Abstract

To examine interactions among spatial scales in disparity processing, we have measured the upper disparity limit for binocular single vision (the diplopia threshold) for high-spatial-frequency test stimuli in the presence of cosine gratings of lower spatial frequency that defined a surface in depth. When the frequency of this grating surface was 2.0 octaves below that of the test, the test fusion range was reduced by a factor of 3–4 relative to the condition in which no grating surface was present. However, gratings 4.0 octaves below the test frequency had no effect, and the test and grating were seen transparently at different depths. Further experiments indicate that the effect is orientation specific and that high-frequency gratings do not affect low-frequency tests. Finally, experiments using grating surfaces tilted in depth indicate that fusion at high spatial frequencies is constrained to a range centered on the local disparity of the surface defined by the lower frequency. These results are important for computational models for stereopsis that are based on coarse-to-fine matching strategies.

© 1991 Optical Society of America

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    [PubMed]
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    [PubMed]
  3. N. Graham, J. Nachmias, “Detection of grating patterns containing two spatial frequencies: a comparison of single-channel and multiple-channel models,” Vision Res. 11, 251–259 (1971).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  5. H. R. Wilson, D. K. McFarlane, G. C. Phillips, “Spatial frequency tuning of orientation selective units estimated by oblique masking,” Vision Res. 23, 873–882 (1983).
    [CrossRef] [PubMed]
  6. B. Julesz, R. A. Schumer, “Early visual perception,” Ann. Rev. Psychol. 32, 575–627 (1981).
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    [CrossRef]
  8. R. L. DeValois, K. K. DeValois, Spatial Vision (Oxford U. Press, New York, 1988).
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    [CrossRef]
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  14. L. H. Quam, “Hierarchical warp stereo,” in Readings in Computer Vision, M. A. Fischler, O. Firschein, eds. (Kauffman, Los Altos, Calif., 1987), pp. 80–86.
  15. C. H. Anderson, D. C. VanEssen, “Shifter circuits: a computational strategy for dynamic aspects of visual processing,” Proc. Natl. Acad. Sci. USA 84, 6297–6301 (1987).
    [CrossRef] [PubMed]
  16. D. Marr, T. Poggio, “A theory of human stereopsis,” Proc. R. Soc. London Ser. B 204, 301–328 (1979).
    [CrossRef]
  17. W. H. Swanson, H. R. Wilson, S. C. Giese, “Contrast matching data predicted from contrast increment thresholds,” Vision Res. 24, 63–75 (1984).
    [CrossRef] [PubMed]
  18. G. E. Legge, J. M. Foley, “Contrast masking in human vision,”J. Opt. Soc. Am. 70, 1458–1470 (1980).
    [CrossRef] [PubMed]
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    [CrossRef]
  20. W. A. Weibull, “A statistical distribution function of wide applicability,”J. Appl. Mech. 18, 292–297 (1951).
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    [CrossRef] [PubMed]
  22. C. Blakemore, “A new kind of stereoscopic vision,” Vision Res. 10, 1181–1199 (1970).
    [CrossRef] [PubMed]
  23. V. S. Ramachandran, P. Cavanagh, “Subjective contours capture stereopsis,” Nature 317, 527–530 (1985).
    [CrossRef]
  24. G. Westheimer, “Cooperative neural processes involved in stereoscopic acuity,” Exp. Brain Res. 36, 585–597 (1979).
    [CrossRef] [PubMed]
  25. G. Westheimer, “Spatial interaction in the domain of disparity signals in human stereoscopic vision,”J. Physiol. 370, 619–629 (1986).
    [PubMed]
  26. G. J. Mitchison, S. P. McKee, “The resolution of ambiguous stereoscopic matches by interpolation,” Vision Res. 27, 285–294 (1987).
    [CrossRef] [PubMed]
  27. G. J. Mitchison, S. P. McKee, “Interpolation and the detection of fine structure in stereoscopic matching,” Vision Res. 27, 295–302 (1987).
    [CrossRef] [PubMed]
  28. R. Blake, Y. Yang, H. R. Wilson, “On the coexistence of stereopsis and binocular rivalry,” submitted to Vision Res.
  29. K. Prazdny, “On the coarse-to-fine strategy in stereomatching,” Bull. Psychon. Soc. 25, 92–94 (1987).
  30. A. M. Rohaly, H. R. Wilson, “Constraints on binocular fusion do not depend on temporal frequency or color,” Suppl. Invest. Ophthalmol. Vis. Sci. 31, 304 (1990).
  31. R. Blake, “A neural theory of binocular rivalry,” Psych. Rev. 96, 145–167 (1989).
    [CrossRef]
  32. W. Richards, “Anomalous stereoscopic depth perception,”J. Opt. Soc. Am. 61, 410–414 (1971).
    [CrossRef] [PubMed]
  33. G. F. Poggio, B. Fischer, “Binocular interaction and depth sensitivity in striate and prestriate cortex of behaving rhesus monkey,”J. Neurophysiol. 40, 1392–1405 (1977).
    [PubMed]
  34. 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]
  35. C. W. Tyler, “Stereoscopic vision: cortical limitations and a disparity scaling effect,” Science 181, 276–278 (1973).
    [CrossRef] [PubMed]
  36. P. Burt, B. Julesz, “A disparity gradient limit for binocular fusion,” Science 208, 615–617 (1980).
    [CrossRef] [PubMed]
  37. H. R. Wilson, R. Blake, J. Pokorny, “Limits of binocular fusion in the short wave sensitive (‘blue’) cones,” Vision Res. 28, 555–562 (1988).
    [CrossRef]

1990 (1)

A. M. Rohaly, H. R. Wilson, “Constraints on binocular fusion do not depend on temporal frequency or color,” Suppl. Invest. Ophthalmol. Vis. Sci. 31, 304 (1990).

1989 (1)

R. Blake, “A neural theory of binocular rivalry,” Psych. Rev. 96, 145–167 (1989).
[CrossRef]

1988 (2)

R. A. Akerstrom, J. T. Todd, “The perception of stereoscopic transparency,” Percept. Psychophys. 44, 421–432 (1988).
[CrossRef] [PubMed]

H. R. Wilson, R. Blake, J. Pokorny, “Limits of binocular fusion in the short wave sensitive (‘blue’) cones,” Vision Res. 28, 555–562 (1988).
[CrossRef]

1987 (4)

C. H. Anderson, D. C. VanEssen, “Shifter circuits: a computational strategy for dynamic aspects of visual processing,” Proc. Natl. Acad. Sci. USA 84, 6297–6301 (1987).
[CrossRef] [PubMed]

G. J. Mitchison, S. P. McKee, “The resolution of ambiguous stereoscopic matches by interpolation,” Vision Res. 27, 285–294 (1987).
[CrossRef] [PubMed]

G. J. Mitchison, S. P. McKee, “Interpolation and the detection of fine structure in stereoscopic matching,” Vision Res. 27, 295–302 (1987).
[CrossRef] [PubMed]

K. Prazdny, “On the coarse-to-fine strategy in stereomatching,” Bull. Psychon. Soc. 25, 92–94 (1987).

1986 (1)

G. Westheimer, “Spatial interaction in the domain of disparity signals in human stereoscopic vision,”J. Physiol. 370, 619–629 (1986).
[PubMed]

1985 (2)

1984 (2)

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

W. H. Swanson, H. R. Wilson, S. C. Giese, “Contrast matching data predicted from contrast increment thresholds,” Vision Res. 24, 63–75 (1984).
[CrossRef] [PubMed]

1983 (1)

H. R. Wilson, D. K. McFarlane, G. C. Phillips, “Spatial frequency tuning of orientation selective units estimated by oblique masking,” Vision Res. 23, 873–882 (1983).
[CrossRef] [PubMed]

1981 (2)

B. Julesz, R. A. Schumer, “Early visual perception,” Ann. Rev. Psychol. 32, 575–627 (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]

1980 (3)

P. Burt, B. Julesz, “A disparity gradient limit for binocular fusion,” Science 208, 615–617 (1980).
[CrossRef] [PubMed]

G. E. Legge, J. M. Foley, “Contrast masking in human vision,”J. Opt. Soc. Am. 70, 1458–1470 (1980).
[CrossRef] [PubMed]

R. L. DeValois, K. K. DeValois, “Spatial vision,” Ann. Rev. Psychol. 31, 309–341 (1980).
[CrossRef]

1979 (3)

H. R. Wilson, J. R. Bergen, “A four mechanism model for threshold spatial vision,” Vision Res. 19, 19–32 (1979).
[CrossRef] [PubMed]

G. Westheimer, “Cooperative neural processes involved in stereoscopic acuity,” Exp. Brain Res. 36, 585–597 (1979).
[CrossRef] [PubMed]

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

1977 (1)

G. F. Poggio, B. Fischer, “Binocular interaction and depth sensitivity in striate and prestriate cortex of behaving rhesus monkey,”J. Neurophysiol. 40, 1392–1405 (1977).
[PubMed]

1975 (1)

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

1974 (1)

R. F. Quick, “A vector-magnitude model of contrast detection,” Kybernetik 16, 1299–1302 (1974).
[CrossRef]

1973 (1)

C. W. Tyler, “Stereoscopic vision: cortical limitations and a disparity scaling effect,” Science 181, 276–278 (1973).
[CrossRef] [PubMed]

1971 (2)

W. Richards, “Anomalous stereoscopic depth perception,”J. Opt. Soc. Am. 61, 410–414 (1971).
[CrossRef] [PubMed]

N. Graham, J. Nachmias, “Detection of grating patterns containing two spatial frequencies: a comparison of single-channel and multiple-channel models,” Vision Res. 11, 251–259 (1971).
[CrossRef] [PubMed]

1970 (1)

C. Blakemore, “A new kind of stereoscopic vision,” Vision Res. 10, 1181–1199 (1970).
[CrossRef] [PubMed]

1969 (1)

C. Blakemore, F. W. Campbell, “On the existence of neurones in the human visual system selectively sensitive to the orientation and size of retinal images,”J. Physiol. 203, 237–260 (1969).
[PubMed]

1968 (1)

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

1951 (1)

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

Akerstrom, R. A.

R. A. Akerstrom, J. T. Todd, “The perception of stereoscopic transparency,” Percept. Psychophys. 44, 421–432 (1988).
[CrossRef] [PubMed]

Anderson, C. H.

C. H. Anderson, D. C. VanEssen, “Shifter circuits: a computational strategy for dynamic aspects of visual processing,” Proc. Natl. Acad. Sci. USA 84, 6297–6301 (1987).
[CrossRef] [PubMed]

Badcock, D. R.

Bergen, J. R.

H. R. Wilson, J. R. Bergen, “A four mechanism model for threshold spatial vision,” Vision Res. 19, 19–32 (1979).
[CrossRef] [PubMed]

Blake, R.

R. Blake, “A neural theory of binocular rivalry,” Psych. Rev. 96, 145–167 (1989).
[CrossRef]

H. R. Wilson, R. Blake, J. Pokorny, “Limits of binocular fusion in the short wave sensitive (‘blue’) cones,” Vision Res. 28, 555–562 (1988).
[CrossRef]

R. Blake, Y. Yang, H. R. Wilson, “On the coexistence of stereopsis and binocular rivalry,” submitted to Vision Res.

Blakemore, C.

C. Blakemore, “A new kind of stereoscopic vision,” Vision Res. 10, 1181–1199 (1970).
[CrossRef] [PubMed]

C. Blakemore, F. W. Campbell, “On the existence of neurones in the human visual system selectively sensitive to the orientation and size of retinal images,”J. Physiol. 203, 237–260 (1969).
[PubMed]

Burt, P.

P. Burt, B. Julesz, “A disparity gradient limit for binocular fusion,” Science 208, 615–617 (1980).
[CrossRef] [PubMed]

Campbell, F. W.

C. Blakemore, F. W. Campbell, “On the existence of neurones in the human visual system selectively sensitive to the orientation and size of retinal images,”J. Physiol. 203, 237–260 (1969).
[PubMed]

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

Cavanagh, P.

V. S. Ramachandran, P. Cavanagh, “Subjective contours capture stereopsis,” Nature 317, 527–530 (1985).
[CrossRef]

DeValois, K. K.

R. L. DeValois, K. K. DeValois, “Spatial vision,” Ann. Rev. Psychol. 31, 309–341 (1980).
[CrossRef]

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

DeValois, R. L.

R. L. DeValois, K. K. DeValois, “Spatial vision,” Ann. Rev. Psychol. 31, 309–341 (1980).
[CrossRef]

H. R. Wilson, D. Levi, L. Maffei, J. Rovamo, R. L. DeValois, “The perception of form: retina to striate cortex,” in The Neurophysiological Foundations of Visual Perception, L. Spillmann, J. S. Werner, eds. (Academic, New York, 1990).

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

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]

Fischer, B.

G. F. Poggio, B. Fischer, “Binocular interaction and depth sensitivity in striate and prestriate cortex of behaving rhesus monkey,”J. Neurophysiol. 40, 1392–1405 (1977).
[PubMed]

Foley, J. M.

Giese, S. C.

W. H. Swanson, H. R. Wilson, S. C. Giese, “Contrast matching data predicted from contrast increment thresholds,” Vision Res. 24, 63–75 (1984).
[CrossRef] [PubMed]

Graham, N.

N. Graham, J. Nachmias, “Detection of grating patterns containing two spatial frequencies: a comparison of single-channel and multiple-channel models,” Vision Res. 11, 251–259 (1971).
[CrossRef] [PubMed]

Julesz, B.

B. Julesz, R. A. Schumer, “Early visual perception,” Ann. Rev. Psychol. 32, 575–627 (1981).
[CrossRef]

P. Burt, B. Julesz, “A disparity gradient limit for binocular fusion,” Science 208, 615–617 (1980).
[CrossRef] [PubMed]

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

Legge, G. E.

Levi, D.

H. R. Wilson, D. Levi, L. Maffei, J. Rovamo, R. L. DeValois, “The perception of form: retina to striate cortex,” in The Neurophysiological Foundations of Visual Perception, L. Spillmann, J. S. Werner, eds. (Academic, New York, 1990).

Maffei, L.

H. R. Wilson, D. Levi, L. Maffei, J. Rovamo, R. L. DeValois, “The perception of form: retina to striate cortex,” in The Neurophysiological Foundations of Visual Perception, L. Spillmann, J. S. Werner, eds. (Academic, New York, 1990).

Marr, D.

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

McFarlane, D. K.

H. R. Wilson, D. K. McFarlane, G. C. Phillips, “Spatial frequency tuning of orientation selective units estimated by oblique masking,” Vision Res. 23, 873–882 (1983).
[CrossRef] [PubMed]

McKee, S. P.

G. J. Mitchison, S. P. McKee, “The resolution of ambiguous stereoscopic matches by interpolation,” Vision Res. 27, 285–294 (1987).
[CrossRef] [PubMed]

G. J. Mitchison, S. P. McKee, “Interpolation and the detection of fine structure in stereoscopic matching,” Vision Res. 27, 295–302 (1987).
[CrossRef] [PubMed]

Miller, J. E.

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

Mitchison, G. J.

G. J. Mitchison, S. P. McKee, “The resolution of ambiguous stereoscopic matches by interpolation,” Vision Res. 27, 285–294 (1987).
[CrossRef] [PubMed]

G. J. Mitchison, S. P. McKee, “Interpolation and the detection of fine structure in stereoscopic matching,” Vision Res. 27, 295–302 (1987).
[CrossRef] [PubMed]

Nachmias, J.

N. Graham, J. Nachmias, “Detection of grating patterns containing two spatial frequencies: a comparison of single-channel and multiple-channel models,” Vision Res. 11, 251–259 (1971).
[CrossRef] [PubMed]

Nishihara, H. K.

H. K. Nishihara, “Practical real time imaging stereo matcher,” in Readings in Computer Vision, M. A. Fischler, O. Firschein, eds. (Kauffman, Los Altos, Calif., 1987), pp. 63–72.

Ogawa, J.

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

Phillips, G. C.

H. R. Wilson, D. K. McFarlane, G. C. Phillips, “Spatial frequency tuning of orientation selective units estimated by oblique masking,” Vision Res. 23, 873–882 (1983).
[CrossRef] [PubMed]

Poggio, G. F.

G. F. Poggio, B. Fischer, “Binocular interaction and depth sensitivity in striate and prestriate cortex of behaving rhesus monkey,”J. Neurophysiol. 40, 1392–1405 (1977).
[PubMed]

Poggio, T.

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

Pokorny, J.

H. R. Wilson, R. Blake, J. Pokorny, “Limits of binocular fusion in the short wave sensitive (‘blue’) cones,” Vision Res. 28, 555–562 (1988).
[CrossRef]

Prazdny, K.

K. Prazdny, “On the coarse-to-fine strategy in stereomatching,” Bull. Psychon. Soc. 25, 92–94 (1987).

Quam, L. H.

L. H. Quam, “Hierarchical warp stereo,” in Readings in Computer Vision, M. A. Fischler, O. Firschein, eds. (Kauffman, Los Altos, Calif., 1987), pp. 80–86.

Quick, R. F.

R. F. Quick, “A vector-magnitude model of contrast detection,” Kybernetik 16, 1299–1302 (1974).
[CrossRef]

Ramachandran, V. S.

V. S. Ramachandran, P. Cavanagh, “Subjective contours capture stereopsis,” Nature 317, 527–530 (1985).
[CrossRef]

Richards, W.

Robson, J. G.

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

Rohaly, A. M.

A. M. Rohaly, H. R. Wilson, “Constraints on binocular fusion do not depend on temporal frequency or color,” Suppl. Invest. Ophthalmol. Vis. Sci. 31, 304 (1990).

Rovamo, J.

H. R. Wilson, D. Levi, L. Maffei, J. Rovamo, R. L. DeValois, “The perception of form: retina to striate cortex,” in The Neurophysiological Foundations of Visual Perception, L. Spillmann, J. S. Werner, eds. (Academic, New York, 1990).

Schor, C.

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

Schor, C. M.

Schumer, R. A.

B. Julesz, R. A. Schumer, “Early visual perception,” Ann. Rev. Psychol. 32, 575–627 (1981).
[CrossRef]

Swanson, W. H.

W. H. Swanson, H. R. Wilson, S. C. Giese, “Contrast matching data predicted from contrast increment thresholds,” Vision Res. 24, 63–75 (1984).
[CrossRef] [PubMed]

Todd, J. T.

R. A. Akerstrom, J. T. Todd, “The perception of stereoscopic transparency,” Percept. Psychophys. 44, 421–432 (1988).
[CrossRef] [PubMed]

Tyler, C. W.

C. W. Tyler, “Stereoscopic vision: cortical limitations and a disparity scaling effect,” Science 181, 276–278 (1973).
[CrossRef] [PubMed]

VanEssen, D. C.

C. H. Anderson, D. C. VanEssen, “Shifter circuits: a computational strategy for dynamic aspects of visual processing,” Proc. Natl. Acad. Sci. USA 84, 6297–6301 (1987).
[CrossRef] [PubMed]

Weibull, W. A.

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

Westheimer, G.

G. Westheimer, “Spatial interaction in the domain of disparity signals in human stereoscopic vision,”J. Physiol. 370, 619–629 (1986).
[PubMed]

G. Westheimer, “Cooperative neural processes involved in stereoscopic acuity,” Exp. Brain Res. 36, 585–597 (1979).
[CrossRef] [PubMed]

Wilson, H. R.

A. M. Rohaly, H. R. Wilson, “Constraints on binocular fusion do not depend on temporal frequency or color,” Suppl. Invest. Ophthalmol. Vis. Sci. 31, 304 (1990).

H. R. Wilson, R. Blake, J. Pokorny, “Limits of binocular fusion in the short wave sensitive (‘blue’) cones,” Vision Res. 28, 555–562 (1988).
[CrossRef]

W. H. Swanson, H. R. Wilson, S. C. Giese, “Contrast matching data predicted from contrast increment thresholds,” Vision Res. 24, 63–75 (1984).
[CrossRef] [PubMed]

H. R. Wilson, D. K. McFarlane, G. C. Phillips, “Spatial frequency tuning of orientation selective units estimated by oblique masking,” Vision Res. 23, 873–882 (1983).
[CrossRef] [PubMed]

H. R. Wilson, J. R. Bergen, “A four mechanism model for threshold spatial vision,” Vision Res. 19, 19–32 (1979).
[CrossRef] [PubMed]

H. R. Wilson, D. Levi, L. Maffei, J. Rovamo, R. L. DeValois, “The perception of form: retina to striate cortex,” in The Neurophysiological Foundations of Visual Perception, L. Spillmann, J. S. Werner, eds. (Academic, New York, 1990).

R. Blake, Y. Yang, H. R. Wilson, “On the coexistence of stereopsis and binocular rivalry,” submitted to Vision Res.

Wood, I.

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

Yang, Y.

R. Blake, Y. Yang, H. R. Wilson, “On the coexistence of stereopsis and binocular rivalry,” submitted to Vision Res.

Ann. Rev. Psychol. (2)

B. Julesz, R. A. Schumer, “Early visual perception,” Ann. Rev. Psychol. 32, 575–627 (1981).
[CrossRef]

R. L. DeValois, K. K. DeValois, “Spatial vision,” Ann. Rev. Psychol. 31, 309–341 (1980).
[CrossRef]

Bull. Psychon. Soc. (1)

K. Prazdny, “On the coarse-to-fine strategy in stereomatching,” Bull. Psychon. Soc. 25, 92–94 (1987).

Exp. Brain Res. (1)

G. Westheimer, “Cooperative neural processes involved in stereoscopic acuity,” Exp. Brain Res. 36, 585–597 (1979).
[CrossRef] [PubMed]

J. Appl. Mech. (1)

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

J. Neurophysiol. (1)

G. F. Poggio, B. Fischer, “Binocular interaction and depth sensitivity in striate and prestriate cortex of behaving rhesus monkey,”J. Neurophysiol. 40, 1392–1405 (1977).
[PubMed]

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (1)

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]

G. Westheimer, “Spatial interaction in the domain of disparity signals in human stereoscopic vision,”J. Physiol. 370, 619–629 (1986).
[PubMed]

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

C. Blakemore, F. W. Campbell, “On the existence of neurones in the human visual system selectively sensitive to the orientation and size of retinal images,”J. Physiol. 203, 237–260 (1969).
[PubMed]

Kybernetik (1)

R. F. Quick, “A vector-magnitude model of contrast detection,” Kybernetik 16, 1299–1302 (1974).
[CrossRef]

Nature (1)

V. S. Ramachandran, P. Cavanagh, “Subjective contours capture stereopsis,” Nature 317, 527–530 (1985).
[CrossRef]

Percept. Psychophys. (1)

R. A. Akerstrom, J. T. Todd, “The perception of stereoscopic transparency,” Percept. Psychophys. 44, 421–432 (1988).
[CrossRef] [PubMed]

Perception (1)

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

Proc. Natl. Acad. Sci. USA (1)

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Figures (10)

Fig. 1
Fig. 1

Stereograms used in these experiments. A, High-frequency D6 stimuli are more widely separated in the left-hand than in the right-hand image. Fusing these images will therefore cause one D6 to appear in front of the other in depth. B, These same high-frequency D6’s are added to cosine gratings two octaves lower in frequency. Note that the left-hand D6 can no longer be fused and remains diplopic. C, the gratings are four octaves lower in frequency, and both D6’s can now be fused and seen transparently in depth.

Fig. 2
Fig. 2

Illustration of depth relationships among elements of the stereograms used in these experiments. A, The two D6 test stimuli (black–white–black bars) were presented with a fixed horizontal separation. One of the two was in the fixation plane, while the disparity of the second was varied so that it appeared either nearer or farther than the other (arrows). B, the D6’s were added to a cosine grating lying in the frontoparallel plane. The left D6 was in the same plane as the grating, while the right D6 was presented with a disparity corresponding to a nearer or farther location (arrows).

Fig. 3
Fig. 3

Diplopia thresholds for three subjects using high-spatial-frequency D6 test stimuli. The D6 spatial frequency was 12.0 c/deg for RB (dark hatch) and HRW (light hatch) and 8.0 c/deg for DLH (gray). In this and subsequent graphs, crossed disparities are plotted as positive and uncrossed as negative. Relative to the threshold for D6’s alone (left-hand side), the presence of a grating surface 2 octaves lower in frequency reduced diplopia thresholds by a factor of 3.9 (center). However, surfaces 4 octaves below the D6 frequency had no effect (right-hand side), and depth transparency was seen.

Fig. 4
Fig. 4

Diplopia thresholds measured with 3.0-c/deg (RB and HRW) or 2.0-c/deg (DLH) D6 test patterns. Thresholds for D6’s alone (left-hand side) were reduced by a factor averaging 2.4 in the presence of a grating 2.0 octaves lower in frequency (center). However, when a grating 2.0 octaves higher in frequency was used, diplopia thresholds returned to a level comparable with that of the unmasked condition (right-hand side).

Fig. 5
Fig. 5

Stereoacuity for two subjects using 12.0-c/deg and 3.0-c/deg D6 test patterns. The left-hand side of each graph shows thresholds for the D6’s alone, while the right-hand side shows thresholds when the D6’s were superimposed on a cosine grating 2.0 octaves lower in spatial frequency. While the grating raised stereo thresholds for HRW (light hatch) somewhat, the gratings actually improved performance for RB (dark hatch).

Fig. 6
Fig. 6

Effect of relative phase on diplopia thresholds. Data for HRW and RB were obtained with a 12.0-c/deg D6 added to a 3.0-c/deg cosine grating, while data for DLH were obtained with an 8.0-c/deg D6 plus a 2.0-c/deg grating. The right-hand D6, which was varied in disparity in order to measure diplopia thresholds, was located at the indicated phase relative to the center of a bright bar of the cosine grating. Clearly, there is little effect of relative phase on the reduction of the fusion range produced by a grating 2.0 octaves lower in spatial frequency. For reference, the average diplopia threshold for the D6’s alone is indicated by the arrow.

Fig. 7
Fig. 7

Dependence of diplopia thresholds on grating orientation. Thresholds for D6’s alone averaged 14.4 min (right-hand side). Addition of a 3.0-c/deg cosine grating reduced this to 3.7 min, a factor of 3.9 (left-hand side). However, a plaid composed of two 3.0-c/deg gratings at ±45 deg produced thresholds averaging 13.5 min (center), which was not significantly different from the condition with no grating present. Thus the reduction of the fusion range for high spatial frequencies by lower-frequency gratings is orientation dependent.

Fig. 8
Fig. 8

Illustration of the depth relationships between a cosine grating tilted in depth and two D6 test patterns (dark–light–dark bars superimposed on the grating). The tilt of the cosine about a vertical axis running through the left-hand D6 was produced by the introduction of a 12.5% spatial-frequency difference between the two monocular gratings. The disparity of the right-hand D6 was then varied (arrows) to measure diplopia thresholds.

Fig. 9
Fig. 9

Diplopia thresholds for D6’s added to a tilted cosine grating 2 octaves lower in spatial frequency. The tilt was produced by introducing a 12.5% spatial-frequency difference between the gratings in the two monocular views. Solid and open circles are averages for RB and HRW using 12.0-c/deg D6’s, and standard errors are shown if they are greater than the height of the plotting symbols. Solid and open triangles are data for DLH obtained with 8.0-c/deg D6’s. Diplopia thresholds for the test stimulus were reduced to a range averaging 5.1 min centered on the local disparity of the grating (heavy line).

Fig. 10
Fig. 10

Neural network that implements a coarse-to-fine constraint on stereo processing.

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