Abstract

Monocular and binocular abutting line vernier acuities were measured as a function of contrast. Over a range of contrasts from near the line-detection threshold to approximately 20 times threshold, binocular vernier thresholds are lower (better) than monocular thresholds by approximately 50–60%, similar to the binocular improvement found for the detection of both a thin line and a dipole. At higher contrasts the binocular advantage diminishes, apparently as a result of saturation.

© 1991 Optical Society of America

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  1. R. J. Lythgoe, L. R. Phillips, “Binocular summation during dark adaptation,”J. Physiol. 91, 427–436 (1938).
    [PubMed]
  2. G. Collier, “Probability of response and intertrial association as functions of monocular and binocular stimulation,”J. Exp. Psychol. 47, 75–83 (1954).
    [CrossRef] [PubMed]
  3. F. W. Campbell, D. G. Green, “Optical and retinal factors affecting visual resolution,”J. Physiol. 181, 576–593 (1965).
    [PubMed]
  4. F. Thorn, R. M. Boynton, “Human binocular summation at absolute threshold,” Vision Res. 14, 445–458 (1976).
    [CrossRef]
  5. R. Blake, E. Levinson, “Spatial properties of binocular neurones in the human visual system,” Exp. Brain Res. 27, 221–223 (1977).
    [CrossRef] [PubMed]
  6. R. Blake, R. Fox, “The psychophysical inquiry into binocular summation,” Percept. Psychophys. 14, 161–185 (1973).
    [CrossRef]
  7. R. Blake, M. Sloane, R. Fox, “Further developments in binocular summation,” Percept. Psychophys. 30, 266–276 (1981).
    [CrossRef] [PubMed]
  8. T. E. Cohn, D. J. Lasley, “Binocular vision: two possible central interactions between signals from two eyes,” Science 192, 561–563 (1976).
    [CrossRef] [PubMed]
  9. D. W. Curtis, S. Rule, “Binocular processing of brightness information: a vector sum model,”J. Exp. Psychol. Human Percept. Perform. 4, 132–143 (1978).
    [CrossRef]
  10. G. E. Legge, “Binocular contrast summation—II. Quadratic summation,” Vision Res. 24, 385–394 (1984).
    [CrossRef]
  11. A. I. Cogan, “Human binocular interaction: towards a neural model,” Vision Res. 27, 2125–2139 (1987).
    [CrossRef] [PubMed]
  12. P. A. Anderson, J. A. Movshon, “Binocular combination of contrast signals,” Vision Res. 29, 1115–1132 (1989).
    [CrossRef] [PubMed]
  13. R. Blake, C. Rush, “Temporal properties of binocular mechanisms in the human visual system,” Exp. Brain Res. 38, 333–340 (1980).
    [CrossRef] [PubMed]
  14. R. N. Berry, “Quantitative relations in vernier, real depth and stereoscopic depth acuities,”J. Exp. Psychol. 38, 708–721 (1948).
    [CrossRef] [PubMed]
  15. L. Frisen, B. Lindblom, “Binocular summation in humans: evidence for a hierarchical model,”J. Physiol. 402, 773–782 (1988).
  16. R. J. Watt, M. J. Morgan, “A theory of the primitive spatial code in human vision,” Vision Res. 25, 1661–1674 (1985).
    [CrossRef] [PubMed]
  17. H. R. Wilson, “Responses of spatial mechanisms can explain hyperacuity,” Vision Res. 26, 453–469 (1986).
    [CrossRef] [PubMed]
  18. B. Lindblom, G. Westheimer, “Binocular summation of hyperacuity tasks,” J. Opt. Soc. Am. A 6, 585–589 (1989).
    [CrossRef]
  19. G. E. Legge, “Binocular contrast summation—I. Detection and discrimination,” Vision Res. 23, 373–383 (1984).
    [CrossRef]
  20. S. A. Klein, E. Casson, T. Carney, “Vernier acuity as line and dipole detection,” Vision Res. 30, 1703–1719 (1990).
    [CrossRef] [PubMed]
  21. D. M. Levi, S. A. Klein, “Spatial localization in normal and amblyopic vision,” Vision Res. 23, 1005–1017 (1983).
    [CrossRef] [PubMed]
  22. M. J. Morgan, T. S. Aiba, “Vernier acuity predicted from changes in the light distribution of the retinal image,” Spatial Vision 1, 151–161 (1986).
    [CrossRef]
  23. G. Westheimer, S. P. McKee, “Spatial configurations for visual hyperacuity,” Vision Res. 17, 941–947 (1977).
    [CrossRef] [PubMed]
  24. D. M. Levi, G. Westheimer, “Spatial-interval discrimination in the human fovea: what delimits the interval?” J. Opt. Soc. Am. A 4, 1304–1313 (1987).
    [CrossRef] [PubMed]
  25. S. A. Klein, D. M. Levi, “The position sense of the peripheral retina,” J. Opt. Soc. Am. A 4, 1544–1553 (1987).
    [CrossRef]
  26. S. A. Klein, C. F. Stromeyer, “On inhibition between spatial frequency channels: adaptation to complex gratings,” Vision Res. 20, 459–466 (1980).
    [CrossRef] [PubMed]
  27. D. M. Levi, S. A. Klein, “Equivalent intrinsic blur in spatial vision,” Vision Res. 30, 1971–1993 (1990).
    [CrossRef] [PubMed]
  28. A. Bradley, B. C. Skottun, “Effects of contrast and spatial frequency on vernier acuity,” Vision Res. 27, 1817–1824 (1987).
    [CrossRef] [PubMed]
  29. S. P. McKee, G. Westheimer, “Improvement in vernier acuity with practice,” Percept. Psychophys. 24, 258–262 (1978).
    [CrossRef] [PubMed]
  30. T. Carney, S. A. Klein, “Parameter free prediction of bisection threshold,” Invest. Ophthalmol. Vis. Sci. Suppl. 30, 453 (1989).
  31. M. J. Morgan, D. Regan, “Opponent model for line interval discrimination: interval and vernier performance compared,” Vision Res. 27, 107–118 (1987).
    [CrossRef] [PubMed]
  32. S. A. Klein, D. M. Levi, “A simple model of resolution and position thresholds for blurred lines,” Invest. Ophthalmol. Vis. Sci. Suppl. 30, 486 (1989).
  33. S. F. Bowne, “Contrast discrimination cannot explain spatial frequency, orientation or temporal frequency discrimination,” Vision Res. 30, 449–461 (1990).
    [CrossRef] [PubMed]
  34. H. R. Wilson, “Pattern discrimination, visual filters, and spatial sampling irregularity,” in Computational Models of Visual Processing, M. Landy, J. A. Movshon, eds. (MIT Press, Cambridge, Mass., to be published).
  35. C. F. Stromeyer, S. A. Klein, “Spatial frequency channels in human vision as asymmetric (edge) mechanisms,” Vision Res. 14, 1409–1420 (1974).
    [CrossRef] [PubMed]
  36. H. R. Wilson, “A transducer function for threshold and supra-threshold spatial vision,” Biol. Cybernet. 38, 171–178 (1980).
    [CrossRef]
  37. G. E. Legge, J. M. Foley, “Contrast masking in human vision,”J. Opt. Soc. Am. 70, 1458–1470 (1980).
    [CrossRef] [PubMed]
  38. S. A. Klein, D. M. Levi, “Hyperacuity thresholds of 1.0 second: theoretical predictions and empirical validation,” J. Opt. Soc. Am. A 2, 1170–1190 (1985).
    [CrossRef] [PubMed]
  39. D. L. Levi, S. A. Klein, “The role of separation and eccentricity in encoding position,” Vision Res. 30, 557–585 (1990).
    [CrossRef] [PubMed]

1990 (4)

D. M. Levi, S. A. Klein, “Equivalent intrinsic blur in spatial vision,” Vision Res. 30, 1971–1993 (1990).
[CrossRef] [PubMed]

S. F. Bowne, “Contrast discrimination cannot explain spatial frequency, orientation or temporal frequency discrimination,” Vision Res. 30, 449–461 (1990).
[CrossRef] [PubMed]

S. A. Klein, E. Casson, T. Carney, “Vernier acuity as line and dipole detection,” Vision Res. 30, 1703–1719 (1990).
[CrossRef] [PubMed]

D. L. Levi, S. A. Klein, “The role of separation and eccentricity in encoding position,” Vision Res. 30, 557–585 (1990).
[CrossRef] [PubMed]

1989 (4)

S. A. Klein, D. M. Levi, “A simple model of resolution and position thresholds for blurred lines,” Invest. Ophthalmol. Vis. Sci. Suppl. 30, 486 (1989).

T. Carney, S. A. Klein, “Parameter free prediction of bisection threshold,” Invest. Ophthalmol. Vis. Sci. Suppl. 30, 453 (1989).

P. A. Anderson, J. A. Movshon, “Binocular combination of contrast signals,” Vision Res. 29, 1115–1132 (1989).
[CrossRef] [PubMed]

B. Lindblom, G. Westheimer, “Binocular summation of hyperacuity tasks,” J. Opt. Soc. Am. A 6, 585–589 (1989).
[CrossRef]

1988 (1)

L. Frisen, B. Lindblom, “Binocular summation in humans: evidence for a hierarchical model,”J. Physiol. 402, 773–782 (1988).

1987 (5)

A. I. Cogan, “Human binocular interaction: towards a neural model,” Vision Res. 27, 2125–2139 (1987).
[CrossRef] [PubMed]

M. J. Morgan, D. Regan, “Opponent model for line interval discrimination: interval and vernier performance compared,” Vision Res. 27, 107–118 (1987).
[CrossRef] [PubMed]

A. Bradley, B. C. Skottun, “Effects of contrast and spatial frequency on vernier acuity,” Vision Res. 27, 1817–1824 (1987).
[CrossRef] [PubMed]

S. A. Klein, D. M. Levi, “The position sense of the peripheral retina,” J. Opt. Soc. Am. A 4, 1544–1553 (1987).
[CrossRef]

D. M. Levi, G. Westheimer, “Spatial-interval discrimination in the human fovea: what delimits the interval?” J. Opt. Soc. Am. A 4, 1304–1313 (1987).
[CrossRef] [PubMed]

1986 (2)

M. J. Morgan, T. S. Aiba, “Vernier acuity predicted from changes in the light distribution of the retinal image,” Spatial Vision 1, 151–161 (1986).
[CrossRef]

H. R. Wilson, “Responses of spatial mechanisms can explain hyperacuity,” Vision Res. 26, 453–469 (1986).
[CrossRef] [PubMed]

1985 (2)

1984 (2)

G. E. Legge, “Binocular contrast summation—II. Quadratic summation,” Vision Res. 24, 385–394 (1984).
[CrossRef]

G. E. Legge, “Binocular contrast summation—I. Detection and discrimination,” Vision Res. 23, 373–383 (1984).
[CrossRef]

1983 (1)

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

1981 (1)

R. Blake, M. Sloane, R. Fox, “Further developments in binocular summation,” Percept. Psychophys. 30, 266–276 (1981).
[CrossRef] [PubMed]

1980 (4)

R. Blake, C. Rush, “Temporal properties of binocular mechanisms in the human visual system,” Exp. Brain Res. 38, 333–340 (1980).
[CrossRef] [PubMed]

H. R. Wilson, “A transducer function for threshold and supra-threshold spatial vision,” Biol. Cybernet. 38, 171–178 (1980).
[CrossRef]

S. A. Klein, C. F. Stromeyer, “On inhibition between spatial frequency channels: adaptation to complex gratings,” Vision Res. 20, 459–466 (1980).
[CrossRef] [PubMed]

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

1978 (2)

S. P. McKee, G. Westheimer, “Improvement in vernier acuity with practice,” Percept. Psychophys. 24, 258–262 (1978).
[CrossRef] [PubMed]

D. W. Curtis, S. Rule, “Binocular processing of brightness information: a vector sum model,”J. Exp. Psychol. Human Percept. Perform. 4, 132–143 (1978).
[CrossRef]

1977 (2)

R. Blake, E. Levinson, “Spatial properties of binocular neurones in the human visual system,” Exp. Brain Res. 27, 221–223 (1977).
[CrossRef] [PubMed]

G. Westheimer, S. P. McKee, “Spatial configurations for visual hyperacuity,” Vision Res. 17, 941–947 (1977).
[CrossRef] [PubMed]

1976 (2)

T. E. Cohn, D. J. Lasley, “Binocular vision: two possible central interactions between signals from two eyes,” Science 192, 561–563 (1976).
[CrossRef] [PubMed]

F. Thorn, R. M. Boynton, “Human binocular summation at absolute threshold,” Vision Res. 14, 445–458 (1976).
[CrossRef]

1974 (1)

C. F. Stromeyer, S. A. Klein, “Spatial frequency channels in human vision as asymmetric (edge) mechanisms,” Vision Res. 14, 1409–1420 (1974).
[CrossRef] [PubMed]

1973 (1)

R. Blake, R. Fox, “The psychophysical inquiry into binocular summation,” Percept. Psychophys. 14, 161–185 (1973).
[CrossRef]

1965 (1)

F. W. Campbell, D. G. Green, “Optical and retinal factors affecting visual resolution,”J. Physiol. 181, 576–593 (1965).
[PubMed]

1954 (1)

G. Collier, “Probability of response and intertrial association as functions of monocular and binocular stimulation,”J. Exp. Psychol. 47, 75–83 (1954).
[CrossRef] [PubMed]

1948 (1)

R. N. Berry, “Quantitative relations in vernier, real depth and stereoscopic depth acuities,”J. Exp. Psychol. 38, 708–721 (1948).
[CrossRef] [PubMed]

1938 (1)

R. J. Lythgoe, L. R. Phillips, “Binocular summation during dark adaptation,”J. Physiol. 91, 427–436 (1938).
[PubMed]

Aiba, T. S.

M. J. Morgan, T. S. Aiba, “Vernier acuity predicted from changes in the light distribution of the retinal image,” Spatial Vision 1, 151–161 (1986).
[CrossRef]

Anderson, P. A.

P. A. Anderson, J. A. Movshon, “Binocular combination of contrast signals,” Vision Res. 29, 1115–1132 (1989).
[CrossRef] [PubMed]

Berry, R. N.

R. N. Berry, “Quantitative relations in vernier, real depth and stereoscopic depth acuities,”J. Exp. Psychol. 38, 708–721 (1948).
[CrossRef] [PubMed]

Blake, R.

R. Blake, M. Sloane, R. Fox, “Further developments in binocular summation,” Percept. Psychophys. 30, 266–276 (1981).
[CrossRef] [PubMed]

R. Blake, C. Rush, “Temporal properties of binocular mechanisms in the human visual system,” Exp. Brain Res. 38, 333–340 (1980).
[CrossRef] [PubMed]

R. Blake, E. Levinson, “Spatial properties of binocular neurones in the human visual system,” Exp. Brain Res. 27, 221–223 (1977).
[CrossRef] [PubMed]

R. Blake, R. Fox, “The psychophysical inquiry into binocular summation,” Percept. Psychophys. 14, 161–185 (1973).
[CrossRef]

Bowne, S. F.

S. F. Bowne, “Contrast discrimination cannot explain spatial frequency, orientation or temporal frequency discrimination,” Vision Res. 30, 449–461 (1990).
[CrossRef] [PubMed]

Boynton, R. M.

F. Thorn, R. M. Boynton, “Human binocular summation at absolute threshold,” Vision Res. 14, 445–458 (1976).
[CrossRef]

Bradley, A.

A. Bradley, B. C. Skottun, “Effects of contrast and spatial frequency on vernier acuity,” Vision Res. 27, 1817–1824 (1987).
[CrossRef] [PubMed]

Campbell, F. W.

F. W. Campbell, D. G. Green, “Optical and retinal factors affecting visual resolution,”J. Physiol. 181, 576–593 (1965).
[PubMed]

Carney, T.

S. A. Klein, E. Casson, T. Carney, “Vernier acuity as line and dipole detection,” Vision Res. 30, 1703–1719 (1990).
[CrossRef] [PubMed]

T. Carney, S. A. Klein, “Parameter free prediction of bisection threshold,” Invest. Ophthalmol. Vis. Sci. Suppl. 30, 453 (1989).

Casson, E.

S. A. Klein, E. Casson, T. Carney, “Vernier acuity as line and dipole detection,” Vision Res. 30, 1703–1719 (1990).
[CrossRef] [PubMed]

Cogan, A. I.

A. I. Cogan, “Human binocular interaction: towards a neural model,” Vision Res. 27, 2125–2139 (1987).
[CrossRef] [PubMed]

Cohn, T. E.

T. E. Cohn, D. J. Lasley, “Binocular vision: two possible central interactions between signals from two eyes,” Science 192, 561–563 (1976).
[CrossRef] [PubMed]

Collier, G.

G. Collier, “Probability of response and intertrial association as functions of monocular and binocular stimulation,”J. Exp. Psychol. 47, 75–83 (1954).
[CrossRef] [PubMed]

Curtis, D. W.

D. W. Curtis, S. Rule, “Binocular processing of brightness information: a vector sum model,”J. Exp. Psychol. Human Percept. Perform. 4, 132–143 (1978).
[CrossRef]

Foley, J. M.

Fox, R.

R. Blake, M. Sloane, R. Fox, “Further developments in binocular summation,” Percept. Psychophys. 30, 266–276 (1981).
[CrossRef] [PubMed]

R. Blake, R. Fox, “The psychophysical inquiry into binocular summation,” Percept. Psychophys. 14, 161–185 (1973).
[CrossRef]

Frisen, L.

L. Frisen, B. Lindblom, “Binocular summation in humans: evidence for a hierarchical model,”J. Physiol. 402, 773–782 (1988).

Green, D. G.

F. W. Campbell, D. G. Green, “Optical and retinal factors affecting visual resolution,”J. Physiol. 181, 576–593 (1965).
[PubMed]

Klein, S. A.

D. L. Levi, S. A. Klein, “The role of separation and eccentricity in encoding position,” Vision Res. 30, 557–585 (1990).
[CrossRef] [PubMed]

S. A. Klein, E. Casson, T. Carney, “Vernier acuity as line and dipole detection,” Vision Res. 30, 1703–1719 (1990).
[CrossRef] [PubMed]

D. M. Levi, S. A. Klein, “Equivalent intrinsic blur in spatial vision,” Vision Res. 30, 1971–1993 (1990).
[CrossRef] [PubMed]

S. A. Klein, D. M. Levi, “A simple model of resolution and position thresholds for blurred lines,” Invest. Ophthalmol. Vis. Sci. Suppl. 30, 486 (1989).

T. Carney, S. A. Klein, “Parameter free prediction of bisection threshold,” Invest. Ophthalmol. Vis. Sci. Suppl. 30, 453 (1989).

S. A. Klein, D. M. Levi, “The position sense of the peripheral retina,” J. Opt. Soc. Am. A 4, 1544–1553 (1987).
[CrossRef]

S. A. Klein, D. M. Levi, “Hyperacuity thresholds of 1.0 second: theoretical predictions and empirical validation,” J. Opt. Soc. Am. A 2, 1170–1190 (1985).
[CrossRef] [PubMed]

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

S. A. Klein, C. F. Stromeyer, “On inhibition between spatial frequency channels: adaptation to complex gratings,” Vision Res. 20, 459–466 (1980).
[CrossRef] [PubMed]

C. F. Stromeyer, S. A. Klein, “Spatial frequency channels in human vision as asymmetric (edge) mechanisms,” Vision Res. 14, 1409–1420 (1974).
[CrossRef] [PubMed]

Lasley, D. J.

T. E. Cohn, D. J. Lasley, “Binocular vision: two possible central interactions between signals from two eyes,” Science 192, 561–563 (1976).
[CrossRef] [PubMed]

Legge, G. E.

G. E. Legge, “Binocular contrast summation—I. Detection and discrimination,” Vision Res. 23, 373–383 (1984).
[CrossRef]

G. E. Legge, “Binocular contrast summation—II. Quadratic summation,” Vision Res. 24, 385–394 (1984).
[CrossRef]

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

Levi, D. L.

D. L. Levi, S. A. Klein, “The role of separation and eccentricity in encoding position,” Vision Res. 30, 557–585 (1990).
[CrossRef] [PubMed]

Levi, D. M.

D. M. Levi, S. A. Klein, “Equivalent intrinsic blur in spatial vision,” Vision Res. 30, 1971–1993 (1990).
[CrossRef] [PubMed]

S. A. Klein, D. M. Levi, “A simple model of resolution and position thresholds for blurred lines,” Invest. Ophthalmol. Vis. Sci. Suppl. 30, 486 (1989).

D. M. Levi, G. Westheimer, “Spatial-interval discrimination in the human fovea: what delimits the interval?” J. Opt. Soc. Am. A 4, 1304–1313 (1987).
[CrossRef] [PubMed]

S. A. Klein, D. M. Levi, “The position sense of the peripheral retina,” J. Opt. Soc. Am. A 4, 1544–1553 (1987).
[CrossRef]

S. A. Klein, D. M. Levi, “Hyperacuity thresholds of 1.0 second: theoretical predictions and empirical validation,” J. Opt. Soc. Am. A 2, 1170–1190 (1985).
[CrossRef] [PubMed]

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

Levinson, E.

R. Blake, E. Levinson, “Spatial properties of binocular neurones in the human visual system,” Exp. Brain Res. 27, 221–223 (1977).
[CrossRef] [PubMed]

Lindblom, B.

B. Lindblom, G. Westheimer, “Binocular summation of hyperacuity tasks,” J. Opt. Soc. Am. A 6, 585–589 (1989).
[CrossRef]

L. Frisen, B. Lindblom, “Binocular summation in humans: evidence for a hierarchical model,”J. Physiol. 402, 773–782 (1988).

Lythgoe, R. J.

R. J. Lythgoe, L. R. Phillips, “Binocular summation during dark adaptation,”J. Physiol. 91, 427–436 (1938).
[PubMed]

McKee, S. P.

S. P. McKee, G. Westheimer, “Improvement in vernier acuity with practice,” Percept. Psychophys. 24, 258–262 (1978).
[CrossRef] [PubMed]

G. Westheimer, S. P. McKee, “Spatial configurations for visual hyperacuity,” Vision Res. 17, 941–947 (1977).
[CrossRef] [PubMed]

Morgan, M. J.

M. J. Morgan, D. Regan, “Opponent model for line interval discrimination: interval and vernier performance compared,” Vision Res. 27, 107–118 (1987).
[CrossRef] [PubMed]

M. J. Morgan, T. S. Aiba, “Vernier acuity predicted from changes in the light distribution of the retinal image,” Spatial Vision 1, 151–161 (1986).
[CrossRef]

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

Movshon, J. A.

P. A. Anderson, J. A. Movshon, “Binocular combination of contrast signals,” Vision Res. 29, 1115–1132 (1989).
[CrossRef] [PubMed]

Phillips, L. R.

R. J. Lythgoe, L. R. Phillips, “Binocular summation during dark adaptation,”J. Physiol. 91, 427–436 (1938).
[PubMed]

Regan, D.

M. J. Morgan, D. Regan, “Opponent model for line interval discrimination: interval and vernier performance compared,” Vision Res. 27, 107–118 (1987).
[CrossRef] [PubMed]

Rule, S.

D. W. Curtis, S. Rule, “Binocular processing of brightness information: a vector sum model,”J. Exp. Psychol. Human Percept. Perform. 4, 132–143 (1978).
[CrossRef]

Rush, C.

R. Blake, C. Rush, “Temporal properties of binocular mechanisms in the human visual system,” Exp. Brain Res. 38, 333–340 (1980).
[CrossRef] [PubMed]

Skottun, B. C.

A. Bradley, B. C. Skottun, “Effects of contrast and spatial frequency on vernier acuity,” Vision Res. 27, 1817–1824 (1987).
[CrossRef] [PubMed]

Sloane, M.

R. Blake, M. Sloane, R. Fox, “Further developments in binocular summation,” Percept. Psychophys. 30, 266–276 (1981).
[CrossRef] [PubMed]

Stromeyer, C. F.

S. A. Klein, C. F. Stromeyer, “On inhibition between spatial frequency channels: adaptation to complex gratings,” Vision Res. 20, 459–466 (1980).
[CrossRef] [PubMed]

C. F. Stromeyer, S. A. Klein, “Spatial frequency channels in human vision as asymmetric (edge) mechanisms,” Vision Res. 14, 1409–1420 (1974).
[CrossRef] [PubMed]

Thorn, F.

F. Thorn, R. M. Boynton, “Human binocular summation at absolute threshold,” Vision Res. 14, 445–458 (1976).
[CrossRef]

Watt, R. 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]

Westheimer, G.

B. Lindblom, G. Westheimer, “Binocular summation of hyperacuity tasks,” J. Opt. Soc. Am. A 6, 585–589 (1989).
[CrossRef]

D. M. Levi, G. Westheimer, “Spatial-interval discrimination in the human fovea: what delimits the interval?” J. Opt. Soc. Am. A 4, 1304–1313 (1987).
[CrossRef] [PubMed]

S. P. McKee, G. Westheimer, “Improvement in vernier acuity with practice,” Percept. Psychophys. 24, 258–262 (1978).
[CrossRef] [PubMed]

G. Westheimer, S. P. McKee, “Spatial configurations for visual hyperacuity,” Vision Res. 17, 941–947 (1977).
[CrossRef] [PubMed]

Wilson, H. R.

H. R. Wilson, “Responses of spatial mechanisms can explain hyperacuity,” Vision Res. 26, 453–469 (1986).
[CrossRef] [PubMed]

H. R. Wilson, “A transducer function for threshold and supra-threshold spatial vision,” Biol. Cybernet. 38, 171–178 (1980).
[CrossRef]

H. R. Wilson, “Pattern discrimination, visual filters, and spatial sampling irregularity,” in Computational Models of Visual Processing, M. Landy, J. A. Movshon, eds. (MIT Press, Cambridge, Mass., to be published).

Biol. Cybernet. (1)

H. R. Wilson, “A transducer function for threshold and supra-threshold spatial vision,” Biol. Cybernet. 38, 171–178 (1980).
[CrossRef]

Exp. Brain Res. (2)

R. Blake, E. Levinson, “Spatial properties of binocular neurones in the human visual system,” Exp. Brain Res. 27, 221–223 (1977).
[CrossRef] [PubMed]

R. Blake, C. Rush, “Temporal properties of binocular mechanisms in the human visual system,” Exp. Brain Res. 38, 333–340 (1980).
[CrossRef] [PubMed]

Invest. Ophthalmol. Vis. Sci. Suppl. (2)

T. Carney, S. A. Klein, “Parameter free prediction of bisection threshold,” Invest. Ophthalmol. Vis. Sci. Suppl. 30, 453 (1989).

S. A. Klein, D. M. Levi, “A simple model of resolution and position thresholds for blurred lines,” Invest. Ophthalmol. Vis. Sci. Suppl. 30, 486 (1989).

J. Exp. Psychol. (2)

G. Collier, “Probability of response and intertrial association as functions of monocular and binocular stimulation,”J. Exp. Psychol. 47, 75–83 (1954).
[CrossRef] [PubMed]

R. N. Berry, “Quantitative relations in vernier, real depth and stereoscopic depth acuities,”J. Exp. Psychol. 38, 708–721 (1948).
[CrossRef] [PubMed]

J. Exp. Psychol. Human Percept. Perform. (1)

D. W. Curtis, S. Rule, “Binocular processing of brightness information: a vector sum model,”J. Exp. Psychol. Human Percept. Perform. 4, 132–143 (1978).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (4)

J. Physiol. (3)

F. W. Campbell, D. G. Green, “Optical and retinal factors affecting visual resolution,”J. Physiol. 181, 576–593 (1965).
[PubMed]

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Figures (4)

Fig. 1
Fig. 1

Schematic representation of the stimuli used in our study: A, thin (0.32 arcmin) dark horizontal line, presented on the right half of the screen; B, dipole (an adjacent pair of horizontal, opposite-polarity, thin lines) presented on the right half of the field; C, line vernier stimulus, which consisted of a pair of abutting thin (0.64 arcmin) horizontal dark lines, with a vertical offset between the left and right halves of the screen; D, addition of a dipole to a line is equivalent to shifting the position of the line (after Ref. 20).

Fig. 2
Fig. 2

Monocular (open squares, right eye; open triangles, left eye) and binocular (filled circles) vernier thresholds for each observer are plotted as a function of the line strength (contrast × width). The symbols plotted along the abscissa (at an ordinate value of 4.0) show the monocular and binocular line detection thresholds. The line in each plot shows the best-fitting straight line on log–log coordinates (determined by nonlinear analysis) to the binocular vernier data of each observer.

Fig. 3
Fig. 3

Binocular summation ratios calculated from the vernier data of Fig. 2 are plotted as a function of line strength (circles). The ratios reflect monocular/binocular thresholds, with the monocular value being either the smaller of the right- and left-eye thresholds (open circles) or the mean monocular value (filled circles). Also shown are the summation ratios for both line and dipole detection (det.). Each have been plotted at abscissa values corresponding to the binocular detection threshold. Note that, for the dipole, the appropriate scale is actually in square percent minutes (%min sq). Summation ratios for the dipole integration width (triangles) are plotted arbitrarily at a value of 1 on the abscissa. In this figure, a ratio of 1 (shown by the line) indicates no summation. Note that all subjects showed binocular summation, both for the detection tasks and for vernier discrimination. Little or no summation is found for integration width, however.

Fig. 4
Fig. 4

Mean summation ratios (averaged across observers) for line detection (det.), dipole detection, integration width, and vernier discrimination are plotted as in the previous figure. The ratios reflect monocular/binocular thresholds, with the monocular being either the smaller of the right- and the left-eye thresholds (open circles) and the mean monocular value (filled circles).

Tables (2)

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Table 2 High-Visibility Verniera

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