Abstract

Contrast thresholds for 75% correct depth identification in narrow-band filtered random dot stereograms were determined for different center spatial frequencies and binocular disparities. Rigorous control over vergence was maintained during testing, and a forced-choice procedure was used. The resulting contrast sensitivity function for stereopsis revealed sensitivity over a greater range of disparities at low than at high spatial frequencies. Sensitivity peaked for large disparities at low spatial frequencies and for small disparities at high spatial frequencies. When disparities were converted to effective binocular phase differences, the variation of contrast sensitivity with phase followed a consistent pattern across spatial frequencies, with peak sensitivity occurring mainly for binocular phases of between 90° and 180°. These results have implications for the extent of spatial integration at the input to the disparity sensing mechanism. A model postulating a spread of positional disparities independent of the spatial frequency selectivity of disparity-sensitive units cannot account for the results. But the size–disparity correlation strongly evident in our data is predicted by certain models of stereopsis, such as phase disparity encoding. An ideal observer analysis is developed that demonstrates that our results were not forced by the nature of the stimulus employed; rather, the quantum efficiency for stereopsis at contrast threshold follows the size–disparity correlation.

© 1994 Optical Society of America

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  1. F. W. Campbell, J. G. Robson, “Application of Fourier analysis to the visibility of gratings,” J. Physiol. 197, 551–566 (1968).
    [PubMed]
  2. R. L. DeValois, K. K. DeValois, Spatial Vision (Oxford U. Press, New York, 1988).
  3. H. R. Wilson, D. Levi, L. Maffei, J. Rovamo, R. L. DeValois, “The perception of form: retina to striate cortex,” in Visual Perception: The Neurophysiological Foundations, L. Spillman, J. S. Werner, eds. (Academic, San Diego, Calif., 1990), pp. 317–347.
  4. B. Julesz, Foundations of Cyclopean Perception (U. Chicago Press, Chicago, Ill., 1971), pp. 100–102.
  5. J. E. W. Mayhew, J. P. Frisby, “Rivalrous texture stereograms,” Nature (London) 264, 53–56 (1976).
    [CrossRef]
  6. B. Julesz, J. E. Miller, “Independent spatial-frequencytuned channels in binocular fusion and rivalry,” Perception 4, 125–143 (1975).
    [CrossRef]
  7. Y. Yang, R. Blake, “Spatial frequency tuning of human stereopsis,” Vision Res. 31, 1177–1189 (1991).
    [CrossRef] [PubMed]
  8. H. R. Wilson, R. Blake, D. L. Halpern, “Coarse spatial scales constrain the range of binocular fusion on fine scales,” J. Opt. Soc. Am. A 8, 229–236 (1991).
    [CrossRef] [PubMed]
  9. R. Blake, H. R. Wilson, “Neural models of stereoscopic vision,” Trends Neurosci. 14, 445–452 (1991).
    [CrossRef] [PubMed]
  10. D. Marr, T. Poggio, “A computational theory of human stereo vision,” Proc. R. Soc. London Ser. B 204, 301–328 (1979).
    [CrossRef]
  11. I. Ohzawa, G. C. DeAngelis, R. D. Freeman, “Stereoscopic depth discrimination in the visual cortex: neurons ideally suited as disparity detectors,” Science 249, 1037–1041 (1990).
    [CrossRef]
  12. G. C. DeAngelis, I. Ohzawa, R. D. Freeman, “Depth is encoded in the visual cortex by a specialized receptive field structure,” Nature (London) 352, 156–159 (1991).
    [CrossRef]
  13. E. H. Adelson, J. R. Bergen, “Spatiotemporal energy models for the perception of motion,” J. Opt. Soc. Am. A 2, 284–299 (1985).
    [CrossRef]
  14. S. F. Bowne, S. P. McKee, C. W. Tyler, “A disparity energy model of early stereo processing,” Invest. Ophthalmol. Vis. Sci. Suppl. 31, 303 (1990).
  15. C. M. Schor, I. Wood, “Disparity range for local stereopsis as a function of luminance spatial frequency,” Vision Res. 23, 1649–1654 (1983).
    [CrossRef] [PubMed]
  16. T. B. Felton, W. Richards, R. A. Smith, “Disparity processing of spatial frequencies in man,” J. Physiol. 225, 340–362 (1972).
  17. J. J. Kulikowski, “Limit of single vision in stereopsis depends on contour sharpness,” Nature (London) 275, 126–127 (1978).
    [CrossRef]
  18. C. M. Schor, I. C. Wood, J. Ogawa, “Binocular sensory fusion is limited by spatial resolution,” Vision Res. 24, 661–665 (1984).
    [CrossRef] [PubMed]
  19. K. Pulliam, “Spatial frequency analysis of three-dimensional vision,” in Visual Simulation and Image Realism II, K. S. Setty, ed., Proc. Soc. Photo-Opt. Instrum. Eng.303, 17–23 (1981).
  20. C. W. Tyler, “Depth perception in disparity gratings,” Nature (London) 251, 140–142 (1974).
    [CrossRef]
  21. J. D. Pettigrew, T. Nikara, P. O. Bishop, “Binocular interaction on single units in cat striate cortex: simultaneous stimulation by single moving slits with receptive fields in correspondence,” Exp. Brain Res. 6, 391–410 (1968).
  22. D. Ferster, “A comparison of binocular depth mechanisms in areas 17 and 18 of the cat visual cortex,” J. Physiol. 311, 623–655 (1981).
    [PubMed]
  23. J. E. P. Frisby, J. E. W. Mayhew, “Contrast sensitivity function for stereopsis,” Perception 7, 423–429 (1978).
    [CrossRef] [PubMed]
  24. J. S. Mansfield, D. R. Simmons, “Contrast threshold for the identification of depth in bandpass-filtered stereograms,” Invest. Ophthalmol. Vis. Sci. Suppl. 30, 251 (1989).
  25. C. M. Schor, I. C. Wood, J. Ogawa, “Spatial tuning of static and dynamic local stereopsis,” Vision Res. 24, 573–578 (1984).
    [CrossRef] [PubMed]
  26. J. E. W. Mayhew, J. P. Frisby, “Convergent disparity discrimination in narrow-band-filtered random dot stereograms,” Vision Res. 19, 63–71 (1979).
    [CrossRef]
  27. D. R. Badcock, C. M. Schor, “Depth-increment detection function for individual spatial channels,” J. Opt. Soc. Am. A 2, 1211–1215 (1985).
    [CrossRef] [PubMed]
  28. Using only a fixation spot to constrain vergence state without verification by nonius lines is unsatisfactory because of the ability of the eye to fuse with fixation disparities up to Panum’s limit. Additionally, the sole use of convergent disparities in this study could have permitted observers to develop an anticipatory fixation disparity. It is interesting, further, to consider that such a fixation disparity would have reduced the 2.6′ disparity between the panels of highest spatial frequency in the Mayhew–Frisby study to a 168-deg phase disparity, which is close to the point at which we find peak contrast sensitivity in the present study. Our results make the counterintuitive prediction that the use of a bigger disparity difference between the two Mayhew–Frisby panels would have made the discrimination harder.
  29. L. L. Kontsevich, C. W. Tyler, “Analysis of stereothresholds for stimuli below 2.5 cy/deg,” Vision Res. (to be published).
  30. G. E. Legge, Y. Gu, “Stereopsis and contrast,” Vision Res. 29, 989–1004 (1989).
    [CrossRef] [PubMed]
  31. D. L. Halpern, R. Blake, “How contrast affects stereoacuity,” Perception 17, 483–495 (1988).
    [CrossRef] [PubMed]
  32. D. G. Pelli, L. Zhang, “Accurate control of contrast on microcomputer displays,” Vision Res. 7/8, 1337–1350 (1991).
    [CrossRef]
  33. After extensive use of this procedure it was decided that it was unnecessary to inquire of the subject the collinearity of the nonius lines before every trial. Instead, subjects were asked to redo trials in which they judged that the nonius lines were incorrectly aligned.
  34. C. Rashbass, G. Westheimer, “Independence of conjunctive and disjunctive eye movements,” J. Physiol. 159, 361–364 (1961).
  35. H. Levitt, “Transformed up–down methods in psychoacoustics,” J. Acoust. Soc. Am. 4, 467–477 (1971).
    [CrossRef]
  36. J. B. Mulligan, D. I. A. MacLeod, “Reciprocity between luminance and dot density in the perception of brightness,” Vision Res. 28, 503–519 (1988).
    [CrossRef] [PubMed]
  37. This prediction applies to the model in its simplest form employing solely vertically oriented mechanisms finely covering the range of spatial frequencies tested here and with no absolute positional disparity between the locations of the left and right eye’s receptive fields.
  38. A. M. Norcia, C. W. Tyler, “Temporal frequency limits for stereoscopic apparent motion processes,” Vision Res. 24, 395–401 (1984).
    [CrossRef] [PubMed]
  39. C. M. Schor, C. W. Tyler, “Spatio-temporal properties of Panum’s fusional area,” Vision Res. 21, 683–692 (1981).
    [CrossRef]
  40. G. C. S. Woo, “The effect of exposure time on the foveal size of Panum’s area,” Vision Res. 14, 473–480 (1974).
    [CrossRef] [PubMed]
  41. O. R. Mitchell, “Effect of spatial frequency on the visibility of unstructured patterns,” J. Opt. Soc. Am. 66, 327–332 (1976).
    [CrossRef] [PubMed]
  42. R. D. Freeman, I. Ohzawa, “On the neurophysiological organization of binocular vision,” Vision Res. 30, 1161–1675 (1990).
    [CrossRef]
  43. A. B. Watson, J. G. Robson, “Detection at threshold: labelled detectors in human vision,” Vision Res. 21, 1115–1122 (1981).
    [CrossRef]
  44. D. M. Levi, S. A. Klein, “Spatial localization in normal and amblyopic vision,” Vision Res. 23, 1005–1017 (1983).
    [CrossRef] [PubMed]
  45. J. E. W. Mayhew, J. P. Frisby, “The computation of binocular edges,” Perception 9, 69–86 (1980).
    [CrossRef] [PubMed]
  46. D. G. Jones, J. Malik, “A computational framework for determining stereo correspondence from a set of linear spatial filters,” Tech. Rep. 91-657 (University of California, Berkeley, Berkeley, Calif., 1991).
  47. L. Liu, C. W. Tyler, C. M. Schor, V. S. Ramachandran, “Position disparity is more efficient in encoding depth than phase disparity,” Invest. Ophthalmol. Vis. Sci. Suppl. 33/4, 1373 (1992).
  48. L. D. Jacobsen, J. P. Gaska, D. A. Pollen, “Phase, displacement, and hybrid models for disparity coding,” Invest. Ophthalmol. Vis. Sci. Suppl. 34/4, 908 (1993).
  49. S. P McKee, D. M. Levi, S. F. Bowne, “The imprecision of stereopsis,” Vision Res. 30, 1763–1779 (1990).
    [CrossRef] [PubMed]
  50. H. B. Barlow, “A method for determining the overall quantum efficiency of visual discrimination,” J. Physiol. (London) 160, 155–168 (1962).
  51. D. G. Pelli, “The quantum efficiency of vision,” in Vision: Coding and Efficiency, C. Blakemore, ed. (Cambridge U. Press, Cambridge, 1990), pp. 1–24.
  52. J. M. Harris, A. J. Parker, “Efficiency of stereopsis in random-dot stereograms,” J. Opt. Soc. Am. A. 9, 14–24 (1992).
    [CrossRef] [PubMed]
  53. J. S. Mansfield, A. J. Parker, “An orientation-tuned component in the contrast masking of stereopsis,” Vision Res. 33, 1535–1544 (1993).
    [CrossRef] [PubMed]
  54. S. R. Lehky, T. J. Sejnowski, “Neural model of stereoacuity and depth interpolation based on a distributed representation of stereo disparity,” J. Neurosci. 10, 2281–2299 (1990).
  55. S. B. Stevenson, L. K. Cormack, C. M. Schor, C. W. Tyler, “Disparity tuning in mechanisms of human stereopsis,” Vision Res. 32, 1685–1694 (1992).
    [CrossRef] [PubMed]
  56. L. K Cormack, S. B. Stevenson, C. M. Schor, “Disparitytuned channels of the human visual system,” Visual Neurosci. 10, 585–596 (1993).
    [CrossRef]
  57. G. Westheimer, S. P. McKee, “Stereoscopic acuity with defocused and spatially filtered retinal images,” J. Opt. Soc. Am. 70, 772–778 (1980).
    [CrossRef]
  58. P. Mowforth, J. E. Mayhew, J. P. Frisby, “Vergence eye movements made in response to spatial frequency-filtered random-dot stereograms,” Perception 10, 299–304 (1981).
    [CrossRef]
  59. H. S. Smallman, D. I. A. MacLeod, “Fine-to-coarse scale disambiguation in stereopsis,” Invest. Ophthalmol. Vis. Sci. Suppl. 33, 1369 (1992).
  60. H. S. Smallman, D. I. A. MacLeod, “Interactions across spatial scales and the size–disparity correlation in stereopsis,” in Annual Meeting, Vol. 16 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), p. 186.
  61. H. S. Smallman, D. I. A. MacLeod, “A size disparity correlation in stereopsis at contrast threshold,” in International Conference and NATO Workshop on Binocular Stereopsis and Optic Flow, June 22nd-26th 1993 (Centre for Vision Research, Toronto, Canada, 1993), p. 18.
  62. Included in this plot, but not shown in Fig. 2, are data taken at 1 cpd with 25-arcmin disparity.
  63. D. Brewster, “On the knowledge of distance given by binocular vision,” Trans. R. Soc. Edinburgh 15, 663–674 (1844).
    [CrossRef]
  64. K. Nakayama, G. H. Silverman, “Detection and discrimination of sinusoidal grating displacements,” J. Opt. Soc. Am. A. 2, 267–274 (1985).
    [CrossRef] [PubMed]
  65. D. M. Green, J. A. Swets, Signal Detection Theory and Psychophysics (Wiley, New York, 1966), p. 174.
  66. H. L. Van Trees, Detection, Estimation and Modulation Theory: Part 1 (Wiley, New York, 1968), p. 108.

1993 (3)

L. D. Jacobsen, J. P. Gaska, D. A. Pollen, “Phase, displacement, and hybrid models for disparity coding,” Invest. Ophthalmol. Vis. Sci. Suppl. 34/4, 908 (1993).

J. S. Mansfield, A. J. Parker, “An orientation-tuned component in the contrast masking of stereopsis,” Vision Res. 33, 1535–1544 (1993).
[CrossRef] [PubMed]

L. K Cormack, S. B. Stevenson, C. M. Schor, “Disparitytuned channels of the human visual system,” Visual Neurosci. 10, 585–596 (1993).
[CrossRef]

1992 (4)

H. S. Smallman, D. I. A. MacLeod, “Fine-to-coarse scale disambiguation in stereopsis,” Invest. Ophthalmol. Vis. Sci. Suppl. 33, 1369 (1992).

L. Liu, C. W. Tyler, C. M. Schor, V. S. Ramachandran, “Position disparity is more efficient in encoding depth than phase disparity,” Invest. Ophthalmol. Vis. Sci. Suppl. 33/4, 1373 (1992).

J. M. Harris, A. J. Parker, “Efficiency of stereopsis in random-dot stereograms,” J. Opt. Soc. Am. A. 9, 14–24 (1992).
[CrossRef] [PubMed]

S. B. Stevenson, L. K. Cormack, C. M. Schor, C. W. Tyler, “Disparity tuning in mechanisms of human stereopsis,” Vision Res. 32, 1685–1694 (1992).
[CrossRef] [PubMed]

1991 (5)

H. R. Wilson, R. Blake, D. L. Halpern, “Coarse spatial scales constrain the range of binocular fusion on fine scales,” J. Opt. Soc. Am. A 8, 229–236 (1991).
[CrossRef] [PubMed]

D. G. Pelli, L. Zhang, “Accurate control of contrast on microcomputer displays,” Vision Res. 7/8, 1337–1350 (1991).
[CrossRef]

Y. Yang, R. Blake, “Spatial frequency tuning of human stereopsis,” Vision Res. 31, 1177–1189 (1991).
[CrossRef] [PubMed]

R. Blake, H. R. Wilson, “Neural models of stereoscopic vision,” Trends Neurosci. 14, 445–452 (1991).
[CrossRef] [PubMed]

G. C. DeAngelis, I. Ohzawa, R. D. Freeman, “Depth is encoded in the visual cortex by a specialized receptive field structure,” Nature (London) 352, 156–159 (1991).
[CrossRef]

1990 (5)

S. F. Bowne, S. P. McKee, C. W. Tyler, “A disparity energy model of early stereo processing,” Invest. Ophthalmol. Vis. Sci. Suppl. 31, 303 (1990).

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

S. P McKee, D. M. Levi, S. F. Bowne, “The imprecision of stereopsis,” Vision Res. 30, 1763–1779 (1990).
[CrossRef] [PubMed]

R. D. Freeman, I. Ohzawa, “On the neurophysiological organization of binocular vision,” Vision Res. 30, 1161–1675 (1990).
[CrossRef]

S. R. Lehky, T. J. Sejnowski, “Neural model of stereoacuity and depth interpolation based on a distributed representation of stereo disparity,” J. Neurosci. 10, 2281–2299 (1990).

1989 (2)

G. E. Legge, Y. Gu, “Stereopsis and contrast,” Vision Res. 29, 989–1004 (1989).
[CrossRef] [PubMed]

J. S. Mansfield, D. R. Simmons, “Contrast threshold for the identification of depth in bandpass-filtered stereograms,” Invest. Ophthalmol. Vis. Sci. Suppl. 30, 251 (1989).

1988 (2)

D. L. Halpern, R. Blake, “How contrast affects stereoacuity,” Perception 17, 483–495 (1988).
[CrossRef] [PubMed]

J. B. Mulligan, D. I. A. MacLeod, “Reciprocity between luminance and dot density in the perception of brightness,” Vision Res. 28, 503–519 (1988).
[CrossRef] [PubMed]

1985 (3)

1984 (3)

A. M. Norcia, C. W. Tyler, “Temporal frequency limits for stereoscopic apparent motion processes,” Vision Res. 24, 395–401 (1984).
[CrossRef] [PubMed]

C. M. Schor, I. C. Wood, J. Ogawa, “Spatial tuning of static and dynamic local stereopsis,” Vision Res. 24, 573–578 (1984).
[CrossRef] [PubMed]

C. M. Schor, I. C. Wood, J. Ogawa, “Binocular sensory fusion is limited by spatial resolution,” Vision Res. 24, 661–665 (1984).
[CrossRef] [PubMed]

1983 (2)

C. M. Schor, I. Wood, “Disparity range for local stereopsis as a function of luminance spatial frequency,” Vision Res. 23, 1649–1654 (1983).
[CrossRef] [PubMed]

D. M. Levi, S. A. Klein, “Spatial localization in normal and amblyopic vision,” Vision Res. 23, 1005–1017 (1983).
[CrossRef] [PubMed]

1981 (4)

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

C. M. Schor, C. W. Tyler, “Spatio-temporal properties of Panum’s fusional area,” Vision Res. 21, 683–692 (1981).
[CrossRef]

D. Ferster, “A comparison of binocular depth mechanisms in areas 17 and 18 of the cat visual cortex,” J. Physiol. 311, 623–655 (1981).
[PubMed]

P. Mowforth, J. E. Mayhew, J. P. Frisby, “Vergence eye movements made in response to spatial frequency-filtered random-dot stereograms,” Perception 10, 299–304 (1981).
[CrossRef]

1980 (2)

1979 (2)

J. E. W. Mayhew, J. P. Frisby, “Convergent disparity discrimination in narrow-band-filtered random dot stereograms,” Vision Res. 19, 63–71 (1979).
[CrossRef]

D. Marr, T. Poggio, “A computational theory of human stereo vision,” Proc. R. Soc. London Ser. B 204, 301–328 (1979).
[CrossRef]

1978 (2)

J. E. P. Frisby, J. E. W. Mayhew, “Contrast sensitivity function for stereopsis,” Perception 7, 423–429 (1978).
[CrossRef] [PubMed]

J. J. Kulikowski, “Limit of single vision in stereopsis depends on contour sharpness,” Nature (London) 275, 126–127 (1978).
[CrossRef]

1976 (2)

1975 (1)

B. Julesz, J. E. Miller, “Independent spatial-frequencytuned channels in binocular fusion and rivalry,” Perception 4, 125–143 (1975).
[CrossRef]

1974 (2)

C. W. Tyler, “Depth perception in disparity gratings,” Nature (London) 251, 140–142 (1974).
[CrossRef]

G. C. S. Woo, “The effect of exposure time on the foveal size of Panum’s area,” Vision Res. 14, 473–480 (1974).
[CrossRef] [PubMed]

1972 (1)

T. B. Felton, W. Richards, R. A. Smith, “Disparity processing of spatial frequencies in man,” J. Physiol. 225, 340–362 (1972).

1971 (1)

H. Levitt, “Transformed up–down methods in psychoacoustics,” J. Acoust. Soc. Am. 4, 467–477 (1971).
[CrossRef]

1968 (2)

J. D. Pettigrew, T. Nikara, P. O. Bishop, “Binocular interaction on single units in cat striate cortex: simultaneous stimulation by single moving slits with receptive fields in correspondence,” Exp. Brain Res. 6, 391–410 (1968).

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

1962 (1)

H. B. Barlow, “A method for determining the overall quantum efficiency of visual discrimination,” J. Physiol. (London) 160, 155–168 (1962).

1961 (1)

C. Rashbass, G. Westheimer, “Independence of conjunctive and disjunctive eye movements,” J. Physiol. 159, 361–364 (1961).

1844 (1)

D. Brewster, “On the knowledge of distance given by binocular vision,” Trans. R. Soc. Edinburgh 15, 663–674 (1844).
[CrossRef]

Adelson, E. H.

Badcock, D. R.

Barlow, H. B.

H. B. Barlow, “A method for determining the overall quantum efficiency of visual discrimination,” J. Physiol. (London) 160, 155–168 (1962).

Bergen, J. R.

Bishop, P. O.

J. D. Pettigrew, T. Nikara, P. O. Bishop, “Binocular interaction on single units in cat striate cortex: simultaneous stimulation by single moving slits with receptive fields in correspondence,” Exp. Brain Res. 6, 391–410 (1968).

Blake, R.

Y. Yang, R. Blake, “Spatial frequency tuning of human stereopsis,” Vision Res. 31, 1177–1189 (1991).
[CrossRef] [PubMed]

H. R. Wilson, R. Blake, D. L. Halpern, “Coarse spatial scales constrain the range of binocular fusion on fine scales,” J. Opt. Soc. Am. A 8, 229–236 (1991).
[CrossRef] [PubMed]

R. Blake, H. R. Wilson, “Neural models of stereoscopic vision,” Trends Neurosci. 14, 445–452 (1991).
[CrossRef] [PubMed]

D. L. Halpern, R. Blake, “How contrast affects stereoacuity,” Perception 17, 483–495 (1988).
[CrossRef] [PubMed]

Bowne, S. F.

S. F. Bowne, S. P. McKee, C. W. Tyler, “A disparity energy model of early stereo processing,” Invest. Ophthalmol. Vis. Sci. Suppl. 31, 303 (1990).

S. P McKee, D. M. Levi, S. F. Bowne, “The imprecision of stereopsis,” Vision Res. 30, 1763–1779 (1990).
[CrossRef] [PubMed]

Brewster, D.

D. Brewster, “On the knowledge of distance given by binocular vision,” Trans. R. Soc. Edinburgh 15, 663–674 (1844).
[CrossRef]

Campbell, F. W.

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

Cormack, L. K

L. K Cormack, S. B. Stevenson, C. M. Schor, “Disparitytuned channels of the human visual system,” Visual Neurosci. 10, 585–596 (1993).
[CrossRef]

Cormack, L. K.

S. B. Stevenson, L. K. Cormack, C. M. Schor, C. W. Tyler, “Disparity tuning in mechanisms of human stereopsis,” Vision Res. 32, 1685–1694 (1992).
[CrossRef] [PubMed]

DeAngelis, G. C.

G. C. DeAngelis, I. Ohzawa, R. D. Freeman, “Depth is encoded in the visual cortex by a specialized receptive field structure,” Nature (London) 352, 156–159 (1991).
[CrossRef]

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

DeValois, K. K.

R. L. DeValois, K. K. DeValois, Spatial Vision (Oxford U. Press, New York, 1988).

DeValois, R. L.

H. R. Wilson, D. Levi, L. Maffei, J. Rovamo, R. L. DeValois, “The perception of form: retina to striate cortex,” in Visual Perception: The Neurophysiological Foundations, L. Spillman, J. S. Werner, eds. (Academic, San Diego, Calif., 1990), pp. 317–347.

R. L. DeValois, K. K. DeValois, Spatial Vision (Oxford U. Press, New York, 1988).

Felton, T. B.

T. B. Felton, W. Richards, R. A. Smith, “Disparity processing of spatial frequencies in man,” J. Physiol. 225, 340–362 (1972).

Ferster, D.

D. Ferster, “A comparison of binocular depth mechanisms in areas 17 and 18 of the cat visual cortex,” J. Physiol. 311, 623–655 (1981).
[PubMed]

Freeman, R. D.

G. C. DeAngelis, I. Ohzawa, R. D. Freeman, “Depth is encoded in the visual cortex by a specialized receptive field structure,” Nature (London) 352, 156–159 (1991).
[CrossRef]

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

R. D. Freeman, I. Ohzawa, “On the neurophysiological organization of binocular vision,” Vision Res. 30, 1161–1675 (1990).
[CrossRef]

Frisby, J. E. P.

J. E. P. Frisby, J. E. W. Mayhew, “Contrast sensitivity function for stereopsis,” Perception 7, 423–429 (1978).
[CrossRef] [PubMed]

Frisby, J. P.

P. Mowforth, J. E. Mayhew, J. P. Frisby, “Vergence eye movements made in response to spatial frequency-filtered random-dot stereograms,” Perception 10, 299–304 (1981).
[CrossRef]

J. E. W. Mayhew, J. P. Frisby, “The computation of binocular edges,” Perception 9, 69–86 (1980).
[CrossRef] [PubMed]

J. E. W. Mayhew, J. P. Frisby, “Convergent disparity discrimination in narrow-band-filtered random dot stereograms,” Vision Res. 19, 63–71 (1979).
[CrossRef]

J. E. W. Mayhew, J. P. Frisby, “Rivalrous texture stereograms,” Nature (London) 264, 53–56 (1976).
[CrossRef]

Gaska, J. P.

L. D. Jacobsen, J. P. Gaska, D. A. Pollen, “Phase, displacement, and hybrid models for disparity coding,” Invest. Ophthalmol. Vis. Sci. Suppl. 34/4, 908 (1993).

Green, D. M.

D. M. Green, J. A. Swets, Signal Detection Theory and Psychophysics (Wiley, New York, 1966), p. 174.

Gu, Y.

G. E. Legge, Y. Gu, “Stereopsis and contrast,” Vision Res. 29, 989–1004 (1989).
[CrossRef] [PubMed]

Halpern, D. L.

Harris, J. M.

J. M. Harris, A. J. Parker, “Efficiency of stereopsis in random-dot stereograms,” J. Opt. Soc. Am. A. 9, 14–24 (1992).
[CrossRef] [PubMed]

Jacobsen, L. D.

L. D. Jacobsen, J. P. Gaska, D. A. Pollen, “Phase, displacement, and hybrid models for disparity coding,” Invest. Ophthalmol. Vis. Sci. Suppl. 34/4, 908 (1993).

Jones, D. G.

D. G. Jones, J. Malik, “A computational framework for determining stereo correspondence from a set of linear spatial filters,” Tech. Rep. 91-657 (University of California, Berkeley, Berkeley, Calif., 1991).

Julesz, B.

B. Julesz, J. E. Miller, “Independent spatial-frequencytuned channels in binocular fusion and rivalry,” Perception 4, 125–143 (1975).
[CrossRef]

B. Julesz, Foundations of Cyclopean Perception (U. Chicago Press, Chicago, Ill., 1971), pp. 100–102.

Klein, S. A.

D. M. Levi, S. A. Klein, “Spatial localization in normal and amblyopic vision,” Vision Res. 23, 1005–1017 (1983).
[CrossRef] [PubMed]

Kontsevich, L. L.

L. L. Kontsevich, C. W. Tyler, “Analysis of stereothresholds for stimuli below 2.5 cy/deg,” Vision Res. (to be published).

Kulikowski, J. J.

J. J. Kulikowski, “Limit of single vision in stereopsis depends on contour sharpness,” Nature (London) 275, 126–127 (1978).
[CrossRef]

Legge, G. E.

G. E. Legge, Y. Gu, “Stereopsis and contrast,” Vision Res. 29, 989–1004 (1989).
[CrossRef] [PubMed]

Lehky, S. R.

S. R. Lehky, T. J. Sejnowski, “Neural model of stereoacuity and depth interpolation based on a distributed representation of stereo disparity,” J. Neurosci. 10, 2281–2299 (1990).

Levi, D.

H. R. Wilson, D. Levi, L. Maffei, J. Rovamo, R. L. DeValois, “The perception of form: retina to striate cortex,” in Visual Perception: The Neurophysiological Foundations, L. Spillman, J. S. Werner, eds. (Academic, San Diego, Calif., 1990), pp. 317–347.

Levi, D. M.

S. P McKee, D. M. Levi, S. F. Bowne, “The imprecision of stereopsis,” Vision Res. 30, 1763–1779 (1990).
[CrossRef] [PubMed]

D. M. Levi, S. A. Klein, “Spatial localization in normal and amblyopic vision,” Vision Res. 23, 1005–1017 (1983).
[CrossRef] [PubMed]

Levitt, H.

H. Levitt, “Transformed up–down methods in psychoacoustics,” J. Acoust. Soc. Am. 4, 467–477 (1971).
[CrossRef]

Liu, L.

L. Liu, C. W. Tyler, C. M. Schor, V. S. Ramachandran, “Position disparity is more efficient in encoding depth than phase disparity,” Invest. Ophthalmol. Vis. Sci. Suppl. 33/4, 1373 (1992).

MacLeod, D. I. A.

H. S. Smallman, D. I. A. MacLeod, “Fine-to-coarse scale disambiguation in stereopsis,” Invest. Ophthalmol. Vis. Sci. Suppl. 33, 1369 (1992).

J. B. Mulligan, D. I. A. MacLeod, “Reciprocity between luminance and dot density in the perception of brightness,” Vision Res. 28, 503–519 (1988).
[CrossRef] [PubMed]

H. S. Smallman, D. I. A. MacLeod, “Interactions across spatial scales and the size–disparity correlation in stereopsis,” in Annual Meeting, Vol. 16 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), p. 186.

H. S. Smallman, D. I. A. MacLeod, “A size disparity correlation in stereopsis at contrast threshold,” in International Conference and NATO Workshop on Binocular Stereopsis and Optic Flow, June 22nd-26th 1993 (Centre for Vision Research, Toronto, Canada, 1993), p. 18.

Maffei, L.

H. R. Wilson, D. Levi, L. Maffei, J. Rovamo, R. L. DeValois, “The perception of form: retina to striate cortex,” in Visual Perception: The Neurophysiological Foundations, L. Spillman, J. S. Werner, eds. (Academic, San Diego, Calif., 1990), pp. 317–347.

Malik, J.

D. G. Jones, J. Malik, “A computational framework for determining stereo correspondence from a set of linear spatial filters,” Tech. Rep. 91-657 (University of California, Berkeley, Berkeley, Calif., 1991).

Mansfield, J. S.

J. S. Mansfield, A. J. Parker, “An orientation-tuned component in the contrast masking of stereopsis,” Vision Res. 33, 1535–1544 (1993).
[CrossRef] [PubMed]

J. S. Mansfield, D. R. Simmons, “Contrast threshold for the identification of depth in bandpass-filtered stereograms,” Invest. Ophthalmol. Vis. Sci. Suppl. 30, 251 (1989).

Marr, D.

D. Marr, T. Poggio, “A computational theory of human stereo vision,” Proc. R. Soc. London Ser. B 204, 301–328 (1979).
[CrossRef]

Mayhew, J. E.

P. Mowforth, J. E. Mayhew, J. P. Frisby, “Vergence eye movements made in response to spatial frequency-filtered random-dot stereograms,” Perception 10, 299–304 (1981).
[CrossRef]

Mayhew, J. E. W.

J. E. W. Mayhew, J. P. Frisby, “The computation of binocular edges,” Perception 9, 69–86 (1980).
[CrossRef] [PubMed]

J. E. W. Mayhew, J. P. Frisby, “Convergent disparity discrimination in narrow-band-filtered random dot stereograms,” Vision Res. 19, 63–71 (1979).
[CrossRef]

J. E. P. Frisby, J. E. W. Mayhew, “Contrast sensitivity function for stereopsis,” Perception 7, 423–429 (1978).
[CrossRef] [PubMed]

J. E. W. Mayhew, J. P. Frisby, “Rivalrous texture stereograms,” Nature (London) 264, 53–56 (1976).
[CrossRef]

McKee, S. P

S. P McKee, D. M. Levi, S. F. Bowne, “The imprecision of stereopsis,” Vision Res. 30, 1763–1779 (1990).
[CrossRef] [PubMed]

McKee, S. P.

S. F. Bowne, S. P. McKee, C. W. Tyler, “A disparity energy model of early stereo processing,” Invest. Ophthalmol. Vis. Sci. Suppl. 31, 303 (1990).

G. Westheimer, S. P. McKee, “Stereoscopic acuity with defocused and spatially filtered retinal images,” J. Opt. Soc. Am. 70, 772–778 (1980).
[CrossRef]

Miller, J. E.

B. Julesz, J. E. Miller, “Independent spatial-frequencytuned channels in binocular fusion and rivalry,” Perception 4, 125–143 (1975).
[CrossRef]

Mitchell, O. R.

Mowforth, P.

P. Mowforth, J. E. Mayhew, J. P. Frisby, “Vergence eye movements made in response to spatial frequency-filtered random-dot stereograms,” Perception 10, 299–304 (1981).
[CrossRef]

Mulligan, J. B.

J. B. Mulligan, D. I. A. MacLeod, “Reciprocity between luminance and dot density in the perception of brightness,” Vision Res. 28, 503–519 (1988).
[CrossRef] [PubMed]

Nakayama, K.

K. Nakayama, G. H. Silverman, “Detection and discrimination of sinusoidal grating displacements,” J. Opt. Soc. Am. A. 2, 267–274 (1985).
[CrossRef] [PubMed]

Nikara, T.

J. D. Pettigrew, T. Nikara, P. O. Bishop, “Binocular interaction on single units in cat striate cortex: simultaneous stimulation by single moving slits with receptive fields in correspondence,” Exp. Brain Res. 6, 391–410 (1968).

Norcia, A. M.

A. M. Norcia, C. W. Tyler, “Temporal frequency limits for stereoscopic apparent motion processes,” Vision Res. 24, 395–401 (1984).
[CrossRef] [PubMed]

Ogawa, J.

C. M. Schor, I. C. Wood, J. Ogawa, “Spatial tuning of static and dynamic local stereopsis,” Vision Res. 24, 573–578 (1984).
[CrossRef] [PubMed]

C. M. Schor, I. C. Wood, J. Ogawa, “Binocular sensory fusion is limited by spatial resolution,” Vision Res. 24, 661–665 (1984).
[CrossRef] [PubMed]

Ohzawa, I.

G. C. DeAngelis, I. Ohzawa, R. D. Freeman, “Depth is encoded in the visual cortex by a specialized receptive field structure,” Nature (London) 352, 156–159 (1991).
[CrossRef]

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

R. D. Freeman, I. Ohzawa, “On the neurophysiological organization of binocular vision,” Vision Res. 30, 1161–1675 (1990).
[CrossRef]

Parker, A. J.

J. S. Mansfield, A. J. Parker, “An orientation-tuned component in the contrast masking of stereopsis,” Vision Res. 33, 1535–1544 (1993).
[CrossRef] [PubMed]

J. M. Harris, A. J. Parker, “Efficiency of stereopsis in random-dot stereograms,” J. Opt. Soc. Am. A. 9, 14–24 (1992).
[CrossRef] [PubMed]

Pelli, D. G.

D. G. Pelli, L. Zhang, “Accurate control of contrast on microcomputer displays,” Vision Res. 7/8, 1337–1350 (1991).
[CrossRef]

D. G. Pelli, “The quantum efficiency of vision,” in Vision: Coding and Efficiency, C. Blakemore, ed. (Cambridge U. Press, Cambridge, 1990), pp. 1–24.

Pettigrew, J. D.

J. D. Pettigrew, T. Nikara, P. O. Bishop, “Binocular interaction on single units in cat striate cortex: simultaneous stimulation by single moving slits with receptive fields in correspondence,” Exp. Brain Res. 6, 391–410 (1968).

Poggio, T.

D. Marr, T. Poggio, “A computational theory of human stereo vision,” Proc. R. Soc. London Ser. B 204, 301–328 (1979).
[CrossRef]

Pollen, D. A.

L. D. Jacobsen, J. P. Gaska, D. A. Pollen, “Phase, displacement, and hybrid models for disparity coding,” Invest. Ophthalmol. Vis. Sci. Suppl. 34/4, 908 (1993).

Pulliam, K.

K. Pulliam, “Spatial frequency analysis of three-dimensional vision,” in Visual Simulation and Image Realism II, K. S. Setty, ed., Proc. Soc. Photo-Opt. Instrum. Eng.303, 17–23 (1981).

Ramachandran, V. S.

L. Liu, C. W. Tyler, C. M. Schor, V. S. Ramachandran, “Position disparity is more efficient in encoding depth than phase disparity,” Invest. Ophthalmol. Vis. Sci. Suppl. 33/4, 1373 (1992).

Rashbass, C.

C. Rashbass, G. Westheimer, “Independence of conjunctive and disjunctive eye movements,” J. Physiol. 159, 361–364 (1961).

Richards, W.

T. B. Felton, W. Richards, R. A. Smith, “Disparity processing of spatial frequencies in man,” J. Physiol. 225, 340–362 (1972).

Robson, J. G.

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

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

Rovamo, J.

H. R. Wilson, D. Levi, L. Maffei, J. Rovamo, R. L. DeValois, “The perception of form: retina to striate cortex,” in Visual Perception: The Neurophysiological Foundations, L. Spillman, J. S. Werner, eds. (Academic, San Diego, Calif., 1990), pp. 317–347.

Schor, C. M.

L. K Cormack, S. B. Stevenson, C. M. Schor, “Disparitytuned channels of the human visual system,” Visual Neurosci. 10, 585–596 (1993).
[CrossRef]

S. B. Stevenson, L. K. Cormack, C. M. Schor, C. W. Tyler, “Disparity tuning in mechanisms of human stereopsis,” Vision Res. 32, 1685–1694 (1992).
[CrossRef] [PubMed]

L. Liu, C. W. Tyler, C. M. Schor, V. S. Ramachandran, “Position disparity is more efficient in encoding depth than phase disparity,” Invest. Ophthalmol. Vis. Sci. Suppl. 33/4, 1373 (1992).

D. R. Badcock, C. M. Schor, “Depth-increment detection function for individual spatial channels,” J. Opt. Soc. Am. A 2, 1211–1215 (1985).
[CrossRef] [PubMed]

C. M. Schor, I. C. Wood, J. Ogawa, “Spatial tuning of static and dynamic local stereopsis,” Vision Res. 24, 573–578 (1984).
[CrossRef] [PubMed]

C. M. Schor, I. C. Wood, J. Ogawa, “Binocular sensory fusion is limited by spatial resolution,” Vision Res. 24, 661–665 (1984).
[CrossRef] [PubMed]

C. M. Schor, I. Wood, “Disparity range for local stereopsis as a function of luminance spatial frequency,” Vision Res. 23, 1649–1654 (1983).
[CrossRef] [PubMed]

C. M. Schor, C. W. Tyler, “Spatio-temporal properties of Panum’s fusional area,” Vision Res. 21, 683–692 (1981).
[CrossRef]

Sejnowski, T. J.

S. R. Lehky, T. J. Sejnowski, “Neural model of stereoacuity and depth interpolation based on a distributed representation of stereo disparity,” J. Neurosci. 10, 2281–2299 (1990).

Silverman, G. H.

K. Nakayama, G. H. Silverman, “Detection and discrimination of sinusoidal grating displacements,” J. Opt. Soc. Am. A. 2, 267–274 (1985).
[CrossRef] [PubMed]

Simmons, D. R.

J. S. Mansfield, D. R. Simmons, “Contrast threshold for the identification of depth in bandpass-filtered stereograms,” Invest. Ophthalmol. Vis. Sci. Suppl. 30, 251 (1989).

Smallman, H. S.

H. S. Smallman, D. I. A. MacLeod, “Fine-to-coarse scale disambiguation in stereopsis,” Invest. Ophthalmol. Vis. Sci. Suppl. 33, 1369 (1992).

H. S. Smallman, D. I. A. MacLeod, “Interactions across spatial scales and the size–disparity correlation in stereopsis,” in Annual Meeting, Vol. 16 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), p. 186.

H. S. Smallman, D. I. A. MacLeod, “A size disparity correlation in stereopsis at contrast threshold,” in International Conference and NATO Workshop on Binocular Stereopsis and Optic Flow, June 22nd-26th 1993 (Centre for Vision Research, Toronto, Canada, 1993), p. 18.

Smith, R. A.

T. B. Felton, W. Richards, R. A. Smith, “Disparity processing of spatial frequencies in man,” J. Physiol. 225, 340–362 (1972).

Stevenson, S. B.

L. K Cormack, S. B. Stevenson, C. M. Schor, “Disparitytuned channels of the human visual system,” Visual Neurosci. 10, 585–596 (1993).
[CrossRef]

S. B. Stevenson, L. K. Cormack, C. M. Schor, C. W. Tyler, “Disparity tuning in mechanisms of human stereopsis,” Vision Res. 32, 1685–1694 (1992).
[CrossRef] [PubMed]

Swets, J. A.

D. M. Green, J. A. Swets, Signal Detection Theory and Psychophysics (Wiley, New York, 1966), p. 174.

Tyler, C. W.

S. B. Stevenson, L. K. Cormack, C. M. Schor, C. W. Tyler, “Disparity tuning in mechanisms of human stereopsis,” Vision Res. 32, 1685–1694 (1992).
[CrossRef] [PubMed]

L. Liu, C. W. Tyler, C. M. Schor, V. S. Ramachandran, “Position disparity is more efficient in encoding depth than phase disparity,” Invest. Ophthalmol. Vis. Sci. Suppl. 33/4, 1373 (1992).

S. F. Bowne, S. P. McKee, C. W. Tyler, “A disparity energy model of early stereo processing,” Invest. Ophthalmol. Vis. Sci. Suppl. 31, 303 (1990).

A. M. Norcia, C. W. Tyler, “Temporal frequency limits for stereoscopic apparent motion processes,” Vision Res. 24, 395–401 (1984).
[CrossRef] [PubMed]

C. M. Schor, C. W. Tyler, “Spatio-temporal properties of Panum’s fusional area,” Vision Res. 21, 683–692 (1981).
[CrossRef]

C. W. Tyler, “Depth perception in disparity gratings,” Nature (London) 251, 140–142 (1974).
[CrossRef]

L. L. Kontsevich, C. W. Tyler, “Analysis of stereothresholds for stimuli below 2.5 cy/deg,” Vision Res. (to be published).

Van Trees, H. L.

H. L. Van Trees, Detection, Estimation and Modulation Theory: Part 1 (Wiley, New York, 1968), p. 108.

Watson, A. B.

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

Westheimer, G.

G. Westheimer, S. P. McKee, “Stereoscopic acuity with defocused and spatially filtered retinal images,” J. Opt. Soc. Am. 70, 772–778 (1980).
[CrossRef]

C. Rashbass, G. Westheimer, “Independence of conjunctive and disjunctive eye movements,” J. Physiol. 159, 361–364 (1961).

Wilson, H. R.

R. Blake, H. R. Wilson, “Neural models of stereoscopic vision,” Trends Neurosci. 14, 445–452 (1991).
[CrossRef] [PubMed]

H. R. Wilson, R. Blake, D. L. Halpern, “Coarse spatial scales constrain the range of binocular fusion on fine scales,” J. Opt. Soc. Am. A 8, 229–236 (1991).
[CrossRef] [PubMed]

H. R. Wilson, D. Levi, L. Maffei, J. Rovamo, R. L. DeValois, “The perception of form: retina to striate cortex,” in Visual Perception: The Neurophysiological Foundations, L. Spillman, J. S. Werner, eds. (Academic, San Diego, Calif., 1990), pp. 317–347.

Woo, G. C. S.

G. C. S. Woo, “The effect of exposure time on the foveal size of Panum’s area,” Vision Res. 14, 473–480 (1974).
[CrossRef] [PubMed]

Wood, I.

C. M. Schor, I. Wood, “Disparity range for local stereopsis as a function of luminance spatial frequency,” Vision Res. 23, 1649–1654 (1983).
[CrossRef] [PubMed]

Wood, I. C.

C. M. Schor, I. C. Wood, J. Ogawa, “Binocular sensory fusion is limited by spatial resolution,” Vision Res. 24, 661–665 (1984).
[CrossRef] [PubMed]

C. M. Schor, I. C. Wood, J. Ogawa, “Spatial tuning of static and dynamic local stereopsis,” Vision Res. 24, 573–578 (1984).
[CrossRef] [PubMed]

Yang, Y.

Y. Yang, R. Blake, “Spatial frequency tuning of human stereopsis,” Vision Res. 31, 1177–1189 (1991).
[CrossRef] [PubMed]

Zhang, L.

D. G. Pelli, L. Zhang, “Accurate control of contrast on microcomputer displays,” Vision Res. 7/8, 1337–1350 (1991).
[CrossRef]

Exp. Brain Res. (1)

J. D. Pettigrew, T. Nikara, P. O. Bishop, “Binocular interaction on single units in cat striate cortex: simultaneous stimulation by single moving slits with receptive fields in correspondence,” Exp. Brain Res. 6, 391–410 (1968).

Invest. Ophthalmol. Vis. Sci. Suppl. (5)

L. Liu, C. W. Tyler, C. M. Schor, V. S. Ramachandran, “Position disparity is more efficient in encoding depth than phase disparity,” Invest. Ophthalmol. Vis. Sci. Suppl. 33/4, 1373 (1992).

L. D. Jacobsen, J. P. Gaska, D. A. Pollen, “Phase, displacement, and hybrid models for disparity coding,” Invest. Ophthalmol. Vis. Sci. Suppl. 34/4, 908 (1993).

S. F. Bowne, S. P. McKee, C. W. Tyler, “A disparity energy model of early stereo processing,” Invest. Ophthalmol. Vis. Sci. Suppl. 31, 303 (1990).

J. S. Mansfield, D. R. Simmons, “Contrast threshold for the identification of depth in bandpass-filtered stereograms,” Invest. Ophthalmol. Vis. Sci. Suppl. 30, 251 (1989).

H. S. Smallman, D. I. A. MacLeod, “Fine-to-coarse scale disambiguation in stereopsis,” Invest. Ophthalmol. Vis. Sci. Suppl. 33, 1369 (1992).

J. Acoust. Soc. Am. (1)

H. Levitt, “Transformed up–down methods in psychoacoustics,” J. Acoust. Soc. Am. 4, 467–477 (1971).
[CrossRef]

J. Neurosci. (1)

S. R. Lehky, T. J. Sejnowski, “Neural model of stereoacuity and depth interpolation based on a distributed representation of stereo disparity,” J. Neurosci. 10, 2281–2299 (1990).

J. Opt. Soc. Am. (2)

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

J. Opt. Soc. Am. A. (2)

K. Nakayama, G. H. Silverman, “Detection and discrimination of sinusoidal grating displacements,” J. Opt. Soc. Am. A. 2, 267–274 (1985).
[CrossRef] [PubMed]

J. M. Harris, A. J. Parker, “Efficiency of stereopsis in random-dot stereograms,” J. Opt. Soc. Am. A. 9, 14–24 (1992).
[CrossRef] [PubMed]

J. Physiol. (4)

D. Ferster, “A comparison of binocular depth mechanisms in areas 17 and 18 of the cat visual cortex,” J. Physiol. 311, 623–655 (1981).
[PubMed]

T. B. Felton, W. Richards, R. A. Smith, “Disparity processing of spatial frequencies in man,” J. Physiol. 225, 340–362 (1972).

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

C. Rashbass, G. Westheimer, “Independence of conjunctive and disjunctive eye movements,” J. Physiol. 159, 361–364 (1961).

J. Physiol. (London) (1)

H. B. Barlow, “A method for determining the overall quantum efficiency of visual discrimination,” J. Physiol. (London) 160, 155–168 (1962).

Nature (London) (4)

C. W. Tyler, “Depth perception in disparity gratings,” Nature (London) 251, 140–142 (1974).
[CrossRef]

J. E. W. Mayhew, J. P. Frisby, “Rivalrous texture stereograms,” Nature (London) 264, 53–56 (1976).
[CrossRef]

J. J. Kulikowski, “Limit of single vision in stereopsis depends on contour sharpness,” Nature (London) 275, 126–127 (1978).
[CrossRef]

G. C. DeAngelis, I. Ohzawa, R. D. Freeman, “Depth is encoded in the visual cortex by a specialized receptive field structure,” Nature (London) 352, 156–159 (1991).
[CrossRef]

Perception (5)

P. Mowforth, J. E. Mayhew, J. P. Frisby, “Vergence eye movements made in response to spatial frequency-filtered random-dot stereograms,” Perception 10, 299–304 (1981).
[CrossRef]

D. L. Halpern, R. Blake, “How contrast affects stereoacuity,” Perception 17, 483–495 (1988).
[CrossRef] [PubMed]

B. Julesz, J. E. Miller, “Independent spatial-frequencytuned channels in binocular fusion and rivalry,” Perception 4, 125–143 (1975).
[CrossRef]

J. E. P. Frisby, J. E. W. Mayhew, “Contrast sensitivity function for stereopsis,” Perception 7, 423–429 (1978).
[CrossRef] [PubMed]

J. E. W. Mayhew, J. P. Frisby, “The computation of binocular edges,” Perception 9, 69–86 (1980).
[CrossRef] [PubMed]

Proc. R. Soc. London Ser. B (1)

D. Marr, T. Poggio, “A computational theory of human stereo vision,” Proc. R. Soc. London Ser. B 204, 301–328 (1979).
[CrossRef]

Science (1)

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

Trans. R. Soc. Edinburgh (1)

D. Brewster, “On the knowledge of distance given by binocular vision,” Trans. R. Soc. Edinburgh 15, 663–674 (1844).
[CrossRef]

Trends Neurosci. (1)

R. Blake, H. R. Wilson, “Neural models of stereoscopic vision,” Trends Neurosci. 14, 445–452 (1991).
[CrossRef] [PubMed]

Vision Res. (17)

D. G. Pelli, L. Zhang, “Accurate control of contrast on microcomputer displays,” Vision Res. 7/8, 1337–1350 (1991).
[CrossRef]

J. B. Mulligan, D. I. A. MacLeod, “Reciprocity between luminance and dot density in the perception of brightness,” Vision Res. 28, 503–519 (1988).
[CrossRef] [PubMed]

A. M. Norcia, C. W. Tyler, “Temporal frequency limits for stereoscopic apparent motion processes,” Vision Res. 24, 395–401 (1984).
[CrossRef] [PubMed]

C. M. Schor, C. W. Tyler, “Spatio-temporal properties of Panum’s fusional area,” Vision Res. 21, 683–692 (1981).
[CrossRef]

G. C. S. Woo, “The effect of exposure time on the foveal size of Panum’s area,” Vision Res. 14, 473–480 (1974).
[CrossRef] [PubMed]

S. P McKee, D. M. Levi, S. F. Bowne, “The imprecision of stereopsis,” Vision Res. 30, 1763–1779 (1990).
[CrossRef] [PubMed]

G. E. Legge, Y. Gu, “Stereopsis and contrast,” Vision Res. 29, 989–1004 (1989).
[CrossRef] [PubMed]

J. S. Mansfield, A. J. Parker, “An orientation-tuned component in the contrast masking of stereopsis,” Vision Res. 33, 1535–1544 (1993).
[CrossRef] [PubMed]

S. B. Stevenson, L. K. Cormack, C. M. Schor, C. W. Tyler, “Disparity tuning in mechanisms of human stereopsis,” Vision Res. 32, 1685–1694 (1992).
[CrossRef] [PubMed]

Y. Yang, R. Blake, “Spatial frequency tuning of human stereopsis,” Vision Res. 31, 1177–1189 (1991).
[CrossRef] [PubMed]

C. M. Schor, I. Wood, “Disparity range for local stereopsis as a function of luminance spatial frequency,” Vision Res. 23, 1649–1654 (1983).
[CrossRef] [PubMed]

C. M. Schor, I. C. Wood, J. Ogawa, “Binocular sensory fusion is limited by spatial resolution,” Vision Res. 24, 661–665 (1984).
[CrossRef] [PubMed]

C. M. Schor, I. C. Wood, J. Ogawa, “Spatial tuning of static and dynamic local stereopsis,” Vision Res. 24, 573–578 (1984).
[CrossRef] [PubMed]

J. E. W. Mayhew, J. P. Frisby, “Convergent disparity discrimination in narrow-band-filtered random dot stereograms,” Vision Res. 19, 63–71 (1979).
[CrossRef]

R. D. Freeman, I. Ohzawa, “On the neurophysiological organization of binocular vision,” Vision Res. 30, 1161–1675 (1990).
[CrossRef]

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

D. M. Levi, S. A. Klein, “Spatial localization in normal and amblyopic vision,” Vision Res. 23, 1005–1017 (1983).
[CrossRef] [PubMed]

Visual Neurosci. (1)

L. K Cormack, S. B. Stevenson, C. M. Schor, “Disparitytuned channels of the human visual system,” Visual Neurosci. 10, 585–596 (1993).
[CrossRef]

Other (15)

Using only a fixation spot to constrain vergence state without verification by nonius lines is unsatisfactory because of the ability of the eye to fuse with fixation disparities up to Panum’s limit. Additionally, the sole use of convergent disparities in this study could have permitted observers to develop an anticipatory fixation disparity. It is interesting, further, to consider that such a fixation disparity would have reduced the 2.6′ disparity between the panels of highest spatial frequency in the Mayhew–Frisby study to a 168-deg phase disparity, which is close to the point at which we find peak contrast sensitivity in the present study. Our results make the counterintuitive prediction that the use of a bigger disparity difference between the two Mayhew–Frisby panels would have made the discrimination harder.

L. L. Kontsevich, C. W. Tyler, “Analysis of stereothresholds for stimuli below 2.5 cy/deg,” Vision Res. (to be published).

D. G. Pelli, “The quantum efficiency of vision,” in Vision: Coding and Efficiency, C. Blakemore, ed. (Cambridge U. Press, Cambridge, 1990), pp. 1–24.

D. G. Jones, J. Malik, “A computational framework for determining stereo correspondence from a set of linear spatial filters,” Tech. Rep. 91-657 (University of California, Berkeley, Berkeley, Calif., 1991).

K. Pulliam, “Spatial frequency analysis of three-dimensional vision,” in Visual Simulation and Image Realism II, K. S. Setty, ed., Proc. Soc. Photo-Opt. Instrum. Eng.303, 17–23 (1981).

R. L. DeValois, K. K. DeValois, Spatial Vision (Oxford U. Press, New York, 1988).

H. R. Wilson, D. Levi, L. Maffei, J. Rovamo, R. L. DeValois, “The perception of form: retina to striate cortex,” in Visual Perception: The Neurophysiological Foundations, L. Spillman, J. S. Werner, eds. (Academic, San Diego, Calif., 1990), pp. 317–347.

B. Julesz, Foundations of Cyclopean Perception (U. Chicago Press, Chicago, Ill., 1971), pp. 100–102.

This prediction applies to the model in its simplest form employing solely vertically oriented mechanisms finely covering the range of spatial frequencies tested here and with no absolute positional disparity between the locations of the left and right eye’s receptive fields.

After extensive use of this procedure it was decided that it was unnecessary to inquire of the subject the collinearity of the nonius lines before every trial. Instead, subjects were asked to redo trials in which they judged that the nonius lines were incorrectly aligned.

D. M. Green, J. A. Swets, Signal Detection Theory and Psychophysics (Wiley, New York, 1966), p. 174.

H. L. Van Trees, Detection, Estimation and Modulation Theory: Part 1 (Wiley, New York, 1968), p. 108.

H. S. Smallman, D. I. A. MacLeod, “Interactions across spatial scales and the size–disparity correlation in stereopsis,” in Annual Meeting, Vol. 16 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), p. 186.

H. S. Smallman, D. I. A. MacLeod, “A size disparity correlation in stereopsis at contrast threshold,” in International Conference and NATO Workshop on Binocular Stereopsis and Optic Flow, June 22nd-26th 1993 (Centre for Vision Research, Toronto, Canada, 1993), p. 18.

Included in this plot, but not shown in Fig. 2, are data taken at 1 cpd with 25-arcmin disparity.

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Figures (13)

Fig. 1
Fig. 1

Schematic diagram depicting the stimulus and the depth relationships to which it gave rise. (a) The left and right eyes’ views that constituted the stereogram. The observer fixated the central cross, and filtered texture patterns with equal and opposite disparities were presented to the left and right eyes. (b) Possible depth relationships present during a trial. The left patch could have crossed disparity and the right uncrossed (the case depicted) or left uncrossed and right crossed, at random from trial to trial. The observer’s task was to determine which patch lay in front of fixation as the contrast was staircased on successive trials to find that which yielded 75% correct depth identification. Rigorous control over the subjects’ state of vergence was maintained during testing.

Fig. 2
Fig. 2

CSF for stereopsis for observer LW. Sensitivity (reciprocal of threshold rms contrast) is plotted (on a logarithmic scale) against center spatial frequency for a range of different disparities; higher disparities are plotted as dashed curves (see key). The CSF is disparity variant, with sensitivity to small disparities best at high spatial frequencies and sensitivity to large disparities greatest at low frequencies. The conventional binocular contrast sensitivity data for detection (line–dot curve) are also shown for comparison.

Fig. 3
Fig. 3

CSF data of LW from Fig. 2 replotted to show the 3D nature of the data. Increasing log contrast sensitivity for depth identification is plotted as increasingly darker grays in a cube with dimensions of spatial frequency, disparity, and log contrast sensitivity. The conventional function for binocular detection is projected onto the rear face of the cube. This representation of the data highlights the size–disparity correlation in the data, for sensitivity forms a ridge in the 3D space, with no sensitivity for pairings of large disparity–high center spatial frequency.

Fig. 4
Fig. 4

LW’s contrast sensitivity data from Fig. 2 replotted to show sensitivity as a function of binocular phase for each spatial frequency tested62; higher frequencies are plotted as dashed curves (see key). Disparities are converted into binocular phases with this simple formula: phase (in degrees) = 360[disparity (in arcmin)/60] spatial frequency (in cpd); thus a disparity of 20 arcmin at a center frequency of 1 cpd corresponded to a 120° binocular phase. The arrow indicates the phase that should give optimal sensitivity predicted by the model of Ohzawa et al.11 extracting disparity with vertically oriented mechanisms arranged in quadrature. The number of spatial periods of center spatial frequency represented by a certain binocular phase is shown on the top axis.

Fig. 5
Fig. 5

Contrast sensitivity plotted as in Fig. 4, for the data of the two observers of Frisby and Mayhew23 for each of the spatial frequencies that they tested. Note the difference in scale on the abscissa between this figure and Fig. 4. Sensitivity is essentially independent of phase. The two panels represent the data from the two observers in the Frisby–Mayhew study.

Fig. 6
Fig. 6

Log contrast sensitivity as a function of disparity for all spatial frequencies superimposed. The fitted curve is a Gaussian derivative of contrast sensitivity as a function of disparity, thus making sensitivity proportional to disparity for small disparities. We accomplished the superimposition by scaling each curve by the disparity range parameter d0(f) factor to establish horizontal congruence and by adding the sensitivity scaling factor S0(f) to line the curves up vertically (see text). The key for spatial frequency is the same as for Fig. 4.

Fig. 7
Fig. 7

Scatter plot of range of disparities processed as a function of center spatial frequency of the filtered texture for the two observers LW and SPM, with best-fitting straight lines shown. The left-hand axis plots the disparity range factor d0(f), defined as the space constant of the Gaussian derivatives used to fit the curves of Fig. 6. The right-hand axis, for the same data, indicates the disparities giving optimal contrast sensitivity at each spatial frequency. There is at least a fivefold reduction in the range of disparities processed from the lowest to the highest center frequency; that is, the data exhibit a strong size–isparity correlation.

Fig. 8
Fig. 8

(a) CSF for stereopsis for observer HSS plotted as in Fig. 2, determined for a display duration of 2 s. Sensitivity (reciprocal of threshold rms contrast) is plotted against center spatial frequency. The variation of sensitivity with disparity is in close accordance with that found for observer LW, shown in Fig. 2. This establishes that the results found above are not specific for a short display duration (used in that case to guard against eye movements). (b) Data from (a) replotted to show sensitivity as a function of binocular phase for each spatial frequency tested; the curves were constructed in exactly the same way as for Fig. 4. The 90° phase prediction for optimal sensitivity from the model of Ohzawa et al.11 is shown by the arrow. The number of spatial periods of center spatial frequency represented by a certain binocular phase is shown on the top axis.

Fig. 9
Fig. 9

Contrast sensitivity plotted as a function of disparity for HSS for filtered patterns of center spatial frequency 13 cpd for three different filter bandwidths; see key. Binocular detection sensitivity for the three different conditions is shown at the left. Error bars are ±1 standard error. A tenfold increase in filter bandwidth results in only marginal improvement in sensitivity.

Fig. 10
Fig. 10

Depiction of how the position- and phase-encoding schemes of Freeman and Ohzawa42 could accommodate the size–disparity correlation evident in our data. The three rows correspond to fine, medium, and coarse spatial scales of the monocular input neuron’s receptive field. The two leftmost columns show how a binocular neuron could exhibit disparity selectivity that is due to a receptive field shift between the two eyes. At the right an alternative scheme is presented, phase-disparity encoding of Freeman and Ohzawa,42 whereby a change in receptive field substructure between the two eyes without a shift in the receptive field envelope can impart a selectivity for disparity. Corresponding retinal points are shown by vertical arrows. Optimal disparities at each spatial scale are indicated by vertical dashed lines. The phase-encoding scheme must predict a size–disparity correlation, but the position-encoding scheme can, too, if the jitter in the receptive field locations between the two eyes is different for the different spatial scales. The present data constrain the mean positional jitters of the latter account; see text.

Fig. 11
Fig. 11

DSQE as a function of disparity for several center spatial frequencies employed in the contrast threshold experiment, for observer LW’s data. DSQE is defined in Eq. (A17) below and is a measure of the efficiency of information usage by a human compared with the ideal observer. Efficiency is best at large disparities for low center spatial frequencies, suggestive of a size–disparity correlation in the mechanisms processing binocular disparities.

Fig. 12
Fig. 12

At the right, a robotic ideal observer faced with the disparity-discrimination task; the observer must decide between stimulus presentation alternatives A and B. To do so it makes use of information in the autocorrelation function of the stimulus as a function of disparity (an example of which is shown at the left). The ideal observer that we develop in Eq. (A8) has a predicted contrast sensitivity proportional to the square root of the length of the thick black bar depicted at the extreme left of the figure, which is the difference in the autocorrelation function of a 2d shift. Ripples in the autocorrelation function affect predicted sensitivity only weakly. See text for details.

Fig. 13
Fig. 13

Predicted contrast sensitivity for stereopsis for the ideal observer of Eq. (A8) plotted against disparity (dashed curves) for three different center spatial frequencies. Also plotted are the data of observer LW (open symbols, solid curve). The center spatial frequency is (a) 1 cpd, (b) 3 cpd, and (c) 9 cpd. The ideal observer continues to possess good sensitivity as disparity is increased across spatial frequency, whereas the human’s sensitivity drops off precipitously as disparity gets larger for the higher spatial frequencies. The ideal observer, in short, does not predict a size–disparity correlation.

Equations (18)

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S ( f ) = S 0 ( f ) d / d 0 ( f ) exp { [ d / d 0 ( f ) ] 2 } .
p ( n i ) = 1 ( 4 π σ 2 ) 1 / 2 exp [ ( n i ) 2 4 σ 2 ] ,
p ( n i ) = 1 ( 4 π σ 2 ) 1 / 2 exp [ ( n i Δ I i ) 2 4 σ 2 ] .
LLR i = [ ( n i Δ I i ) 2 n i 2 ] / 4 σ 2 = [ ( Δ I i ) 2 2 Δ I i n i ] / 4 σ 2 .
LLR = 2 N [ ( Δ I i ) 2 2 Δ I i n i ] 4 σ 2 ,
E ( LLR ) = 2 N [ ( Δ I i ) 2 4 σ 2 ] ,
Var ( LLR ) = 2 N [ ( Δ I i ) 2 2 σ 2 ] .
( Δ I i ) 2 = 4 N ( I C ) 2 [ 1 r ( 2 d ) ] .
d discrim = ( N / σ 2 ) I C 1 r ( 2 d ) .
1 / C = 1 r ( 2 d ) .
E ( SS n ) = 2 N t σ 2 .
Var ( SS n ) = 8 N t σ 4 .
E ( SS s n ) = 4 N ( I C ) 2 + 2 N t σ 2 ,
Var ( SS s n ) = 8 N t [ 2 N ( I C ) 2 / N t + σ 2 ] 2 .
E ( Δ SS ) = 4 N ( I C ) 2 ,
Var ( Δ SS ) = 8 N t [ 2 N ( I C ) 2 / N t + σ 2 ] 2 + 8 N t σ 4 .
d detect = N I C [ 2 σ 2 + 2 N N t ( I C ) 2 + N t σ 4 N ( I C ) 2 ] 1 / 2 .
DSQE = ( C discrim * C ideal , discrim * ) 2 ,

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