Abstract

To address the issue of whether the luminance-dependent (linear) and contrast-dependent (nonlinear) processes in stereo and motion have a common computational basis, we compare both carrier-dependent and envelope-dependent performance for these two modalities by using the same stimulus and task: two-flash apparent motion/depth for a wide range of displacements. We do this for different densities, bandwidths, contrasts, spatial frequencies, and exposure durations. The results suggest that there is concordance not only between the luminance-dependent (linear) processes of motion and stereo but also between the envelope-dependent (nonlinear) processes of both modalities. Only one exception was found, but we show this to be amenable to an explanation based on a different contrast dependence for the nonlinear mechanisms of stereo and motion. This suggests that the computational basis of linear and nonlinear processes may be similar for stereopsis and motion.

© 1999 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef]
  3. R. F. Hess, L. M. Wilcox, “Linear and non-linear filtering in stereopsis,” Vision Res. 34, 2431–2438 (1994).
    [CrossRef] [PubMed]
  4. L. Lin, H. R. Wilson, “Stereoscopic integration of Fourier and non-Fourier patterns,” Invest. Ophthalmol. Visual Sci. Suppl. 36, S364 (1995).
  5. I. Kovács, A. Fehér, “Non-Fourier information in bandpass noise patterns,” Vision Res. 37, 1167–1177 (1997).
    [CrossRef] [PubMed]
  6. J. C. Boulton, C. L. Baker, “Different parameters control motion perception above and below a critical density,” Vision Res. 33, 1803–1811 (1993).
    [CrossRef] [PubMed]
  7. J. C. Boulton, C. L. Baker, “Dependence on stimulus onset asynchrony in apparent motion: evidence for two mechanisms,” Vision Res. 33, 2013–2019 (1993).
    [CrossRef] [PubMed]
  8. Y. X. Zhou, C. L. Baker, “A processing stream in mammalian visual cortex neurons for non-Fourier responses,” Science 261, 98–101 (1993).
    [CrossRef] [PubMed]
  9. Y. X. Zhou, C. L. Baker, “Envelope-responsive neurons in areas 17 and 18 of cat,” J. Neurophysiol. 72, 2134–2150 (1994).
    [PubMed]
  10. Y. X. Zhou, C. L. Baker, “Spatial properties of envelope-responsive cells in area 17 and 18 neurons of the cat,” J. Neurophysiol. 75, 1038–1050 (1996).
    [PubMed]
  11. C. L. Baker, R. F. Hess, “Two mechanisms underlie processing of stochastic motion stimuli,” Vision Res. 38, 1211–1222 (1998).
    [CrossRef] [PubMed]
  12. R. Cleary, O. J. Braddick, “Direction discrimination for bandpass filtered random dot kinematograms,” Vision Res. 30, 303–316 (1990).
    [CrossRef]
  13. W. F. Bischof, V. Di Lollo, “On the half-cycle displacement limit of sampled directional motion,” Vision Res. 31, 649–660 (1991).
    [CrossRef] [PubMed]
  14. I. Ohzawa, G. C. DeAngelis, R. D. Freeman, “Stereoscopic depth discrimination in the visual cortex: neurones ideally suited as disparity detectors,” Science 249, 1037–1041 (1990).
    [CrossRef] [PubMed]
  15. D. J. Fleet, K. Langley, “Computational analysis of non-Fourier motion,” Vision Res. 34, 3057–3059 (1994).
    [CrossRef] [PubMed]
  16. N. Qian, “Computing stereo disparity and motion with known binocular cell properties,” Neural Comput. 6, 390–404 (1994).
    [CrossRef]
  17. N. Qian, R. A. Andersen, “A physiological model for motion–stereo integration and a unified explanation for the Pulfrich-like phenomena,” Vision Res. 37, 1683–1698 (1997).
    [CrossRef] [PubMed]
  18. L. M. Wilcox, R. F. Hess, “Is the site of non-linear filtering in stereopsis before or after binocular combination?” Vision Res. 36, 391–399 (1996).
    [CrossRef] [PubMed]
  19. L. M. Wilcox, R. F. Hess, “When stereopsis does not improve with increasing contrast,” Vision Res. 38, 3671–3680 (1998).
    [CrossRef]
  20. A. Glennerster, “Dmax for stereopsis and motion in random dot displays,” Vision Res. 38, 925–935 (1998).
    [CrossRef] [PubMed]
  21. A. Sutter, G. Sperling, C. Chubb, “Measuring the spatial frequency selectivity of second-order texture mechanisms,” Vision Res. 35, 915–924 (1995).
    [CrossRef] [PubMed]
  22. D. D. Landers, L. K. Cormack, “Some spatio-temporal interactions in stereopsis,” Invest. Ophthalmol. Visual Sci. Suppl. 38, S907 (1997).
  23. M. Edwards, D. Pope, C. M. Schor, “Orientation tuning of the transient-disparity stereopsis system” Invest. Ophthalmol. Visual Sci. Suppl. 39, S191 (1998).
  24. E. H. Adelson, J. R. Bergen, “Spatio-temporal energy models for the perception of motion,” J. Opt. Soc. Am. A 2, 284–299 (1985).
    [CrossRef] [PubMed]
  25. G. J. Burton, “Evidence for non-linear response processes in the human visual system from measurements on the thresholds of spatial beat frequencies,” Vision Res. 13, 1211–1225 (1973).
    [CrossRef] [PubMed]
  26. E. Taub, J. D. Victor, M. M. Conte, “Nonlinear preprocessing in short-range motion,” Vision Res. 37, 1459–1477 (1997).
    [CrossRef] [PubMed]
  27. A. Derrington, P. Lennie, “Spatial and temporal contrast sensitivities of neurones in lateral geniculate nucleus of macaque,” J. Physiol. (London) 357, 219–240 (1984).
  28. A. M. Derrington, D. R. Badcock, “Separate detectors for simple and complex grating patterns,” Vision Res. 25, 1869–1878 (1985).
    [CrossRef]
  29. T. D. Albright, “Form-cue invariant motion processing in primate visual cortex,” Science 255, 1141–1143 (1992).
    [CrossRef] [PubMed]
  30. I. Mareschal, C. L. Baker, “A cortical locus for the processing of contrast-defined contours,” Nature Neurosci. 1, 150–154 (1998).
    [CrossRef]
  31. R. J. Watt, M. J. Morgan, “A theory of the primitive spatial code in human vision,” Vision Res. 25, 1661–1674 (1985).
    [CrossRef] [PubMed]
  32. R. A. Eagle, B. J. Rogers, “Effects of dot density, patch size and contrast on the upper spatial limit for direction discrimination in random dot kinematograms,” Vision Res. 37, 545–558 (1997).
    [CrossRef]
  33. C. L. Baker, J. C. Boulton, K. T. Mullen, “A nonlinear chromatic motion mechanism,” Vision Res. 38, 291–302 (1998).
    [CrossRef] [PubMed]
  34. P. J. Bex, C. L. Baker, “The effects of distractor elements on direction discrimination in random Gabor kinematograms,” Vision Res. 37, 1761–1767 (1997).
    [CrossRef] [PubMed]
  35. P. J. Bex, N. Brady, R. E. Fredericksen, R. F. Hess, “Energetic motion detection,” Nature (London) 378, 670–671 (1995).
    [CrossRef]
  36. T. Ledgeway, A. T. Smith, “Evidence for separate motion-detecting mechanisms for first- and second-order motion in human vision,” Vision Res. 34, 2727–2740 (1994).
    [CrossRef] [PubMed]
  37. Information is available from R. F. Hess at the address on the title page.
  38. N. Graham, J. Beck, A. Sutter, “Nonlinear processes in spatial-frequency channel models of perceived texture segregation: effects of sign and amount of contrast,” Vision Res. 32, 719–743 (1992).
    [CrossRef] [PubMed]
  39. H. R. Wilson, P. Ferrera, C. Yo, “A psychophysically motivated model for two-dimensional motion perception,” Visual Neurosci. 9, 79–97 (1992).
    [CrossRef]
  40. A. T. Wells, D. R. Simmons, “The influence of first-order orientation information on second-order stereopsis,” Invest. Ophthalmol. Visual Sci. Suppl. 38, S906 (1997).
  41. L. Ziegler, R. F. Hess, “Linear and non-linear stereoscopic contributions distinguished by task,” Invest. Ophthalmol. Visual Sci. Suppl. 38, S906 (1997).
  42. L. Ziegler, R. F. Hess, “Why is there depth but no shape from uncorrelated micropatterns?” Invest. Ophthalmol. Visual Sci. Suppl. 39, S614 (1998).

1998 (7)

C. L. Baker, R. F. Hess, “Two mechanisms underlie processing of stochastic motion stimuli,” Vision Res. 38, 1211–1222 (1998).
[CrossRef] [PubMed]

L. M. Wilcox, R. F. Hess, “When stereopsis does not improve with increasing contrast,” Vision Res. 38, 3671–3680 (1998).
[CrossRef]

A. Glennerster, “Dmax for stereopsis and motion in random dot displays,” Vision Res. 38, 925–935 (1998).
[CrossRef] [PubMed]

M. Edwards, D. Pope, C. M. Schor, “Orientation tuning of the transient-disparity stereopsis system” Invest. Ophthalmol. Visual Sci. Suppl. 39, S191 (1998).

I. Mareschal, C. L. Baker, “A cortical locus for the processing of contrast-defined contours,” Nature Neurosci. 1, 150–154 (1998).
[CrossRef]

C. L. Baker, J. C. Boulton, K. T. Mullen, “A nonlinear chromatic motion mechanism,” Vision Res. 38, 291–302 (1998).
[CrossRef] [PubMed]

L. Ziegler, R. F. Hess, “Why is there depth but no shape from uncorrelated micropatterns?” Invest. Ophthalmol. Visual Sci. Suppl. 39, S614 (1998).

1997 (8)

A. T. Wells, D. R. Simmons, “The influence of first-order orientation information on second-order stereopsis,” Invest. Ophthalmol. Visual Sci. Suppl. 38, S906 (1997).

L. Ziegler, R. F. Hess, “Linear and non-linear stereoscopic contributions distinguished by task,” Invest. Ophthalmol. Visual Sci. Suppl. 38, S906 (1997).

P. J. Bex, C. L. Baker, “The effects of distractor elements on direction discrimination in random Gabor kinematograms,” Vision Res. 37, 1761–1767 (1997).
[CrossRef] [PubMed]

R. A. Eagle, B. J. Rogers, “Effects of dot density, patch size and contrast on the upper spatial limit for direction discrimination in random dot kinematograms,” Vision Res. 37, 545–558 (1997).
[CrossRef]

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

D. D. Landers, L. K. Cormack, “Some spatio-temporal interactions in stereopsis,” Invest. Ophthalmol. Visual Sci. Suppl. 38, S907 (1997).

N. Qian, R. A. Andersen, “A physiological model for motion–stereo integration and a unified explanation for the Pulfrich-like phenomena,” Vision Res. 37, 1683–1698 (1997).
[CrossRef] [PubMed]

I. Kovács, A. Fehér, “Non-Fourier information in bandpass noise patterns,” Vision Res. 37, 1167–1177 (1997).
[CrossRef] [PubMed]

1996 (2)

Y. X. Zhou, C. L. Baker, “Spatial properties of envelope-responsive cells in area 17 and 18 neurons of the cat,” J. Neurophysiol. 75, 1038–1050 (1996).
[PubMed]

L. M. Wilcox, R. F. Hess, “Is the site of non-linear filtering in stereopsis before or after binocular combination?” Vision Res. 36, 391–399 (1996).
[CrossRef] [PubMed]

1995 (3)

L. Lin, H. R. Wilson, “Stereoscopic integration of Fourier and non-Fourier patterns,” Invest. Ophthalmol. Visual Sci. Suppl. 36, S364 (1995).

A. Sutter, G. Sperling, C. Chubb, “Measuring the spatial frequency selectivity of second-order texture mechanisms,” Vision Res. 35, 915–924 (1995).
[CrossRef] [PubMed]

P. J. Bex, N. Brady, R. E. Fredericksen, R. F. Hess, “Energetic motion detection,” Nature (London) 378, 670–671 (1995).
[CrossRef]

1994 (5)

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

R. F. Hess, L. M. Wilcox, “Linear and non-linear filtering in stereopsis,” Vision Res. 34, 2431–2438 (1994).
[CrossRef] [PubMed]

Y. X. Zhou, C. L. Baker, “Envelope-responsive neurons in areas 17 and 18 of cat,” J. Neurophysiol. 72, 2134–2150 (1994).
[PubMed]

D. J. Fleet, K. Langley, “Computational analysis of non-Fourier motion,” Vision Res. 34, 3057–3059 (1994).
[CrossRef] [PubMed]

N. Qian, “Computing stereo disparity and motion with known binocular cell properties,” Neural Comput. 6, 390–404 (1994).
[CrossRef]

1993 (3)

J. C. Boulton, C. L. Baker, “Different parameters control motion perception above and below a critical density,” Vision Res. 33, 1803–1811 (1993).
[CrossRef] [PubMed]

J. C. Boulton, C. L. Baker, “Dependence on stimulus onset asynchrony in apparent motion: evidence for two mechanisms,” Vision Res. 33, 2013–2019 (1993).
[CrossRef] [PubMed]

Y. X. Zhou, C. L. Baker, “A processing stream in mammalian visual cortex neurons for non-Fourier responses,” Science 261, 98–101 (1993).
[CrossRef] [PubMed]

1992 (3)

N. Graham, J. Beck, A. Sutter, “Nonlinear processes in spatial-frequency channel models of perceived texture segregation: effects of sign and amount of contrast,” Vision Res. 32, 719–743 (1992).
[CrossRef] [PubMed]

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

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

1991 (1)

W. F. Bischof, V. Di Lollo, “On the half-cycle displacement limit of sampled directional motion,” Vision Res. 31, 649–660 (1991).
[CrossRef] [PubMed]

1990 (2)

I. Ohzawa, G. C. DeAngelis, R. D. Freeman, “Stereoscopic depth discrimination in the visual cortex: neurones ideally suited as disparity detectors,” Science 249, 1037–1041 (1990).
[CrossRef] [PubMed]

R. Cleary, O. J. Braddick, “Direction discrimination for bandpass filtered random dot kinematograms,” Vision Res. 30, 303–316 (1990).
[CrossRef]

1988 (1)

1985 (3)

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

R. J. Watt, M. J. Morgan, “A theory of the primitive spatial code in human vision,” Vision Res. 25, 1661–1674 (1985).
[CrossRef] [PubMed]

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

1984 (1)

A. Derrington, P. Lennie, “Spatial and temporal contrast sensitivities of neurones in lateral geniculate nucleus of macaque,” J. Physiol. (London) 357, 219–240 (1984).

1973 (1)

G. J. Burton, “Evidence for non-linear response processes in the human visual system from measurements on the thresholds of spatial beat frequencies,” Vision Res. 13, 1211–1225 (1973).
[CrossRef] [PubMed]

Adelson, E. H.

Albright, T. D.

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

Andersen, R. A.

N. Qian, R. A. Andersen, “A physiological model for motion–stereo integration and a unified explanation for the Pulfrich-like phenomena,” Vision Res. 37, 1683–1698 (1997).
[CrossRef] [PubMed]

Badcock, D. R.

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

Baker, C. L.

I. Mareschal, C. L. Baker, “A cortical locus for the processing of contrast-defined contours,” Nature Neurosci. 1, 150–154 (1998).
[CrossRef]

C. L. Baker, R. F. Hess, “Two mechanisms underlie processing of stochastic motion stimuli,” Vision Res. 38, 1211–1222 (1998).
[CrossRef] [PubMed]

C. L. Baker, J. C. Boulton, K. T. Mullen, “A nonlinear chromatic motion mechanism,” Vision Res. 38, 291–302 (1998).
[CrossRef] [PubMed]

P. J. Bex, C. L. Baker, “The effects of distractor elements on direction discrimination in random Gabor kinematograms,” Vision Res. 37, 1761–1767 (1997).
[CrossRef] [PubMed]

Y. X. Zhou, C. L. Baker, “Spatial properties of envelope-responsive cells in area 17 and 18 neurons of the cat,” J. Neurophysiol. 75, 1038–1050 (1996).
[PubMed]

Y. X. Zhou, C. L. Baker, “Envelope-responsive neurons in areas 17 and 18 of cat,” J. Neurophysiol. 72, 2134–2150 (1994).
[PubMed]

J. C. Boulton, C. L. Baker, “Dependence on stimulus onset asynchrony in apparent motion: evidence for two mechanisms,” Vision Res. 33, 2013–2019 (1993).
[CrossRef] [PubMed]

Y. X. Zhou, C. L. Baker, “A processing stream in mammalian visual cortex neurons for non-Fourier responses,” Science 261, 98–101 (1993).
[CrossRef] [PubMed]

J. C. Boulton, C. L. Baker, “Different parameters control motion perception above and below a critical density,” Vision Res. 33, 1803–1811 (1993).
[CrossRef] [PubMed]

J. C. Boulton, C. L. Baker, “Psychophysical evidence for both a ‘quasi-linear’ and a ‘nonlinear’ mechanism for the detection of motion,” in Computational Vision Based on Neurobiology, T. B. Lawton, ed., Proc. SPIE2054, 124–133 (1993).
[CrossRef]

Beck, J.

N. Graham, J. Beck, A. Sutter, “Nonlinear processes in spatial-frequency channel models of perceived texture segregation: effects of sign and amount of contrast,” Vision Res. 32, 719–743 (1992).
[CrossRef] [PubMed]

Bergen, J. R.

Bex, P. J.

P. J. Bex, C. L. Baker, “The effects of distractor elements on direction discrimination in random Gabor kinematograms,” Vision Res. 37, 1761–1767 (1997).
[CrossRef] [PubMed]

P. J. Bex, N. Brady, R. E. Fredericksen, R. F. Hess, “Energetic motion detection,” Nature (London) 378, 670–671 (1995).
[CrossRef]

Bischof, W. F.

W. F. Bischof, V. Di Lollo, “On the half-cycle displacement limit of sampled directional motion,” Vision Res. 31, 649–660 (1991).
[CrossRef] [PubMed]

Boulton, J. C.

C. L. Baker, J. C. Boulton, K. T. Mullen, “A nonlinear chromatic motion mechanism,” Vision Res. 38, 291–302 (1998).
[CrossRef] [PubMed]

J. C. Boulton, C. L. Baker, “Dependence on stimulus onset asynchrony in apparent motion: evidence for two mechanisms,” Vision Res. 33, 2013–2019 (1993).
[CrossRef] [PubMed]

J. C. Boulton, C. L. Baker, “Different parameters control motion perception above and below a critical density,” Vision Res. 33, 1803–1811 (1993).
[CrossRef] [PubMed]

J. C. Boulton, C. L. Baker, “Psychophysical evidence for both a ‘quasi-linear’ and a ‘nonlinear’ mechanism for the detection of motion,” in Computational Vision Based on Neurobiology, T. B. Lawton, ed., Proc. SPIE2054, 124–133 (1993).
[CrossRef]

Braddick, O. J.

R. Cleary, O. J. Braddick, “Direction discrimination for bandpass filtered random dot kinematograms,” Vision Res. 30, 303–316 (1990).
[CrossRef]

Brady, N.

P. J. Bex, N. Brady, R. E. Fredericksen, R. F. Hess, “Energetic motion detection,” Nature (London) 378, 670–671 (1995).
[CrossRef]

Burton, G. J.

G. J. Burton, “Evidence for non-linear response processes in the human visual system from measurements on the thresholds of spatial beat frequencies,” Vision Res. 13, 1211–1225 (1973).
[CrossRef] [PubMed]

Chubb, C.

A. Sutter, G. Sperling, C. Chubb, “Measuring the spatial frequency selectivity of second-order texture mechanisms,” Vision Res. 35, 915–924 (1995).
[CrossRef] [PubMed]

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

Cleary, R.

R. Cleary, O. J. Braddick, “Direction discrimination for bandpass filtered random dot kinematograms,” Vision Res. 30, 303–316 (1990).
[CrossRef]

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]

Cormack, L. K.

D. D. Landers, L. K. Cormack, “Some spatio-temporal interactions in stereopsis,” Invest. Ophthalmol. Visual Sci. Suppl. 38, S907 (1997).

DeAngelis, G. C.

I. Ohzawa, G. C. DeAngelis, R. D. Freeman, “Stereoscopic depth discrimination in the visual cortex: neurones ideally suited as disparity detectors,” Science 249, 1037–1041 (1990).
[CrossRef] [PubMed]

Derrington, A.

A. Derrington, P. Lennie, “Spatial and temporal contrast sensitivities of neurones in lateral geniculate nucleus of macaque,” J. Physiol. (London) 357, 219–240 (1984).

Derrington, A. M.

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

Di Lollo, V.

W. F. Bischof, V. Di Lollo, “On the half-cycle displacement limit of sampled directional motion,” Vision Res. 31, 649–660 (1991).
[CrossRef] [PubMed]

Eagle, R. A.

R. A. Eagle, B. J. Rogers, “Effects of dot density, patch size and contrast on the upper spatial limit for direction discrimination in random dot kinematograms,” Vision Res. 37, 545–558 (1997).
[CrossRef]

Edwards, M.

M. Edwards, D. Pope, C. M. Schor, “Orientation tuning of the transient-disparity stereopsis system” Invest. Ophthalmol. Visual Sci. Suppl. 39, S191 (1998).

Fehér, A.

I. Kovács, A. Fehér, “Non-Fourier information in bandpass noise patterns,” Vision Res. 37, 1167–1177 (1997).
[CrossRef] [PubMed]

Ferrera, P.

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

Fleet, D. J.

D. J. Fleet, K. Langley, “Computational analysis of non-Fourier motion,” Vision Res. 34, 3057–3059 (1994).
[CrossRef] [PubMed]

Fredericksen, R. E.

P. J. Bex, N. Brady, R. E. Fredericksen, R. F. Hess, “Energetic motion detection,” Nature (London) 378, 670–671 (1995).
[CrossRef]

Freeman, R. D.

I. Ohzawa, G. C. DeAngelis, R. D. Freeman, “Stereoscopic depth discrimination in the visual cortex: neurones ideally suited as disparity detectors,” Science 249, 1037–1041 (1990).
[CrossRef] [PubMed]

Glennerster, A.

A. Glennerster, “Dmax for stereopsis and motion in random dot displays,” Vision Res. 38, 925–935 (1998).
[CrossRef] [PubMed]

Graham, N.

N. Graham, J. Beck, A. Sutter, “Nonlinear processes in spatial-frequency channel models of perceived texture segregation: effects of sign and amount of contrast,” Vision Res. 32, 719–743 (1992).
[CrossRef] [PubMed]

Hess, R. F.

L. M. Wilcox, R. F. Hess, “When stereopsis does not improve with increasing contrast,” Vision Res. 38, 3671–3680 (1998).
[CrossRef]

L. Ziegler, R. F. Hess, “Why is there depth but no shape from uncorrelated micropatterns?” Invest. Ophthalmol. Visual Sci. Suppl. 39, S614 (1998).

C. L. Baker, R. F. Hess, “Two mechanisms underlie processing of stochastic motion stimuli,” Vision Res. 38, 1211–1222 (1998).
[CrossRef] [PubMed]

L. Ziegler, R. F. Hess, “Linear and non-linear stereoscopic contributions distinguished by task,” Invest. Ophthalmol. Visual Sci. Suppl. 38, S906 (1997).

L. M. Wilcox, R. F. Hess, “Is the site of non-linear filtering in stereopsis before or after binocular combination?” Vision Res. 36, 391–399 (1996).
[CrossRef] [PubMed]

P. J. Bex, N. Brady, R. E. Fredericksen, R. F. Hess, “Energetic motion detection,” Nature (London) 378, 670–671 (1995).
[CrossRef]

R. F. Hess, L. M. Wilcox, “Linear and non-linear filtering in stereopsis,” Vision Res. 34, 2431–2438 (1994).
[CrossRef] [PubMed]

Kovács, I.

I. Kovács, A. Fehér, “Non-Fourier information in bandpass noise patterns,” Vision Res. 37, 1167–1177 (1997).
[CrossRef] [PubMed]

Landers, D. D.

D. D. Landers, L. K. Cormack, “Some spatio-temporal interactions in stereopsis,” Invest. Ophthalmol. Visual Sci. Suppl. 38, S907 (1997).

Langley, K.

D. J. Fleet, K. Langley, “Computational analysis of non-Fourier motion,” Vision Res. 34, 3057–3059 (1994).
[CrossRef] [PubMed]

Ledgeway, T.

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

Lennie, P.

A. Derrington, P. Lennie, “Spatial and temporal contrast sensitivities of neurones in lateral geniculate nucleus of macaque,” J. Physiol. (London) 357, 219–240 (1984).

Lin, L.

L. Lin, H. R. Wilson, “Stereoscopic integration of Fourier and non-Fourier patterns,” Invest. Ophthalmol. Visual Sci. Suppl. 36, S364 (1995).

Mareschal, I.

I. Mareschal, C. L. Baker, “A cortical locus for the processing of contrast-defined contours,” Nature Neurosci. 1, 150–154 (1998).
[CrossRef]

Morgan, M. J.

R. J. Watt, M. J. Morgan, “A theory of the primitive spatial code in human vision,” Vision Res. 25, 1661–1674 (1985).
[CrossRef] [PubMed]

Mullen, K. T.

C. L. Baker, J. C. Boulton, K. T. Mullen, “A nonlinear chromatic motion mechanism,” Vision Res. 38, 291–302 (1998).
[CrossRef] [PubMed]

Ohzawa, I.

I. Ohzawa, G. C. DeAngelis, R. D. Freeman, “Stereoscopic depth discrimination in the visual cortex: neurones ideally suited as disparity detectors,” Science 249, 1037–1041 (1990).
[CrossRef] [PubMed]

Pope, D.

M. Edwards, D. Pope, C. M. Schor, “Orientation tuning of the transient-disparity stereopsis system” Invest. Ophthalmol. Visual Sci. Suppl. 39, S191 (1998).

Qian, N.

N. Qian, R. A. Andersen, “A physiological model for motion–stereo integration and a unified explanation for the Pulfrich-like phenomena,” Vision Res. 37, 1683–1698 (1997).
[CrossRef] [PubMed]

N. Qian, “Computing stereo disparity and motion with known binocular cell properties,” Neural Comput. 6, 390–404 (1994).
[CrossRef]

Rogers, B. J.

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Other (2)

Information is available from R. F. Hess at the address on the title page.

J. C. Boulton, C. L. Baker, “Psychophysical evidence for both a ‘quasi-linear’ and a ‘nonlinear’ mechanism for the detection of motion,” in Computational Vision Based on Neurobiology, T. B. Lawton, ed., Proc. SPIE2054, 124–133 (1993).
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Figures (7)

Fig. 1
Fig. 1

Spatial arrangement of the stimuli used. Fixation was always on the center of the screen. Arrays of either sparse (A and C) or dense (B and D) micropatterns were displayed. The micropatterns were either spatial-frequency broadband (C and D) or spatial-frequency narrow band (A and B). The screen size was 10×15 deg.

Fig. 2
Fig. 2

Motion and stereo psychometric performance plotted as a function of spatial displacement in fractions of the carrier wavelength for Gabor stimuli in either a two-flash motion task or a two-flash stereo task. Results are shown for two subjects and for two densities (low density, open symbols; high density, filled symbols). The bandwidth of the Gabors is narrow (0.29 octave).

Fig. 3
Fig. 3

Same as for Fig. 2, except that now the spatial bandwidth of the Gabors is broad (0.74 octave).

Fig. 4
Fig. 4

Psychometric performance plotted as a function of spatial displacement in fractions of the carrier wavelength for either a two-flash Gabor motion task or a one-flash Gabor stereo task. The orientation of the carrier went through a 90° rotation on alternate flashes of the 2-flash sequence. Results are shown for two subjects and for two densities (low density, open symbols; high density, filled symbols). The bandwidth of the Gabors is narrow (0.29 octave).

Fig. 5
Fig. 5

Same as for Fig. 4, except that now the spatial bandwidth of the Gabors is broad (0.74 octave).

Fig. 6
Fig. 6

Psychometric stereo data for subject LMW as a function of spatial displacement for broadband Gabor stimuli (low density, unfilled symbols; high density, filled symbols) of differing carrier frequency, exposure duration, and contrast. Contrast was effective in producing the linear oscillatory behavior at small displacements that characterized the motion response to the same stimuli (see Fig. 3).

Fig. 7
Fig. 7

Same as for Fig. 6, but for subject RFH.

Equations (1)

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L(x, y)=L0{1+C exp[-(x2/2σx2+y2/2σy2)]×sin(2πx/λ+ϕ)},

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