Abstract

We assessed the accuracy of contrast-defined shape detection of stimuli of constant aspect ratio, namely, circular bandpass stimuli whose radii were sinusoidally varied about a mean radius. Performance for these contrast-defined shapes, which we show is determined by the global rather than the local attributes of the stimulus, is 2–8 times worse than that for their luminance-defined counterparts, suggesting separate processing limitations. By spatially and orientationally filtering the two-dimensional fractal-noise carriers of which these stimuli were composed, we determined whether there are specific rules concerning the spatial and orientational input to shape detectors from mechanisms sensitive to the carrier structure. The results suggest that second-order circularity detectors receive mixed input from spatial-frequency-tuned and orientationally tuned cells.

© 2001 Optical Society of America

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    [CrossRef] [PubMed]
  2. F. Wilkinson, H. R. Wilson, C. Habak, “Detection and recognition of radial frequency patterns,” Vision Res. 38, 3555–3568 (1998).
    [CrossRef]
  3. H. R. Wilson, “Non-Fourier cortical processes in texture, form, and motion perception,” in Cerebral Cortex: Models of Cortical Circuitry, P. S. Ulinski, E. G. Jones, eds. (Plenum, New York, 1999), pp. 445–477.
  4. R. F. Hess, Y.-Z. Wang, S. C. Dakin, “Are judgments of circularity local or global?” Vision Res. 39, 4354–4360 (1999).
    [CrossRef]
  5. J. L. Gallant, J. Braun, D. C. Van Essen, “Selectivity for polar, hyperbolic, and Cartesian gratings in macaque visual cortex,” Science 259, 100–103 (1993).
    [CrossRef] [PubMed]
  6. J. L. Gallant, C. E. Connor, S. Rakshit, J. W. Lewis, D. C. Van Essen, “Neural responses to polar, hyperbolic, and Cartesian gratings in area V4 of the macaque monkey,” J. Neurophysiol. 76, 2718–2739 (1996).
    [PubMed]
  7. F. W. Wilkinson, T. W. James, H. R. Wilson, J. S. Gati, R. S. Menon, M. A. Goodale, “Radial and concentric gratings selectivity activate high-level form vision areas in human extra-striate cortex: an fMRI study,” Curr. Biol. 10, 1455–1458 (2000).
    [CrossRef] [PubMed]
  8. Second-order mechanisms have been shown to have two types of spatial frequency and orientational tuning (see Refs. 12and 15), one for luminance modulation (carrier tuning) and another for contrast modulation (envelope tuning). The present study concerns only the former.
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    [CrossRef] [PubMed]
  10. A. Sutter, G. Sperling, C. Chubb, “Measuring the spatial frequency selectivity of second-order texture mechanisms,” Vision Res. 35, 915–924 (1995).
    [CrossRef] [PubMed]
  11. K. Langley, D. J. Fleet, P. B. Hibbard, “Linear filtering precedes nonlinear processing in early vision,” Curr. Biol. 6, 891–896 (1996).
    [CrossRef] [PubMed]
  12. Y. X. Zhou, C. L. Baker, “A processing stream in mammalian visual cortex neurons for non-Fourier responses,” Science 261, 98–101 (1993).
    [CrossRef] [PubMed]
  13. Y. X. Zhou, C. L. Baker, “Envelope-responsive neutrons in areas 17 and 18 of cat,” J. Neurophysiol. 72, 2134–2150 (1994).
    [PubMed]
  14. 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]
  15. I. Mareschal, C. L. Baker, “A cortical locus for the processing of contrast-defined contours,” Nat. Neurosci. 1, 150–154 (1998).
    [CrossRef]
  16. J. M. Zanker, “Interactions between primary and secondary mechanisms in human motion detection,” Vision Res. 34, 2863–2877 (1994).
    [CrossRef]
  17. S. S. Wolfson, M. S. Landy, “Discrimination of orientation-defined texture edges,” Vision Res. 35, 2863–2877 (1995).
    [CrossRef] [PubMed]
  18. S. C. Dakin, I. Mareschal, “Sensitivity to contrast modulation depends on carrier spatial frequency and orientation,” Vision Res. 40, 311–329 (2000).
    [CrossRef] [PubMed]
  19. F. Wilkinson, H. R. Wilson, “Discrimination of curvilinear patterns: beyond simple cells,” Invest. Ophthalmol. Visual Sci. Suppl. 37, S955 (1996).
  20. D. H. Brainard, “The Psychophysics Toolbox,” Spatial Vision 10, 433–446 (1997).
    [CrossRef] [PubMed]
  21. D. G. Pelli, “The VideoToolbox software for visual psychophysics: transforming numbers into movies,” Spatial Vision 10, 437–442 (1997).
    [CrossRef] [PubMed]
  22. W. Weibull, “A statistical distribution function of wide applicability,” J. Appl. Mech. 18, 292–297 (1951).
  23. J. Nachmias, “On the psychometric function for contrast detection,” Vision Res. 21, 215–223 (1981).
    [CrossRef] [PubMed]
  24. A. T. Smith, “The detection of second-order motion,” in Visual Detection of Motion, A. T. Smith, R. J. Snowden, eds. (Academic, London, 1994), pp. 145–176.
  25. A. T. Smith, T. Ledgeway, “Separate detection of moving luminance and contrast modulations: fact or artifact?” Vision Res. 37, 45–62 (1997).
    [CrossRef] [PubMed]
  26. A. M. Derrington, D. R. Badcock, “Separate detectors for simple and complex grating patterns,” Vision Res. 25, 1869–1878 (1985).
    [CrossRef]
  27. I. E. Holliday, S. J. Anderson, “Different processes underlie the detection of second-order motion at low and high temporal frequencies,” Proc. R. Soc. London Ser. B 257, 165–173 (1994).
    [CrossRef]
  28. A. T. Smith, T. Ledgeway, “Sensitivity to second-order motion as a function of temporal frequency and eccentricity,” Vision Res. 38, 403–410 (1998).
    [CrossRef] [PubMed]
  29. J. M. Zanker, I. S. Hupgens, “Interaction between primary and secondary mechanisms in human motion perception,” Vision Res. 34, 1255–1266 (1994).
    [CrossRef] [PubMed]

2000

F. W. Wilkinson, T. W. James, H. R. Wilson, J. S. Gati, R. S. Menon, M. A. Goodale, “Radial and concentric gratings selectivity activate high-level form vision areas in human extra-striate cortex: an fMRI study,” Curr. Biol. 10, 1455–1458 (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

R. F. Hess, Y.-Z. Wang, S. C. Dakin, “Are judgments of circularity local or global?” Vision Res. 39, 4354–4360 (1999).
[CrossRef]

1998

F. Wilkinson, H. R. Wilson, C. Habak, “Detection and recognition of radial frequency patterns,” Vision Res. 38, 3555–3568 (1998).
[CrossRef]

I. Mareschal, C. L. Baker, “A cortical locus for the processing of contrast-defined contours,” Nat. Neurosci. 1, 150–154 (1998).
[CrossRef]

A. T. Smith, T. Ledgeway, “Sensitivity to second-order motion as a function of temporal frequency and eccentricity,” Vision Res. 38, 403–410 (1998).
[CrossRef] [PubMed]

1997

A. T. Smith, T. Ledgeway, “Separate detection of moving luminance and contrast modulations: fact or artifact?” Vision Res. 37, 45–62 (1997).
[CrossRef] [PubMed]

D. H. Brainard, “The Psychophysics Toolbox,” Spatial Vision 10, 433–446 (1997).
[CrossRef] [PubMed]

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

1996

F. Wilkinson, H. R. Wilson, “Discrimination of curvilinear patterns: beyond simple cells,” Invest. Ophthalmol. Visual Sci. Suppl. 37, S955 (1996).

K. Langley, D. J. Fleet, P. B. Hibbard, “Linear filtering precedes nonlinear processing in early vision,” Curr. Biol. 6, 891–896 (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]

J. L. Gallant, C. E. Connor, S. Rakshit, J. W. Lewis, D. C. Van Essen, “Neural responses to polar, hyperbolic, and Cartesian gratings in area V4 of the macaque monkey,” J. Neurophysiol. 76, 2718–2739 (1996).
[PubMed]

1995

A. Sutter, G. Sperling, C. Chubb, “Measuring the spatial frequency selectivity of second-order texture mechanisms,” Vision Res. 35, 915–924 (1995).
[CrossRef] [PubMed]

S. S. Wolfson, M. S. Landy, “Discrimination of orientation-defined texture edges,” Vision Res. 35, 2863–2877 (1995).
[CrossRef] [PubMed]

1994

J. M. Zanker, I. S. Hupgens, “Interaction between primary and secondary mechanisms in human motion perception,” Vision Res. 34, 1255–1266 (1994).
[CrossRef] [PubMed]

I. E. Holliday, S. J. Anderson, “Different processes underlie the detection of second-order motion at low and high temporal frequencies,” Proc. R. Soc. London Ser. B 257, 165–173 (1994).
[CrossRef]

Y. X. Zhou, C. L. Baker, “Envelope-responsive neutrons in areas 17 and 18 of cat,” J. Neurophysiol. 72, 2134–2150 (1994).
[PubMed]

J. M. Zanker, “Interactions between primary and secondary mechanisms in human motion detection,” Vision Res. 34, 2863–2877 (1994).
[CrossRef]

1993

Y. X. Zhou, C. L. Baker, “A processing stream in mammalian visual cortex neurons for non-Fourier responses,” Science 261, 98–101 (1993).
[CrossRef] [PubMed]

P. Werkhoven, G. Sperling, C. Chubb, “The dimensionality of texture-defined motion: a single channel theory,” Vision Res. 33, 463–485 (1993).
[CrossRef] [PubMed]

J. L. Gallant, J. Braun, D. C. Van Essen, “Selectivity for polar, hyperbolic, and Cartesian gratings in macaque visual cortex,” Science 259, 100–103 (1993).
[CrossRef] [PubMed]

1992

D. Regan, S. J. Hamstra, “Shape discrimination and the judgment of perfect symmetry: dissociation of shape from size,” Vision Res. 32, 1845–1864 (1992).
[CrossRef] [PubMed]

1985

A. M. Derrington, D. R. Badcock, “Separate detectors for simple and complex grating patterns,” Vision Res. 25, 1869–1878 (1985).
[CrossRef]

1981

J. Nachmias, “On the psychometric function for contrast detection,” Vision Res. 21, 215–223 (1981).
[CrossRef] [PubMed]

1951

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

Anderson, S. J.

I. E. Holliday, S. J. Anderson, “Different processes underlie the detection of second-order motion at low and high temporal frequencies,” Proc. R. Soc. London Ser. B 257, 165–173 (1994).
[CrossRef]

Badcock, D. R.

A. M. Derrington, D. R. Badcock, “Separate detectors for simple and complex grating patterns,” Vision Res. 25, 1869–1878 (1985).
[CrossRef]

Baker, C. L.

I. Mareschal, C. L. Baker, “A cortical locus for the processing of contrast-defined contours,” Nat. Neurosci. 1, 150–154 (1998).
[CrossRef]

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]

Y. X. Zhou, C. L. Baker, “Envelope-responsive neutrons in areas 17 and 18 of cat,” J. Neurophysiol. 72, 2134–2150 (1994).
[PubMed]

Y. X. Zhou, C. L. Baker, “A processing stream in mammalian visual cortex neurons for non-Fourier responses,” Science 261, 98–101 (1993).
[CrossRef] [PubMed]

Brainard, D. H.

D. H. Brainard, “The Psychophysics Toolbox,” Spatial Vision 10, 433–446 (1997).
[CrossRef] [PubMed]

Braun, J.

J. L. Gallant, J. Braun, D. C. Van Essen, “Selectivity for polar, hyperbolic, and Cartesian gratings in macaque visual cortex,” Science 259, 100–103 (1993).
[CrossRef] [PubMed]

Chubb, C.

A. Sutter, G. Sperling, C. Chubb, “Measuring the spatial frequency selectivity of second-order texture mechanisms,” Vision Res. 35, 915–924 (1995).
[CrossRef] [PubMed]

P. Werkhoven, G. Sperling, C. Chubb, “The dimensionality of texture-defined motion: a single channel theory,” Vision Res. 33, 463–485 (1993).
[CrossRef] [PubMed]

Connor, C. E.

J. L. Gallant, C. E. Connor, S. Rakshit, J. W. Lewis, D. C. Van Essen, “Neural responses to polar, hyperbolic, and Cartesian gratings in area V4 of the macaque monkey,” J. Neurophysiol. 76, 2718–2739 (1996).
[PubMed]

Dakin, S. C.

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, Y.-Z. Wang, S. C. Dakin, “Are judgments of circularity local or global?” Vision Res. 39, 4354–4360 (1999).
[CrossRef]

Derrington, A. M.

A. M. Derrington, D. R. Badcock, “Separate detectors for simple and complex grating patterns,” Vision Res. 25, 1869–1878 (1985).
[CrossRef]

Fleet, D. J.

K. Langley, D. J. Fleet, P. B. Hibbard, “Linear filtering precedes nonlinear processing in early vision,” Curr. Biol. 6, 891–896 (1996).
[CrossRef] [PubMed]

Gallant, J. L.

J. L. Gallant, C. E. Connor, S. Rakshit, J. W. Lewis, D. C. Van Essen, “Neural responses to polar, hyperbolic, and Cartesian gratings in area V4 of the macaque monkey,” J. Neurophysiol. 76, 2718–2739 (1996).
[PubMed]

J. L. Gallant, J. Braun, D. C. Van Essen, “Selectivity for polar, hyperbolic, and Cartesian gratings in macaque visual cortex,” Science 259, 100–103 (1993).
[CrossRef] [PubMed]

Gati, J. S.

F. W. Wilkinson, T. W. James, H. R. Wilson, J. S. Gati, R. S. Menon, M. A. Goodale, “Radial and concentric gratings selectivity activate high-level form vision areas in human extra-striate cortex: an fMRI study,” Curr. Biol. 10, 1455–1458 (2000).
[CrossRef] [PubMed]

Goodale, M. A.

F. W. Wilkinson, T. W. James, H. R. Wilson, J. S. Gati, R. S. Menon, M. A. Goodale, “Radial and concentric gratings selectivity activate high-level form vision areas in human extra-striate cortex: an fMRI study,” Curr. Biol. 10, 1455–1458 (2000).
[CrossRef] [PubMed]

Habak, C.

F. Wilkinson, H. R. Wilson, C. Habak, “Detection and recognition of radial frequency patterns,” Vision Res. 38, 3555–3568 (1998).
[CrossRef]

Hamstra, S. J.

D. Regan, S. J. Hamstra, “Shape discrimination and the judgment of perfect symmetry: dissociation of shape from size,” Vision Res. 32, 1845–1864 (1992).
[CrossRef] [PubMed]

Hess, R. F.

R. F. Hess, Y.-Z. Wang, S. C. Dakin, “Are judgments of circularity local or global?” Vision Res. 39, 4354–4360 (1999).
[CrossRef]

Hibbard, P. B.

K. Langley, D. J. Fleet, P. B. Hibbard, “Linear filtering precedes nonlinear processing in early vision,” Curr. Biol. 6, 891–896 (1996).
[CrossRef] [PubMed]

Holliday, I. E.

I. E. Holliday, S. J. Anderson, “Different processes underlie the detection of second-order motion at low and high temporal frequencies,” Proc. R. Soc. London Ser. B 257, 165–173 (1994).
[CrossRef]

Hupgens, I. S.

J. M. Zanker, I. S. Hupgens, “Interaction between primary and secondary mechanisms in human motion perception,” Vision Res. 34, 1255–1266 (1994).
[CrossRef] [PubMed]

James, T. W.

F. W. Wilkinson, T. W. James, H. R. Wilson, J. S. Gati, R. S. Menon, M. A. Goodale, “Radial and concentric gratings selectivity activate high-level form vision areas in human extra-striate cortex: an fMRI study,” Curr. Biol. 10, 1455–1458 (2000).
[CrossRef] [PubMed]

Landy, M. S.

S. S. Wolfson, M. S. Landy, “Discrimination of orientation-defined texture edges,” Vision Res. 35, 2863–2877 (1995).
[CrossRef] [PubMed]

Langley, K.

K. Langley, D. J. Fleet, P. B. Hibbard, “Linear filtering precedes nonlinear processing in early vision,” Curr. Biol. 6, 891–896 (1996).
[CrossRef] [PubMed]

Ledgeway, T.

A. T. Smith, T. Ledgeway, “Sensitivity to second-order motion as a function of temporal frequency and eccentricity,” Vision Res. 38, 403–410 (1998).
[CrossRef] [PubMed]

A. T. Smith, T. Ledgeway, “Separate detection of moving luminance and contrast modulations: fact or artifact?” Vision Res. 37, 45–62 (1997).
[CrossRef] [PubMed]

Lewis, J. W.

J. L. Gallant, C. E. Connor, S. Rakshit, J. W. Lewis, D. C. Van Essen, “Neural responses to polar, hyperbolic, and Cartesian gratings in area V4 of the macaque monkey,” J. Neurophysiol. 76, 2718–2739 (1996).
[PubMed]

Mareschal, I.

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

I. Mareschal, C. L. Baker, “A cortical locus for the processing of contrast-defined contours,” Nat. Neurosci. 1, 150–154 (1998).
[CrossRef]

Menon, R. S.

F. W. Wilkinson, T. W. James, H. R. Wilson, J. S. Gati, R. S. Menon, M. A. Goodale, “Radial and concentric gratings selectivity activate high-level form vision areas in human extra-striate cortex: an fMRI study,” Curr. Biol. 10, 1455–1458 (2000).
[CrossRef] [PubMed]

Nachmias, J.

J. Nachmias, “On the psychometric function for contrast detection,” Vision Res. 21, 215–223 (1981).
[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]

Rakshit, S.

J. L. Gallant, C. E. Connor, S. Rakshit, J. W. Lewis, D. C. Van Essen, “Neural responses to polar, hyperbolic, and Cartesian gratings in area V4 of the macaque monkey,” J. Neurophysiol. 76, 2718–2739 (1996).
[PubMed]

Regan, D.

D. Regan, S. J. Hamstra, “Shape discrimination and the judgment of perfect symmetry: dissociation of shape from size,” Vision Res. 32, 1845–1864 (1992).
[CrossRef] [PubMed]

Smith, A. T.

A. T. Smith, T. Ledgeway, “Sensitivity to second-order motion as a function of temporal frequency and eccentricity,” Vision Res. 38, 403–410 (1998).
[CrossRef] [PubMed]

A. T. Smith, T. Ledgeway, “Separate detection of moving luminance and contrast modulations: fact or artifact?” Vision Res. 37, 45–62 (1997).
[CrossRef] [PubMed]

A. T. Smith, “The detection of second-order motion,” in Visual Detection of Motion, A. T. Smith, R. J. Snowden, eds. (Academic, London, 1994), pp. 145–176.

Sperling, G.

A. Sutter, G. Sperling, C. Chubb, “Measuring the spatial frequency selectivity of second-order texture mechanisms,” Vision Res. 35, 915–924 (1995).
[CrossRef] [PubMed]

P. Werkhoven, G. Sperling, C. Chubb, “The dimensionality of texture-defined motion: a single channel theory,” Vision Res. 33, 463–485 (1993).
[CrossRef] [PubMed]

Sutter, A.

A. Sutter, G. Sperling, C. Chubb, “Measuring the spatial frequency selectivity of second-order texture mechanisms,” Vision Res. 35, 915–924 (1995).
[CrossRef] [PubMed]

Van Essen, D. C.

J. L. Gallant, C. E. Connor, S. Rakshit, J. W. Lewis, D. C. Van Essen, “Neural responses to polar, hyperbolic, and Cartesian gratings in area V4 of the macaque monkey,” J. Neurophysiol. 76, 2718–2739 (1996).
[PubMed]

J. L. Gallant, J. Braun, D. C. Van Essen, “Selectivity for polar, hyperbolic, and Cartesian gratings in macaque visual cortex,” Science 259, 100–103 (1993).
[CrossRef] [PubMed]

Wang, Y.-Z.

R. F. Hess, Y.-Z. Wang, S. C. Dakin, “Are judgments of circularity local or global?” Vision Res. 39, 4354–4360 (1999).
[CrossRef]

Weibull, W.

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

Werkhoven, P.

P. Werkhoven, G. Sperling, C. Chubb, “The dimensionality of texture-defined motion: a single channel theory,” Vision Res. 33, 463–485 (1993).
[CrossRef] [PubMed]

Wilkinson, F.

F. Wilkinson, H. R. Wilson, C. Habak, “Detection and recognition of radial frequency patterns,” Vision Res. 38, 3555–3568 (1998).
[CrossRef]

F. Wilkinson, H. R. Wilson, “Discrimination of curvilinear patterns: beyond simple cells,” Invest. Ophthalmol. Visual Sci. Suppl. 37, S955 (1996).

Wilkinson, F. W.

F. W. Wilkinson, T. W. James, H. R. Wilson, J. S. Gati, R. S. Menon, M. A. Goodale, “Radial and concentric gratings selectivity activate high-level form vision areas in human extra-striate cortex: an fMRI study,” Curr. Biol. 10, 1455–1458 (2000).
[CrossRef] [PubMed]

Wilson, H. R.

F. W. Wilkinson, T. W. James, H. R. Wilson, J. S. Gati, R. S. Menon, M. A. Goodale, “Radial and concentric gratings selectivity activate high-level form vision areas in human extra-striate cortex: an fMRI study,” Curr. Biol. 10, 1455–1458 (2000).
[CrossRef] [PubMed]

F. Wilkinson, H. R. Wilson, C. Habak, “Detection and recognition of radial frequency patterns,” Vision Res. 38, 3555–3568 (1998).
[CrossRef]

F. Wilkinson, H. R. Wilson, “Discrimination of curvilinear patterns: beyond simple cells,” Invest. Ophthalmol. Visual Sci. Suppl. 37, S955 (1996).

H. R. Wilson, “Non-Fourier cortical processes in texture, form, and motion perception,” in Cerebral Cortex: Models of Cortical Circuitry, P. S. Ulinski, E. G. Jones, eds. (Plenum, New York, 1999), pp. 445–477.

Wolfson, S. S.

S. S. Wolfson, M. S. Landy, “Discrimination of orientation-defined texture edges,” Vision Res. 35, 2863–2877 (1995).
[CrossRef] [PubMed]

Zanker, J. M.

J. M. Zanker, “Interactions between primary and secondary mechanisms in human motion detection,” Vision Res. 34, 2863–2877 (1994).
[CrossRef]

J. M. Zanker, I. S. Hupgens, “Interaction between primary and secondary mechanisms in human motion perception,” Vision Res. 34, 1255–1266 (1994).
[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]

Y. X. Zhou, C. L. Baker, “Envelope-responsive neutrons in areas 17 and 18 of cat,” J. Neurophysiol. 72, 2134–2150 (1994).
[PubMed]

Y. X. Zhou, C. L. Baker, “A processing stream in mammalian visual cortex neurons for non-Fourier responses,” Science 261, 98–101 (1993).
[CrossRef] [PubMed]

Curr. Biol.

F. W. Wilkinson, T. W. James, H. R. Wilson, J. S. Gati, R. S. Menon, M. A. Goodale, “Radial and concentric gratings selectivity activate high-level form vision areas in human extra-striate cortex: an fMRI study,” Curr. Biol. 10, 1455–1458 (2000).
[CrossRef] [PubMed]

K. Langley, D. J. Fleet, P. B. Hibbard, “Linear filtering precedes nonlinear processing in early vision,” Curr. Biol. 6, 891–896 (1996).
[CrossRef] [PubMed]

Invest. Ophthalmol. Visual Sci. Suppl.

F. Wilkinson, H. R. Wilson, “Discrimination of curvilinear patterns: beyond simple cells,” Invest. Ophthalmol. Visual Sci. Suppl. 37, S955 (1996).

J. Appl. Mech.

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

J. Neurophysiol.

J. L. Gallant, C. E. Connor, S. Rakshit, J. W. Lewis, D. C. Van Essen, “Neural responses to polar, hyperbolic, and Cartesian gratings in area V4 of the macaque monkey,” J. Neurophysiol. 76, 2718–2739 (1996).
[PubMed]

Y. X. Zhou, C. L. Baker, “Envelope-responsive neutrons in areas 17 and 18 of cat,” J. Neurophysiol. 72, 2134–2150 (1994).
[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]

Nat. Neurosci.

I. Mareschal, C. L. Baker, “A cortical locus for the processing of contrast-defined contours,” Nat. Neurosci. 1, 150–154 (1998).
[CrossRef]

Proc. R. Soc. London Ser. B

I. E. Holliday, S. J. Anderson, “Different processes underlie the detection of second-order motion at low and high temporal frequencies,” Proc. R. Soc. London Ser. B 257, 165–173 (1994).
[CrossRef]

Science

Y. X. Zhou, C. L. Baker, “A processing stream in mammalian visual cortex neurons for non-Fourier responses,” Science 261, 98–101 (1993).
[CrossRef] [PubMed]

J. L. Gallant, J. Braun, D. C. Van Essen, “Selectivity for polar, hyperbolic, and Cartesian gratings in macaque visual cortex,” Science 259, 100–103 (1993).
[CrossRef] [PubMed]

Spatial Vision

D. H. Brainard, “The Psychophysics Toolbox,” Spatial Vision 10, 433–446 (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.

J. M. Zanker, “Interactions between primary and secondary mechanisms in human motion detection,” Vision Res. 34, 2863–2877 (1994).
[CrossRef]

S. S. Wolfson, M. S. Landy, “Discrimination of orientation-defined texture edges,” Vision Res. 35, 2863–2877 (1995).
[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]

R. F. Hess, Y.-Z. Wang, S. C. Dakin, “Are judgments of circularity local or global?” Vision Res. 39, 4354–4360 (1999).
[CrossRef]

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Second-order mechanisms have been shown to have two types of spatial frequency and orientational tuning (see Refs. 12and 15), one for luminance modulation (carrier tuning) and another for contrast modulation (envelope tuning). The present study concerns only the former.

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Figures (5)

Fig. 1
Fig. 1

Examples of sinusoidally modulated RF stimuli. At a viewing distance of 1.5 m, the D4 peak spatial frequency is 5 c/deg and the mean radius is 0.5°. The amplitude of radial motion is 1%. RF is 4c/360° with a modulation phase of 90°. (a) RF4 with no noise; (b), (c) luminance-defined RF4s with no background noise and background noise, respectively; (d),(e) contrast-defined RF4s with no background noise and background noise, respectively.

Fig. 2
Fig. 2

Comparison of modulation thresholds of two subjects (RFH and RLA) for various types of RF patterns at several different radial frequencies (4, 6, 8, or 10 c/360°). Solid symbols, luminance-defined stimuli; open symbols, contrast-defined stimuli. Triangles, control condition of a RF4 with no noise; circles, background-noise condition; squares, no-background-noise condition. Vertical bars represent one standard deviation.

Fig. 3
Fig. 3

Control conditions of the contrast-defined stimuli where we altered either contrast or duration. Circles, no-background-noise condition; squares, background-noise condition. There is no strong dependence on exposure duration or noise amplitude.

Fig. 4
Fig. 4

(a),(b) Effect of phase for two subjects in three conditions [no noise; contrast-defined (CD) RF patterns with no background noise (Stim 1); and CD RFs with background noise (Stim 2)]. In the CD conditions, sensitivity for both the 90° and the 270° phases is significantly different from that of the 0° and the 180° phases. (c),(d) Shape-detection sensitivity for intact RF patterns and patterns that were cut into four pieces. Results show a higher threshold for detecting the intact CD pattern than for detecting the same modulation in its constituent pieces.

Fig. 5
Fig. 5

Modulation thresholds of two subjects for contrast-defined RF4s with and without background noise. (a) Spatially unfiltered condition (cutoff at infinity), (b) spatial low-pass-filtering condition (cutoff at 5c/deg). In both conditions, thresholds are similar regardless of the orientational filtering used (isotropic, horizontal/vertical, or oblique).

Equations (10)

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RF4=Lm1+c1-4r2+43r4exp(-r)2,
r=(x2+y2)1/2-Rσ,
σ=2πωp,
R=Rm{1+A sin[frarctan(y/x)+θ]},
luminance-defined RF4
=Lm[1+cnoiseRF4],
contrast-definedRF4NoBackgroundNoise
=Lm[1+cnoisenoiseRF4],
contrast-definedCD4global
=Lm[1+cnoisenoise(0.5+0.5CD4)],

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