Abstract

It is generally assumed that the perception of non-Fourier motion requires the operation of some nonlinearity before motion analysis. We apply a computational model of biological motion processing to a class of non-Fourier motion stimuli designed to investigate nonlinearity in human visual processing. The model correctly detects direction of motion in these non-Fourier stimuli without recourse to any preprocessing nonlinearity. This demonstrates that the non-Fourier motion in some non-Fourier stimuli is directly available to luminance-based motion mechanisms operating on measurements of local spatial and temporal gradients.

© 2001 Optical Society of America

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References

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  1. A. B. Watson, A. J. Ahumada, A Look at Motion in the Frequency Domain (Ames Research Center, Moffett Field, Calif., 1983).
  2. A. B. Watson, A. J. Ahumada, “Model of human visual-motion sensing,” J. Opt. Soc. Am. A 2, 322–341 (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. 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.
  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. Johnston, P. W. McOwan, H. Buxton, “A computational model of the analysis of some first-order and second-order motion patterns by simple and complex cells,” Proc. R. Soc. London Ser. B 250, 297–306 (1992).
    [CrossRef]
  8. A. Johnston, P. W. McOwan, C. P. Benton, “Robust velocity computation from a biologically motivated model of motion perception,” Proc. R. Soc. London Ser. B 266, 509–518 (1999).
    [CrossRef]
  9. C. Chubb, G. Sperling, “Drift-balanced random dot stimuli: a general basis for studying non-Fourier motion perception,” J. Opt. Soc. Am. A 5, 1986–2007 (1988).
    [CrossRef] [PubMed]
  10. C. P. Benton, A. Johnston, “First-order motion from contrast modulated noise?” Vision Res. 37, 3073–3078 (1997).
    [CrossRef]
  11. E. Taub, J. D. Victor, M. M. Conte, “Nonlinear preprocessing in short-range motion,” Vision Res. 37, 1459–1477 (1997).
    [CrossRef] [PubMed]
  12. C. P. Benton, A. Johnston, P. W. McOwan, “Computational modelling of interleaved first-and second-order motion sequences and translating 3f+4f beat patterns,” Vision Res. 40, 1135–1142 (2000).
    [CrossRef]
  13. C. L. Fennema, W. B. Thompson, “Velocity determination in scenes containing several moving objects,” Comput. Graph. Image Process. 9, 301–315 (1979).
    [CrossRef]
  14. B. K. P. Horn, B. G. Schunck, “Determining optical flow,” Artif. Intel. 17, 185–203 (1981).
    [CrossRef]
  15. A. Johnston, C. W. G. Clifford, “A unified account of three apparent motion illusions,” Vision Res. 35, 1109–1123 (1995).
    [CrossRef] [PubMed]
  16. A. Johnston, C. P. Benton, P. W. McOwan, “Induced motion at texture-define motion boundaries,” Proc. R. Soc. London Ser. B 266, 2441–2459 (1999).
    [CrossRef]
  17. C. P. Benton, A. Johnston, P. W. McOwan, “Perception of motion direction in luminance- and contrast-defined reversed-phi motion sequences,” Vision Res. 37, 2381–2399 (1997).
    [CrossRef] [PubMed]
  18. C. Chubb, G. Sperling, “Two motion perception mechanisms revealed through distance-driven reversal of apparent motion,” Proc. Natl. Acad. Sci. U.S.A. 86, 2985–2989 (1989).
    [CrossRef] [PubMed]
  19. S. Shioiri, P. Cavanagh, “ISI produces reverse apparent motion,” Vision Res. 30, 757–768 (1990).
    [CrossRef] [PubMed]
  20. M. A. Georgeson, M. G. Harris, “The temporal range of motion sensing and motion perception,” Vision Res. 30, 615–619 (1990).
    [CrossRef] [PubMed]
  21. A. Pantle, K. Turano, “Visual resolution of motion ambiguity with periodic luminance- and contrast-domain stimuli,” Vision Res. 32, 2093–2106 (1992).
    [CrossRef] [PubMed]
  22. S. T. Hammett, T. Ledgeway, A. T. Smith, “Transparent motion from feature- and luminance-based processes,” Vision Res. 33, 1119–1122 (1993).
    [CrossRef] [PubMed]
  23. T. Ledgeway, A. T. Smith, “Evidence for separate mechanisms for first- and second-order motion in human vision,” Vision Res. 34, 2727–2740 (1994).
    [CrossRef] [PubMed]

2000 (1)

C. P. Benton, A. Johnston, P. W. McOwan, “Computational modelling of interleaved first-and second-order motion sequences and translating 3f+4f beat patterns,” Vision Res. 40, 1135–1142 (2000).
[CrossRef]

1999 (2)

A. Johnston, C. P. Benton, P. W. McOwan, “Induced motion at texture-define motion boundaries,” Proc. R. Soc. London Ser. B 266, 2441–2459 (1999).
[CrossRef]

A. Johnston, P. W. McOwan, C. P. Benton, “Robust velocity computation from a biologically motivated model of motion perception,” Proc. R. Soc. London Ser. B 266, 509–518 (1999).
[CrossRef]

1997 (3)

C. P. Benton, A. Johnston, P. W. McOwan, “Perception of motion direction in luminance- and contrast-defined reversed-phi motion sequences,” Vision Res. 37, 2381–2399 (1997).
[CrossRef] [PubMed]

C. P. Benton, A. Johnston, “First-order motion from contrast modulated noise?” Vision Res. 37, 3073–3078 (1997).
[CrossRef]

E. Taub, J. D. Victor, M. M. Conte, “Nonlinear preprocessing in short-range motion,” Vision Res. 37, 1459–1477 (1997).
[CrossRef] [PubMed]

1995 (1)

A. Johnston, C. W. G. Clifford, “A unified account of three apparent motion illusions,” Vision Res. 35, 1109–1123 (1995).
[CrossRef] [PubMed]

1994 (1)

T. Ledgeway, A. T. Smith, “Evidence for separate mechanisms for first- and second-order motion in human vision,” Vision Res. 34, 2727–2740 (1994).
[CrossRef] [PubMed]

1993 (1)

S. T. Hammett, T. Ledgeway, A. T. Smith, “Transparent motion from feature- and luminance-based processes,” Vision Res. 33, 1119–1122 (1993).
[CrossRef] [PubMed]

1992 (2)

A. Pantle, K. Turano, “Visual resolution of motion ambiguity with periodic luminance- and contrast-domain stimuli,” Vision Res. 32, 2093–2106 (1992).
[CrossRef] [PubMed]

A. Johnston, P. W. McOwan, H. Buxton, “A computational model of the analysis of some first-order and second-order motion patterns by simple and complex cells,” Proc. R. Soc. London Ser. B 250, 297–306 (1992).
[CrossRef]

1990 (2)

S. Shioiri, P. Cavanagh, “ISI produces reverse apparent motion,” Vision Res. 30, 757–768 (1990).
[CrossRef] [PubMed]

M. A. Georgeson, M. G. Harris, “The temporal range of motion sensing and motion perception,” Vision Res. 30, 615–619 (1990).
[CrossRef] [PubMed]

1989 (1)

C. Chubb, G. Sperling, “Two motion perception mechanisms revealed through distance-driven reversal of apparent motion,” Proc. Natl. Acad. Sci. U.S.A. 86, 2985–2989 (1989).
[CrossRef] [PubMed]

1988 (1)

1985 (3)

1984 (1)

1981 (1)

B. K. P. Horn, B. G. Schunck, “Determining optical flow,” Artif. Intel. 17, 185–203 (1981).
[CrossRef]

1979 (1)

C. L. Fennema, W. B. Thompson, “Velocity determination in scenes containing several moving objects,” Comput. Graph. Image Process. 9, 301–315 (1979).
[CrossRef]

Adelson, E. H.

Ahumada, A. J.

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

A. B. Watson, A. J. Ahumada, A Look at Motion in the Frequency Domain (Ames Research Center, Moffett Field, Calif., 1983).

Benton, C. P.

C. P. Benton, A. Johnston, P. W. McOwan, “Computational modelling of interleaved first-and second-order motion sequences and translating 3f+4f beat patterns,” Vision Res. 40, 1135–1142 (2000).
[CrossRef]

A. Johnston, P. W. McOwan, C. P. Benton, “Robust velocity computation from a biologically motivated model of motion perception,” Proc. R. Soc. London Ser. B 266, 509–518 (1999).
[CrossRef]

A. Johnston, C. P. Benton, P. W. McOwan, “Induced motion at texture-define motion boundaries,” Proc. R. Soc. London Ser. B 266, 2441–2459 (1999).
[CrossRef]

C. P. Benton, A. Johnston, “First-order motion from contrast modulated noise?” Vision Res. 37, 3073–3078 (1997).
[CrossRef]

C. P. Benton, A. Johnston, P. W. McOwan, “Perception of motion direction in luminance- and contrast-defined reversed-phi motion sequences,” Vision Res. 37, 2381–2399 (1997).
[CrossRef] [PubMed]

Bergen, J. R.

Buxton, H.

A. Johnston, P. W. McOwan, H. Buxton, “A computational model of the analysis of some first-order and second-order motion patterns by simple and complex cells,” Proc. R. Soc. London Ser. B 250, 297–306 (1992).
[CrossRef]

Cavanagh, P.

S. Shioiri, P. Cavanagh, “ISI produces reverse apparent motion,” Vision Res. 30, 757–768 (1990).
[CrossRef] [PubMed]

Chubb, C.

C. Chubb, G. Sperling, “Two motion perception mechanisms revealed through distance-driven reversal of apparent motion,” Proc. Natl. Acad. Sci. U.S.A. 86, 2985–2989 (1989).
[CrossRef] [PubMed]

C. Chubb, G. Sperling, “Drift-balanced random dot stimuli: a general basis for studying non-Fourier motion perception,” J. Opt. Soc. Am. A 5, 1986–2007 (1988).
[CrossRef] [PubMed]

Clifford, C. W. G.

A. Johnston, C. W. G. Clifford, “A unified account of three apparent motion illusions,” Vision Res. 35, 1109–1123 (1995).
[CrossRef] [PubMed]

Conte, M. M.

E. Taub, J. D. Victor, M. M. Conte, “Nonlinear preprocessing in short-range motion,” Vision Res. 37, 1459–1477 (1997).
[CrossRef] [PubMed]

Fennema, C. L.

C. L. Fennema, W. B. Thompson, “Velocity determination in scenes containing several moving objects,” Comput. Graph. Image Process. 9, 301–315 (1979).
[CrossRef]

Georgeson, M. A.

M. A. Georgeson, M. G. Harris, “The temporal range of motion sensing and motion perception,” Vision Res. 30, 615–619 (1990).
[CrossRef] [PubMed]

Hammett, S. T.

S. T. Hammett, T. Ledgeway, A. T. Smith, “Transparent motion from feature- and luminance-based processes,” Vision Res. 33, 1119–1122 (1993).
[CrossRef] [PubMed]

Harris, M. G.

M. A. Georgeson, M. G. Harris, “The temporal range of motion sensing and motion perception,” Vision Res. 30, 615–619 (1990).
[CrossRef] [PubMed]

Horn, B. K. P.

B. K. P. Horn, B. G. Schunck, “Determining optical flow,” Artif. Intel. 17, 185–203 (1981).
[CrossRef]

Johnston, A.

C. P. Benton, A. Johnston, P. W. McOwan, “Computational modelling of interleaved first-and second-order motion sequences and translating 3f+4f beat patterns,” Vision Res. 40, 1135–1142 (2000).
[CrossRef]

A. Johnston, P. W. McOwan, C. P. Benton, “Robust velocity computation from a biologically motivated model of motion perception,” Proc. R. Soc. London Ser. B 266, 509–518 (1999).
[CrossRef]

A. Johnston, C. P. Benton, P. W. McOwan, “Induced motion at texture-define motion boundaries,” Proc. R. Soc. London Ser. B 266, 2441–2459 (1999).
[CrossRef]

C. P. Benton, A. Johnston, “First-order motion from contrast modulated noise?” Vision Res. 37, 3073–3078 (1997).
[CrossRef]

C. P. Benton, A. Johnston, P. W. McOwan, “Perception of motion direction in luminance- and contrast-defined reversed-phi motion sequences,” Vision Res. 37, 2381–2399 (1997).
[CrossRef] [PubMed]

A. Johnston, C. W. G. Clifford, “A unified account of three apparent motion illusions,” Vision Res. 35, 1109–1123 (1995).
[CrossRef] [PubMed]

A. Johnston, P. W. McOwan, H. Buxton, “A computational model of the analysis of some first-order and second-order motion patterns by simple and complex cells,” Proc. R. Soc. London Ser. B 250, 297–306 (1992).
[CrossRef]

Ledgeway, T.

T. Ledgeway, A. T. Smith, “Evidence for separate mechanisms for first- and second-order motion in human vision,” Vision Res. 34, 2727–2740 (1994).
[CrossRef] [PubMed]

S. T. Hammett, T. Ledgeway, A. T. Smith, “Transparent motion from feature- and luminance-based processes,” Vision Res. 33, 1119–1122 (1993).
[CrossRef] [PubMed]

McOwan, P. W.

C. P. Benton, A. Johnston, P. W. McOwan, “Computational modelling of interleaved first-and second-order motion sequences and translating 3f+4f beat patterns,” Vision Res. 40, 1135–1142 (2000).
[CrossRef]

A. Johnston, P. W. McOwan, C. P. Benton, “Robust velocity computation from a biologically motivated model of motion perception,” Proc. R. Soc. London Ser. B 266, 509–518 (1999).
[CrossRef]

A. Johnston, C. P. Benton, P. W. McOwan, “Induced motion at texture-define motion boundaries,” Proc. R. Soc. London Ser. B 266, 2441–2459 (1999).
[CrossRef]

C. P. Benton, A. Johnston, P. W. McOwan, “Perception of motion direction in luminance- and contrast-defined reversed-phi motion sequences,” Vision Res. 37, 2381–2399 (1997).
[CrossRef] [PubMed]

A. Johnston, P. W. McOwan, H. Buxton, “A computational model of the analysis of some first-order and second-order motion patterns by simple and complex cells,” Proc. R. Soc. London Ser. B 250, 297–306 (1992).
[CrossRef]

Pantle, A.

A. Pantle, K. Turano, “Visual resolution of motion ambiguity with periodic luminance- and contrast-domain stimuli,” Vision Res. 32, 2093–2106 (1992).
[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.

Schunck, B. G.

B. K. P. Horn, B. G. Schunck, “Determining optical flow,” Artif. Intel. 17, 185–203 (1981).
[CrossRef]

Shioiri, S.

S. Shioiri, P. Cavanagh, “ISI produces reverse apparent motion,” Vision Res. 30, 757–768 (1990).
[CrossRef] [PubMed]

Smith, A. T.

T. Ledgeway, A. T. Smith, “Evidence for separate mechanisms for first- and second-order motion in human vision,” Vision Res. 34, 2727–2740 (1994).
[CrossRef] [PubMed]

S. T. Hammett, T. Ledgeway, A. T. Smith, “Transparent motion from feature- and luminance-based processes,” Vision Res. 33, 1119–1122 (1993).
[CrossRef] [PubMed]

Sperling, G.

Taub, E.

E. Taub, J. D. Victor, M. M. Conte, “Nonlinear preprocessing in short-range motion,” Vision Res. 37, 1459–1477 (1997).
[CrossRef] [PubMed]

Thompson, W. B.

C. L. Fennema, W. B. Thompson, “Velocity determination in scenes containing several moving objects,” Comput. Graph. Image Process. 9, 301–315 (1979).
[CrossRef]

Turano, K.

A. Pantle, K. Turano, “Visual resolution of motion ambiguity with periodic luminance- and contrast-domain stimuli,” Vision Res. 32, 2093–2106 (1992).
[CrossRef] [PubMed]

van Santen, J. P. H.

Victor, J. D.

E. Taub, J. D. Victor, M. M. Conte, “Nonlinear preprocessing in short-range motion,” Vision Res. 37, 1459–1477 (1997).
[CrossRef] [PubMed]

Watson, A. B.

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

A. B. Watson, A. J. Ahumada, A Look at Motion in the Frequency Domain (Ames Research Center, Moffett Field, Calif., 1983).

Artif. Intel. (1)

B. K. P. Horn, B. G. Schunck, “Determining optical flow,” Artif. Intel. 17, 185–203 (1981).
[CrossRef]

Comput. Graph. Image Process. (1)

C. L. Fennema, W. B. Thompson, “Velocity determination in scenes containing several moving objects,” Comput. Graph. Image Process. 9, 301–315 (1979).
[CrossRef]

J. Opt. Soc. Am. A (5)

Proc. Natl. Acad. Sci. U.S.A. (1)

C. Chubb, G. Sperling, “Two motion perception mechanisms revealed through distance-driven reversal of apparent motion,” Proc. Natl. Acad. Sci. U.S.A. 86, 2985–2989 (1989).
[CrossRef] [PubMed]

Proc. R. Soc. London Ser. B (3)

A. Johnston, C. P. Benton, P. W. McOwan, “Induced motion at texture-define motion boundaries,” Proc. R. Soc. London Ser. B 266, 2441–2459 (1999).
[CrossRef]

A. Johnston, P. W. McOwan, H. Buxton, “A computational model of the analysis of some first-order and second-order motion patterns by simple and complex cells,” Proc. R. Soc. London Ser. B 250, 297–306 (1992).
[CrossRef]

A. Johnston, P. W. McOwan, C. P. Benton, “Robust velocity computation from a biologically motivated model of motion perception,” Proc. R. Soc. London Ser. B 266, 509–518 (1999).
[CrossRef]

Vision Res. (10)

C. P. Benton, A. Johnston, P. W. McOwan, “Perception of motion direction in luminance- and contrast-defined reversed-phi motion sequences,” Vision Res. 37, 2381–2399 (1997).
[CrossRef] [PubMed]

A. Johnston, C. W. G. Clifford, “A unified account of three apparent motion illusions,” Vision Res. 35, 1109–1123 (1995).
[CrossRef] [PubMed]

C. P. Benton, A. Johnston, “First-order motion from contrast modulated noise?” Vision Res. 37, 3073–3078 (1997).
[CrossRef]

E. Taub, J. D. Victor, M. M. Conte, “Nonlinear preprocessing in short-range motion,” Vision Res. 37, 1459–1477 (1997).
[CrossRef] [PubMed]

C. P. Benton, A. Johnston, P. W. McOwan, “Computational modelling of interleaved first-and second-order motion sequences and translating 3f+4f beat patterns,” Vision Res. 40, 1135–1142 (2000).
[CrossRef]

S. Shioiri, P. Cavanagh, “ISI produces reverse apparent motion,” Vision Res. 30, 757–768 (1990).
[CrossRef] [PubMed]

M. A. Georgeson, M. G. Harris, “The temporal range of motion sensing and motion perception,” Vision Res. 30, 615–619 (1990).
[CrossRef] [PubMed]

A. Pantle, K. Turano, “Visual resolution of motion ambiguity with periodic luminance- and contrast-domain stimuli,” Vision Res. 32, 2093–2106 (1992).
[CrossRef] [PubMed]

S. T. Hammett, T. Ledgeway, A. T. Smith, “Transparent motion from feature- and luminance-based processes,” Vision Res. 33, 1119–1122 (1993).
[CrossRef] [PubMed]

T. Ledgeway, A. T. Smith, “Evidence for separate mechanisms for first- and second-order motion in human vision,” Vision Res. 34, 2727–2740 (1994).
[CrossRef] [PubMed]

Other (2)

A. B. Watson, A. J. Ahumada, A Look at Motion in the Frequency Domain (Ames Research Center, Moffett Field, Calif., 1983).

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 (2)

Fig. 1
Fig. 1

(a) Binary noise pattern. (b) Two sine waves separated by half a cycle. (c) Snapshot of a contrast modulation of noise created by sampling the two sine waves shown in (b) with the noise sample shown in (a). When the value of the noise is 1, then the dotted sine wave is selected; when the value of the noise is -1, then the sine wave indicated by the solid curve is selected. Note that in the example shown here there is spatial variation within noise elements. However, for the stimuli used in this study there was no spatial variation within noise elements.

Fig. 2
Fig. 2

Mean directional index as a function of stimulus type [see Eq. (5)]. Error bars show standard deviations. The dotted horizontal line marks a directional index of zero, where no overall motion is indicated by the model.

Equations (5)

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

I(x, y, t)=I0[1+cos(ky+ωt)R(x, y)],
K(r, t)=14πσexp(-r2/4σ) 1πτα exp(τ2/4)×exp{-[ln(t/α)/τ]2},
I(x, y, t)=I0[1+Pn(x, y, t)],
Pn(x, y, t)=cos[ky+ωt+(2π/n)R(x, y)].
Directionalindex=(|V|-|V|)/(|V|+|V|).

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