Abstract

Motion in the retinal image may occur either in the form of spatiotemporal variations in luminance (first-order motion) or as spatiotemporal variations in characteristics derived from luminance, such as contrast (second-order motion). Second-order motion patterns were employed in an attempt to establish the principles used for the detection of image motion in the human visual system. In principle, one can detect motion at a high level of visual analysis by identifying features of the image and tracking their positions (correspondence-based detection) or at a low level by analysis of spatiotemporal luminance variations without reference to features (intensity-based detection). Prevailing models favor the latter approach, which has been adapted to account for the visibility of second-order motion by postulation of a stage of rectification that precedes motion energy detection [ J. Opt. Soc. Am. A 5, 1986 ( 1988)]. In two experiments it is shown that second-order motion is indeed detected normally by use of the strategy of transformation plus energy detection but that detection can also be achieved by use of the feature-correspondence strategy when the intensity strategy fails. In the first experiment, a stimulus is employed in which opposite directions of motion perception are predicted by the two strategies. It is shown that normally the direction associated with motion energy in the rectified image is seen but that the direction associated with feature motion is seen when the energy system is disabled by the use of an interstimulus interval. In the second experiment, masking of features is shown to have little effect on motion detection under normal conditions but a marked effect when an interstimulus interval is employed, suggesting that features are used in the latter case but not in the former.

© 1994 Optical Society of America

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References

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  1. S. Ullman, The Interpretation of Visual Motion (MIT Press, Cambridge, Mass., 1979).
  2. 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]
  3. O. Braddick, “A short-range process in apparent motion,” Vision Res. 14, 519–527 (1974).
    [CrossRef] [PubMed]
  4. O. J. Braddick, “Low-level and high-level processes in apparent motion,” Phil. Trans. R. Soc. London B 290, 137–151 (1980).
    [CrossRef]
  5. S. M. Anstis, “The perception of apparent movement,” Phil. Trans. R. Soc. London B 290, 153–168 (1980).
    [CrossRef]
  6. P. Cavanagh, G. Mather, “Motion: the long and short of it,” Spatial Vis. 4, 103–129 (1989).
    [CrossRef]
  7. P. Cavanagh, “Short-range vs. long-range motion: not a valid distinction,” Spatial Vis. 5, 303–309 (1991).
    [CrossRef]
  8. P. Cavanagh, “Attention-based motion perception,” Science 257, 1563–1565 (1992).
    [CrossRef] [PubMed]
  9. C. Chubb, G. Sperling, “Drift-balanced random stimuli: a general basis for studying non-Fourier motion perception,” J. Opt. Soc. Am. A 5, 1986–2006 (1988).
    [CrossRef] [PubMed]
  10. H. R. Wilson, V. P. Ferrera, C. Yo, “A psychophysically motivated model for two-dimensional motion perception,” Vis. Neurosci. 9, 79–97 (1992).
    [CrossRef] [PubMed]
  11. E. H. Adelson, “Some new motion illusions, and some old ones, analyzed in terms of their Fourier components,” Invest. Ophthalmol. Vis. Sci. Suppl. 34, 144 (1982).
  12. M. A. Georgeson, T. M. Shackleton, “Monocular motion sensing, binocular motion perception,” Vision Res. 29, 1511–1523 (1989).
    [CrossRef] [PubMed]
  13. M. A. Georgeson, M. G. Harris, “The temporal range of motion sensing and motion perception,” Vision Res. 30, 615–619 (1990).
    [CrossRef] [PubMed]
  14. S. T. Hamett, T. Ledgeway, A. T. Smith, “Transparent motion from feature and luminance-based processes,” Vision Res. 33, 1119–1122 (1993).
    [CrossRef]
  15. G. B. Henning, B. G. Hertz, D. E. Broadbent, “Some experiments bearing on the hypothesis that the visual system analyses spatial patterns in independent bands of spatial frequency,” Vision Res. 15, 887–897 (1975).
    [CrossRef] [PubMed]
  16. W. Weibull, “A statistical distribution function of wide applicability,” J. Appl. Mech. 18, 292–297 (1951).
  17. A. T. Smith, R. F. Hess, J. C. L. Baker, “Direction identification thresholds for second-order motion in central and peripheral vision,” J. Opt. Soc. Am. A 11, 506–514 (1994).
    [CrossRef]
  18. S. J. Anderson, D. C. Burr, “Spatial and temporal selectivity of the human motion detecting system,” Vision Res. 25, 1147–1154 (1985).
    [CrossRef]
  19. A. Johnston, P. W. McOwen, 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 B 250, 297–306 (1992).
    [CrossRef]
  20. N. M. Grzywacz, “One-path model for contrast-independent perception of Fourier and non-Fourier motions,” Invest. Ophthalmol. Vis. Sci. 33, 954 (1992).
  21. A. M. Derrington, D. Badcock, “Separate detectors for simple and complex patterns?” Vision Res. 25, 1869–1878 (1985).
    [CrossRef]
  22. G. Mather, S. West, “Evidence for second-order motion detectors,” Vision Res. 33, 1109–1112 (1993).
    [CrossRef] [PubMed]
  23. T. Ledgeway, A. T. Smith, “Evidence for separate motion-detecting mechanisms for first- and second-order motion in human vision,” Vision Res. (to be published).
  24. L. R. Harris, A. T. Smith, “Motion defined exclusively by second-order characteristics does not evoke optokinetic nystagmus,” Visual Neurosci. 9, 565–570 (1992).
    [CrossRef]
  25. K.-P. Hoffmann, “Visual input relevant for the optokinetic nystagmus in mammals,” in Progress in Brain Research, H. -J. Freund, U. Büttner, B. Cohen, J. Noth, eds. (Elsevier, Amsterdam, 1986).
    [CrossRef]
  26. K. Turano, “Evidence for a common motion mechanism of luminance-modulated and contrast-modulated patterns: selective adaptation,” Perception 20, 455–466 (1991).
    [CrossRef] [PubMed]
  27. T. D. Albright, “Form-cue invariant motion processing in primate visual cortex,” Science 255, 1141–1143 (1992).
    [CrossRef] [PubMed]
  28. Y.-X. Zhou, C. L. Baker, “A processing stream in mammalian visual cortex neurons for non-Fourier responses,” Science 261, 98–100 (1993).
    [CrossRef] [PubMed]
  29. A. T. Smith, “Two mechanisms for detecting second-order motion,” Invest. Ophthalmol. Vis. Sci. 34, 1363 (1993).
  30. A. T. Smith, “Energy-based and feature-based mechanisms for detecting second-order motion,” Perception 22, 31 (1993).

1994 (1)

1993 (5)

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

G. Mather, S. West, “Evidence for second-order motion detectors,” Vision Res. 33, 1109–1112 (1993).
[CrossRef] [PubMed]

Y.-X. Zhou, C. L. Baker, “A processing stream in mammalian visual cortex neurons for non-Fourier responses,” Science 261, 98–100 (1993).
[CrossRef] [PubMed]

A. T. Smith, “Two mechanisms for detecting second-order motion,” Invest. Ophthalmol. Vis. Sci. 34, 1363 (1993).

A. T. Smith, “Energy-based and feature-based mechanisms for detecting second-order motion,” Perception 22, 31 (1993).

1992 (6)

L. R. Harris, A. T. Smith, “Motion defined exclusively by second-order characteristics does not evoke optokinetic nystagmus,” Visual Neurosci. 9, 565–570 (1992).
[CrossRef]

T. D. Albright, “Form-cue invariant motion processing in primate visual cortex,” Science 255, 1141–1143 (1992).
[CrossRef] [PubMed]

A. Johnston, P. W. McOwen, 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 B 250, 297–306 (1992).
[CrossRef]

N. M. Grzywacz, “One-path model for contrast-independent perception of Fourier and non-Fourier motions,” Invest. Ophthalmol. Vis. Sci. 33, 954 (1992).

H. R. Wilson, V. P. Ferrera, C. Yo, “A psychophysically motivated model for two-dimensional motion perception,” Vis. Neurosci. 9, 79–97 (1992).
[CrossRef] [PubMed]

P. Cavanagh, “Attention-based motion perception,” Science 257, 1563–1565 (1992).
[CrossRef] [PubMed]

1991 (2)

P. Cavanagh, “Short-range vs. long-range motion: not a valid distinction,” Spatial Vis. 5, 303–309 (1991).
[CrossRef]

K. Turano, “Evidence for a common motion mechanism of luminance-modulated and contrast-modulated patterns: selective adaptation,” Perception 20, 455–466 (1991).
[CrossRef] [PubMed]

1990 (1)

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

1989 (2)

M. A. Georgeson, T. M. Shackleton, “Monocular motion sensing, binocular motion perception,” Vision Res. 29, 1511–1523 (1989).
[CrossRef] [PubMed]

P. Cavanagh, G. Mather, “Motion: the long and short of it,” Spatial Vis. 4, 103–129 (1989).
[CrossRef]

1988 (1)

1985 (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]

A. M. Derrington, D. Badcock, “Separate detectors for simple and complex patterns?” Vision Res. 25, 1869–1878 (1985).
[CrossRef]

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

1982 (1)

E. H. Adelson, “Some new motion illusions, and some old ones, analyzed in terms of their Fourier components,” Invest. Ophthalmol. Vis. Sci. Suppl. 34, 144 (1982).

1980 (2)

O. J. Braddick, “Low-level and high-level processes in apparent motion,” Phil. Trans. R. Soc. London B 290, 137–151 (1980).
[CrossRef]

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

1975 (1)

G. B. Henning, B. G. Hertz, D. E. Broadbent, “Some experiments bearing on the hypothesis that the visual system analyses spatial patterns in independent bands of spatial frequency,” Vision Res. 15, 887–897 (1975).
[CrossRef] [PubMed]

1974 (1)

O. Braddick, “A short-range process in apparent motion,” Vision Res. 14, 519–527 (1974).
[CrossRef] [PubMed]

1951 (1)

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

Adelson, E. H.

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, “Some new motion illusions, and some old ones, analyzed in terms of their Fourier components,” Invest. Ophthalmol. Vis. Sci. Suppl. 34, 144 (1982).

Albright, T. D.

T. D. Albright, “Form-cue invariant motion processing in primate visual cortex,” Science 255, 1141–1143 (1992).
[CrossRef] [PubMed]

Anderson, S. J.

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

Anstis, S. M.

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

Badcock, D.

A. M. Derrington, D. Badcock, “Separate detectors for simple and complex patterns?” Vision Res. 25, 1869–1878 (1985).
[CrossRef]

Baker, C. L.

Y.-X. Zhou, C. L. Baker, “A processing stream in mammalian visual cortex neurons for non-Fourier responses,” Science 261, 98–100 (1993).
[CrossRef] [PubMed]

Baker, J. C. L.

Bergen, J. R.

Braddick, O.

O. Braddick, “A short-range process in apparent motion,” Vision Res. 14, 519–527 (1974).
[CrossRef] [PubMed]

Braddick, O. J.

O. J. Braddick, “Low-level and high-level processes in apparent motion,” Phil. Trans. R. Soc. London B 290, 137–151 (1980).
[CrossRef]

Broadbent, D. E.

G. B. Henning, B. G. Hertz, D. E. Broadbent, “Some experiments bearing on the hypothesis that the visual system analyses spatial patterns in independent bands of spatial frequency,” Vision Res. 15, 887–897 (1975).
[CrossRef] [PubMed]

Burr, D. C.

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

Buxton, H.

A. Johnston, P. W. McOwen, 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 B 250, 297–306 (1992).
[CrossRef]

Cavanagh, P.

P. Cavanagh, “Attention-based motion perception,” Science 257, 1563–1565 (1992).
[CrossRef] [PubMed]

P. Cavanagh, “Short-range vs. long-range motion: not a valid distinction,” Spatial Vis. 5, 303–309 (1991).
[CrossRef]

P. Cavanagh, G. Mather, “Motion: the long and short of it,” Spatial Vis. 4, 103–129 (1989).
[CrossRef]

Chubb, C.

Derrington, A. M.

A. M. Derrington, D. Badcock, “Separate detectors for simple and complex patterns?” Vision Res. 25, 1869–1878 (1985).
[CrossRef]

Ferrera, V. P.

H. R. Wilson, V. P. Ferrera, C. Yo, “A psychophysically motivated model for two-dimensional motion perception,” Vis. Neurosci. 9, 79–97 (1992).
[CrossRef] [PubMed]

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]

M. A. Georgeson, T. M. Shackleton, “Monocular motion sensing, binocular motion perception,” Vision Res. 29, 1511–1523 (1989).
[CrossRef] [PubMed]

Grzywacz, N. M.

N. M. Grzywacz, “One-path model for contrast-independent perception of Fourier and non-Fourier motions,” Invest. Ophthalmol. Vis. Sci. 33, 954 (1992).

Hamett, S. T.

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

Harris, L. R.

L. R. Harris, A. T. Smith, “Motion defined exclusively by second-order characteristics does not evoke optokinetic nystagmus,” Visual Neurosci. 9, 565–570 (1992).
[CrossRef]

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]

Henning, G. B.

G. B. Henning, B. G. Hertz, D. E. Broadbent, “Some experiments bearing on the hypothesis that the visual system analyses spatial patterns in independent bands of spatial frequency,” Vision Res. 15, 887–897 (1975).
[CrossRef] [PubMed]

Hertz, B. G.

G. B. Henning, B. G. Hertz, D. E. Broadbent, “Some experiments bearing on the hypothesis that the visual system analyses spatial patterns in independent bands of spatial frequency,” Vision Res. 15, 887–897 (1975).
[CrossRef] [PubMed]

Hess, R. F.

Hoffmann, K.-P.

K.-P. Hoffmann, “Visual input relevant for the optokinetic nystagmus in mammals,” in Progress in Brain Research, H. -J. Freund, U. Büttner, B. Cohen, J. Noth, eds. (Elsevier, Amsterdam, 1986).
[CrossRef]

Johnston, A.

A. Johnston, P. W. McOwen, 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 B 250, 297–306 (1992).
[CrossRef]

Ledgeway, T.

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

T. Ledgeway, A. T. Smith, “Evidence for separate motion-detecting mechanisms for first- and second-order motion in human vision,” Vision Res. (to be published).

Mather, G.

G. Mather, S. West, “Evidence for second-order motion detectors,” Vision Res. 33, 1109–1112 (1993).
[CrossRef] [PubMed]

P. Cavanagh, G. Mather, “Motion: the long and short of it,” Spatial Vis. 4, 103–129 (1989).
[CrossRef]

McOwen, P. W.

A. Johnston, P. W. McOwen, 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 B 250, 297–306 (1992).
[CrossRef]

Shackleton, T. M.

M. A. Georgeson, T. M. Shackleton, “Monocular motion sensing, binocular motion perception,” Vision Res. 29, 1511–1523 (1989).
[CrossRef] [PubMed]

Smith, A. T.

A. T. Smith, R. F. Hess, J. C. L. Baker, “Direction identification thresholds for second-order motion in central and peripheral vision,” J. Opt. Soc. Am. A 11, 506–514 (1994).
[CrossRef]

A. T. Smith, “Energy-based and feature-based mechanisms for detecting second-order motion,” Perception 22, 31 (1993).

A. T. Smith, “Two mechanisms for detecting second-order motion,” Invest. Ophthalmol. Vis. Sci. 34, 1363 (1993).

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

L. R. Harris, A. T. Smith, “Motion defined exclusively by second-order characteristics does not evoke optokinetic nystagmus,” Visual Neurosci. 9, 565–570 (1992).
[CrossRef]

T. Ledgeway, A. T. Smith, “Evidence for separate motion-detecting mechanisms for first- and second-order motion in human vision,” Vision Res. (to be published).

Sperling, G.

Turano, K.

K. Turano, “Evidence for a common motion mechanism of luminance-modulated and contrast-modulated patterns: selective adaptation,” Perception 20, 455–466 (1991).
[CrossRef] [PubMed]

Ullman, S.

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

Weibull, W.

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

West, S.

G. Mather, S. West, “Evidence for second-order motion detectors,” Vision Res. 33, 1109–1112 (1993).
[CrossRef] [PubMed]

Wilson, H. R.

H. R. Wilson, V. P. Ferrera, C. Yo, “A psychophysically motivated model for two-dimensional motion perception,” Vis. Neurosci. 9, 79–97 (1992).
[CrossRef] [PubMed]

Yo, C.

H. R. Wilson, V. P. Ferrera, C. Yo, “A psychophysically motivated model for two-dimensional motion perception,” Vis. Neurosci. 9, 79–97 (1992).
[CrossRef] [PubMed]

Zhou, Y.-X.

Y.-X. Zhou, C. L. Baker, “A processing stream in mammalian visual cortex neurons for non-Fourier responses,” Science 261, 98–100 (1993).
[CrossRef] [PubMed]

Invest. Ophthalmol. Vis. Sci. (2)

N. M. Grzywacz, “One-path model for contrast-independent perception of Fourier and non-Fourier motions,” Invest. Ophthalmol. Vis. Sci. 33, 954 (1992).

A. T. Smith, “Two mechanisms for detecting second-order motion,” Invest. Ophthalmol. Vis. Sci. 34, 1363 (1993).

Invest. Ophthalmol. Vis. Sci. Suppl. (1)

E. H. Adelson, “Some new motion illusions, and some old ones, analyzed in terms of their Fourier components,” Invest. Ophthalmol. Vis. Sci. Suppl. 34, 144 (1982).

J. Appl. Mech. (1)

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

J. Opt. Soc. Am. A (3)

Perception (2)

A. T. Smith, “Energy-based and feature-based mechanisms for detecting second-order motion,” Perception 22, 31 (1993).

K. Turano, “Evidence for a common motion mechanism of luminance-modulated and contrast-modulated patterns: selective adaptation,” Perception 20, 455–466 (1991).
[CrossRef] [PubMed]

Phil. Trans. R. Soc. London B (2)

O. J. Braddick, “Low-level and high-level processes in apparent motion,” Phil. Trans. R. Soc. London B 290, 137–151 (1980).
[CrossRef]

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

Proc. R. Soc. London B (1)

A. Johnston, P. W. McOwen, 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 B 250, 297–306 (1992).
[CrossRef]

Science (3)

T. D. Albright, “Form-cue invariant motion processing in primate visual cortex,” Science 255, 1141–1143 (1992).
[CrossRef] [PubMed]

Y.-X. Zhou, C. L. Baker, “A processing stream in mammalian visual cortex neurons for non-Fourier responses,” Science 261, 98–100 (1993).
[CrossRef] [PubMed]

P. Cavanagh, “Attention-based motion perception,” Science 257, 1563–1565 (1992).
[CrossRef] [PubMed]

Spatial Vis. (2)

P. Cavanagh, G. Mather, “Motion: the long and short of it,” Spatial Vis. 4, 103–129 (1989).
[CrossRef]

P. Cavanagh, “Short-range vs. long-range motion: not a valid distinction,” Spatial Vis. 5, 303–309 (1991).
[CrossRef]

Vis. Neurosci. (1)

H. R. Wilson, V. P. Ferrera, C. Yo, “A psychophysically motivated model for two-dimensional motion perception,” Vis. Neurosci. 9, 79–97 (1992).
[CrossRef] [PubMed]

Vision Res. (8)

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

M. A. Georgeson, T. M. Shackleton, “Monocular motion sensing, binocular motion perception,” Vision Res. 29, 1511–1523 (1989).
[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]

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

G. B. Henning, B. G. Hertz, D. E. Broadbent, “Some experiments bearing on the hypothesis that the visual system analyses spatial patterns in independent bands of spatial frequency,” Vision Res. 15, 887–897 (1975).
[CrossRef] [PubMed]

O. Braddick, “A short-range process in apparent motion,” Vision Res. 14, 519–527 (1974).
[CrossRef] [PubMed]

A. M. Derrington, D. Badcock, “Separate detectors for simple and complex patterns?” Vision Res. 25, 1869–1878 (1985).
[CrossRef]

G. Mather, S. West, “Evidence for second-order motion detectors,” Vision Res. 33, 1109–1112 (1993).
[CrossRef] [PubMed]

Visual Neurosci. (1)

L. R. Harris, A. T. Smith, “Motion defined exclusively by second-order characteristics does not evoke optokinetic nystagmus,” Visual Neurosci. 9, 565–570 (1992).
[CrossRef]

Other (3)

K.-P. Hoffmann, “Visual input relevant for the optokinetic nystagmus in mammals,” in Progress in Brain Research, H. -J. Freund, U. Büttner, B. Cohen, J. Noth, eds. (Elsevier, Amsterdam, 1986).
[CrossRef]

T. Ledgeway, A. T. Smith, “Evidence for separate motion-detecting mechanisms for first- and second-order motion in human vision,” Vision Res. (to be published).

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

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Figures (7)

Fig. 1
Fig. 1

Illustration of the contrast-modulated images used in the experiments. Top left, the contrast of a sample of 2D noise is modulated sinusoidally in the horizontal dimension. Top right, the image used in experiment 1. Contrast is modulated by a 3f + 4f waveform. In the animation sequences used, the modulating waveform moved while the noise remained static, to give second-order motion. Bottom left, the contrast of a sample of 2D noise is randomly modulated in the horizontal dimension. The (stationary) features so created were used to mask those of a (moving) target contrast modulation (not shown) in experiment 2. Bottom right, the appearance of a sinusoidal contrast modulation identical to that shown at top left in the presence of the second-order mask shown at bottom left. Because of luminance nonlinearities inherent in the process of photographic reproduction, the images in this figure contain brightness variations that are correlated with the contrast variations; there were no such luminance variations in the images used in the experiments.

Fig. 2
Fig. 2

Luminance profiles of the patterns used in the experiments. Each trace represents a horizontal slice through an image and shows luminance as a function of spatial position. (a) Visual noise formed by assignment of each pixel to be either light or dark at random; (b) the 3f + 4f waveform formed by addition of two sinusoids of equal amplitude whose periods are in the ratio 3:4, resulting in a beat pattern that repeats with a period of f; (c) contrast-modulated noise formed from the product of waveforms (a) and (b). The waveform of the envelope repeats with a period of f. Also shown (straight line) is the mean luminance of the image locally averaged over a patch of pixels: contrast waxes and wanes symmetrically about a constant mean luminance value; (d) the result of half-wave rectifying (and rescaling) the image represented in (c), together with the mean luminance profile of the transformed image. The mean luminance now varies in the horizontal dimension. The waveform describing this variation is identical in form (though not in amplitude) to that in (b); i.e., its Fourier spectrum contains energy at 3f and at 4f.

Fig. 3
Fig. 3

Performance on a direction judgment task, shown separately for the author (AS) and a naïve observer (PB), as a function of the amplitude of a 3f + 4f contrast modulation that moves continuously in one direction in steps of one quarter of a period of f (noise remains static). Results are shown for three conditions: static noise, no isi (filled circles); static noise, 60-ms isi (squares) and dynamic noise, no isi (open circles).

Fig. 4
Fig. 4

Performance of the author (AS) on a direction judgment task as a function of the amplitude of a sinusoidal contrast modulation that drifted smoothly either rightward or leftward in the presence of a static second-order mask. Results are shown for four mask modulation depths: zero (open circles), 12.5% (circles), 25% (squares), and 50% (triangles). Results obtained (a) without an interstimulus interval and (b) when successive updates of the animation were separated by a 60-ms isi.

Fig. 5
Fig. 5

As for Fig. 4 but showing results for a naive observer (TF).

Fig. 6
Fig. 6

As for Fig. 4 but showing mean results for a group of six observers, for two mask modulation depths only: zero (circles) and 50% (triangles).

Fig. 7
Fig. 7

Direction-detection thresholds for condition 1 (no isi, open symbols) and condition 2 (60-ms isi, filled symbols) as a function of mask amplitude. Data are shown for subject AS (squares, solid line, data from Fig. 4), for subject TF (circles, dashed line, from Fig. 5), and for the mean of six subjects (triangles, 0 and 50% modulation depth only, from Fig. 6).

Equations (4)

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L ( x , y ) = L m { 1 + r ( x , y ) [ 1 + a sin ( 2 π f x + ϕ ) ] } ,
L ( x , y ) = L m { 1 + r ( x , y ) [ 1 + a sin ( 6 π f 1 x + ϕ ) + a sin ( 8 π f 2 x + ϕ ) ] } .
M = ( C max C min ) / ( C max + C min ) ,
L ( x , y ) = L m { 1 + r 2 ( x , y ) r 1 ( x ) [ 1 + a sin ( 2 π f x + ϕ ) ] } ,

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