Abstract

The problem of how visual information such as orientation is combined across space bears on key visual abilities, such as texture perception. Orientation signals can be derived from both luminance and contrast, but it is not well understood how such information is pooled or how these different orientation signals interact in the integration process. We measured orientation discrimination thresholds for arrays of equivisible first-order and second-order Gabors. Thresholds were measured as the orientation variability in the arrays increased, and we estimated the number of samples (or efficiency) and internal noise of the mechanism being used. Observers were able to judge the mean orientation of arrays of either first- or second-order Gabors. For arrays of first-order and arrays of second-order Gabors, estimates of the number of samples used increased as the number of Gabors increased. When judging the orientation of arrays of either order, observers were able to ignore randomly oriented Gabors of the opposite order. If observers did not know which Gabor type carried the more useful orientation information, they tended to use the information from first-order Gabors (even when this was poorer information). Observers were unable to combine information from first- and second-order Gabors, though this would have improved their performance. The visual system appears to have separate integrators for combining local orientation across space for luminance- and contrast-defined features.

© 2003 Optical Society of America

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    [CrossRef] [PubMed]
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  26. Z. Lu, B. A. Dosher, “External noise distinguishes attention mechanisms,” Vision Res. 38, 1183–1198 (1998).
    [CrossRef] [PubMed]
  27. S. C. Dakin, “An information limit on the spatial integration of local orientation signals,” J. Opt. Soc. Am. A 18, 1016–1026 (2001).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  31. S. C. Dakin, I. Mareschal, “Sensitivity to contrast modulation depends on carrier spatial frequency and orientation,” Vision Res. 40, 311–329 (2000).
    [CrossRef] [PubMed]
  32. T. Ledgeway, R. F. Hess, “Failure of direction-identification for briefly presented second-order motion stimuli: evidence for weak direction-selectivity of the mechanisms encoding motion,” Vision Res. 42, 1739–1758 (2002).
    [CrossRef] [PubMed]
  33. R. J. Watt, D. Andrews, “APE. Adaptive probit estimation of the psychometric functions,” Curr. Psychol. Rev. 1, 205–214 (1981).
  34. D. H. Foster, W. F. Bischof, “Bootstrap estimates of the statistical accuracy of thresholds obtained from psychometric functions,” Spatial Vision 11, 135–139 (1997).
    [PubMed]
  35. G. Westheimer, “Simultaneous orientation contrast for lines in the human fovea,” Vision Res. 30, 1913–1921 (1990).
    [CrossRef] [PubMed]
  36. C. D. Gilbert, A. Das, M. Ito, M. Kapadia, G. Westheimer, “Spatial integration and cortical dynamics,” Proc. Natl. Acad. Sci. USA 93, 615–622 (1996).
    [CrossRef]
  37. C. D. Gilbert, T. N. Wiesel, “The influence of contextual stimuli on the orientation selectivity of cells in primary visual cortex of the cat,” Vision Res. 30, 1689–1701 (1990).
    [CrossRef] [PubMed]
  38. D. J. Field, A. Hayes, R. F. Hess, “Contour integration by the human visual system: evidence for a local ‘association field,’ ” Vision Res. 33, 173–193 (1993).
    [CrossRef] [PubMed]
  39. R. F. Hess, S. C. Dakin, “Contour integration in the peripheral field,” Vision Res. 39, 947–959 (1999).
    [CrossRef] [PubMed]
  40. L. Parkes, J. Lund, A. Angelucci, J. A. Solomon, M. Morgan, “Compulsory averaging of crowded orientation signals in human vision,” Nat. Neurosci. 4, 739–744 (2001).
    [CrossRef] [PubMed]
  41. W. H. Mcllhagga, K. T. Mullen, “Contour integration with colour and luminance contrast,” Vision Res. 36, 1265–1279 (1996).
    [CrossRef]
  42. D. J. Field, A. Hayes, R. F. Hess, “The roles of polarity and symmetry in the perceptual grouping of contour fragments,” Vision Res. 13, 51–66 (2000).
  43. A. T. Smith, N. E. Scott-Samuel, “First-order and second-order signals combine to improve perceptual accuracy,” J. Opt. Soc. Am. A 18, 2267–2272 (2001).
    [CrossRef]
  44. M. Edwards, D. R. Badcock, “Global motion perception: no interaction between the first- and second-order motion pathways,” Vision Res. 35, 2589–2602 (1995).
    [CrossRef] [PubMed]
  45. S. C. Dakin, C. B. Williams, R. F. Hess, “The interaction of first- and second-order cues to orientation,” Vision Res. 39, 2867–2884 (1999).
    [CrossRef] [PubMed]
  46. M. J. Morgan, A. J. S. Mason, S. Baldassi, “Are there separate first-order and second-order mechanisms for orientation discrimination?” Vision Res. 40, 1751–1763 (2000).
    [CrossRef] [PubMed]
  47. A. J. Schofield, M. A. Georgeson, “Sensitivity to modulations of luminance and contrast in visual white noise: separate mechanisms with similar behaviour,” Vision Res. 39, 2697–2716 (1999).
    [CrossRef] [PubMed]
  48. I. Mareschal, M. P. Sceniak, R. M. Shapley, “Contextual influences on orientation discrimination: binding local and global cues,” Vision Res. 41, 1915–1930 (2001).
    [CrossRef] [PubMed]

2002

T. Ledgeway, R. F. Hess, “Failure of direction-identification for briefly presented second-order motion stimuli: evidence for weak direction-selectivity of the mechanisms encoding motion,” Vision Res. 42, 1739–1758 (2002).
[CrossRef] [PubMed]

2001

S. C. Dakin, “An information limit on the spatial integration of local orientation signals,” J. Opt. Soc. Am. A 18, 1016–1026 (2001).
[CrossRef]

S. Smith, P. Wenderoth, R. van der Zwan, “Orientation processing mechanisms revealed by the plaid tilt illusion,” Vision Res. 41, 483–494 (2001).
[CrossRef] [PubMed]

S. Smith, C. W. G. Clifford, P. Wenderoth, “Interaction between first- and second-order orientation channels revealed by the tilt illusion: psychophysics and computational modeling,” Vision Res. 41, 1057–1071 (2001).
[CrossRef] [PubMed]

H. Ashida, A. E. Seiffert, N. Osaka, “Inefficient visual search for second-order motion,” J. Opt. Soc. Am. A 18, 2255–2266 (2001).
[CrossRef]

L. Parkes, J. Lund, A. Angelucci, J. A. Solomon, M. Morgan, “Compulsory averaging of crowded orientation signals in human vision,” Nat. Neurosci. 4, 739–744 (2001).
[CrossRef] [PubMed]

A. T. Smith, N. E. Scott-Samuel, “First-order and second-order signals combine to improve perceptual accuracy,” J. Opt. Soc. Am. A 18, 2267–2272 (2001).
[CrossRef]

I. Mareschal, M. P. Sceniak, R. M. Shapley, “Contextual influences on orientation discrimination: binding local and global cues,” Vision Res. 41, 1915–1930 (2001).
[CrossRef] [PubMed]

2000

M. J. Morgan, A. J. S. Mason, S. Baldassi, “Are there separate first-order and second-order mechanisms for orientation discrimination?” Vision Res. 40, 1751–1763 (2000).
[CrossRef] [PubMed]

D. J. Field, A. Hayes, R. F. Hess, “The roles of polarity and symmetry in the perceptual grouping of contour fragments,” Vision Res. 13, 51–66 (2000).

H. A. Allen, A. M. Derrington, “Slow discrimination of contrast-defined expansion patterns,” Vision Res. 40, 735–744 (2000).
[CrossRef] [PubMed]

R. F. Hess, L. R. Ziegler, “What limits the contribution of second-order motion to the perception of surface shape?” Vision Res. 40, 2125–2133 (2000).
[CrossRef] [PubMed]

R. F. Hess, T. Ledgeway, S. Dakin, “Impoverished second-order input to global linking in human vision,” Vision Res. 40, 3309–3318 (2000).
[CrossRef] [PubMed]

S. C. Dakin, I. Mareschal, “Sensitivity to contrast modulation depends on carrier spatial frequency and orientation,” Vision Res. 40, 311–329 (2000).
[CrossRef] [PubMed]

1999

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

P. V. McGraw, D. M. Levi, D. Whitaker, “Spatial characterististics of the second-order visual pathway revealed by positional adaptation,” Nat. Neurosci. 2, 479–484 (1999).
[CrossRef] [PubMed]

A. A. Baloch, S. Grossberg, E. Mingolla, C. A. M. Nogueira, “Neural model of first-order and second-order motion perception and magnocellular dymanics,” J. Opt. Soc. Am. A 16, 953–978 (1999).
[CrossRef]

S. C. Dakin, C. B. Williams, R. F. Hess, “The interaction of first- and second-order cues to orientation,” Vision Res. 39, 2867–2884 (1999).
[CrossRef] [PubMed]

R. F. Hess, S. C. Dakin, “Contour integration in the peripheral field,” Vision Res. 39, 947–959 (1999).
[CrossRef] [PubMed]

A. J. Schofield, M. A. Georgeson, “Sensitivity to modulations of luminance and contrast in visual white noise: separate mechanisms with similar behaviour,” Vision Res. 39, 2697–2716 (1999).
[CrossRef] [PubMed]

1998

Z. Lu, B. A. Dosher, “External noise distinguishes attention mechanisms,” Vision Res. 38, 1183–1198 (1998).
[CrossRef] [PubMed]

1997

D. H. Foster, W. F. Bischof, “Bootstrap estimates of the statistical accuracy of thresholds obtained from psychometric functions,” Spatial Vision 11, 135–139 (1997).
[PubMed]

D. W. Heeley, H. M. Buchanan Smith, J. A. Cromwell, J. S. Wright, “The oblique effect in orientation acuity,” Vision Res. 37, 235–242 (1997).
[CrossRef] [PubMed]

D. H. Brainard, “The Psychophysics Toolbox,” Spatial Vision 10, 433–436 (1997).
[CrossRef] [PubMed]

D. G. Pelli, “The VideoToolbox software for visual psychophysics: transforming numbers into movies,” Spatial Vision 10, 437–442 (1997).
[CrossRef] [PubMed]

S. C. Dakin, R. J. Watt, “The computation of orientation statistics from visual texture,” Vision Res. 37, 3181–3192 (1997).
[CrossRef]

1996

P. W. McOwan, A. Johnston, “A second-order pattern reveals separate strategies for encoding orientation in two-dimensional space and space-time,” Vision Res. 36, 425–430 (1996).
[CrossRef] [PubMed]

L. M. Lin, H. R. Wilson, “Fourier and non-Fourier pattern discrimination compared,” Vision Res. 36, 1907–1918 (1996).
[CrossRef] [PubMed]

Y. X. Zhou, C. L. Baker, “Spatial properties of envelope-responsive cells in area 17 and 18 neurons of the cat,” J. Neurophysiol. 75, 1038–1050 (1996).
[PubMed]

C. D. Gilbert, A. Das, M. Ito, M. Kapadia, G. Westheimer, “Spatial integration and cortical dynamics,” Proc. Natl. Acad. Sci. USA 93, 615–622 (1996).
[CrossRef]

W. H. Mcllhagga, K. T. Mullen, “Contour integration with colour and luminance contrast,” Vision Res. 36, 1265–1279 (1996).
[CrossRef]

1995

M. Edwards, D. R. Badcock, “Global motion perception: no interaction between the first- and second-order motion pathways,” Vision Res. 35, 2589–2602 (1995).
[CrossRef] [PubMed]

Z. Lu, G. Sperling, “The functional architecture of human visual motion perception,” Vision Res. 35, 2697–2722 (1995).
[CrossRef] [PubMed]

A. Johnston, C. W. G. Clifford, “Perceived motion of contrast-modulated gratings—predictions of the multichannel gradient model and the role of full-wave rectification,” Vision Res. 35, 1771–1783 (1995).
[CrossRef] [PubMed]

R. van der Zwan, P. Wenderoth, “Mechanisms of purely subjective contour tilt aftereffects,” Vision Res. 35, 2547–2557 (1995).
[CrossRef] [PubMed]

1993

D. J. Field, A. Hayes, R. F. Hess, “Contour integration by the human visual system: evidence for a local ‘association field,’ ” Vision Res. 33, 173–193 (1993).
[CrossRef] [PubMed]

1992

H. R. Wilson, V. P. Ferrera, C. Yo, “A psychophysically motivated model for two-dimensional motion perception,” Visual Neurosci. 9, 79–97 (1992).
[CrossRef]

N. Graham, J. Beck, A. Sutter, “Nonlinear processes in spatial-frequency channel models of perceived texture segregation—effects of sign and amount of contrast,” Vision Res. 32, 719–743 (1992).
[CrossRef] [PubMed]

1991

D. G. Pelli, L. Zhang, “Accurate control of contrast on microcomputer displays,” Vision Res. 31, 1337–1350 (1991).
[CrossRef] [PubMed]

1990

C. D. Gilbert, T. N. Wiesel, “The influence of contextual stimuli on the orientation selectivity of cells in primary visual cortex of the cat,” Vision Res. 30, 1689–1701 (1990).
[CrossRef] [PubMed]

G. Westheimer, “Simultaneous orientation contrast for lines in the human fovea,” Vision Res. 30, 1913–1921 (1990).
[CrossRef] [PubMed]

J. Malik, P. Perona, “Preattentive texture discrimination with early vision mechanisms,” J. Opt. Soc. Am. A 7, 923–932 (1990).
[CrossRef] [PubMed]

1988

1985

1981

R. J. Watt, D. Andrews, “APE. Adaptive probit estimation of the psychometric functions,” Curr. Psychol. Rev. 1, 205–214 (1981).

1968

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

1957

H. B. Barlow, “Increment thresholds at low intensities considered as signal/noise discriminations,” J. Physiol. (London) 136, 469–488 (1957).

Ahumada, A. J.

Allen, H. A.

H. A. Allen, A. M. Derrington, “Slow discrimination of contrast-defined expansion patterns,” Vision Res. 40, 735–744 (2000).
[CrossRef] [PubMed]

Andrews, D.

R. J. Watt, D. Andrews, “APE. Adaptive probit estimation of the psychometric functions,” Curr. Psychol. Rev. 1, 205–214 (1981).

Angelucci, A.

L. Parkes, J. Lund, A. Angelucci, J. A. Solomon, M. Morgan, “Compulsory averaging of crowded orientation signals in human vision,” Nat. Neurosci. 4, 739–744 (2001).
[CrossRef] [PubMed]

Ashida, H.

Badcock, D. R.

M. Edwards, D. R. Badcock, “Global motion perception: no interaction between the first- and second-order motion pathways,” Vision Res. 35, 2589–2602 (1995).
[CrossRef] [PubMed]

Baker, C. L.

Y. X. Zhou, C. L. Baker, “Spatial properties of envelope-responsive cells in area 17 and 18 neurons of the cat,” J. Neurophysiol. 75, 1038–1050 (1996).
[PubMed]

Baldassi, S.

M. J. Morgan, A. J. S. Mason, S. Baldassi, “Are there separate first-order and second-order mechanisms for orientation discrimination?” Vision Res. 40, 1751–1763 (2000).
[CrossRef] [PubMed]

Baloch, A. A.

Barlow, H. B.

H. B. Barlow, “Increment thresholds at low intensities considered as signal/noise discriminations,” J. Physiol. (London) 136, 469–488 (1957).

Beck, J.

N. Graham, J. Beck, A. Sutter, “Nonlinear processes in spatial-frequency channel models of perceived texture segregation—effects of sign and amount of contrast,” Vision Res. 32, 719–743 (1992).
[CrossRef] [PubMed]

Bischof, W. F.

D. H. Foster, W. F. Bischof, “Bootstrap estimates of the statistical accuracy of thresholds obtained from psychometric functions,” Spatial Vision 11, 135–139 (1997).
[PubMed]

Brainard, D. H.

D. H. Brainard, “The Psychophysics Toolbox,” Spatial Vision 10, 433–436 (1997).
[CrossRef] [PubMed]

Buchanan Smith, H. M.

D. W. Heeley, H. M. Buchanan Smith, J. A. Cromwell, J. S. Wright, “The oblique effect in orientation acuity,” Vision Res. 37, 235–242 (1997).
[CrossRef] [PubMed]

Campbell, F. W.

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

Chubb, C.

Clifford, C. W. G.

S. Smith, C. W. G. Clifford, P. Wenderoth, “Interaction between first- and second-order orientation channels revealed by the tilt illusion: psychophysics and computational modeling,” Vision Res. 41, 1057–1071 (2001).
[CrossRef] [PubMed]

A. Johnston, C. W. G. Clifford, “Perceived motion of contrast-modulated gratings—predictions of the multichannel gradient model and the role of full-wave rectification,” Vision Res. 35, 1771–1783 (1995).
[CrossRef] [PubMed]

Cromwell, J. A.

D. W. Heeley, H. M. Buchanan Smith, J. A. Cromwell, J. S. Wright, “The oblique effect in orientation acuity,” Vision Res. 37, 235–242 (1997).
[CrossRef] [PubMed]

Dakin, S.

R. F. Hess, T. Ledgeway, S. Dakin, “Impoverished second-order input to global linking in human vision,” Vision Res. 40, 3309–3318 (2000).
[CrossRef] [PubMed]

Dakin, S. C.

S. C. Dakin, “An information limit on the spatial integration of local orientation signals,” J. Opt. Soc. Am. A 18, 1016–1026 (2001).
[CrossRef]

S. C. Dakin, I. Mareschal, “Sensitivity to contrast modulation depends on carrier spatial frequency and orientation,” Vision Res. 40, 311–329 (2000).
[CrossRef] [PubMed]

R. F. Hess, S. C. Dakin, “Contour integration in the peripheral field,” Vision Res. 39, 947–959 (1999).
[CrossRef] [PubMed]

S. C. Dakin, C. B. Williams, R. F. Hess, “The interaction of first- and second-order cues to orientation,” Vision Res. 39, 2867–2884 (1999).
[CrossRef] [PubMed]

S. C. Dakin, R. J. Watt, “The computation of orientation statistics from visual texture,” Vision Res. 37, 3181–3192 (1997).
[CrossRef]

Das, A.

C. D. Gilbert, A. Das, M. Ito, M. Kapadia, G. Westheimer, “Spatial integration and cortical dynamics,” Proc. Natl. Acad. Sci. USA 93, 615–622 (1996).
[CrossRef]

Derrington, A. M.

H. A. Allen, A. M. Derrington, “Slow discrimination of contrast-defined expansion patterns,” Vision Res. 40, 735–744 (2000).
[CrossRef] [PubMed]

Dosher, B. A.

Z. Lu, B. A. Dosher, “External noise distinguishes attention mechanisms,” Vision Res. 38, 1183–1198 (1998).
[CrossRef] [PubMed]

Edwards, M.

M. Edwards, D. R. Badcock, “Global motion perception: no interaction between the first- and second-order motion pathways,” Vision Res. 35, 2589–2602 (1995).
[CrossRef] [PubMed]

Ferrera, V. P.

H. R. Wilson, V. P. Ferrera, C. Yo, “A psychophysically motivated model for two-dimensional motion perception,” Visual Neurosci. 9, 79–97 (1992).
[CrossRef]

Field, D. J.

D. J. Field, A. Hayes, R. F. Hess, “The roles of polarity and symmetry in the perceptual grouping of contour fragments,” Vision Res. 13, 51–66 (2000).

D. J. Field, A. Hayes, R. F. Hess, “Contour integration by the human visual system: evidence for a local ‘association field,’ ” Vision Res. 33, 173–193 (1993).
[CrossRef] [PubMed]

Foster, D. H.

D. H. Foster, W. F. Bischof, “Bootstrap estimates of the statistical accuracy of thresholds obtained from psychometric functions,” Spatial Vision 11, 135–139 (1997).
[PubMed]

Georgeson, M. A.

A. J. Schofield, M. A. Georgeson, “Sensitivity to modulations of luminance and contrast in visual white noise: separate mechanisms with similar behaviour,” Vision Res. 39, 2697–2716 (1999).
[CrossRef] [PubMed]

Gilbert, C. D.

C. D. Gilbert, A. Das, M. Ito, M. Kapadia, G. Westheimer, “Spatial integration and cortical dynamics,” Proc. Natl. Acad. Sci. USA 93, 615–622 (1996).
[CrossRef]

C. D. Gilbert, T. N. Wiesel, “The influence of contextual stimuli on the orientation selectivity of cells in primary visual cortex of the cat,” Vision Res. 30, 1689–1701 (1990).
[CrossRef] [PubMed]

Graham, N.

N. Graham, J. Beck, A. Sutter, “Nonlinear processes in spatial-frequency channel models of perceived texture segregation—effects of sign and amount of contrast,” Vision Res. 32, 719–743 (1992).
[CrossRef] [PubMed]

Grossberg, S.

Hayes, A.

D. J. Field, A. Hayes, R. F. Hess, “The roles of polarity and symmetry in the perceptual grouping of contour fragments,” Vision Res. 13, 51–66 (2000).

D. J. Field, A. Hayes, R. F. Hess, “Contour integration by the human visual system: evidence for a local ‘association field,’ ” Vision Res. 33, 173–193 (1993).
[CrossRef] [PubMed]

Heeley, D. W.

D. W. Heeley, H. M. Buchanan Smith, J. A. Cromwell, J. S. Wright, “The oblique effect in orientation acuity,” Vision Res. 37, 235–242 (1997).
[CrossRef] [PubMed]

Hess, R. F.

T. Ledgeway, R. F. Hess, “Failure of direction-identification for briefly presented second-order motion stimuli: evidence for weak direction-selectivity of the mechanisms encoding motion,” Vision Res. 42, 1739–1758 (2002).
[CrossRef] [PubMed]

R. F. Hess, L. R. Ziegler, “What limits the contribution of second-order motion to the perception of surface shape?” Vision Res. 40, 2125–2133 (2000).
[CrossRef] [PubMed]

R. F. Hess, T. Ledgeway, S. Dakin, “Impoverished second-order input to global linking in human vision,” Vision Res. 40, 3309–3318 (2000).
[CrossRef] [PubMed]

D. J. Field, A. Hayes, R. F. Hess, “The roles of polarity and symmetry in the perceptual grouping of contour fragments,” Vision Res. 13, 51–66 (2000).

R. F. Hess, S. C. Dakin, “Contour integration in the peripheral field,” Vision Res. 39, 947–959 (1999).
[CrossRef] [PubMed]

S. C. Dakin, C. B. Williams, R. F. Hess, “The interaction of first- and second-order cues to orientation,” Vision Res. 39, 2867–2884 (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]

D. J. Field, A. Hayes, R. F. Hess, “Contour integration by the human visual system: evidence for a local ‘association field,’ ” Vision Res. 33, 173–193 (1993).
[CrossRef] [PubMed]

Ito, M.

C. D. Gilbert, A. Das, M. Ito, M. Kapadia, G. Westheimer, “Spatial integration and cortical dynamics,” Proc. Natl. Acad. Sci. USA 93, 615–622 (1996).
[CrossRef]

Johnston, A.

P. W. McOwan, A. Johnston, “A second-order pattern reveals separate strategies for encoding orientation in two-dimensional space and space-time,” Vision Res. 36, 425–430 (1996).
[CrossRef] [PubMed]

A. Johnston, C. W. G. Clifford, “Perceived motion of contrast-modulated gratings—predictions of the multichannel gradient model and the role of full-wave rectification,” Vision Res. 35, 1771–1783 (1995).
[CrossRef] [PubMed]

Kapadia, M.

C. D. Gilbert, A. Das, M. Ito, M. Kapadia, G. Westheimer, “Spatial integration and cortical dynamics,” Proc. Natl. Acad. Sci. USA 93, 615–622 (1996).
[CrossRef]

Ledgeway, T.

T. Ledgeway, R. F. Hess, “Failure of direction-identification for briefly presented second-order motion stimuli: evidence for weak direction-selectivity of the mechanisms encoding motion,” Vision Res. 42, 1739–1758 (2002).
[CrossRef] [PubMed]

R. F. Hess, T. Ledgeway, S. Dakin, “Impoverished second-order input to global linking in human vision,” Vision Res. 40, 3309–3318 (2000).
[CrossRef] [PubMed]

Levi, D. M.

P. V. McGraw, D. M. Levi, D. Whitaker, “Spatial characterististics of the second-order visual pathway revealed by positional adaptation,” Nat. Neurosci. 2, 479–484 (1999).
[CrossRef] [PubMed]

Lin, L. M.

L. M. Lin, H. R. Wilson, “Fourier and non-Fourier pattern discrimination compared,” Vision Res. 36, 1907–1918 (1996).
[CrossRef] [PubMed]

Lu, Z.

Z. Lu, B. A. Dosher, “External noise distinguishes attention mechanisms,” Vision Res. 38, 1183–1198 (1998).
[CrossRef] [PubMed]

Z. Lu, G. Sperling, “The functional architecture of human visual motion perception,” Vision Res. 35, 2697–2722 (1995).
[CrossRef] [PubMed]

Lund, J.

L. Parkes, J. Lund, A. Angelucci, J. A. Solomon, M. Morgan, “Compulsory averaging of crowded orientation signals in human vision,” Nat. Neurosci. 4, 739–744 (2001).
[CrossRef] [PubMed]

Malik, J.

Mareschal, I.

I. Mareschal, M. P. Sceniak, R. M. Shapley, “Contextual influences on orientation discrimination: binding local and global cues,” Vision Res. 41, 1915–1930 (2001).
[CrossRef] [PubMed]

S. C. Dakin, I. Mareschal, “Sensitivity to contrast modulation depends on carrier spatial frequency and orientation,” Vision Res. 40, 311–329 (2000).
[CrossRef] [PubMed]

Mason, A. J. S.

M. J. Morgan, A. J. S. Mason, S. Baldassi, “Are there separate first-order and second-order mechanisms for orientation discrimination?” Vision Res. 40, 1751–1763 (2000).
[CrossRef] [PubMed]

McGraw, P. V.

P. V. McGraw, D. M. Levi, D. Whitaker, “Spatial characterististics of the second-order visual pathway revealed by positional adaptation,” Nat. Neurosci. 2, 479–484 (1999).
[CrossRef] [PubMed]

Mcllhagga, W. H.

W. H. Mcllhagga, K. T. Mullen, “Contour integration with colour and luminance contrast,” Vision Res. 36, 1265–1279 (1996).
[CrossRef]

McOwan, P. W.

P. W. McOwan, A. Johnston, “A second-order pattern reveals separate strategies for encoding orientation in two-dimensional space and space-time,” Vision Res. 36, 425–430 (1996).
[CrossRef] [PubMed]

Mingolla, E.

Morgan, M.

L. Parkes, J. Lund, A. Angelucci, J. A. Solomon, M. Morgan, “Compulsory averaging of crowded orientation signals in human vision,” Nat. Neurosci. 4, 739–744 (2001).
[CrossRef] [PubMed]

Morgan, M. J.

M. J. Morgan, A. J. S. Mason, S. Baldassi, “Are there separate first-order and second-order mechanisms for orientation discrimination?” Vision Res. 40, 1751–1763 (2000).
[CrossRef] [PubMed]

Mullen, K. T.

W. H. Mcllhagga, K. T. Mullen, “Contour integration with colour and luminance contrast,” Vision Res. 36, 1265–1279 (1996).
[CrossRef]

Nogueira, C. A. M.

Osaka, N.

Parkes, L.

L. Parkes, J. Lund, A. Angelucci, J. A. Solomon, M. Morgan, “Compulsory averaging of crowded orientation signals in human vision,” Nat. Neurosci. 4, 739–744 (2001).
[CrossRef] [PubMed]

Pelli, D. G.

D. G. Pelli, “The VideoToolbox software for visual psychophysics: transforming numbers into movies,” Spatial Vision 10, 437–442 (1997).
[CrossRef] [PubMed]

D. G. Pelli, L. Zhang, “Accurate control of contrast on microcomputer displays,” Vision Res. 31, 1337–1350 (1991).
[CrossRef] [PubMed]

D. G. Pelli, “Effects of visual noise,” Ph.D. thesis (University of Cambridge, Cambridge, UK, 1981).

Perona, P.

Robson, J. G.

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

Sceniak, M. P.

I. Mareschal, M. P. Sceniak, R. M. Shapley, “Contextual influences on orientation discrimination: binding local and global cues,” Vision Res. 41, 1915–1930 (2001).
[CrossRef] [PubMed]

Schofield, A. J.

A. J. Schofield, M. A. Georgeson, “Sensitivity to modulations of luminance and contrast in visual white noise: separate mechanisms with similar behaviour,” Vision Res. 39, 2697–2716 (1999).
[CrossRef] [PubMed]

Scott-Samuel, N. E.

Seiffert, A. E.

Shapley, R. M.

I. Mareschal, M. P. Sceniak, R. M. Shapley, “Contextual influences on orientation discrimination: binding local and global cues,” Vision Res. 41, 1915–1930 (2001).
[CrossRef] [PubMed]

Smith, A. T.

Smith, S.

S. Smith, P. Wenderoth, R. van der Zwan, “Orientation processing mechanisms revealed by the plaid tilt illusion,” Vision Res. 41, 483–494 (2001).
[CrossRef] [PubMed]

S. Smith, C. W. G. Clifford, P. Wenderoth, “Interaction between first- and second-order orientation channels revealed by the tilt illusion: psychophysics and computational modeling,” Vision Res. 41, 1057–1071 (2001).
[CrossRef] [PubMed]

Solomon, J. A.

L. Parkes, J. Lund, A. Angelucci, J. A. Solomon, M. Morgan, “Compulsory averaging of crowded orientation signals in human vision,” Nat. Neurosci. 4, 739–744 (2001).
[CrossRef] [PubMed]

Sperling, G.

Sutter, A.

N. Graham, J. Beck, A. Sutter, “Nonlinear processes in spatial-frequency channel models of perceived texture segregation—effects of sign and amount of contrast,” Vision Res. 32, 719–743 (1992).
[CrossRef] [PubMed]

van der Zwan, R.

S. Smith, P. Wenderoth, R. van der Zwan, “Orientation processing mechanisms revealed by the plaid tilt illusion,” Vision Res. 41, 483–494 (2001).
[CrossRef] [PubMed]

R. van der Zwan, P. Wenderoth, “Mechanisms of purely subjective contour tilt aftereffects,” Vision Res. 35, 2547–2557 (1995).
[CrossRef] [PubMed]

Watson, A. B.

Watt, R. J.

S. C. Dakin, R. J. Watt, “The computation of orientation statistics from visual texture,” Vision Res. 37, 3181–3192 (1997).
[CrossRef]

R. J. Watt, D. Andrews, “APE. Adaptive probit estimation of the psychometric functions,” Curr. Psychol. Rev. 1, 205–214 (1981).

Wenderoth, P.

S. Smith, P. Wenderoth, R. van der Zwan, “Orientation processing mechanisms revealed by the plaid tilt illusion,” Vision Res. 41, 483–494 (2001).
[CrossRef] [PubMed]

S. Smith, C. W. G. Clifford, P. Wenderoth, “Interaction between first- and second-order orientation channels revealed by the tilt illusion: psychophysics and computational modeling,” Vision Res. 41, 1057–1071 (2001).
[CrossRef] [PubMed]

R. van der Zwan, P. Wenderoth, “Mechanisms of purely subjective contour tilt aftereffects,” Vision Res. 35, 2547–2557 (1995).
[CrossRef] [PubMed]

Westheimer, G.

C. D. Gilbert, A. Das, M. Ito, M. Kapadia, G. Westheimer, “Spatial integration and cortical dynamics,” Proc. Natl. Acad. Sci. USA 93, 615–622 (1996).
[CrossRef]

G. Westheimer, “Simultaneous orientation contrast for lines in the human fovea,” Vision Res. 30, 1913–1921 (1990).
[CrossRef] [PubMed]

Whitaker, D.

P. V. McGraw, D. M. Levi, D. Whitaker, “Spatial characterististics of the second-order visual pathway revealed by positional adaptation,” Nat. Neurosci. 2, 479–484 (1999).
[CrossRef] [PubMed]

Wiesel, T. N.

C. D. Gilbert, T. N. Wiesel, “The influence of contextual stimuli on the orientation selectivity of cells in primary visual cortex of the cat,” Vision Res. 30, 1689–1701 (1990).
[CrossRef] [PubMed]

Williams, C. B.

S. C. Dakin, C. B. Williams, R. F. Hess, “The interaction of first- and second-order cues to orientation,” Vision Res. 39, 2867–2884 (1999).
[CrossRef] [PubMed]

Wilson, H. R.

L. M. Lin, H. R. Wilson, “Fourier and non-Fourier pattern discrimination compared,” Vision Res. 36, 1907–1918 (1996).
[CrossRef] [PubMed]

H. R. Wilson, V. P. Ferrera, C. Yo, “A psychophysically motivated model for two-dimensional motion perception,” Visual Neurosci. 9, 79–97 (1992).
[CrossRef]

Wright, J. S.

D. W. Heeley, H. M. Buchanan Smith, J. A. Cromwell, J. S. Wright, “The oblique effect in orientation acuity,” Vision Res. 37, 235–242 (1997).
[CrossRef] [PubMed]

Yo, C.

H. R. Wilson, V. P. Ferrera, C. Yo, “A psychophysically motivated model for two-dimensional motion perception,” Visual Neurosci. 9, 79–97 (1992).
[CrossRef]

Zhang, L.

D. G. Pelli, L. Zhang, “Accurate control of contrast on microcomputer displays,” Vision Res. 31, 1337–1350 (1991).
[CrossRef] [PubMed]

Zhou, Y. X.

Y. X. Zhou, C. L. Baker, “Spatial properties of envelope-responsive cells in area 17 and 18 neurons of the cat,” J. Neurophysiol. 75, 1038–1050 (1996).
[PubMed]

Ziegler, L. R.

R. F. Hess, L. R. Ziegler, “What limits the contribution of second-order motion to the perception of surface shape?” Vision Res. 40, 2125–2133 (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]

Curr. Psychol. Rev.

R. J. Watt, D. Andrews, “APE. Adaptive probit estimation of the psychometric functions,” Curr. Psychol. Rev. 1, 205–214 (1981).

J. Neurophysiol.

Y. X. Zhou, C. L. Baker, “Spatial properties of envelope-responsive cells in area 17 and 18 neurons of the cat,” J. Neurophysiol. 75, 1038–1050 (1996).
[PubMed]

J. Opt. Soc. Am. A

J. Physiol. (London)

H. B. Barlow, “Increment thresholds at low intensities considered as signal/noise discriminations,” J. Physiol. (London) 136, 469–488 (1957).

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

Nat. Neurosci.

P. V. McGraw, D. M. Levi, D. Whitaker, “Spatial characterististics of the second-order visual pathway revealed by positional adaptation,” Nat. Neurosci. 2, 479–484 (1999).
[CrossRef] [PubMed]

L. Parkes, J. Lund, A. Angelucci, J. A. Solomon, M. Morgan, “Compulsory averaging of crowded orientation signals in human vision,” Nat. Neurosci. 4, 739–744 (2001).
[CrossRef] [PubMed]

Proc. Natl. Acad. Sci. USA

C. D. Gilbert, A. Das, M. Ito, M. Kapadia, G. Westheimer, “Spatial integration and cortical dynamics,” Proc. Natl. Acad. Sci. USA 93, 615–622 (1996).
[CrossRef]

Spatial Vision

D. H. Foster, W. F. Bischof, “Bootstrap estimates of the statistical accuracy of thresholds obtained from psychometric functions,” Spatial Vision 11, 135–139 (1997).
[PubMed]

D. H. Brainard, “The Psychophysics Toolbox,” Spatial Vision 10, 433–436 (1997).
[CrossRef] [PubMed]

D. G. Pelli, “The VideoToolbox software for visual psychophysics: transforming numbers into movies,” Spatial Vision 10, 437–442 (1997).
[CrossRef] [PubMed]

Vision Res.

D. G. Pelli, L. Zhang, “Accurate control of contrast on microcomputer displays,” Vision Res. 31, 1337–1350 (1991).
[CrossRef] [PubMed]

S. C. Dakin, I. Mareschal, “Sensitivity to contrast modulation depends on carrier spatial frequency and orientation,” Vision Res. 40, 311–329 (2000).
[CrossRef] [PubMed]

T. Ledgeway, R. F. Hess, “Failure of direction-identification for briefly presented second-order motion stimuli: evidence for weak direction-selectivity of the mechanisms encoding motion,” Vision Res. 42, 1739–1758 (2002).
[CrossRef] [PubMed]

H. A. Allen, A. M. Derrington, “Slow discrimination of contrast-defined expansion patterns,” Vision Res. 40, 735–744 (2000).
[CrossRef] [PubMed]

R. F. Hess, L. R. Ziegler, “What limits the contribution of second-order motion to the perception of surface shape?” Vision Res. 40, 2125–2133 (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]

S. C. Dakin, R. J. Watt, “The computation of orientation statistics from visual texture,” Vision Res. 37, 3181–3192 (1997).
[CrossRef]

G. Westheimer, “Simultaneous orientation contrast for lines in the human fovea,” Vision Res. 30, 1913–1921 (1990).
[CrossRef] [PubMed]

D. W. Heeley, H. M. Buchanan Smith, J. A. Cromwell, J. S. Wright, “The oblique effect in orientation acuity,” Vision Res. 37, 235–242 (1997).
[CrossRef] [PubMed]

Z. Lu, B. A. Dosher, “External noise distinguishes attention mechanisms,” Vision Res. 38, 1183–1198 (1998).
[CrossRef] [PubMed]

C. D. Gilbert, T. N. Wiesel, “The influence of contextual stimuli on the orientation selectivity of cells in primary visual cortex of the cat,” Vision Res. 30, 1689–1701 (1990).
[CrossRef] [PubMed]

D. J. Field, A. Hayes, R. F. Hess, “Contour integration by the human visual system: evidence for a local ‘association field,’ ” Vision Res. 33, 173–193 (1993).
[CrossRef] [PubMed]

R. F. Hess, S. C. Dakin, “Contour integration in the peripheral field,” Vision Res. 39, 947–959 (1999).
[CrossRef] [PubMed]

R. F. Hess, T. Ledgeway, S. Dakin, “Impoverished second-order input to global linking in human vision,” Vision Res. 40, 3309–3318 (2000).
[CrossRef] [PubMed]

N. Graham, J. Beck, A. Sutter, “Nonlinear processes in spatial-frequency channel models of perceived texture segregation—effects of sign and amount of contrast,” Vision Res. 32, 719–743 (1992).
[CrossRef] [PubMed]

Z. Lu, G. Sperling, “The functional architecture of human visual motion perception,” Vision Res. 35, 2697–2722 (1995).
[CrossRef] [PubMed]

A. Johnston, C. W. G. Clifford, “Perceived motion of contrast-modulated gratings—predictions of the multichannel gradient model and the role of full-wave rectification,” Vision Res. 35, 1771–1783 (1995).
[CrossRef] [PubMed]

P. W. McOwan, A. Johnston, “A second-order pattern reveals separate strategies for encoding orientation in two-dimensional space and space-time,” Vision Res. 36, 425–430 (1996).
[CrossRef] [PubMed]

L. M. Lin, H. R. Wilson, “Fourier and non-Fourier pattern discrimination compared,” Vision Res. 36, 1907–1918 (1996).
[CrossRef] [PubMed]

R. van der Zwan, P. Wenderoth, “Mechanisms of purely subjective contour tilt aftereffects,” Vision Res. 35, 2547–2557 (1995).
[CrossRef] [PubMed]

S. Smith, P. Wenderoth, R. van der Zwan, “Orientation processing mechanisms revealed by the plaid tilt illusion,” Vision Res. 41, 483–494 (2001).
[CrossRef] [PubMed]

S. Smith, C. W. G. Clifford, P. Wenderoth, “Interaction between first- and second-order orientation channels revealed by the tilt illusion: psychophysics and computational modeling,” Vision Res. 41, 1057–1071 (2001).
[CrossRef] [PubMed]

W. H. Mcllhagga, K. T. Mullen, “Contour integration with colour and luminance contrast,” Vision Res. 36, 1265–1279 (1996).
[CrossRef]

D. J. Field, A. Hayes, R. F. Hess, “The roles of polarity and symmetry in the perceptual grouping of contour fragments,” Vision Res. 13, 51–66 (2000).

M. Edwards, D. R. Badcock, “Global motion perception: no interaction between the first- and second-order motion pathways,” Vision Res. 35, 2589–2602 (1995).
[CrossRef] [PubMed]

S. C. Dakin, C. B. Williams, R. F. Hess, “The interaction of first- and second-order cues to orientation,” Vision Res. 39, 2867–2884 (1999).
[CrossRef] [PubMed]

M. J. Morgan, A. J. S. Mason, S. Baldassi, “Are there separate first-order and second-order mechanisms for orientation discrimination?” Vision Res. 40, 1751–1763 (2000).
[CrossRef] [PubMed]

A. J. Schofield, M. A. Georgeson, “Sensitivity to modulations of luminance and contrast in visual white noise: separate mechanisms with similar behaviour,” Vision Res. 39, 2697–2716 (1999).
[CrossRef] [PubMed]

I. Mareschal, M. P. Sceniak, R. M. Shapley, “Contextual influences on orientation discrimination: binding local and global cues,” Vision Res. 41, 1915–1930 (2001).
[CrossRef] [PubMed]

Visual Neurosci.

H. R. Wilson, V. P. Ferrera, C. Yo, “A psychophysically motivated model for two-dimensional motion perception,” Visual Neurosci. 9, 79–97 (1992).
[CrossRef]

Other

D. G. Pelli, “Effects of visual noise,” Ph.D. thesis (University of Cambridge, Cambridge, UK, 1981).

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Figures (8)

Fig. 1
Fig. 1

Examples of stimuli: (a)–(c) Typical arrays of first-order and (d)–(f) second-order Gabors are shown. The orientation of each Gabor is drawn from a Gaussian distribution with standard deviation as shown in the leftmost column. Observers judged whether the mean orientation of all the Gabors in the array was tilted left or right of vertical.

Fig. 2
Fig. 2

Orientation discrimination thresholds for one Gabor. Data are shown for one observer, HAA. The discrimination thresholds for a range of contrasts of first-order Gabors are shown compared with the discrimination threshold for a second-order Gabor at maximum modulation depth.

Fig. 3
Fig. 3

Summary of parameters derived from fits of the equivalent noise model. (a),(b) Results of conditions in which the radius remained constant, so that as more Gabor patches are presented there is a corresponding increase in density. (c),(d) Results of conditions in which the density remained constant, so that as more Gabor patches are presented the stimulus area increased. (a),(c) show the estimated internal noise for the observers, and (b),(d) show the estimated number of samples used by the observers. In all four plots the parameter is plotted against the number of Gabor patches. Curves represent the mean estimate (solid, first order; dashed, second order). Points represent the estimated parameters from each observer. Each shape represents a different observer. Solid shapes and stars are data from first-order conditions; open symbols and ×’s are data from second-order conditions.

Fig. 4
Fig. 4

Graphs comparing observers’ performance judging the mean orientation of arrays of first-order Gabors with, or without, intermixed randomly oriented Gabors. Orientation thresholds were measured as the standard deviation of the distribution of orientations in the signal population increased. Each plot shows thresholds and the fitted equivalent noise model for performance when there were 32 first-order signal Gabors (dashed curves, diamonds) and 32 first-order signal Gabors and 32 second-order random Gabors (solid curves, triangles). The data from the case with 32 first-order signal plus 32 random first-order Gabors are summarized by the fitted function (dotted curves, circles). JHD: naïve observer. RH, HAA, and BM: authors. FO, first order; SO, second order; s.d., standard deviation.

Fig. 5
Fig. 5

Graphs comparing observers’ performance judging the mean orientation of arrays of second-order Gabors either with or without intermixed randomly oriented Gabors. Orientation thresholds were measured as the standard deviation of the distribution of orientations in the signal population increased. Each plot shows thresholds and the fitted model for performance when there were 32 second-order signal Gabors (dashed curves, diamonds) and 32 second-order signal Gabors and 32 first-order random Gabors (solid curves, triangles). The data from the case with 32 second-order signal plus 32 random second-order Gabors are summarized by the fitted function (dotted curves, circles).

Fig. 6
Fig. 6

Graphs comparing observers’ performance judging the mean orientation of arrays of Gabors with, or without, randomly oriented noise Gabors of the opposite order being present. Observers did not know whether the first-order or second-order Gabors were the signal Gabors. Orientation thresholds were measured as the standard deviation of the distribution of orientations in the signal population increased. Each plot shows thresholds and the fitted model for performance when there were 32 signal Gabors (dashed curve, triangles) compared with 32 signal Gabors plus 32 noise Gabors (solid curves, diamonds). (a)–(c) Conditions when the signal was first order (noise was second order). (d)–(f) Conditions when the signal was second order (noise was first order).

Fig. 7
Fig. 7

Graphs of observers’ performance judging the mean orientation of arrays containing either 32 first-order or 32 second-order Gabors (dashed curves, triangles) and their performance judging the mean orientation of arrays containing both 32 first-order and 32 second-order Gabors (solid curves, diamonds). Orientation thresholds were measured as the standard deviation of the distribution of orientations in the signal population increased. Each subplot shows a different observer’s data. Performance in the mixed Gabor condition is compared with performance with 32 first-order Gabors for HAA, BM, and MW (naïve observer) and with 32 second-order Gabors for JHD and RH (see text).

Fig. 8
Fig. 8

Summary of possible mechanisms underlying the judgment of mean orientation.

Equations (3)

Equations on this page are rendered with MathJax. Learn more.

σobs=(σint2+σext2/n)1/2,
L(x,y)=L(mean)+[1+cos(αθ+ϕ)]RC(x,y)env,
L(x,y)=L(mean)+[R(x,y)+C cos(αθ+ϕ)]env,

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