mechanisms in human vision,” J. Opt. Soc. Am. A 1, 876–884 (1984).
[Crossref] [PubMed]

1983 (2)

T. J. Long, “Why not compatible high-definition television?”IBA Tech. Rev. 21, 4–12 (1983); T. S. Robson, “Extended-definition television service,” Proc. IEE 129, 485–489 (1982).

E. H. Adelson and J. R. Bergen, “Spatio-temporal energy models for the Perception of Motion,”J. Opt. Soc. Am. 73, 1861 (1983).

1982 (3)

E. H. Adelson, “Some new illusions, and some old ones, analyzed in terms of their Fourier components,” Invest. Opthalmol. Vis. Sci. Suppl. 22, 144 (1982).

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

E. H. Adelson and J. A. Movshon “Phenomenal coherence of moving gratings,” Nature 200, 523–525 (1982).
[Crossref]

1981 (4)

M. Fahle and T. Poggio, “Visual hyperacuity: spatio-temporal interpolation in human vision,” Proc. R. Soc. London Ser. B 213, 451–477 (1981).
[Crossref]

A. B. Watson and J. G. Robson, “Discrimination at threshold: labelled detectors in human vision,” Vision Res. 21, 1115–1122 (1981).
[Crossref] [PubMed]

D. Marr and S. Ullman, “Direction selectivity and its use in early visual processing,” Proc. R. Soc. London Ser. B 211, 151–180 (1981).
[Crossref]

P. Burt and G. Sperling, “Time, distance, and feature trade-offs in visual apparent motion,” Psych. Rev. 88, 171–195 (1981).
[Crossref]

1980 (2)

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

A. B. Watson, P. G. Thompson, B. J. Murphy, and J. Nachmias, “Summation and discrimination of gratings moving in opposite directions,” Vision Res. 20, 341–347 (1980).
[Crossref] [PubMed]

1979 (3)

D. H. Kelly, “Motion and vision, II. Stabilized spatio-temporal threshold surface,”J. Opt. Soc. Am. 69, 1340–349 (1979).
[Crossref] [PubMed]

M. J. Morgan, “Perception of continuity in stroboscopic motion: a temporal frequency analysis.” Vision Res 19, 491–500 (1979); “Analogue models of motion perception,” Phil. Trans. R. Soc. London Ser. B 290, 117–135 (1980).
[Crossref] [PubMed]

H. R. Wilson and J. R. Bergen, “A four mechanism model for threshold spatial vision,” Vision Res. 19, 19–33 (1979).
[Crossref] [PubMed]

1978 (2)

J. A. Movshon, I. D. Thompson, and D. J. Tolhurst, “Spatial summation in the receptive fields of simple cells in the cat’s striate cortex.”J. Physiol. (London) 283, 79–99 (1978).

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

1976 (2)

A. J. Pantle and L. Picciano, “A multi-stable movement display: Evidence for two separate motion systems in humans,” Science 193, 500–502 (1976).
[Crossref] [PubMed]

G. Sperling, “Movement perception in computer-driven visual displays,” Behav. Res. Methods Instrum. 8, 144–151 (1976).
[Crossref]

1975 (4)

D. H. Tolhurst and J. A. Movshon, “Spatial and temporal contrast sensitivity of striate cortical neurons,” Nature 257, 674–675 (1975).
[Crossref] [PubMed]

D. J. Tolhurst, “Sustained and transient channels in human vision,” Vision Res. 15, 1151–1155 (1975).
[Crossref] [PubMed]

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

S. M. Anstis and B. J. Rogers, “Illusory reversal of visual depth and movement during changes of contrast,” Vision Res. 15, 957–961 (1975).
[Crossref] [PubMed]

1974 (1)

O. Braddick, “A short-range process in apparent motion,” Vision Res. 14, 519–529, (1974); “Low-level and high-level processes in apparent motion,” Phil. Trans. R. Soc. London B 290, 137–151 (1980).
[Crossref] [PubMed]

1972 (1)

J. S. Lappin and H. H. Bell, “Perceptual differentiation of sequential visual patterns,” Percept. Psychophys. 12, 129–134 (1972).
[Crossref]

1969 (1)

A. Pantle and R. Sekuler, “Contrast response of human visual mechanisms sensitive to orientation and motion.” Vision Res. 9, 397–406 (1969).
[Crossref] [PubMed]

1968 (1)

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

1966 (2)

C. Enroth-Cugell and J. G. Robson, “The contrast sensitivity of retinal ganglion cells of the cat,”J. Physiol. London 187, 517–552 (1966).
[PubMed]

J. G. Robson, “Spatial and temporal contrast sensitivity functions of the visual system,”J. Opt. Soc. Am. 56, 1141–1142 (1966).
[Crossref]

1959 (1)

D. H. Hubel and T. N. Wiesel, “Receptive fields of single neurones in the cat’s striate cortex,”J. Physiol. (London) 148, 574–591 (1959).

Adelson, E. H.

E. H. Adelson and J. R. Bergen, “Spatio-temporal energy models for the Perception of Motion,”J. Opt. Soc. Am. 73, 1861 (1983).

E. H. Adelson, “Some new illusions, and some old ones, analyzed in terms of their Fourier components,” Invest. Opthalmol. Vis. Sci. Suppl. 22, 144 (1982).

E. H. Adelson and J. A. Movshon “Phenomenal coherence of moving gratings,” Nature 200, 523–525 (1982).
[Crossref]

Ahumada, A.

A. B. Watson, A. Ahumada, and J. E. Farrell, “The window of visibility: a psychophysical theory of fidelity in time-sampled visual motion displays,”NASA Tech. Paper TP-2211 (1983).

Ahumada, A. J.

A. B. Watson and A. J. Ahumada, “A model of how humans sense image motion,” Invest. Opthalmol. Vis. Sci. Suppl. 25, 14 (1984).

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

Anstis, S. M.

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

S. M. Anstis and B. J. Rogers, “Illusory reversal of visual depth and movement during changes of contrast,” Vision Res. 15, 957–961 (1975).
[Crossref] [PubMed]

S. M. Anstis, Department of Psychology, York University, Toronto, Ontario, Canada (personal communication, 1981).

S. M. Anstis, “Apparent Movement,” in Handbook of Sensory Physiology, Vol. VIII, Perception, R. Held, H. W. Leibowitz, and H.-L. Teuber, eds. (Springer-Verlag, New York, 1977).

Bell, H. H.

J. S. Lappin and H. H. Bell, “Perceptual differentiation of sequential visual patterns,” Percept. Psychophys. 12, 129–134 (1972).
[Crossref]

Bergen, J. R.

E. H. Adelson and J. R. Bergen, “Spatio-temporal energy models for the Perception of Motion,”J. Opt. Soc. Am. 73, 1861 (1983).

H. R. Wilson and J. R. Bergen, “A four mechanism model for threshold spatial vision,” Vision Res. 19, 19–33 (1979).
[Crossref] [PubMed]

J. R. Bergen and H. R. Wilson, “Prediction of flicker sensitivities from temporal three pulse data,” Vision Res. (to be published).

Braddick, O.

O. Braddick, “A short-range process in apparent motion,” Vision Res. 14, 519–529, (1974); “Low-level and high-level processes in apparent motion,” Phil. Trans. R. Soc. London B 290, 137–151 (1980).
[Crossref] [PubMed]

Brooks, V.

J. Hochberg and V. Brooks, “The perception of motion pictures,” in Handbook of Perception, E. C. Carterette and M. Friedmen, eds. (Academic, New York, 1978), Vol. 10.

Burr, D.

J. Ross and D. Burr, “The psychophysics of motion,” in Proceedings of the Workshop of Vision, Brain, and Cooperative Computation, M. A. Arbib and A. R. Hanson eds. (U. Massachusetts Press, Amherst, Mass., 1983); Vision, Brain, and Cooperative Computation (Bradford, Amherst, Mass., to be published).

Burt, P.

P. Burt and G. Sperling, “Time, distance, and feature trade-offs in visual apparent motion,” Psych. Rev. 88, 171–195 (1981).
[Crossref]

Campbell, F. W.

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

Enroth-Cugell, C.

C. Enroth-Cugell and J. G. Robson, “The contrast sensitivity of retinal ganglion cells of the cat,”J. Physiol. London 187, 517–552 (1966).
[PubMed]

Fahle, M.

M. Fahle and T. Poggio, “Visual hyperacuity: spatio-temporal interpolation in human vision,” Proc. R. Soc. London Ser. B 213, 451–477 (1981).
[Crossref]

Farrell, J. E.

A. B. Watson, A. Ahumada, and J. E. Farrell, “The window of visibility: a psychophysical theory of fidelity in time-sampled visual motion displays,”NASA Tech. Paper TP-2211 (1983).

Hochberg, J.

J. Hochberg and V. Brooks, “The perception of motion pictures,” in Handbook of Perception, E. C. Carterette and M. Friedmen, eds. (Academic, New York, 1978), Vol. 10.

Hubel, D. H.

D. H. Hubel and T. N. Wiesel, “Receptive fields of single neurones in the cat’s striate cortex,”J. Physiol. (London) 148, 574–591 (1959).

Kelly, D. H.

Klein, S. A.

Kronauer, R. E.

Lappin, J. S.

J. S. Lappin and H. H. Bell, “Perceptual differentiation of sequential visual patterns,” Percept. Psychophys. 12, 129–134 (1972).
[Crossref]

Levinson, E.

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

Long, T. J.

T. J. Long, “Why not compatible high-definition television?”IBA Tech. Rev. 21, 4–12 (1983); T. S. Robson, “Extended-definition television service,” Proc. IEE 129, 485–489 (1982).

Madsen, J. C.

Marr, D.

D. Marr and S. Ullman, “Direction selectivity and its use in early visual processing,” Proc. R. Soc. London Ser. B 211, 151–180 (1981).
[Crossref]

Morgan, M. J.

M. J. Morgan, “Perception of continuity in stroboscopic motion: a temporal frequency analysis.” Vision Res 19, 491–500 (1979); “Analogue models of motion perception,” Phil. Trans. R. Soc. London Ser. B 290, 117–135 (1980).
[Crossref] [PubMed]

Movshon, J. A.

E. H. Adelson and J. A. Movshon “Phenomenal coherence of moving gratings,” Nature 200, 523–525 (1982).
[Crossref]

J. A. Movshon, I. D. Thompson, and D. J. Tolhurst, “Spatial summation in the receptive fields of simple cells in the cat’s striate cortex.”J. Physiol. (London) 283, 79–99 (1978).

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

D. H. Tolhurst and J. A. Movshon, “Spatial and temporal contrast sensitivity of striate cortical neurons,” Nature 257, 674–675 (1975).
[Crossref] [PubMed]

Murphy, B. J.

A. B. Watson, P. G. Thompson, B. J. Murphy, and J. Nachmias, “Summation and discrimination of gratings moving in opposite directions,” Vision Res. 20, 341–347 (1980).
[Crossref] [PubMed]

Nachmias, J.

A. B. Watson, P. G. Thompson, B. J. Murphy, and J. Nachmias, “Summation and discrimination of gratings moving in opposite directions,” Vision Res. 20, 341–347 (1980).
[Crossref] [PubMed]

Pantle, A.

A. Pantle and R. Sekuler, “Contrast response of human visual mechanisms sensitive to orientation and motion.” Vision Res. 9, 397–406 (1969).
[Crossref] [PubMed]

Pantle, A. J.

A. J. Pantle and L. Picciano, “A multi-stable movement display: Evidence for two separate motion systems in humans,” Science 193, 500–502 (1976).
[Crossref] [PubMed]

Pearson, D. E.

D. E. Pearson, Transmission and Display of Pictorial Information (Wiley, New York, 1975).

Picciano, L.

A. J. Pantle and L. Picciano, “A multi-stable movement display: Evidence for two separate motion systems in humans,” Science 193, 500–502 (1976).
[Crossref] [PubMed]

Poggio, T.

M. Fahle and T. Poggio, “Visual hyperacuity: spatio-temporal interpolation in human vision,” Proc. R. Soc. London Ser. B 213, 451–477 (1981).
[Crossref]

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).

Robson, J. G.

A. B. Watson and J. G. Robson, “Discrimination at threshold: labelled detectors in human vision,” Vision Res. 21, 1115–1122 (1981).
[Crossref] [PubMed]

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

C. Enroth-Cugell and J. G. Robson, “The contrast sensitivity of retinal ganglion cells of the cat,”J. Physiol. London 187, 517–552 (1966).
[PubMed]

J. G. Robson, “Spatial and temporal contrast sensitivity functions of the visual system,”J. Opt. Soc. Am. 56, 1141–1142 (1966).
[Crossref]

Rogers, B. J.

S. M. Anstis and B. J. Rogers, “Illusory reversal of visual depth and movement during changes of contrast,” Vision Res. 15, 957–961 (1975).
[Crossref] [PubMed]

Ross, J.

J. Ross and D. Burr, “The psychophysics of motion,” in Proceedings of the Workshop of Vision, Brain, and Cooperative Computation, M. A. Arbib and A. R. Hanson eds. (U. Massachusetts Press, Amherst, Mass., 1983); Vision, Brain, and Cooperative Computation (Bradford, Amherst, Mass., to be published).

Sekuler, R.

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

A. Pantle and R. Sekuler, “Contrast response of human visual mechanisms sensitive to orientation and motion.” Vision Res. 9, 397–406 (1969).
[Crossref] [PubMed]

Sperling, G.

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

P. Burt and G. Sperling, “Time, distance, and feature trade-offs in visual apparent motion,” Psych. Rev. 88, 171–195 (1981).
[Crossref]

G. Sperling, “Movement perception in computer-driven visual displays,” Behav. Res. Methods Instrum. 8, 144–151 (1976).
[Crossref]

Stromeyer, C. F.

Thompson, I. D.

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

J. A. Movshon, I. D. Thompson, and D. J. Tolhurst, “Spatial summation in the receptive fields of simple cells in the cat’s striate cortex.”J. Physiol. (London) 283, 79–99 (1978).

Thompson, P.

P. Thompson, “The coding of velocity of movement in the human visual system,” Vision Res. 24, 41–45 (1984).
[Crossref] [PubMed]

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

Thompson, P. G.

A. B. Watson, P. G. Thompson, B. J. Murphy, and J. Nachmias, “Summation and discrimination of gratings moving in opposite directions,” Vision Res. 20, 341–347 (1980).
[Crossref] [PubMed]

Tolhurst, D. H.

D. H. Tolhurst and J. A. Movshon, “Spatial and temporal contrast sensitivity of striate cortical neurons,” Nature 257, 674–675 (1975).
[Crossref] [PubMed]

Tolhurst, D. J.

J. A. Movshon, I. D. Thompson, and D. J. Tolhurst, “Spatial summation in the receptive fields of simple cells in the cat’s striate cortex.”J. Physiol. (London) 283, 79–99 (1978).

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

D. J. Tolhurst, “Sustained and transient channels in human vision,” Vision Res. 15, 1151–1155 (1975).
[Crossref] [PubMed]

Ullman, S.

D. Marr and S. Ullman, “Direction selectivity and its use in early visual processing,” Proc. R. Soc. London Ser. B 211, 151–180 (1981).
[Crossref]

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A. B. Watson, A. Ahumada, and J. E. Farrell, “The window of visibility: a psychophysical theory of fidelity in time-sampled visual motion displays,”NASA Tech. Paper TP-2211 (1983).

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Other (10)

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J. R. Bergen and H. R. Wilson, “Prediction of flicker sensitivities from temporal three pulse data,” Vision Res. (to be published).

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Figures (18)

Fig. 1
Fig. 1 a, A sequence of images presented at times t1, t2, and t3 showing a bar moving to the right. b, A sequence of vertical random noise patterns, also shown at three successive instants of time. Motion is seen in each case. The motion percept is simple in a and complex in b, but a motion model should be able to handle both cases.

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Fig. 2
Fig. 2 a, A picture of a vertical bar moving to the right. b, A spatiotemporal picture of the same stimulus. Time forms the third dimension. c, A spatiotemporal picture of a moving bar sampled in time (i.e., a movie).

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Fig. 3
Fig. 3 a, An (x, t) plot of a bar moving to the right over time. Time proceeds downward. The vertical dimension is not shown. b, An (x, t) plot of the same bar, sampled in time. c, The sampled motion as displayed in a movie in which each frame remains on until the next one appears. d, Continuous motion after spatiotemporal blurring. e, Sampled motion after spatiotemporal blurring. The middle- and low-frequency information is almost the same for the two stimuli.

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Fig. 4
Fig. 4 (x, t) plots of moving bars. a, A movie of a bar moving to the right. b, A bar moving to the right continuously. c, The difference (sampling artifacts) between the sampled and continuous motions. d, A movie sampled at a high frame rate. e, Continuous motion. f, The difference between the finely sampled and continuous motion. When the sampling rate is high, the sampling artifacts become difficult or impossible to see.

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Fig. 5
Fig. 5 a–e, (x, t) plots of bars moving to the left or to the right at various speeds. f, Motion is like orientation in (x, t), and a spatiotemporally oriented receptive field can be used to detect it. g, The same oriented receptive field can respond to sampled motion just as it responds to continuous motion.

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Fig. 6
Fig. 6 A spatiotemporally separable impulse response. The spatial and temporal impulse responses are shown along the margins. Their product is shown schematically in the center. The spatiotemporal impulse response is a weighting function that sums inputs at various positions and times to determine the present output.

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Fig. 7
Fig. 7 One may think of a spatiotemporal impulse response as being fixed, while the spatiotemporal stimulus slides beneath it as if pulled along on a strip. At any moment, the integral of the pointwise product of the two functions determines the output; i.e., the two functions are convolved in time (the impulse response is time reversed here; otherwise the operation would be a correlation). This particular unit will respond strongly when the motion lies within its receptive field but will not respond to blank areas or areas without motion.

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Fig. 8
Fig. 8 a, An (x, t) plot of an edge that is stationary, then moves sinusoidally, and then is stationary again. b, A separable spatiotemporal impulse response, magnified four times for clarity. c, The convolution of a and b, i,e., the output of a separable channel. There is no selectivity for direction of motion. d The stimulus again. e, A spatiotemporally oriented Gabor function, magnified four times. f, The convolution of d and e. The output is strongly selective for rightward motion.

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Fig. 9
Fig. 9 a, Two linear filters, whose responses are 90 deg out of phase, form a quadrature pair. If their responses are squared and summed, the resulting signal gives a phase-independent measure of local motion energy (within a given spatial-frequency band). The filters shown here resemble spatiotemporally oriented Gabor functions. To approximate such functions, a number of separable filters b–e, which are shifted in phase and time, can be summed to form f.

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Fig. 10
Fig. 10 A method for constructing spatiotemporally oriented impulse responses from pairs of separable ones, following Watson and Ahumada.8 Two spatial and two temporal impulse responses are shown in a and b. The four spatiotemporal impulse responses shown across the top of c are the products of two spatial and two temporal impulse responses. The ones across the bottom are sums and differences of those above. The result is a pair of leftward- and a pair of rightward-selective filters. Members of a pair are approximately in quadrature.

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Fig. 11
Fig. 11 The spatiotemporal energy spectrum of a direction-selective filter built as the sum of two separable filters.

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Fig. 12
Fig. 12 A spatiotemporal-frequency plot showing the sensitivities of rightward (R), leftward (L), and stationary (S) units. Similar units are presumed to cover the entire visible region of the spatiotemporal spectrum (the bounds of which are shown by the dashed line).

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Fig. 13
Fig. 13 The time courses of the responses of various stages to a light or a dark bar, moving to the left or to the right. Responses are shown for idealized filters to make the qualitative differences clear. The separable linear stage responds to both polarities and both directions of motion. The spatiotemporally oriented linear stage responds only to rightward motion; the response oscillates and depends on the polarity of the bar. The spatiotemporally oriented energy stage responds to rightward motion only and gives the same positive response regardless of bar polarity. The opponent-energy stage gives a positive response to rightward motion and a negative response to leftward motion, regardless of bar polarity.

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Fig. 14
Fig. 14 The overlapping response curves of three motion units plotted as a function of velocity. Any single unit’s response is a function of both the velocity and the contrast of a stimulus. However, the relative responses of the various units can be used to compute a measure of velocity that is invariant with contrast.

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Fig. 15
Fig. 15 a, An (x, t) plot of a stimulus consisting of a moving light–dark edge. b, The response of a rightward-energy unit. c, A leftward-energy unit. d, An opponent-energy unit; e, A static unit. f, An (x, t) plot of a movie of the stimulus shown in a. g–j, The responses of units selective for rightward energy, leftward energy, opponent energy, and static energy, respectively.

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Fig. 16
Fig. 16 a, An (x, t) plot of a random bar pattern, moving to the right in steps. b The reverse-phi version: The pattern moves to the right and the bars reverse polarity on each step. c, The response of an opponent-energy channel to normal motion. The response is mainly positive, signaling rightward motion. d, The response of the channel to the reverse-phi display. Now the response is mainly negative, signaling leftward motion.

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Fig. 17
Fig. 17 a, An (x, t) plot of a square wave’s motion. b, A (x, t) plot of a fluted square wave’s motion. c, The response of a medium spatial-frequency opponent-motion channel when stimulated by the square wave. Rightward motion (bright) is signaled. d, The response of the same channel when stimulated by the fluted square wave. Leftward motion (dark) is signaled.

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Fig. 18
Fig. 18 (a) A version of the Reichardt model that is formally equivalent to a version of an energy model. The visual input I(x, t) passes the two spatial impulse responses f1(x) and f2(x). Following van Santen and Sperling,6 these functions can be bandpass, differing in phase. or in position. Each output passes through the two temporal functions h1(t) and h2(t), where h2(t) is more low passed or more delayed than h1(t). The four separable responses are labeled A, A′, B, and B′. The products AB′ and BA′ are generated, and their difference constitutes the final output. (b) An equivalent spatiotemporal energy model. The same spatial and temporal filters are used. Sums and differences generate directionally selective filters. Sums of squares of quadrature pairs give motion energy for each direction. The difference between the rightward and leftward signals gives the final output. This turns out to be identical with the output of the Reichardt model. The equivalence holds only for energy models that are based on sums of separable filter pairs.

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Equations (2)

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f ( t ) = ( k t ) n   exp ( - k t ) [ 1 / n ! - ( k t ) 2 / ( n + 2 ) ! ] ,
A ( t ) = h 1 ( t ) * [ I ( x , t ) · f 1 ( x ) ] ,

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