Abstract

Are differences in luminance spatial frequency between surfaces that overlap in depth useful for surface segmentation? We examined this question, using a novel stimulus termed a dual-surface disparity grating. The dual-surface grating was made from Gabor micropatterns and consisted of two superimposed sinusoidal disparity gratings of identical disparity-modulation spatial frequency and orientation but of opposite spatial phase. Corrugation amplitude thresholds for discrimination of the orientation of the dual-surface grating were obtained as a function of the difference in Gabor (luminance) spatial frequency between the two surfaces. When the Gabor micropatterns on the two surfaces were identical in spatial frequency, thresholds were very high and in some instances impossible to obtain. However, with as little as a 1-octave difference in spatial frequency between the surfaces, thresholds fell sharply to near-asymptotic levels. The fall in thresholds paralleled a change in the appearance of the stimulus from one of irregular depth to stereo transparency. The most parsimonious explanation for this finding is that the introduction of a between-surface luminance spatial-frequency difference reduces the number of spurious cross-surface binocular matches, thus helping to reveal the three-dimensional structure of the stimulus.

© 2001 Optical Society of America

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    [CrossRef] [PubMed]
  2. R. A. Akerstrom, J. T. Todd, “The perception of stereoscopic transparency,” Percept. Psychophys. 44, 421–432 (1988).
    [CrossRef] [PubMed]
  3. D. Weinshall, “Perception of multiple transparent planes in stereo vision,” Nature 341, 737–739 (1989).
    [CrossRef] [PubMed]
  4. S. Gephstein, A. Cooperman, “Stereoscopic transparency: A test for binocular disambiguating power,” Vision Res. 38, 2913–2932 (1998).
    [CrossRef]
  5. I. P. Howard, B. J. Rogers, Binocular Vision and Stereopsis (Oxford U. Press, Oxford, UK, 1995). For a discussion of disparity averaging and its limitations as an explanatory concept, see pp. 230–234. For a discussion of the constraints on stereo matching, see pp. 216–229.
  6. J. M. Lankheet, M. Palmen, “Stereoscopic segregation of transparent surfaces and the effect of motion contrast,” Vision Res. 38, 659–668 (1998).
    [CrossRef] [PubMed]
  7. B. Julesz, J. E. Miller, “Independent spatial frequency tuned channels in binocular fusion and rivalry,” Perception 4, 125–143 (1975).
    [CrossRef]
  8. J. E. W. Mayhew, J. P. Frisby, “Rivalrous texture stereograms,” Nature 264, 53–56 (1976).
    [CrossRef] [PubMed]
  9. C. M. Schor, I. Wood, “Disparity range for local stereopsis as a function of luminance spatial frequency,” Vision Res. 23, 1649–1654 (1983).
    [CrossRef] [PubMed]
  10. H. R. Wilson, R. Blake, D. L. Halpern, “Coarse spatial scales constrain the range of fusion of fine spatial scales,” J. Opt. Soc. Am. A 8, 229–236 (1991).
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  11. Y. Yang, R. Blake, “Spatial frequency tuning of human stereopsis,” Vision Res. 31, 1177–1189 (1991).
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    [CrossRef]
  13. G. C. DeAngelis, I. Ohzawa, R. D. Freeman, “Neuronal mechanisms underlying stereopsis: How do simple cells in the visual cortex encode binocular disparity?” Perception 24, 3–31 (1995).
    [CrossRef] [PubMed]
  14. A. M. Rohaly, H. R. Wilson, “Disparity averaging across spatial scales,” Vision Res. 34, 1315–1325 (1994).
    [CrossRef] [PubMed]
  15. B. Julesz, S. C. Johnson, “Stereograms portraying ambiguous perceivable surfaces,” Proc. Natl. Soc. 61, 437–441 (1968).
    [CrossRef]
  16. A. J. Parker, Y. Yang, “Spatial properties of disparity pooling in human stereo vision,” Vision Res. 29, 1525–1538 (1989).
    [CrossRef] [PubMed]
  17. S. B. Stevenson, L. K. Cormack, C. M. Schor, “Depth attraction and repulsion in random dot stereograms,” Vision Res. 31, 805–813 (1991).
    [CrossRef] [PubMed]
  18. C. W. Tyler, “Depth perception in disparity gratings,” Nature 251, 140–142 (1974).
    [CrossRef] [PubMed]
  19. F. A. A. Kingdom, L. R. Ziegler, R. F. Hess, “The role of spatial scale in stereoscopic segmentation,” Perception Suppl. 27, 21 (1998).
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    [CrossRef] [PubMed]
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    [CrossRef]
  22. R. F. Hess, F. A. A. Kingdom, L. R. Ziegler, “On the relationship between the spatial channels for luminance and disparity processing,” Vision Res. 39, 559–568 (1999).
    [CrossRef] [PubMed]
  23. M. A. Georgeson, G. D. Sullivan, “Contrast constancy: Deblurring in human vision by spatial frequency channels,” J. Physiol. (London) 252, 677–656 (1975).
  24. N. Brady, D. J. Field, “What’s constant in contrast constancy? The effect of scaling on the perceived contrast of bandpass patterns,” Vision Res. 35, 739–756 (1995).
    [CrossRef] [PubMed]
  25. R. A. Schumer, L. Ganz, “Independent stereoscopic channels for different extents of spatial pooling,” Vision Res. 19, 1303–1314 (1979).
    [CrossRef] [PubMed]
  26. C. W. Tyler, “Sensory processing of binocular disparity,” in Vergence Eye Movements: Basic and Clinical Aspects, M. C. Schor, K. J. Ciuffreda, eds. (Butterworth, Boston, Mass., 1983), pp. 199–296.
  27. A. B. Cobo-Lewis, Y. Y. Yeh, “Selectivity of cyclopean masking for the spatial frequency of disparity modulation,” Vision Res. 34, 607–620 (1994).
    [CrossRef] [PubMed]
  28. K. Pulliam, “Spatial frequency analysis of three-dimensional vision,” in Visual Simulation and Image Realism II, K. S. Setty, ed., Proc. SPIE303, 71–77 (1981).
    [CrossRef]
  29. B. Lee, B. Rogers, “Disparity modulation sensitivity for narrow-band-filtered stereograms,” Vision Res. 37, 1769–1778 (1997).
    [CrossRef] [PubMed]
  30. R. Blake, H. R. Wilson, “Neural models of stereoscopic vision,” Trends Neurosci. 14, 445–452 (1991).
    [CrossRef] [PubMed]
  31. L. R. Ziegler, R. F. Hess, “Stereoscopic depth but not shape perception from second-order stimuli,” Vision Res. 39, 1491–1507 (1999).
    [CrossRef] [PubMed]
  32. L. R. Ziegler, F. A. A. Kingdom, R. F. Hess, “Local luminance factors that determine the maximum disparity for seeing cyclopean surface shape,” Vision Res. 40, 1157–1165 (2000).
    [CrossRef] [PubMed]
  33. G. Sperling, “Binocular vision: A physical and a neural theory,” Am. J. Psychol. 83, 461–534 (1970).
    [CrossRef]
  34. J. L. Nelson, “Globality and stereoscopic fusion in binocular vision,” J. Theor. Biol. 49, 1–88 (1975).
    [CrossRef] [PubMed]
  35. D. Marr, T. Poggio, “Cooperative computation of stereo disparity,” Science 194, 283–287 (1976).
    [CrossRef] [PubMed]
  36. J. E. W. Mayhew, J. P. Frisby, “The computation of binocular edges,” Perception 9, 69–86 (1980).
    [CrossRef] [PubMed]
  37. J. Gibson, The Perception of the Visual World (Houghton-Mifflin, Boston, Mass., 1950).
  38. J. Cutting, R. Millard, “Three gradients and the perception of flat and curved surfaces,” J. Exp. Psychol. Gen. 113, 198–216 (1984).
    [CrossRef] [PubMed]
  39. J. Todd, R. Akerstrom, “Perception of three-dimensional form from patterns of optical texture,” J. Exp. Psychol. Hum. Percep. 13, 242–255 (1987).
    [CrossRef]
  40. K. Stevens, A. Brookes, “Integrating stereopsis with monocular interpretations of planar surfaces,” Vision Res. 28, 371–386 (1988).
    [CrossRef] [PubMed]

2000

L. R. Ziegler, F. A. A. Kingdom, R. F. Hess, “Local luminance factors that determine the maximum disparity for seeing cyclopean surface shape,” Vision Res. 40, 1157–1165 (2000).
[CrossRef] [PubMed]

1999

R. F. Hess, F. A. A. Kingdom, L. R. Ziegler, “On the relationship between the spatial channels for luminance and disparity processing,” Vision Res. 39, 559–568 (1999).
[CrossRef] [PubMed]

L. R. Ziegler, R. F. Hess, “Stereoscopic depth but not shape perception from second-order stimuli,” Vision Res. 39, 1491–1507 (1999).
[CrossRef] [PubMed]

1998

F. A. A. Kingdom, L. R. Ziegler, R. F. Hess, “The role of spatial scale in stereoscopic segmentation,” Perception Suppl. 27, 21 (1998).

S. Gephstein, A. Cooperman, “Stereoscopic transparency: A test for binocular disambiguating power,” Vision Res. 38, 2913–2932 (1998).
[CrossRef]

J. M. Lankheet, M. Palmen, “Stereoscopic segregation of transparent surfaces and the effect of motion contrast,” Vision Res. 38, 659–668 (1998).
[CrossRef] [PubMed]

1997

B. Lee, B. Rogers, “Disparity modulation sensitivity for narrow-band-filtered stereograms,” Vision Res. 37, 1769–1778 (1997).
[CrossRef] [PubMed]

1995

N. Brady, D. J. Field, “What’s constant in contrast constancy? The effect of scaling on the perceived contrast of bandpass patterns,” Vision Res. 35, 739–756 (1995).
[CrossRef] [PubMed]

H. S. Smallman, S. P. McKee, “A contrast ratio constraint on stereo matching,” Proc. R. Soc. London Ser. B 260, 265–271 (1995).
[CrossRef]

G. C. DeAngelis, I. Ohzawa, R. D. Freeman, “Neuronal mechanisms underlying stereopsis: How do simple cells in the visual cortex encode binocular disparity?” Perception 24, 3–31 (1995).
[CrossRef] [PubMed]

1994

A. M. Rohaly, H. R. Wilson, “Disparity averaging across spatial scales,” Vision Res. 34, 1315–1325 (1994).
[CrossRef] [PubMed]

A. B. Cobo-Lewis, Y. Y. Yeh, “Selectivity of cyclopean masking for the spatial frequency of disparity modulation,” Vision Res. 34, 607–620 (1994).
[CrossRef] [PubMed]

H. S. Smallman, D. I. A. MacLeod, “Size-disparity correlation in stereopsis at contrast threshold,” J. Opt. Soc. Am. A 11, 2169–2183 (1994).
[CrossRef]

1991

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

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

S. B. Stevenson, L. K. Cormack, C. M. Schor, “Depth attraction and repulsion in random dot stereograms,” Vision Res. 31, 805–813 (1991).
[CrossRef] [PubMed]

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

1989

D. Weinshall, “Perception of multiple transparent planes in stereo vision,” Nature 341, 737–739 (1989).
[CrossRef] [PubMed]

A. J. Parker, Y. Yang, “Spatial properties of disparity pooling in human stereo vision,” Vision Res. 29, 1525–1538 (1989).
[CrossRef] [PubMed]

1988

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

K. Stevens, A. Brookes, “Integrating stereopsis with monocular interpretations of planar surfaces,” Vision Res. 28, 371–386 (1988).
[CrossRef] [PubMed]

1987

J. Todd, R. Akerstrom, “Perception of three-dimensional form from patterns of optical texture,” J. Exp. Psychol. Hum. Percep. 13, 242–255 (1987).
[CrossRef]

1985

K. Prazdny, “Detection of binocular disparities,” Biol. Cybern. 52, 93–99 (1985).
[CrossRef] [PubMed]

1984

J. Cutting, R. Millard, “Three gradients and the perception of flat and curved surfaces,” J. Exp. Psychol. Gen. 113, 198–216 (1984).
[CrossRef] [PubMed]

K. Boothroyd, R. Blake, “Stereopsis from disparity of complex grating patterns,” Vision Res. 24, 1205–1222 (1984).
[CrossRef] [PubMed]

1983

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

1980

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

1979

R. A. Schumer, L. Ganz, “Independent stereoscopic channels for different extents of spatial pooling,” Vision Res. 19, 1303–1314 (1979).
[CrossRef] [PubMed]

1976

D. Marr, T. Poggio, “Cooperative computation of stereo disparity,” Science 194, 283–287 (1976).
[CrossRef] [PubMed]

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

1975

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

J. L. Nelson, “Globality and stereoscopic fusion in binocular vision,” J. Theor. Biol. 49, 1–88 (1975).
[CrossRef] [PubMed]

M. A. Georgeson, G. D. Sullivan, “Contrast constancy: Deblurring in human vision by spatial frequency channels,” J. Physiol. (London) 252, 677–656 (1975).

1974

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

1970

G. Sperling, “Binocular vision: A physical and a neural theory,” Am. J. Psychol. 83, 461–534 (1970).
[CrossRef]

1968

B. Julesz, S. C. Johnson, “Stereograms portraying ambiguous perceivable surfaces,” Proc. Natl. Soc. 61, 437–441 (1968).
[CrossRef]

Akerstrom, R.

J. Todd, R. Akerstrom, “Perception of three-dimensional form from patterns of optical texture,” J. Exp. Psychol. Hum. Percep. 13, 242–255 (1987).
[CrossRef]

Akerstrom, R. A.

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

Blake, R.

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

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

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

K. Boothroyd, R. Blake, “Stereopsis from disparity of complex grating patterns,” Vision Res. 24, 1205–1222 (1984).
[CrossRef] [PubMed]

Boothroyd, K.

K. Boothroyd, R. Blake, “Stereopsis from disparity of complex grating patterns,” Vision Res. 24, 1205–1222 (1984).
[CrossRef] [PubMed]

Brady, N.

N. Brady, D. J. Field, “What’s constant in contrast constancy? The effect of scaling on the perceived contrast of bandpass patterns,” Vision Res. 35, 739–756 (1995).
[CrossRef] [PubMed]

Brookes, A.

K. Stevens, A. Brookes, “Integrating stereopsis with monocular interpretations of planar surfaces,” Vision Res. 28, 371–386 (1988).
[CrossRef] [PubMed]

Cobo-Lewis, A. B.

A. B. Cobo-Lewis, Y. Y. Yeh, “Selectivity of cyclopean masking for the spatial frequency of disparity modulation,” Vision Res. 34, 607–620 (1994).
[CrossRef] [PubMed]

Cooperman, A.

S. Gephstein, A. Cooperman, “Stereoscopic transparency: A test for binocular disambiguating power,” Vision Res. 38, 2913–2932 (1998).
[CrossRef]

Cormack, L. K.

S. B. Stevenson, L. K. Cormack, C. M. Schor, “Depth attraction and repulsion in random dot stereograms,” Vision Res. 31, 805–813 (1991).
[CrossRef] [PubMed]

Cutting, J.

J. Cutting, R. Millard, “Three gradients and the perception of flat and curved surfaces,” J. Exp. Psychol. Gen. 113, 198–216 (1984).
[CrossRef] [PubMed]

DeAngelis, G. C.

G. C. DeAngelis, I. Ohzawa, R. D. Freeman, “Neuronal mechanisms underlying stereopsis: How do simple cells in the visual cortex encode binocular disparity?” Perception 24, 3–31 (1995).
[CrossRef] [PubMed]

Field, D. J.

N. Brady, D. J. Field, “What’s constant in contrast constancy? The effect of scaling on the perceived contrast of bandpass patterns,” Vision Res. 35, 739–756 (1995).
[CrossRef] [PubMed]

Freeman, R. D.

G. C. DeAngelis, I. Ohzawa, R. D. Freeman, “Neuronal mechanisms underlying stereopsis: How do simple cells in the visual cortex encode binocular disparity?” Perception 24, 3–31 (1995).
[CrossRef] [PubMed]

Frisby, J. P.

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

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

Ganz, L.

R. A. Schumer, L. Ganz, “Independent stereoscopic channels for different extents of spatial pooling,” Vision Res. 19, 1303–1314 (1979).
[CrossRef] [PubMed]

Georgeson, M. A.

M. A. Georgeson, G. D. Sullivan, “Contrast constancy: Deblurring in human vision by spatial frequency channels,” J. Physiol. (London) 252, 677–656 (1975).

Gephstein, S.

S. Gephstein, A. Cooperman, “Stereoscopic transparency: A test for binocular disambiguating power,” Vision Res. 38, 2913–2932 (1998).
[CrossRef]

Gibson, J.

J. Gibson, The Perception of the Visual World (Houghton-Mifflin, Boston, Mass., 1950).

Halpern, D. L.

Hess, R. F.

L. R. Ziegler, F. A. A. Kingdom, R. F. Hess, “Local luminance factors that determine the maximum disparity for seeing cyclopean surface shape,” Vision Res. 40, 1157–1165 (2000).
[CrossRef] [PubMed]

L. R. Ziegler, R. F. Hess, “Stereoscopic depth but not shape perception from second-order stimuli,” Vision Res. 39, 1491–1507 (1999).
[CrossRef] [PubMed]

R. F. Hess, F. A. A. Kingdom, L. R. Ziegler, “On the relationship between the spatial channels for luminance and disparity processing,” Vision Res. 39, 559–568 (1999).
[CrossRef] [PubMed]

F. A. A. Kingdom, L. R. Ziegler, R. F. Hess, “The role of spatial scale in stereoscopic segmentation,” Perception Suppl. 27, 21 (1998).

Howard, I. P.

I. P. Howard, B. J. Rogers, Binocular Vision and Stereopsis (Oxford U. Press, Oxford, UK, 1995). For a discussion of disparity averaging and its limitations as an explanatory concept, see pp. 230–234. For a discussion of the constraints on stereo matching, see pp. 216–229.

Johnson, S. C.

B. Julesz, S. C. Johnson, “Stereograms portraying ambiguous perceivable surfaces,” Proc. Natl. Soc. 61, 437–441 (1968).
[CrossRef]

Julesz, B.

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

B. Julesz, S. C. Johnson, “Stereograms portraying ambiguous perceivable surfaces,” Proc. Natl. Soc. 61, 437–441 (1968).
[CrossRef]

Kingdom, F. A. A.

L. R. Ziegler, F. A. A. Kingdom, R. F. Hess, “Local luminance factors that determine the maximum disparity for seeing cyclopean surface shape,” Vision Res. 40, 1157–1165 (2000).
[CrossRef] [PubMed]

R. F. Hess, F. A. A. Kingdom, L. R. Ziegler, “On the relationship between the spatial channels for luminance and disparity processing,” Vision Res. 39, 559–568 (1999).
[CrossRef] [PubMed]

F. A. A. Kingdom, L. R. Ziegler, R. F. Hess, “The role of spatial scale in stereoscopic segmentation,” Perception Suppl. 27, 21 (1998).

Lankheet, J. M.

J. M. Lankheet, M. Palmen, “Stereoscopic segregation of transparent surfaces and the effect of motion contrast,” Vision Res. 38, 659–668 (1998).
[CrossRef] [PubMed]

Lee, B.

B. Lee, B. Rogers, “Disparity modulation sensitivity for narrow-band-filtered stereograms,” Vision Res. 37, 1769–1778 (1997).
[CrossRef] [PubMed]

MacLeod, D. I. A.

Marr, D.

D. Marr, T. Poggio, “Cooperative computation of stereo disparity,” Science 194, 283–287 (1976).
[CrossRef] [PubMed]

Mayhew, J. E. W.

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

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

McKee, S. P.

H. S. Smallman, S. P. McKee, “A contrast ratio constraint on stereo matching,” Proc. R. Soc. London Ser. B 260, 265–271 (1995).
[CrossRef]

Millard, R.

J. Cutting, R. Millard, “Three gradients and the perception of flat and curved surfaces,” J. Exp. Psychol. Gen. 113, 198–216 (1984).
[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]

Nelson, J. L.

J. L. Nelson, “Globality and stereoscopic fusion in binocular vision,” J. Theor. Biol. 49, 1–88 (1975).
[CrossRef] [PubMed]

Ohzawa, I.

G. C. DeAngelis, I. Ohzawa, R. D. Freeman, “Neuronal mechanisms underlying stereopsis: How do simple cells in the visual cortex encode binocular disparity?” Perception 24, 3–31 (1995).
[CrossRef] [PubMed]

Palmen, M.

J. M. Lankheet, M. Palmen, “Stereoscopic segregation of transparent surfaces and the effect of motion contrast,” Vision Res. 38, 659–668 (1998).
[CrossRef] [PubMed]

Parker, A. J.

A. J. Parker, Y. Yang, “Spatial properties of disparity pooling in human stereo vision,” Vision Res. 29, 1525–1538 (1989).
[CrossRef] [PubMed]

Poggio, T.

D. Marr, T. Poggio, “Cooperative computation of stereo disparity,” Science 194, 283–287 (1976).
[CrossRef] [PubMed]

Prazdny, K.

K. Prazdny, “Detection of binocular disparities,” Biol. Cybern. 52, 93–99 (1985).
[CrossRef] [PubMed]

Pulliam, K.

K. Pulliam, “Spatial frequency analysis of three-dimensional vision,” in Visual Simulation and Image Realism II, K. S. Setty, ed., Proc. SPIE303, 71–77 (1981).
[CrossRef]

Rogers, B.

B. Lee, B. Rogers, “Disparity modulation sensitivity for narrow-band-filtered stereograms,” Vision Res. 37, 1769–1778 (1997).
[CrossRef] [PubMed]

Rogers, B. J.

I. P. Howard, B. J. Rogers, Binocular Vision and Stereopsis (Oxford U. Press, Oxford, UK, 1995). For a discussion of disparity averaging and its limitations as an explanatory concept, see pp. 230–234. For a discussion of the constraints on stereo matching, see pp. 216–229.

Rohaly, A. M.

A. M. Rohaly, H. R. Wilson, “Disparity averaging across spatial scales,” Vision Res. 34, 1315–1325 (1994).
[CrossRef] [PubMed]

Schor, C. M.

S. B. Stevenson, L. K. Cormack, C. M. Schor, “Depth attraction and repulsion in random dot stereograms,” Vision Res. 31, 805–813 (1991).
[CrossRef] [PubMed]

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

Schumer, R. A.

R. A. Schumer, L. Ganz, “Independent stereoscopic channels for different extents of spatial pooling,” Vision Res. 19, 1303–1314 (1979).
[CrossRef] [PubMed]

Smallman, H. S.

H. S. Smallman, S. P. McKee, “A contrast ratio constraint on stereo matching,” Proc. R. Soc. London Ser. B 260, 265–271 (1995).
[CrossRef]

H. S. Smallman, D. I. A. MacLeod, “Size-disparity correlation in stereopsis at contrast threshold,” J. Opt. Soc. Am. A 11, 2169–2183 (1994).
[CrossRef]

Sperling, G.

G. Sperling, “Binocular vision: A physical and a neural theory,” Am. J. Psychol. 83, 461–534 (1970).
[CrossRef]

Stevens, K.

K. Stevens, A. Brookes, “Integrating stereopsis with monocular interpretations of planar surfaces,” Vision Res. 28, 371–386 (1988).
[CrossRef] [PubMed]

Stevenson, S. B.

S. B. Stevenson, L. K. Cormack, C. M. Schor, “Depth attraction and repulsion in random dot stereograms,” Vision Res. 31, 805–813 (1991).
[CrossRef] [PubMed]

Sullivan, G. D.

M. A. Georgeson, G. D. Sullivan, “Contrast constancy: Deblurring in human vision by spatial frequency channels,” J. Physiol. (London) 252, 677–656 (1975).

Todd, J.

J. Todd, R. Akerstrom, “Perception of three-dimensional form from patterns of optical texture,” J. Exp. Psychol. Hum. Percep. 13, 242–255 (1987).
[CrossRef]

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

C. W. Tyler, “Sensory processing of binocular disparity,” in Vergence Eye Movements: Basic and Clinical Aspects, M. C. Schor, K. J. Ciuffreda, eds. (Butterworth, Boston, Mass., 1983), pp. 199–296.

Weinshall, D.

D. Weinshall, “Perception of multiple transparent planes in stereo vision,” Nature 341, 737–739 (1989).
[CrossRef] [PubMed]

Wilson, H. R.

A. M. Rohaly, H. R. Wilson, “Disparity averaging across spatial scales,” Vision Res. 34, 1315–1325 (1994).
[CrossRef] [PubMed]

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

R. Blake, H. R. Wilson, “Neural models of stereoscopic vision,” Trends Neurosci. 14, 445–452 (1991).
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Figures (6)

Fig. 1
Fig. 1

Fusion by crossed disparity reveals branches of the fem at different depths that are largely camouflaged in the monocular view. The more distant branches will have a slightly higher retinal spatial frequency composition. Could this difference facilitate stereoscopic segmentation?

Fig. 2
Fig. 2

Method of construction of a dual-surface disparity grating from two types of Gabor micropatterns.

Fig. 3
Fig. 3

Example dual-surface disparity gratings. Fusion of the two stereo halves in (a) reveals a 3-D pattern with an obliquely oriented corrugated structure. On closer inspection one can see two interwoven surfaces and an impression of depth transparency. In (a) the micropatterns are of the same size but differ in luminance spatial frequency by 1 octave, or a factor of 2. In (b) the two surfaces are made from the same micropatterns, and the corrugated structure is very difficult to perceive in the fused image. In the main experiment subjects were required to judge the orientation of the corrugations in the stimulus as a function of the difference in Gabor micropattern spatial frequency between the two surfaces (±45 deg).

Fig. 4
Fig. 4

Results of experiment 1. The graphs show dmin, the threshold amplitude of disparity modulation, for identifying the orientation of a dual-surface disparity grating, as a function of the difference in spatial frequency, Δf, between the micropatterns on its two surfaces. The value of zero on the abscissa implies identical micropatterns on the two surfaces. The two curves in each graph are for two different values of fixed micropattern spatial frequency f. For the fixed f=0.42 cpd condition, variable f was always higher, whereas, for the other fixed f conditions variable f was always lower. The dotted curve in LZ’s data finishing at Δf=0.5 indicates that this subject was unable to obtain a threshold below this point. On the right, thresholds for single-surface disparity gratings are shown as a function of micropattern spatial frequency.

Fig. 5
Fig. 5

Results from experiment 2. Dmin is shown for both dual-surface and single-surface disparity gratings, with all stimuli constructed from just two types of Gabors with spatial frequencies 1.0 and 3.0 cpd. (a) Gabors with equal size, σ; (b) Gabors with equal bandwidth (σ inversely proportional to f). Seg, Gabors segregated between surfaces; nonseg, Gabors nonsegregated between surfaces. Single low f, single-surface grating with 1.0 cpd Gabors; single high f, single-surface grating with 3.0 cpd Gabors.

Fig. 6
Fig. 6

Correspondence-noise model of the results. Each figure shows left eye (LE) and right eye (RE) representations of a horizontal slice through a half-cycle of a dual-surface disparity grating. For each eye the set of elements making up the two surfaces are shown one above the other for convenience. Small solid circles and large open circles represent Gabors of different spatial frequencies. Binocular matches are shown along the fixation plane running horizontally between the corners of each figure. The nearest-neighbor rule finds those matches that minimize disparity with respect to the plane of fixation, but the similarity rule restricts those matches to like Gabors. The uniqueness rule allows only one match per element. (a) Single-Gabor stimulus [as in Fig. 3(b)], (b) nonsegregated two-Gabor stimulus, (c) segregated two-Gabor stimulus [as in Fig. 3(a)]. Only in (c) is the dual-surface, sinusoidal structure of the stimulus revealed.

Tables (1)

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Table 1 Contrasts of Various Gabor Spatial Frequencies Obtained by Matching the Perceived Contrast of Each Gabor to a 0.42 cpd Standard Gabor at 14% Contrasta

Equations (1)

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L(x)=M[1+c sin(2πfx)exp(-x2/2σ2)],

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