Abstract

We seek to determine the relationship between threshold and suprathreshold perception for position offset and stereoscopic depth perception under conditions that elevate their respective thresholds. Two threshold-elevating conditions were used: (1) increasing the interline gap and (2) dioptric blur. Although increasing the interline gap increases position (Vernier) offset and stereoscopic disparity thresholds substantially, the perception of suprathreshold position offset and stereoscopic depth remains unchanged. Perception of suprathreshold position offset also remains unchanged when the Vernier threshold is elevated by dioptric blur. We show that such normalization of suprathreshold position offset can be attributed to the topographical-map-based encoding of position. On the other hand, dioptric blur increases the stereoscopic disparity thresholds and reduces the perceived suprathreshold stereoscopic depth, which can be accounted for by a disparity-computation model in which the activities of absolute disparity encoders are multiplied by a Gaussian weighting function that is centered on the horopter. Overall, the statement “equal suprathreshold perception occurs in threshold-elevated and unelevated conditions when the stimuli are equally above their corresponding thresholds” describes the results better than the statement “suprathreshold stimuli are perceived as equal when they are equal multiples of their respective threshold values.”

© 2009 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  42. L. Gantz, S. S. Patel, S. T. Chung, and R. S. Harwerth, “Mechanisms of perceptual learning of depth discrimination in random dot stereograms,” Vision Res. 47, 2170-2178 (2007).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  45. S. B. Stevenson, L. K. Cormack, C. M. Schor, and C. W. Tyler, “Disparity tuning in mechanisms of human stereopsis,” Vision Res. 32, 1685-1694 (1992).
    [CrossRef] [PubMed]
  46. S. J. Prince and R. A. Eagle, “Weighted directional energy model of human stereo correspondence,” Vision Res. 40, 1143-1155 (2000).
    [CrossRef] [PubMed]
  47. H. S. Smallman and D. I. MacLeod, “Spatial scale interactions in stereo sensitivity and the neural representation of binocular disparity,” Perception 26, 977-994 (1997).
    [CrossRef] [PubMed]
  48. C. M. Schor and P. A. Howarth, “Suprathreshold stereo-depth matches as a function of contrast and spatial frequency,” Perception 15, 249-258 (1986).
    [CrossRef] [PubMed]
  49. C. M. Schor and D. R. Badcock, “A comparison of stereo and vernier acuity within spatial channels as a function of distance from fixation,” Vision Res. 25, 1113-1119 (1985).
    [CrossRef] [PubMed]

2007 (1)

L. Gantz, S. S. Patel, S. T. Chung, and R. S. Harwerth, “Mechanisms of perceptual learning of depth discrimination in random dot stereograms,” Vision Res. 47, 2170-2178 (2007).
[CrossRef] [PubMed]

2006 (1)

S. S. Patel, H. E. Bedell, and P. Sampat, “Pooling signals from vertically and non-vertically orientation-tuned disparity mechanisms in human stereopsis,” Vision Res. 46, 1-13 (2006).
[CrossRef]

2003 (2)

R. S. Harwerth, P. M. Fredenburg, and E. L. Smith 3rd, “Temporal integration for stereoscopic vision,” Vision Res. 43, 505-517 (2003).
[CrossRef] [PubMed]

S. S. Patel, M. T. Ukwade, S. B. Stevenson, H. E. Bedell, V. Sampath, and H. Ogmen, “Stereoscopic depth perception from oblique phase disparities,” Vision Res. 43, 2479-2492 (2003).
[CrossRef] [PubMed]

2002 (1)

W. H. Bosking, J. C. Crowley, and D. Fitzpatrick, “Spatial coding of position and orientation in primary visual cortex,” Nat. Neurosci. 5, 874-882 (2002).
[CrossRef] [PubMed]

2001 (1)

S. S. Patel, B. C. Jiang, and H. Ogmen, “Vergence dynamics predict fixation disparity,” Neural Comput. 13, 1495-1525 (2001).
[CrossRef] [PubMed]

2000 (2)

L. M. Wilcox, J. H. Elder, and R. F. Hess, “The effects of blur and size on monocular and stereoscopic localization,” Vision Res. 40, 3575-3584 (2000).
[CrossRef] [PubMed]

S. J. Prince and R. A. Eagle, “Weighted directional energy model of human stereo correspondence,” Vision Res. 40, 1143-1155 (2000).
[CrossRef] [PubMed]

1999 (2)

E. Brenner and W. J. van Damme, “Perceived distance, shape and size,” Vision Res. 39, 975-986 (1999).
[CrossRef] [PubMed]

S. S. Patel, H. E. Bedell, and M. T. Ukwade, “Vernier judgments in the absence of regular shape information,” Vision Res. 39, 2349-2360 (1999).
[CrossRef] [PubMed]

1998 (2)

S. T. Chung and H. E. Bedell, “Vernier and letter acuities for low-pass filtered moving stimuli,” Vision Res. 38, 1967-1982 (1998).
[CrossRef] [PubMed]

C. M. Schor, M. Edwards, and D. R. Pope, “Spatial-frequency and contrast tuning of the transient-stereopsis system,” Vision Res. 38, 3057-3068 (1998).
[CrossRef]

1997 (3)

W. van Damme and E. Brenner, “The distance used for scaling disparities is the same as the one used for scaling retinal size,” Vision Res. 37, 757-764 (1997).
[CrossRef] [PubMed]

N. Qian and Y. Zhu, “Physiological computation of binocular disparity,” Vision Res. 37, 1811-1827 (1997).
[CrossRef] [PubMed]

H. S. Smallman and D. I. MacLeod, “Spatial scale interactions in stereo sensitivity and the neural representation of binocular disparity,” Perception 26, 977-994 (1997).
[CrossRef] [PubMed]

1996 (3)

D. J. Fleet, H. Wagner, and D. J. Heeger, “Neural encoding of binocular disparity: energy models, position shifts and phase shifts,” Vision Res. 36, 1839-1857 (1996).
[CrossRef] [PubMed]

A. J. Mussap and D. M. Levi, “Spatial properties of filters underlying vernier acuity revealed by masking: evidence for collator mechanisms,” Vision Res. 36, 2459-2473 (1996).
[CrossRef] [PubMed]

M. F. Bradshaw, A. Glennerster, and B. J. Rogers, “The effect of display size on disparity scaling from differential perspective and vergence cues,” Vision Res. 36, 1255-1264 (1996).
[CrossRef] [PubMed]

1995 (1)

1993 (1)

S. J. Waugh, D. M. Levi, and T. Carney, “Orientation, masking, and vernier acuity for line targets,” Vision Res. 33, 1619-1638 (1993).
[CrossRef] [PubMed]

1992 (3)

D. M. Levi and S. A. Klein, “Weber's law for position: the role of spatial frequency and contrast,” Vision Res. 32, 2235-2250 (1992).
[CrossRef] [PubMed]

J. P. Roy, H. Komatsu, and R. H. Wurtz, “Disparity sensitivity of neurons in monkey extrastriate area MST,” J. Neurosci. 12, 2478-2492 (1992).
[PubMed]

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

1991 (1)

1990 (1)

H. A. Mallot and H. Bideau, “Binocular vergence influences the assignment of stereo correspondences,” Vision Res. 30, 1521-1523 (1990).
[CrossRef] [PubMed]

1988 (1)

S. P. McKee and G. J. Mitchison, “The role of retinal correspondence in stereoscopic matching,” Vision Res. 28, 1001-1012 (1988).
[CrossRef] [PubMed]

1987 (1)

M. A. Georgeson, “Temporal properties of spatial contrast vision,” Vision Res. 27, 765-780 (1987).
[CrossRef] [PubMed]

1986 (1)

C. M. Schor and P. A. Howarth, “Suprathreshold stereo-depth matches as a function of contrast and spatial frequency,” Perception 15, 249-258 (1986).
[CrossRef] [PubMed]

1985 (2)

C. M. Schor and D. R. Badcock, “A comparison of stereo and vernier acuity within spatial channels as a function of distance from fixation,” Vision Res. 25, 1113-1119 (1985).
[CrossRef] [PubMed]

G. F. Poggio, B. C. Motter, S. Squatrito, and Y. Trotter, “Responses of neurons in visual cortex (V1 and V2) of the alert macaque to dynamic random-dot stereograms,” Vision Res. 25, 397-406 (1985).
[CrossRef] [PubMed]

1984 (1)

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

1983 (1)

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

1980 (1)

1977 (4)

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

D. H. Hubel and T. N. Wiesel, “Ferrier lecture. Functional architecture of macaque monkey visual cortex,” Proc. R. Soc. London 198, 1-59 (1977).
[CrossRef]

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

J. I. Nelson, H. Kato, and P. O. Bishop, “Discrimination of orientation and position disparities by binocularly activated neurons in cat striate cortex,” J. Neurophysiol. 40, 260-283 (1977).
[PubMed]

1976 (1)

J. J. Kulikowski, “Effective contrast constancy and linearity of contrast sensation,” Vision Res. 16, 1419-1431 (1976).
[CrossRef] [PubMed]

1975 (1)

M. A. Georgeson and G. D. Sullivan, “Contrast constancy: deblurring in human vision by spatial frequency channels,” J. Physiol. (London) 252, 627-656 (1975).

1974 (1)

D. H. Hubel and T. N. Wiesel, “Uniformity of monkey striate cortex: a parallel relationship between field size, scatter, and magnification factor,” J. Comp. Neurol. 158, 295-305 (1974).
[CrossRef] [PubMed]

1973 (1)

J. M. Findlay, “Feature detectors and vernier acuity,” Nature (London) 241, 135-137 (1973).
[CrossRef]

1964 (1)

G. Wald, “The receptors of human color vision,” Science 145, 1007-1016 (1964).
[CrossRef] [PubMed]

1948 (1)

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

1941 (1)

A. H. Holoway and E. G. Boring, “Determinants of apparent visual size with distance variant,” Am. J. Psychol. 54, 21-37 (1941).
[CrossRef]

1923 (1)

E. E. Andersen and F. W. Weymouth, “Visual perception and the retinal mosaic,” Am. J. Physiol. 64, 559-594 (1923).

Andersen, E. E.

E. E. Andersen and F. W. Weymouth, “Visual perception and the retinal mosaic,” Am. J. Physiol. 64, 559-594 (1923).

Badcock, D. R.

C. M. Schor and D. R. Badcock, “A comparison of stereo and vernier acuity within spatial channels as a function of distance from fixation,” Vision Res. 25, 1113-1119 (1985).
[CrossRef] [PubMed]

Bedell, H. E.

S. S. Patel, H. E. Bedell, and P. Sampat, “Pooling signals from vertically and non-vertically orientation-tuned disparity mechanisms in human stereopsis,” Vision Res. 46, 1-13 (2006).
[CrossRef]

S. S. Patel, M. T. Ukwade, S. B. Stevenson, H. E. Bedell, V. Sampath, and H. Ogmen, “Stereoscopic depth perception from oblique phase disparities,” Vision Res. 43, 2479-2492 (2003).
[CrossRef] [PubMed]

S. S. Patel, H. E. Bedell, and M. T. Ukwade, “Vernier judgments in the absence of regular shape information,” Vision Res. 39, 2349-2360 (1999).
[CrossRef] [PubMed]

S. T. Chung and H. E. Bedell, “Vernier and letter acuities for low-pass filtered moving stimuli,” Vision Res. 38, 1967-1982 (1998).
[CrossRef] [PubMed]

Berry, R. N.

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

Bideau, H.

H. A. Mallot and H. Bideau, “Binocular vergence influences the assignment of stereo correspondences,” Vision Res. 30, 1521-1523 (1990).
[CrossRef] [PubMed]

Bishop, P. O.

J. I. Nelson, H. Kato, and P. O. Bishop, “Discrimination of orientation and position disparities by binocularly activated neurons in cat striate cortex,” J. Neurophysiol. 40, 260-283 (1977).
[PubMed]

Boring, E. G.

A. H. Holoway and E. G. Boring, “Determinants of apparent visual size with distance variant,” Am. J. Psychol. 54, 21-37 (1941).
[CrossRef]

Bosking, W. H.

W. H. Bosking, J. C. Crowley, and D. Fitzpatrick, “Spatial coding of position and orientation in primary visual cortex,” Nat. Neurosci. 5, 874-882 (2002).
[CrossRef] [PubMed]

Bradshaw, M. F.

M. F. Bradshaw, A. Glennerster, and B. J. Rogers, “The effect of display size on disparity scaling from differential perspective and vergence cues,” Vision Res. 36, 1255-1264 (1996).
[CrossRef] [PubMed]

Brenner, E.

E. Brenner and W. J. van Damme, “Perceived distance, shape and size,” Vision Res. 39, 975-986 (1999).
[CrossRef] [PubMed]

W. van Damme and E. Brenner, “The distance used for scaling disparities is the same as the one used for scaling retinal size,” Vision Res. 37, 757-764 (1997).
[CrossRef] [PubMed]

Carney, T.

S. J. Waugh, D. M. Levi, and T. Carney, “Orientation, masking, and vernier acuity for line targets,” Vision Res. 33, 1619-1638 (1993).
[CrossRef] [PubMed]

Chung, S. T.

L. Gantz, S. S. Patel, S. T. Chung, and R. S. Harwerth, “Mechanisms of perceptual learning of depth discrimination in random dot stereograms,” Vision Res. 47, 2170-2178 (2007).
[CrossRef] [PubMed]

S. T. Chung and H. E. Bedell, “Vernier and letter acuities for low-pass filtered moving stimuli,” Vision Res. 38, 1967-1982 (1998).
[CrossRef] [PubMed]

Comerford, J.

H. Ono and J. Comerford, “Stereoscopic depth constancy,” in Stability and Constancy in Visual Perception, W.Epstein, ed. (Wiley, 1977), pp. 91-128.

Cormack, L. K.

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

Crowley, J. C.

W. H. Bosking, J. C. Crowley, and D. Fitzpatrick, “Spatial coding of position and orientation in primary visual cortex,” Nat. Neurosci. 5, 874-882 (2002).
[CrossRef] [PubMed]

Eagle, R. A.

S. J. Prince and R. A. Eagle, “Weighted directional energy model of human stereo correspondence,” Vision Res. 40, 1143-1155 (2000).
[CrossRef] [PubMed]

Edwards, M.

C. M. Schor, M. Edwards, and D. R. Pope, “Spatial-frequency and contrast tuning of the transient-stereopsis system,” Vision Res. 38, 3057-3068 (1998).
[CrossRef]

Elder, J. H.

L. M. Wilcox, J. H. Elder, and R. F. Hess, “The effects of blur and size on monocular and stereoscopic localization,” Vision Res. 40, 3575-3584 (2000).
[CrossRef] [PubMed]

Fechner, G. T.

G. T. Fechner, in Elemente der Psychophysik (Breitkopf and Hartel, 1860).

Findlay, J. M.

J. M. Findlay, “Feature detectors and vernier acuity,” Nature (London) 241, 135-137 (1973).
[CrossRef]

Fischer, B.

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

Fitzpatrick, D.

W. H. Bosking, J. C. Crowley, and D. Fitzpatrick, “Spatial coding of position and orientation in primary visual cortex,” Nat. Neurosci. 5, 874-882 (2002).
[CrossRef] [PubMed]

Fleet, D. J.

D. J. Fleet, H. Wagner, and D. J. Heeger, “Neural encoding of binocular disparity: energy models, position shifts and phase shifts,” Vision Res. 36, 1839-1857 (1996).
[CrossRef] [PubMed]

Fredenburg, P. M.

R. S. Harwerth, P. M. Fredenburg, and E. L. Smith 3rd, “Temporal integration for stereoscopic vision,” Vision Res. 43, 505-517 (2003).
[CrossRef] [PubMed]

Gantz, L.

L. Gantz, S. S. Patel, S. T. Chung, and R. S. Harwerth, “Mechanisms of perceptual learning of depth discrimination in random dot stereograms,” Vision Res. 47, 2170-2178 (2007).
[CrossRef] [PubMed]

Georgeson, M. A.

M. A. Georgeson, “Contrast overconstancy,” J. Opt. Soc. Am. A 8, 579-586 (1991).
[CrossRef] [PubMed]

M. A. Georgeson, “Temporal properties of spatial contrast vision,” Vision Res. 27, 765-780 (1987).
[CrossRef] [PubMed]

M. A. Georgeson and G. D. Sullivan, “Contrast constancy: deblurring in human vision by spatial frequency channels,” J. Physiol. (London) 252, 627-656 (1975).

Giese, S. C.

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

Glennerster, A.

M. F. Bradshaw, A. Glennerster, and B. J. Rogers, “The effect of display size on disparity scaling from differential perspective and vergence cues,” Vision Res. 36, 1255-1264 (1996).
[CrossRef] [PubMed]

Green, D. M.

D. M. Green and J. A. Swets, Signal Detection Theory and Psychophysics (Krieger, 1974).

Harwerth, R. S.

L. Gantz, S. S. Patel, S. T. Chung, and R. S. Harwerth, “Mechanisms of perceptual learning of depth discrimination in random dot stereograms,” Vision Res. 47, 2170-2178 (2007).
[CrossRef] [PubMed]

R. S. Harwerth, P. M. Fredenburg, and E. L. Smith 3rd, “Temporal integration for stereoscopic vision,” Vision Res. 43, 505-517 (2003).
[CrossRef] [PubMed]

Heeger, D. J.

D. J. Fleet, H. Wagner, and D. J. Heeger, “Neural encoding of binocular disparity: energy models, position shifts and phase shifts,” Vision Res. 36, 1839-1857 (1996).
[CrossRef] [PubMed]

Hess, R. F.

L. M. Wilcox, J. H. Elder, and R. F. Hess, “The effects of blur and size on monocular and stereoscopic localization,” Vision Res. 40, 3575-3584 (2000).
[CrossRef] [PubMed]

Holoway, A. H.

A. H. Holoway and E. G. Boring, “Determinants of apparent visual size with distance variant,” Am. J. Psychol. 54, 21-37 (1941).
[CrossRef]

Howarth, P. A.

C. M. Schor and P. A. Howarth, “Suprathreshold stereo-depth matches as a function of contrast and spatial frequency,” Perception 15, 249-258 (1986).
[CrossRef] [PubMed]

Hubel, D. H.

D. H. Hubel and T. N. Wiesel, “Ferrier lecture. Functional architecture of macaque monkey visual cortex,” Proc. R. Soc. London 198, 1-59 (1977).
[CrossRef]

D. H. Hubel and T. N. Wiesel, “Uniformity of monkey striate cortex: a parallel relationship between field size, scatter, and magnification factor,” J. Comp. Neurol. 158, 295-305 (1974).
[CrossRef] [PubMed]

Jiang, B. C.

S. S. Patel, B. C. Jiang, and H. Ogmen, “Vergence dynamics predict fixation disparity,” Neural Comput. 13, 1495-1525 (2001).
[CrossRef] [PubMed]

Kato, H.

J. I. Nelson, H. Kato, and P. O. Bishop, “Discrimination of orientation and position disparities by binocularly activated neurons in cat striate cortex,” J. Neurophysiol. 40, 260-283 (1977).
[PubMed]

Klein, S. A.

D. M. Levi and S. A. Klein, “Weber's law for position: the role of spatial frequency and contrast,” Vision Res. 32, 2235-2250 (1992).
[CrossRef] [PubMed]

Komatsu, H.

J. P. Roy, H. Komatsu, and R. H. Wurtz, “Disparity sensitivity of neurons in monkey extrastriate area MST,” J. Neurosci. 12, 2478-2492 (1992).
[PubMed]

Kulikowski, J. J.

J. J. Kulikowski, “Effective contrast constancy and linearity of contrast sensation,” Vision Res. 16, 1419-1431 (1976).
[CrossRef] [PubMed]

Levi, D. M.

A. J. Mussap and D. M. Levi, “Spatial properties of filters underlying vernier acuity revealed by masking: evidence for collator mechanisms,” Vision Res. 36, 2459-2473 (1996).
[CrossRef] [PubMed]

S. J. Waugh and D. M. Levi, “Spatial alignment across gaps: contributions of orientation and spatial scale,” J. Opt. Soc. Am. A 12, 2305-2317 (1995).
[CrossRef]

S. J. Waugh, D. M. Levi, and T. Carney, “Orientation, masking, and vernier acuity for line targets,” Vision Res. 33, 1619-1638 (1993).
[CrossRef] [PubMed]

D. M. Levi and S. A. Klein, “Weber's law for position: the role of spatial frequency and contrast,” Vision Res. 32, 2235-2250 (1992).
[CrossRef] [PubMed]

MacLeod, D. I.

H. S. Smallman and D. I. MacLeod, “Spatial scale interactions in stereo sensitivity and the neural representation of binocular disparity,” Perception 26, 977-994 (1997).
[CrossRef] [PubMed]

Mallot, H. A.

H. A. Mallot and H. Bideau, “Binocular vergence influences the assignment of stereo correspondences,” Vision Res. 30, 1521-1523 (1990).
[CrossRef] [PubMed]

McKee, S.

McKee, S. P.

S. P. McKee and G. J. Mitchison, “The role of retinal correspondence in stereoscopic matching,” Vision Res. 28, 1001-1012 (1988).
[CrossRef] [PubMed]

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

Mitchison, G. J.

S. P. McKee and G. J. Mitchison, “The role of retinal correspondence in stereoscopic matching,” Vision Res. 28, 1001-1012 (1988).
[CrossRef] [PubMed]

Motter, B. C.

G. F. Poggio, B. C. Motter, S. Squatrito, and Y. Trotter, “Responses of neurons in visual cortex (V1 and V2) of the alert macaque to dynamic random-dot stereograms,” Vision Res. 25, 397-406 (1985).
[CrossRef] [PubMed]

Mussap, A. J.

A. J. Mussap and D. M. Levi, “Spatial properties of filters underlying vernier acuity revealed by masking: evidence for collator mechanisms,” Vision Res. 36, 2459-2473 (1996).
[CrossRef] [PubMed]

Nelson, J. I.

J. I. Nelson, H. Kato, and P. O. Bishop, “Discrimination of orientation and position disparities by binocularly activated neurons in cat striate cortex,” J. Neurophysiol. 40, 260-283 (1977).
[PubMed]

Ogmen, H.

S. S. Patel, M. T. Ukwade, S. B. Stevenson, H. E. Bedell, V. Sampath, and H. Ogmen, “Stereoscopic depth perception from oblique phase disparities,” Vision Res. 43, 2479-2492 (2003).
[CrossRef] [PubMed]

S. S. Patel, B. C. Jiang, and H. Ogmen, “Vergence dynamics predict fixation disparity,” Neural Comput. 13, 1495-1525 (2001).
[CrossRef] [PubMed]

Ono, H.

H. Ono and J. Comerford, “Stereoscopic depth constancy,” in Stability and Constancy in Visual Perception, W.Epstein, ed. (Wiley, 1977), pp. 91-128.

Patel, S. S.

L. Gantz, S. S. Patel, S. T. Chung, and R. S. Harwerth, “Mechanisms of perceptual learning of depth discrimination in random dot stereograms,” Vision Res. 47, 2170-2178 (2007).
[CrossRef] [PubMed]

S. S. Patel, H. E. Bedell, and P. Sampat, “Pooling signals from vertically and non-vertically orientation-tuned disparity mechanisms in human stereopsis,” Vision Res. 46, 1-13 (2006).
[CrossRef]

S. S. Patel, M. T. Ukwade, S. B. Stevenson, H. E. Bedell, V. Sampath, and H. Ogmen, “Stereoscopic depth perception from oblique phase disparities,” Vision Res. 43, 2479-2492 (2003).
[CrossRef] [PubMed]

S. S. Patel, B. C. Jiang, and H. Ogmen, “Vergence dynamics predict fixation disparity,” Neural Comput. 13, 1495-1525 (2001).
[CrossRef] [PubMed]

S. S. Patel, H. E. Bedell, and M. T. Ukwade, “Vernier judgments in the absence of regular shape information,” Vision Res. 39, 2349-2360 (1999).
[CrossRef] [PubMed]

Pirenne, M. H.

M. H. Pirenne, “Spectral luminous efficiency of radiation,” in The Eye, H.Davson, ed. (Academic, 1962), pp. 65-91.

Poggio, G. F.

G. F. Poggio, B. C. Motter, S. Squatrito, and Y. Trotter, “Responses of neurons in visual cortex (V1 and V2) of the alert macaque to dynamic random-dot stereograms,” Vision Res. 25, 397-406 (1985).
[CrossRef] [PubMed]

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

Pope, D. R.

C. M. Schor, M. Edwards, and D. R. Pope, “Spatial-frequency and contrast tuning of the transient-stereopsis system,” Vision Res. 38, 3057-3068 (1998).
[CrossRef]

Prince, S. J.

S. J. Prince and R. A. Eagle, “Weighted directional energy model of human stereo correspondence,” Vision Res. 40, 1143-1155 (2000).
[CrossRef] [PubMed]

Qian, N.

N. Qian and Y. Zhu, “Physiological computation of binocular disparity,” Vision Res. 37, 1811-1827 (1997).
[CrossRef] [PubMed]

Rogers, B. J.

M. F. Bradshaw, A. Glennerster, and B. J. Rogers, “The effect of display size on disparity scaling from differential perspective and vergence cues,” Vision Res. 36, 1255-1264 (1996).
[CrossRef] [PubMed]

Roy, J. P.

J. P. Roy, H. Komatsu, and R. H. Wurtz, “Disparity sensitivity of neurons in monkey extrastriate area MST,” J. Neurosci. 12, 2478-2492 (1992).
[PubMed]

Sampat, P.

S. S. Patel, H. E. Bedell, and P. Sampat, “Pooling signals from vertically and non-vertically orientation-tuned disparity mechanisms in human stereopsis,” Vision Res. 46, 1-13 (2006).
[CrossRef]

Sampath, V.

S. S. Patel, M. T. Ukwade, S. B. Stevenson, H. E. Bedell, V. Sampath, and H. Ogmen, “Stereoscopic depth perception from oblique phase disparities,” Vision Res. 43, 2479-2492 (2003).
[CrossRef] [PubMed]

Schor, C. M.

C. M. Schor, M. Edwards, and D. R. Pope, “Spatial-frequency and contrast tuning of the transient-stereopsis system,” Vision Res. 38, 3057-3068 (1998).
[CrossRef]

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

C. M. Schor and P. A. Howarth, “Suprathreshold stereo-depth matches as a function of contrast and spatial frequency,” Perception 15, 249-258 (1986).
[CrossRef] [PubMed]

C. M. Schor and D. R. Badcock, “A comparison of stereo and vernier acuity within spatial channels as a function of distance from fixation,” Vision Res. 25, 1113-1119 (1985).
[CrossRef] [PubMed]

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

Smallman, H. S.

H. S. Smallman and D. I. MacLeod, “Spatial scale interactions in stereo sensitivity and the neural representation of binocular disparity,” Perception 26, 977-994 (1997).
[CrossRef] [PubMed]

Smith, E. L.

R. S. Harwerth, P. M. Fredenburg, and E. L. Smith 3rd, “Temporal integration for stereoscopic vision,” Vision Res. 43, 505-517 (2003).
[CrossRef] [PubMed]

Squatrito, S.

G. F. Poggio, B. C. Motter, S. Squatrito, and Y. Trotter, “Responses of neurons in visual cortex (V1 and V2) of the alert macaque to dynamic random-dot stereograms,” Vision Res. 25, 397-406 (1985).
[CrossRef] [PubMed]

Stevenson, S. B.

S. S. Patel, M. T. Ukwade, S. B. Stevenson, H. E. Bedell, V. Sampath, and H. Ogmen, “Stereoscopic depth perception from oblique phase disparities,” Vision Res. 43, 2479-2492 (2003).
[CrossRef] [PubMed]

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

Sullivan, G. D.

M. A. Georgeson and G. D. Sullivan, “Contrast constancy: deblurring in human vision by spatial frequency channels,” J. Physiol. (London) 252, 627-656 (1975).

Swanson, W. H.

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

Swets, J. A.

D. M. Green and J. A. Swets, Signal Detection Theory and Psychophysics (Krieger, 1974).

Trotter, Y.

G. F. Poggio, B. C. Motter, S. Squatrito, and Y. Trotter, “Responses of neurons in visual cortex (V1 and V2) of the alert macaque to dynamic random-dot stereograms,” Vision Res. 25, 397-406 (1985).
[CrossRef] [PubMed]

Tyler, C. W.

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

Ukwade, M. T.

S. S. Patel, M. T. Ukwade, S. B. Stevenson, H. E. Bedell, V. Sampath, and H. Ogmen, “Stereoscopic depth perception from oblique phase disparities,” Vision Res. 43, 2479-2492 (2003).
[CrossRef] [PubMed]

S. S. Patel, H. E. Bedell, and M. T. Ukwade, “Vernier judgments in the absence of regular shape information,” Vision Res. 39, 2349-2360 (1999).
[CrossRef] [PubMed]

van Damme, W.

W. van Damme and E. Brenner, “The distance used for scaling disparities is the same as the one used for scaling retinal size,” Vision Res. 37, 757-764 (1997).
[CrossRef] [PubMed]

van Damme, W. J.

E. Brenner and W. J. van Damme, “Perceived distance, shape and size,” Vision Res. 39, 975-986 (1999).
[CrossRef] [PubMed]

Wagner, H.

D. J. Fleet, H. Wagner, and D. J. Heeger, “Neural encoding of binocular disparity: energy models, position shifts and phase shifts,” Vision Res. 36, 1839-1857 (1996).
[CrossRef] [PubMed]

Wald, G.

G. Wald, “The receptors of human color vision,” Science 145, 1007-1016 (1964).
[CrossRef] [PubMed]

Waugh, S. J.

S. J. Waugh and D. M. Levi, “Spatial alignment across gaps: contributions of orientation and spatial scale,” J. Opt. Soc. Am. A 12, 2305-2317 (1995).
[CrossRef]

S. J. Waugh, D. M. Levi, and T. Carney, “Orientation, masking, and vernier acuity for line targets,” Vision Res. 33, 1619-1638 (1993).
[CrossRef] [PubMed]

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Weymouth, F. W.

E. E. Andersen and F. W. Weymouth, “Visual perception and the retinal mosaic,” Am. J. Physiol. 64, 559-594 (1923).

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D. H. Hubel and T. N. Wiesel, “Ferrier lecture. Functional architecture of macaque monkey visual cortex,” Proc. R. Soc. London 198, 1-59 (1977).
[CrossRef]

D. H. Hubel and T. N. Wiesel, “Uniformity of monkey striate cortex: a parallel relationship between field size, scatter, and magnification factor,” J. Comp. Neurol. 158, 295-305 (1974).
[CrossRef] [PubMed]

Wilcox, L. M.

L. M. Wilcox, J. H. Elder, and R. F. Hess, “The effects of blur and size on monocular and stereoscopic localization,” Vision Res. 40, 3575-3584 (2000).
[CrossRef] [PubMed]

Wilson, H. R.

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

Wood, I.

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

Wurtz, R. H.

J. P. Roy, H. Komatsu, and R. H. Wurtz, “Disparity sensitivity of neurons in monkey extrastriate area MST,” J. Neurosci. 12, 2478-2492 (1992).
[PubMed]

Zhu, Y.

N. Qian and Y. Zhu, “Physiological computation of binocular disparity,” Vision Res. 37, 1811-1827 (1997).
[CrossRef] [PubMed]

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E. E. Andersen and F. W. Weymouth, “Visual perception and the retinal mosaic,” Am. J. Physiol. 64, 559-594 (1923).

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

J. I. Nelson, H. Kato, and P. O. Bishop, “Discrimination of orientation and position disparities by binocularly activated neurons in cat striate cortex,” J. Neurophysiol. 40, 260-283 (1977).
[PubMed]

J. Neurosci. (1)

J. P. Roy, H. Komatsu, and R. H. Wurtz, “Disparity sensitivity of neurons in monkey extrastriate area MST,” J. Neurosci. 12, 2478-2492 (1992).
[PubMed]

J. Opt. Soc. Am. (1)

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

J. Physiol. (London) (1)

M. A. Georgeson and G. D. Sullivan, “Contrast constancy: deblurring in human vision by spatial frequency channels,” J. Physiol. (London) 252, 627-656 (1975).

Nat. Neurosci. (1)

W. H. Bosking, J. C. Crowley, and D. Fitzpatrick, “Spatial coding of position and orientation in primary visual cortex,” Nat. Neurosci. 5, 874-882 (2002).
[CrossRef] [PubMed]

Nature (London) (1)

J. M. Findlay, “Feature detectors and vernier acuity,” Nature (London) 241, 135-137 (1973).
[CrossRef]

Neural Comput. (1)

S. S. Patel, B. C. Jiang, and H. Ogmen, “Vergence dynamics predict fixation disparity,” Neural Comput. 13, 1495-1525 (2001).
[CrossRef] [PubMed]

Perception (2)

H. S. Smallman and D. I. MacLeod, “Spatial scale interactions in stereo sensitivity and the neural representation of binocular disparity,” Perception 26, 977-994 (1997).
[CrossRef] [PubMed]

C. M. Schor and P. A. Howarth, “Suprathreshold stereo-depth matches as a function of contrast and spatial frequency,” Perception 15, 249-258 (1986).
[CrossRef] [PubMed]

Proc. R. Soc. London (1)

D. H. Hubel and T. N. Wiesel, “Ferrier lecture. Functional architecture of macaque monkey visual cortex,” Proc. R. Soc. London 198, 1-59 (1977).
[CrossRef]

Science (1)

G. Wald, “The receptors of human color vision,” Science 145, 1007-1016 (1964).
[CrossRef] [PubMed]

Vision Res. (27)

C. M. Schor and D. R. Badcock, “A comparison of stereo and vernier acuity within spatial channels as a function of distance from fixation,” Vision Res. 25, 1113-1119 (1985).
[CrossRef] [PubMed]

S. S. Patel, H. E. Bedell, and P. Sampat, “Pooling signals from vertically and non-vertically orientation-tuned disparity mechanisms in human stereopsis,” Vision Res. 46, 1-13 (2006).
[CrossRef]

D. M. Levi and S. A. Klein, “Weber's law for position: the role of spatial frequency and contrast,” Vision Res. 32, 2235-2250 (1992).
[CrossRef] [PubMed]

G. F. Poggio, B. C. Motter, S. Squatrito, and Y. Trotter, “Responses of neurons in visual cortex (V1 and V2) of the alert macaque to dynamic random-dot stereograms,” Vision Res. 25, 397-406 (1985).
[CrossRef] [PubMed]

W. van Damme and E. Brenner, “The distance used for scaling disparities is the same as the one used for scaling retinal size,” Vision Res. 37, 757-764 (1997).
[CrossRef] [PubMed]

S. J. Waugh, D. M. Levi, and T. Carney, “Orientation, masking, and vernier acuity for line targets,” Vision Res. 33, 1619-1638 (1993).
[CrossRef] [PubMed]

A. J. Mussap and D. M. Levi, “Spatial properties of filters underlying vernier acuity revealed by masking: evidence for collator mechanisms,” Vision Res. 36, 2459-2473 (1996).
[CrossRef] [PubMed]

S. S. Patel, H. E. Bedell, and M. T. Ukwade, “Vernier judgments in the absence of regular shape information,” Vision Res. 39, 2349-2360 (1999).
[CrossRef] [PubMed]

N. Qian and Y. Zhu, “Physiological computation of binocular disparity,” Vision Res. 37, 1811-1827 (1997).
[CrossRef] [PubMed]

D. J. Fleet, H. Wagner, and D. J. Heeger, “Neural encoding of binocular disparity: energy models, position shifts and phase shifts,” Vision Res. 36, 1839-1857 (1996).
[CrossRef] [PubMed]

S. S. Patel, M. T. Ukwade, S. B. Stevenson, H. E. Bedell, V. Sampath, and H. Ogmen, “Stereoscopic depth perception from oblique phase disparities,” Vision Res. 43, 2479-2492 (2003).
[CrossRef] [PubMed]

L. Gantz, S. S. Patel, S. T. Chung, and R. S. Harwerth, “Mechanisms of perceptual learning of depth discrimination in random dot stereograms,” Vision Res. 47, 2170-2178 (2007).
[CrossRef] [PubMed]

S. P. McKee and G. J. Mitchison, “The role of retinal correspondence in stereoscopic matching,” Vision Res. 28, 1001-1012 (1988).
[CrossRef] [PubMed]

H. A. Mallot and H. Bideau, “Binocular vergence influences the assignment of stereo correspondences,” Vision Res. 30, 1521-1523 (1990).
[CrossRef] [PubMed]

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

S. J. Prince and R. A. Eagle, “Weighted directional energy model of human stereo correspondence,” Vision Res. 40, 1143-1155 (2000).
[CrossRef] [PubMed]

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

M. A. Georgeson, “Temporal properties of spatial contrast vision,” Vision Res. 27, 765-780 (1987).
[CrossRef] [PubMed]

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

J. J. Kulikowski, “Effective contrast constancy and linearity of contrast sensation,” Vision Res. 16, 1419-1431 (1976).
[CrossRef] [PubMed]

S. T. Chung and H. E. Bedell, “Vernier and letter acuities for low-pass filtered moving stimuli,” Vision Res. 38, 1967-1982 (1998).
[CrossRef] [PubMed]

C. M. Schor, M. Edwards, and D. R. Pope, “Spatial-frequency and contrast tuning of the transient-stereopsis system,” Vision Res. 38, 3057-3068 (1998).
[CrossRef]

R. S. Harwerth, P. M. Fredenburg, and E. L. Smith 3rd, “Temporal integration for stereoscopic vision,” Vision Res. 43, 505-517 (2003).
[CrossRef] [PubMed]

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

L. M. Wilcox, J. H. Elder, and R. F. Hess, “The effects of blur and size on monocular and stereoscopic localization,” Vision Res. 40, 3575-3584 (2000).
[CrossRef] [PubMed]

M. F. Bradshaw, A. Glennerster, and B. J. Rogers, “The effect of display size on disparity scaling from differential perspective and vergence cues,” Vision Res. 36, 1255-1264 (1996).
[CrossRef] [PubMed]

E. Brenner and W. J. van Damme, “Perceived distance, shape and size,” Vision Res. 39, 975-986 (1999).
[CrossRef] [PubMed]

Other (4)

H. Ono and J. Comerford, “Stereoscopic depth constancy,” in Stability and Constancy in Visual Perception, W.Epstein, ed. (Wiley, 1977), pp. 91-128.

G. T. Fechner, in Elemente der Psychophysik (Breitkopf and Hartel, 1860).

D. M. Green and J. A. Swets, Signal Detection Theory and Psychophysics (Krieger, 1974).

M. H. Pirenne, “Spectral luminous efficiency of radiation,” in The Eye, H.Davson, ed. (Academic, 1962), pp. 65-91.

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Figures (9)

Fig. 1
Fig. 1

(a) For the stimuli used in the position-offset experiments (top), the horizontal distance p between the vertical dotted lines is defined as the Vernier offset. In the fused percept (bottom), the observer sees the bottom line shifted rightward relative to the top line, with both lines in the same depth plane. (b) The stimuli used in the stereoscopic depth experiments (top) differed from those in (a) in that opposite directions of monocular offsets were presented to each eye to generate stereoscopic disparity. Twice the horizontal distance between the vertical dotted lines (2p) is defined as the relative stereoscopic disparity. In the fused percept (bottom), the observer sees the bottom line in front of (or behind) the top line, with both lines in the same perceived direction.

Fig. 2
Fig. 2

Threshold and matching data from the gap experiments for four observers. In each panel, the squares are data from the Vernier offset experiments and the circles are data from the stereo experiments. The error bars represent ± 1 standard error. The unconnected square and circular symbols just below and above the y axis value of 1 in each panel represent the Vernier offset threshold and stereothreshold, respectively. The y axis value for the threshold data was selected arbitrarily. Small symbols correspond to thresholds for a 10 interline gap (except S2’s gap = 20 ), medium-sized symbols correspond to thresholds for a 100 gap (except S2’s gap = 720 and 240 for Vernier offset and stereothreshold experiments, respectively), and the large filled circle in the lower right panel corresponds to S2’s stereo threshold for a 540 gap. The squares and circles joined by lines are data from suprathreshold Vernier offset and stereo experiments, respectively. The 1:1 diagonal line represents equal suprathreshold perception of the test and matching stimuli in the threshold unelevated and elevated conditions. The filled symbols for S2 denote that the gap of the matching stimuli in the Vernier offset and stereo suprathreshold experiments was 20 .  

Fig. 3
Fig. 3

Threshold and matching data from the blur experiments for three observers. The unfilled symbols indicate that the test target was blurred by + 2 D . Otherwise, the lines and symbols have the same meaning as in Fig. 2. The interline gap was 20 . For observer S3 a test target with 4 D blur also was used (filled symbols).

Fig. 4
Fig. 4

Relationship between blur-induced changes in perceived target distance and perceived position-offset (squares) or stereoscopic depth (circles). The top x axis and the right-hand y axis compare the ratio of the squared perceived distances for blurred versus unblurred targets to the ratio of disparities for unblurred matching and blurred test stimuli, averaged for all of the suprathreshold disparities in Fig. 3. The bottom x axis and left-hand y axis compare the ratio of perceived distances for blurred versus unblurred stimuli to the ratio of the Vernier position offsets for unblurred matching and blurred test stimuli, averaged for all the suprathreshold Vernier offsets in Fig. 3. Each symbol represents the data for one observer, with x and y error bars equal to ± 1 SE. The diagonal line indicates that blur-induced changes in perceived stereoscopic depth or relative position offset can be accounted for by blur-induced changes in perceived distance.

Fig. 5
Fig. 5

Relationship between the threshold and the perception of suprathreshold stimuli as predicted by Kulikowski’s [(a) and (b)] and by proportional models [(c) and (d)] of suprathreshold perception. (a) and (c) plot stimulus strength s versus the perceptual response P ( s ) on linear x and y axes. (b) and (d) replot the same relationships on logarithmic x and y axes. In each plot, the thick black line shows the relationship between stimuli and perceptual responses for stimulus levels above the unelevated threshold Th 0 (black circle). In a threshold-elevating condition, the threshold increases to Th e (gray circle) and perceptual responses to stimuli greater than Th e are defined by the thick dotted line. In the model shown in (a) and (b), the perceptual responses E P in the normal and threshold-elevating conditions match when the suprathreshold stimuli in the corresponding conditions s 0 and s e differ by the amount equal to the difference between the thresholds ( Th e Th 0 ) . In the model shown in (c) and (d), the perceptual responses E P in the normal and threshold-elevating conditions match when the suprathreshold stimuli in the corresponding conditions s 0 and s e have a ratio equal to the ratio of the thresholds Th e Th 0 . Note that the proportional model’s prediction in the logarithmic coordinate system is equivalent to the Kulikowski model’s prediction in a linear coordinate system.

Fig. 6
Fig. 6

Evaluation of the Kulikowski (top row) and proportional models (bottom row) for suprathreshold perception, using data pooled across observers and conditions in the gap (left) and blur (right) position-offset experiments. The x axis in each panel represents the difference between the suprathreshold position offset and the threshold Vernier offset (linear in the top panels and log transformed in the bottom panels) when the Vernier threshold was not elevated. The y axis represents the difference between the suprathreshold position offset and the elevated Vernier threshold in threshold-elevating conditions. Filled circles specify position offsets in the threshold-unelevated and elevated conditions that perceptually match. Solid lines are fit to the plotted data, with the y intercept constrained to be zero. In each panel, the prediction of the Kulikowski or the proportional model is shown by a dotted line.

Fig. 7
Fig. 7

Evaluation of the Kulikowski (top row) and proportional models (bottom row) for suprathreshold perception using the data from the stereoscopic depth experiments. The x axis in each panel represents the difference between the suprathreshold disparity and the stereothreshold (linear in the top panels, log transformed in the bottom panels) when the stereothreshold was not elevated. The y axis represents the difference between the suprathreshold disparity and the elevated stereothreshold in threshold-elevating conditions. Other conventions are as in Fig. 6.

Fig. 8
Fig. 8

Illustration of the effect of stimulus blur and readout weighting on disparity representation. The top row illustrates the retinal activity profiles generated by one object of a binocular stimulus that is composed of two objects. The second object (not shown) is assumed to lie on the horopter with zero disparity. Activity profiles in the two eyes are represented as two Gaussian functions (curves T L and T R ) displaced from the retinal zero location in opposite directions. The difference between the peaks of the two Gaussian functions represents the absolute stimulus disparity (here, 10 ). The middle row shows the absolute disparity representation obtained by cross-correlating the retinal activity profiles in the two eyes in the top row. The gray Gaussian curves ( W f : SD = 20 ) in the bottom row depict a hypothetical weighted readout function for disparity, and the black curves represent the weighted disparity representation computed by multiplying the absolute disparity representation in the middle row by the weighted readout function. The left and right columns show the normalized retinal activation and the corresponding disparity representations for an unblurred (Gaussian SD = 0.5 ) and a blurred stimulus (Gaussian SD = 10 ), respectively. The long vertical dotted lines that span the second and third rows illustrate the relative alignment between the peaks of the disparity representation and the weighted disparity representation.

Fig. 9
Fig. 9

Simulation results for the weighted-disparity-computation model. The x axis represents the absolute disparity of an off-horoptoral binocular stimulus object. (The reference object is assumed to be on the horopter.) For each value of stimulus disparity on the x axis, the y axis represents the centroid of the weighted disparity representation obtained using a Gaussian weighting function W f with its peak on the horopter as described in Fig. 8. Simulation results using two different weighting functions are shown for blurred (medium and large circles connected by slightly thick and thicker lines, respectively) and unblurred stimuli (small circles and thin connecting line). The standard deviation SD of the Gaussian retinal activity profile for the blurred stimulus was 10 . The thin diagonal line indicates veridical model responses.

Tables (4)

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Table 1 Summary of Regression Analysis to Test Kulikowski and Proportional Models a

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Table 2 Parameters of the Relative Position Computation Model (Gap Experiment)

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Table 3 Results of Simulating the Suprathreshold Vernier Gap Experiment

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Table 4 Parameters of the Relative Position Computation Model (Blur Experiments)

Equations (22)

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Perceived Depth = k ( Disparity ) ( Viewing Distance 2 ) ,
k e ( s e Th e ) = k 0 ( s 0 Th 0 ) .
s e Th e = s 0 Th 0 .
k e ( log s e log Th e ) = k 0 ( log s 0 log Th 0 ) .
log s e log Th e = log s 0 log Th 0 .
P = k s + c ,
P Th = k s T + c ,
P = k ( s s T ) + P Th .
P = c s k ,
log P = log c + k log s .
log P Th = log c + k log s T .
log P = k ( log s log s T ) + log P Th .
P = k log s + c ,
P Th = c + k log s T .
P = k ( log s log s T ) + P Th .
P a i = i r a 2 + ψ p ,
x a i = g a exp [ ( i n a c ) 2 σ a 2 ] + ψ x ,
T top = i = 1 round ( 4 r 1 ) P 1 i f 1 ( x 1 i ) i = 1 round ( 4 r 1 ) f 1 ( x 1 i ) ,
T bottom = i = 1 round ( 4 r 2 ) P 2 i f 2 ( x 2 i ) i = 1 round ( 4 r 2 ) f 2 ( x 2 i ) ,
f a ( x ) = { x , if n a c λ a x n a c + λ a 0 , otherwise } .
R P = r 1 T top r 2 T bottom + ψ r p ,
D = { left if R P < 0 right if R P > 0 guess if R P = 0 } .

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