Abstract

Channel-based models of human spatial vision require that the output of spatial filters be pooled across space. This pooling yields global estimates of local feature attributes such as orientation that are useful in situations in which that attribute may be locally variable, as is the case for visual texture. The spatial characteristics of orientation summation are considered in the study. By assessing the effect of orientation variability on observers’ ability to estimate the mean orientation of spatially unstructured textures, one can determine both the internal noise on each orientation sample and the number of samples being pooled. By a combination of fixing and covarying the size of textured regions and the number of elements constituting them, one can then assess the effects of the texture’s size, density, and numerosity (the number of elements present) on the internal noise and the sampling density. Results indicate that internal noise shows a primary dependence on texture density but that, counterintuitively, subjects rely on a sample size approximately equal to a fixed power of the number of samples present, regardless of their spatial arrangement. Orientation pooling is entirely flexible with respect to the position of input features.

© 2001 Optical Society of America

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  1. D. H. Hubel, T. N. Wiesel, “Receptive fields, binocular interaction and function architecture in the cat’s visual cortex,” J. Physiol. 160, 106–154 (1962).
    [PubMed]
  2. A. B. Watson, “Summation of grating patches indicates many types of detectors at one retinal location,” Vision Res. 22, 17–25 (1982).
    [CrossRef]
  3. I. Fogel, D. Sagi, “Gabor filters as texture discriminator,” Biol. Cybern. 61, 103–113 (1989).
    [CrossRef]
  4. A. Bovik, M. Clark, W. Geisler, “Multi-channel texture analysis using localised spatial filters,” IEEE Trans. Pattern Anal. Mach. Intell. 12, 55–73 (1990).
    [CrossRef]
  5. J. Malik, P. Perona, “Preattentive texture discrimination with early visual mechanisms,” J. Opt. Soc. Am. A 7, 923–932 (1990).
    [CrossRef] [PubMed]
  6. J. R. Bergen, M. S. Landy, “Computational modeling of visual texture segmentation,” in Computational Models of Visual Processing, M. S. Landy, J. A. Movshon, eds. (MIT Press, Cambridge, Mass., 1991).
  7. E. R. Howell, R. F. Hess, “The functional area for summation to threshold for sinusoidal gratings,” Vision Res. 18, 369–374 (1978).
    [CrossRef] [PubMed]
  8. J. G. Robson, N. Graham, “Probability summation and regional variation in contrast sensitivity across the visual field,” Vision Res. 21, 409–418 (1981).
    [CrossRef] [PubMed]
  9. N. V. S. Graham, Visual Pattern Analyzers (Oxford U. Press, New York, 1989).
  10. M. J. Mayer, C. W. Tyler, “Invariance of the slope of the psychometric function with spatial summation,” J. Opt. Soc. Am. A 3, 1166–1172 (1986).
    [CrossRef] [PubMed]
  11. T. S. Meese, C. B. Williams, “Probability summation for multiple patches of luminance modulation,” Vision Res. 40, 2101–2113 (2000).
    [CrossRef] [PubMed]
  12. P. Verghese, L. S. Stone, “Perceived visual speed constrained by image segmentation,” Nature 381, 161–163 (1996).
    [CrossRef] [PubMed]
  13. U. Polat, C. W. Tyler, “What pattern the eye sees best,” Vision Res. 39, 887–895 (1999).
    [CrossRef] [PubMed]
  14. P. Verghese, S. N. J. Watnmaniuk, S. P. McKee, N. M. Grzywacz, “Local motion detectors cannot account for the detectability of an extended trajectory in noise,” Vision Res. 39, 19–30 (1999).
    [CrossRef] [PubMed]
  15. 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]
  16. R. F. Hess, S. C. Dakin, “Absence of contour linking in peripheral vision,” Nature (London) 390, 602–604 (1997).
    [CrossRef]
  17. S. C. Dakin, R. J. Watt, “The computation of orientation statistics from visual texture,” Vision Res. 37, 3181–3192 (1997).
    [CrossRef]
  18. F. A. Kingdom, D. R. Keeble, “On the mechanism for scale invariance in orientation-defined textures,” Vision Res. 39, 1477–1489 (1999).
    [CrossRef] [PubMed]
  19. H. C. Nothdurft, “Sensitivity for structure gradient in texture discrimination tasks,” Vision Res. 25, 1957–1968 (1985).
    [CrossRef] [PubMed]
  20. M. S. Landy, J. R. Bergen, “Texture segregation and orientation gradient,” Vision Res. 31, 679–691 (1991).
    [CrossRef] [PubMed]
  21. D. Sagi, B. Julesz, “Short-range limitation on detection of feature differences,” Spatial Vision 2, 39–49 (1987).
    [CrossRef] [PubMed]
  22. M. J. Morgan, R. M. Ward, E. Castet, “Visual search for a tilted target: tests of spatial uncertainty models,” Q. J. Exp. Psychology A 51, 347–370 (1998).
    [CrossRef]
  23. H. C. Nothdurft, C. Y. Li, “Texture discrimination: representation of orientation and luminance differences in cells of the cat striate cortex,” Vision Res. 25, 99–113 (1985).
    [CrossRef] [PubMed]
  24. A. Gorea, T. V. Papathomas, “Local versus global contrasts in texture segregation,” J. Opt. Soc. Am. A 16, 728–741 (1999).
    [CrossRef]
  25. H. B. Barlow, “Retinal noise and absolute threshold,” J. Opt. Soc. Am. A 46, 634–639 (1956).
    [CrossRef]
  26. H. B. Barlow, “Increment thresholds at low intensities considered as signal/noise discrimination,” J. Physiol. (London) 136, 469–488 (1957).
  27. Y. Y. Zeevi, S. S. Mangoubi, “Vernier acuity with noisy lines: estimation of relative position uncertainty,” Biol. Cybern. 50, 371–376 (1984).
    [CrossRef] [PubMed]
  28. R. J. Watt, R. F. Hess, “Spatial information and uncertainty in anisometropic amblyopia,” Vision Res. 27, 661–674 (1987).
    [CrossRef] [PubMed]
  29. R. J. Watt, M. J. Morgan, “The recognition and representation of edge blur: evidence for spatial primitives in human vision,” Vision Res. 23, 1465–1477 (1983).
    [CrossRef] [PubMed]
  30. D. W. Heeley, “Spatial frequency discrimination for sinewave gratings with random, bandpass frequency modulation: evidence for averaging in spatial acuity,” Spatial Vision 2, 317–335 (1987).
    [CrossRef] [PubMed]
  31. D. G. Pelli, “The quantum efficiency of vision,” in Vision Coding and Efficiency, C. Blakemore, ed. (Cambridge U. Press, Cambridge, UK, 1990).
  32. A. J. J. Ahumada, A. B. Watson, “Equivalent-noise model for contrast detection and discrimination,” J. Opt. Soc. Am. A 2, 1133–1139 (1985).
    [CrossRef] [PubMed]
  33. R. F. Hess, S. C. Dakin, “Contour integration in the peripheral field,” Vision Res. 39, 947–959 (1999).
    [CrossRef] [PubMed]
  34. R. J. Watt, Understanding Vision (Academic Press, London, UK, 1991).
  35. D. W. Heeley, H. M. Buchanan-Smith, J. A. Cromwell, J. S. Wright, “The oblique effect in orientation acuity,” Vision Res. 37, p. 235–242 (1997).
    [CrossRef]
  36. Z. L. Lu, B. A. Dosher, “External noise distinguishes attention mechanisms,” Vision Res. 38, 1183–1198 (1998).
    [CrossRef] [PubMed]
  37. D. H. Brainard, “The Psychophysics Toolbox,” Spatial Vision 10, 433–436 (1997).
    [CrossRef] [PubMed]
  38. D. G. Pelli, “The VideoToolbox software for visual psychophysics: transforming number into movies,” Spatial Vision 10, 437–442 (1997).
    [CrossRef]
  39. D. G. Pelli, L. Zhang, “Accurate control of contrast on microcomputer displays,” Vision Res. 31, 1337–1350 (1991).
    [CrossRef] [PubMed]
  40. D. W. Heeley, H. M. Buchanan-Smith, “Recognition of stimulus orientation,” Vision Res. 32, 719–743 (1990).
  41. D. C. Burr, S. A. Wijesundra, “Orientation discrimination depends on spatial frequency,” Vision Res. 31, 1449–1452 (1991).
    [CrossRef] [PubMed]
  42. R. J. Watt, D. Andrews, “APE: Adaptive probit estimation of psychometric functions,” Current Psychol. Rev. 1, 205–214 (1981).
    [CrossRef]
  43. 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]
  44. S. He, P. Cavanagh, J. Intriligator, “Attentional resolution and the locus of visual awareness,” Nature 383, 334–347 (1996).
    [CrossRef] [PubMed]
  45. J. S. Joseph, M. M. Chun, K. Nakayama, “Attentional requirements in a ‘preattentive’ feature search task,” Nature 387, 805–807 (1997).
    [CrossRef] [PubMed]
  46. S. J. M. Rainville, F. A. A. Kingdom, “The functional role of oriented spatial filters in the perception of mirror symmetry,” Vision Res. 40, 2621–2644 (2000).
    [CrossRef]
  47. P. Verghese, D. G. Pelli, “The information capacity of visual attention,” Vision Res. 32, 983–995 (1992).
    [CrossRef] [PubMed]
  48. C. Chubb, G. Sperling, “Drift-balanced random stimuli: a general basis for studying non-Fourier motion perception,” J. Opt. Soc. Am. A 5, 1986–2007 (1988).
    [CrossRef] [PubMed]
  49. H. R. Wilson, P. Ferrera, C. Yo, “A psychophysically motivated model for two-dimensional motion perception,” Vision Res. 9, 79–97 (1992).
  50. S. C. Dakin, I. Mareschal, “Sensitivity to contrast modulation depends on carrier spatial frequency and orientation,” Vision Res. 40, 311–329 (2000).
    [CrossRef] [PubMed]
  51. I. Mareschal, C. L. Baker, “Cortical processing of second-order motion,” Visual Neurosci., 3, 527–540 (1999).
  52. J. J. Knierim, D. C. van Essen, “Neuronal responses to static texture patterns in area V1 of the alert macaque monkey,” J. Neurophysiol. 67, 961–980 (1992).
    [PubMed]

2000 (3)

T. S. Meese, C. B. Williams, “Probability summation for multiple patches of luminance modulation,” Vision Res. 40, 2101–2113 (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]

S. J. M. Rainville, F. A. A. Kingdom, “The functional role of oriented spatial filters in the perception of mirror symmetry,” Vision Res. 40, 2621–2644 (2000).
[CrossRef]

1999 (6)

A. Gorea, T. V. Papathomas, “Local versus global contrasts in texture segregation,” J. Opt. Soc. Am. A 16, 728–741 (1999).
[CrossRef]

I. Mareschal, C. L. Baker, “Cortical processing of second-order motion,” Visual Neurosci., 3, 527–540 (1999).

U. Polat, C. W. Tyler, “What pattern the eye sees best,” Vision Res. 39, 887–895 (1999).
[CrossRef] [PubMed]

P. Verghese, S. N. J. Watnmaniuk, S. P. McKee, N. M. Grzywacz, “Local motion detectors cannot account for the detectability of an extended trajectory in noise,” Vision Res. 39, 19–30 (1999).
[CrossRef] [PubMed]

F. A. Kingdom, D. R. Keeble, “On the mechanism for scale invariance in orientation-defined textures,” Vision Res. 39, 1477–1489 (1999).
[CrossRef] [PubMed]

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

1998 (2)

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

M. J. Morgan, R. M. Ward, E. Castet, “Visual search for a tilted target: tests of spatial uncertainty models,” Q. J. Exp. Psychology A 51, 347–370 (1998).
[CrossRef]

1997 (7)

R. F. Hess, S. C. Dakin, “Absence of contour linking in peripheral vision,” Nature (London) 390, 602–604 (1997).
[CrossRef]

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

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

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

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

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]

J. S. Joseph, M. M. Chun, K. Nakayama, “Attentional requirements in a ‘preattentive’ feature search task,” Nature 387, 805–807 (1997).
[CrossRef] [PubMed]

1996 (2)

S. He, P. Cavanagh, J. Intriligator, “Attentional resolution and the locus of visual awareness,” Nature 383, 334–347 (1996).
[CrossRef] [PubMed]

P. Verghese, L. S. Stone, “Perceived visual speed constrained by image segmentation,” Nature 381, 161–163 (1996).
[CrossRef] [PubMed]

1993 (1)

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 (3)

J. J. Knierim, D. C. van Essen, “Neuronal responses to static texture patterns in area V1 of the alert macaque monkey,” J. Neurophysiol. 67, 961–980 (1992).
[PubMed]

P. Verghese, D. G. Pelli, “The information capacity of visual attention,” Vision Res. 32, 983–995 (1992).
[CrossRef] [PubMed]

H. R. Wilson, P. Ferrera, C. Yo, “A psychophysically motivated model for two-dimensional motion perception,” Vision Res. 9, 79–97 (1992).

1991 (3)

M. S. Landy, J. R. Bergen, “Texture segregation and orientation gradient,” Vision Res. 31, 679–691 (1991).
[CrossRef] [PubMed]

D. C. Burr, S. A. Wijesundra, “Orientation discrimination depends on spatial frequency,” Vision Res. 31, 1449–1452 (1991).
[CrossRef] [PubMed]

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

1990 (3)

D. W. Heeley, H. M. Buchanan-Smith, “Recognition of stimulus orientation,” Vision Res. 32, 719–743 (1990).

A. Bovik, M. Clark, W. Geisler, “Multi-channel texture analysis using localised spatial filters,” IEEE Trans. Pattern Anal. Mach. Intell. 12, 55–73 (1990).
[CrossRef]

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

1989 (1)

I. Fogel, D. Sagi, “Gabor filters as texture discriminator,” Biol. Cybern. 61, 103–113 (1989).
[CrossRef]

1988 (1)

1987 (3)

D. Sagi, B. Julesz, “Short-range limitation on detection of feature differences,” Spatial Vision 2, 39–49 (1987).
[CrossRef] [PubMed]

R. J. Watt, R. F. Hess, “Spatial information and uncertainty in anisometropic amblyopia,” Vision Res. 27, 661–674 (1987).
[CrossRef] [PubMed]

D. W. Heeley, “Spatial frequency discrimination for sinewave gratings with random, bandpass frequency modulation: evidence for averaging in spatial acuity,” Spatial Vision 2, 317–335 (1987).
[CrossRef] [PubMed]

1986 (1)

1985 (3)

A. J. J. Ahumada, A. B. Watson, “Equivalent-noise model for contrast detection and discrimination,” J. Opt. Soc. Am. A 2, 1133–1139 (1985).
[CrossRef] [PubMed]

H. C. Nothdurft, C. Y. Li, “Texture discrimination: representation of orientation and luminance differences in cells of the cat striate cortex,” Vision Res. 25, 99–113 (1985).
[CrossRef] [PubMed]

H. C. Nothdurft, “Sensitivity for structure gradient in texture discrimination tasks,” Vision Res. 25, 1957–1968 (1985).
[CrossRef] [PubMed]

1984 (1)

Y. Y. Zeevi, S. S. Mangoubi, “Vernier acuity with noisy lines: estimation of relative position uncertainty,” Biol. Cybern. 50, 371–376 (1984).
[CrossRef] [PubMed]

1983 (1)

R. J. Watt, M. J. Morgan, “The recognition and representation of edge blur: evidence for spatial primitives in human vision,” Vision Res. 23, 1465–1477 (1983).
[CrossRef] [PubMed]

1982 (1)

A. B. Watson, “Summation of grating patches indicates many types of detectors at one retinal location,” Vision Res. 22, 17–25 (1982).
[CrossRef]

1981 (2)

R. J. Watt, D. Andrews, “APE: Adaptive probit estimation of psychometric functions,” Current Psychol. Rev. 1, 205–214 (1981).
[CrossRef]

J. G. Robson, N. Graham, “Probability summation and regional variation in contrast sensitivity across the visual field,” Vision Res. 21, 409–418 (1981).
[CrossRef] [PubMed]

1978 (1)

E. R. Howell, R. F. Hess, “The functional area for summation to threshold for sinusoidal gratings,” Vision Res. 18, 369–374 (1978).
[CrossRef] [PubMed]

1962 (1)

D. H. Hubel, T. N. Wiesel, “Receptive fields, binocular interaction and function architecture in the cat’s visual cortex,” J. Physiol. 160, 106–154 (1962).
[PubMed]

1957 (1)

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

1956 (1)

H. B. Barlow, “Retinal noise and absolute threshold,” J. Opt. Soc. Am. A 46, 634–639 (1956).
[CrossRef]

Ahumada, A. J. J.

Andrews, D.

R. J. Watt, D. Andrews, “APE: Adaptive probit estimation of psychometric functions,” Current Psychol. Rev. 1, 205–214 (1981).
[CrossRef]

Baker, C. L.

I. Mareschal, C. L. Baker, “Cortical processing of second-order motion,” Visual Neurosci., 3, 527–540 (1999).

Barlow, H. B.

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

H. B. Barlow, “Retinal noise and absolute threshold,” J. Opt. Soc. Am. A 46, 634–639 (1956).
[CrossRef]

Bergen, J. R.

M. S. Landy, J. R. Bergen, “Texture segregation and orientation gradient,” Vision Res. 31, 679–691 (1991).
[CrossRef] [PubMed]

J. R. Bergen, M. S. Landy, “Computational modeling of visual texture segmentation,” in Computational Models of Visual Processing, M. S. Landy, J. A. Movshon, eds. (MIT Press, Cambridge, Mass., 1991).

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]

Bovik, A.

A. Bovik, M. Clark, W. Geisler, “Multi-channel texture analysis using localised spatial filters,” IEEE Trans. Pattern Anal. Mach. Intell. 12, 55–73 (1990).
[CrossRef]

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, p. 235–242 (1997).
[CrossRef]

D. W. Heeley, H. M. Buchanan-Smith, “Recognition of stimulus orientation,” Vision Res. 32, 719–743 (1990).

Burr, D. C.

D. C. Burr, S. A. Wijesundra, “Orientation discrimination depends on spatial frequency,” Vision Res. 31, 1449–1452 (1991).
[CrossRef] [PubMed]

Castet, E.

M. J. Morgan, R. M. Ward, E. Castet, “Visual search for a tilted target: tests of spatial uncertainty models,” Q. J. Exp. Psychology A 51, 347–370 (1998).
[CrossRef]

Cavanagh, P.

S. He, P. Cavanagh, J. Intriligator, “Attentional resolution and the locus of visual awareness,” Nature 383, 334–347 (1996).
[CrossRef] [PubMed]

Chubb, C.

Chun, M. M.

J. S. Joseph, M. M. Chun, K. Nakayama, “Attentional requirements in a ‘preattentive’ feature search task,” Nature 387, 805–807 (1997).
[CrossRef] [PubMed]

Clark, M.

A. Bovik, M. Clark, W. Geisler, “Multi-channel texture analysis using localised spatial filters,” IEEE Trans. Pattern Anal. Mach. Intell. 12, 55–73 (1990).
[CrossRef]

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, p. 235–242 (1997).
[CrossRef]

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

R. F. Hess, S. C. Dakin, “Absence of contour linking in peripheral vision,” Nature (London) 390, 602–604 (1997).
[CrossRef]

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

Dosher, B. A.

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

Ferrera, P.

H. R. Wilson, P. Ferrera, C. Yo, “A psychophysically motivated model for two-dimensional motion perception,” Vision Res. 9, 79–97 (1992).

Field, D. J.

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]

Fogel, I.

I. Fogel, D. Sagi, “Gabor filters as texture discriminator,” Biol. Cybern. 61, 103–113 (1989).
[CrossRef]

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]

Geisler, W.

A. Bovik, M. Clark, W. Geisler, “Multi-channel texture analysis using localised spatial filters,” IEEE Trans. Pattern Anal. Mach. Intell. 12, 55–73 (1990).
[CrossRef]

Gorea, A.

Graham, N.

J. G. Robson, N. Graham, “Probability summation and regional variation in contrast sensitivity across the visual field,” Vision Res. 21, 409–418 (1981).
[CrossRef] [PubMed]

Graham, N. V. S.

N. V. S. Graham, Visual Pattern Analyzers (Oxford U. Press, New York, 1989).

Grzywacz, N. M.

P. Verghese, S. N. J. Watnmaniuk, S. P. McKee, N. M. Grzywacz, “Local motion detectors cannot account for the detectability of an extended trajectory in noise,” Vision Res. 39, 19–30 (1999).
[CrossRef] [PubMed]

Hayes, A.

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]

He, S.

S. He, P. Cavanagh, J. Intriligator, “Attentional resolution and the locus of visual awareness,” Nature 383, 334–347 (1996).
[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, p. 235–242 (1997).
[CrossRef]

D. W. Heeley, H. M. Buchanan-Smith, “Recognition of stimulus orientation,” Vision Res. 32, 719–743 (1990).

D. W. Heeley, “Spatial frequency discrimination for sinewave gratings with random, bandpass frequency modulation: evidence for averaging in spatial acuity,” Spatial Vision 2, 317–335 (1987).
[CrossRef] [PubMed]

Hess, R. F.

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

R. F. Hess, S. C. Dakin, “Absence of contour linking in peripheral vision,” Nature (London) 390, 602–604 (1997).
[CrossRef]

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. J. Watt, R. F. Hess, “Spatial information and uncertainty in anisometropic amblyopia,” Vision Res. 27, 661–674 (1987).
[CrossRef] [PubMed]

E. R. Howell, R. F. Hess, “The functional area for summation to threshold for sinusoidal gratings,” Vision Res. 18, 369–374 (1978).
[CrossRef] [PubMed]

Howell, E. R.

E. R. Howell, R. F. Hess, “The functional area for summation to threshold for sinusoidal gratings,” Vision Res. 18, 369–374 (1978).
[CrossRef] [PubMed]

Hubel, D. H.

D. H. Hubel, T. N. Wiesel, “Receptive fields, binocular interaction and function architecture in the cat’s visual cortex,” J. Physiol. 160, 106–154 (1962).
[PubMed]

Intriligator, J.

S. He, P. Cavanagh, J. Intriligator, “Attentional resolution and the locus of visual awareness,” Nature 383, 334–347 (1996).
[CrossRef] [PubMed]

Joseph, J. S.

J. S. Joseph, M. M. Chun, K. Nakayama, “Attentional requirements in a ‘preattentive’ feature search task,” Nature 387, 805–807 (1997).
[CrossRef] [PubMed]

Julesz, B.

D. Sagi, B. Julesz, “Short-range limitation on detection of feature differences,” Spatial Vision 2, 39–49 (1987).
[CrossRef] [PubMed]

Keeble, D. R.

F. A. Kingdom, D. R. Keeble, “On the mechanism for scale invariance in orientation-defined textures,” Vision Res. 39, 1477–1489 (1999).
[CrossRef] [PubMed]

Kingdom, F. A.

F. A. Kingdom, D. R. Keeble, “On the mechanism for scale invariance in orientation-defined textures,” Vision Res. 39, 1477–1489 (1999).
[CrossRef] [PubMed]

Kingdom, F. A. A.

S. J. M. Rainville, F. A. A. Kingdom, “The functional role of oriented spatial filters in the perception of mirror symmetry,” Vision Res. 40, 2621–2644 (2000).
[CrossRef]

Knierim, J. J.

J. J. Knierim, D. C. van Essen, “Neuronal responses to static texture patterns in area V1 of the alert macaque monkey,” J. Neurophysiol. 67, 961–980 (1992).
[PubMed]

Landy, M. S.

M. S. Landy, J. R. Bergen, “Texture segregation and orientation gradient,” Vision Res. 31, 679–691 (1991).
[CrossRef] [PubMed]

J. R. Bergen, M. S. Landy, “Computational modeling of visual texture segmentation,” in Computational Models of Visual Processing, M. S. Landy, J. A. Movshon, eds. (MIT Press, Cambridge, Mass., 1991).

Li, C. Y.

H. C. Nothdurft, C. Y. Li, “Texture discrimination: representation of orientation and luminance differences in cells of the cat striate cortex,” Vision Res. 25, 99–113 (1985).
[CrossRef] [PubMed]

Lu, Z. L.

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

Malik, J.

Mangoubi, S. S.

Y. Y. Zeevi, S. S. Mangoubi, “Vernier acuity with noisy lines: estimation of relative position uncertainty,” Biol. Cybern. 50, 371–376 (1984).
[CrossRef] [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, “Cortical processing of second-order motion,” Visual Neurosci., 3, 527–540 (1999).

Mayer, M. J.

McKee, S. P.

P. Verghese, S. N. J. Watnmaniuk, S. P. McKee, N. M. Grzywacz, “Local motion detectors cannot account for the detectability of an extended trajectory in noise,” Vision Res. 39, 19–30 (1999).
[CrossRef] [PubMed]

Meese, T. S.

T. S. Meese, C. B. Williams, “Probability summation for multiple patches of luminance modulation,” Vision Res. 40, 2101–2113 (2000).
[CrossRef] [PubMed]

Morgan, M. J.

M. J. Morgan, R. M. Ward, E. Castet, “Visual search for a tilted target: tests of spatial uncertainty models,” Q. J. Exp. Psychology A 51, 347–370 (1998).
[CrossRef]

R. J. Watt, M. J. Morgan, “The recognition and representation of edge blur: evidence for spatial primitives in human vision,” Vision Res. 23, 1465–1477 (1983).
[CrossRef] [PubMed]

Nakayama, K.

J. S. Joseph, M. M. Chun, K. Nakayama, “Attentional requirements in a ‘preattentive’ feature search task,” Nature 387, 805–807 (1997).
[CrossRef] [PubMed]

Nothdurft, H. C.

H. C. Nothdurft, “Sensitivity for structure gradient in texture discrimination tasks,” Vision Res. 25, 1957–1968 (1985).
[CrossRef] [PubMed]

H. C. Nothdurft, C. Y. Li, “Texture discrimination: representation of orientation and luminance differences in cells of the cat striate cortex,” Vision Res. 25, 99–113 (1985).
[CrossRef] [PubMed]

Papathomas, T. V.

Pelli, D. G.

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

P. Verghese, D. G. Pelli, “The information capacity of visual attention,” Vision Res. 32, 983–995 (1992).
[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, “The quantum efficiency of vision,” in Vision Coding and Efficiency, C. Blakemore, ed. (Cambridge U. Press, Cambridge, UK, 1990).

Perona, P.

Polat, U.

U. Polat, C. W. Tyler, “What pattern the eye sees best,” Vision Res. 39, 887–895 (1999).
[CrossRef] [PubMed]

Rainville, S. J. M.

S. J. M. Rainville, F. A. A. Kingdom, “The functional role of oriented spatial filters in the perception of mirror symmetry,” Vision Res. 40, 2621–2644 (2000).
[CrossRef]

Robson, J. G.

J. G. Robson, N. Graham, “Probability summation and regional variation in contrast sensitivity across the visual field,” Vision Res. 21, 409–418 (1981).
[CrossRef] [PubMed]

Sagi, D.

I. Fogel, D. Sagi, “Gabor filters as texture discriminator,” Biol. Cybern. 61, 103–113 (1989).
[CrossRef]

D. Sagi, B. Julesz, “Short-range limitation on detection of feature differences,” Spatial Vision 2, 39–49 (1987).
[CrossRef] [PubMed]

Sperling, G.

Stone, L. S.

P. Verghese, L. S. Stone, “Perceived visual speed constrained by image segmentation,” Nature 381, 161–163 (1996).
[CrossRef] [PubMed]

Tyler, C. W.

van Essen, D. C.

J. J. Knierim, D. C. van Essen, “Neuronal responses to static texture patterns in area V1 of the alert macaque monkey,” J. Neurophysiol. 67, 961–980 (1992).
[PubMed]

Verghese, P.

P. Verghese, S. N. J. Watnmaniuk, S. P. McKee, N. M. Grzywacz, “Local motion detectors cannot account for the detectability of an extended trajectory in noise,” Vision Res. 39, 19–30 (1999).
[CrossRef] [PubMed]

P. Verghese, L. S. Stone, “Perceived visual speed constrained by image segmentation,” Nature 381, 161–163 (1996).
[CrossRef] [PubMed]

P. Verghese, D. G. Pelli, “The information capacity of visual attention,” Vision Res. 32, 983–995 (1992).
[CrossRef] [PubMed]

Ward, R. M.

M. J. Morgan, R. M. Ward, E. Castet, “Visual search for a tilted target: tests of spatial uncertainty models,” Q. J. Exp. Psychology A 51, 347–370 (1998).
[CrossRef]

Watnmaniuk, S. N. J.

P. Verghese, S. N. J. Watnmaniuk, S. P. McKee, N. M. Grzywacz, “Local motion detectors cannot account for the detectability of an extended trajectory in noise,” Vision Res. 39, 19–30 (1999).
[CrossRef] [PubMed]

Watson, A. B.

A. J. J. Ahumada, A. B. Watson, “Equivalent-noise model for contrast detection and discrimination,” J. Opt. Soc. Am. A 2, 1133–1139 (1985).
[CrossRef] [PubMed]

A. B. Watson, “Summation of grating patches indicates many types of detectors at one retinal location,” Vision Res. 22, 17–25 (1982).
[CrossRef]

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, R. F. Hess, “Spatial information and uncertainty in anisometropic amblyopia,” Vision Res. 27, 661–674 (1987).
[CrossRef] [PubMed]

R. J. Watt, M. J. Morgan, “The recognition and representation of edge blur: evidence for spatial primitives in human vision,” Vision Res. 23, 1465–1477 (1983).
[CrossRef] [PubMed]

R. J. Watt, D. Andrews, “APE: Adaptive probit estimation of psychometric functions,” Current Psychol. Rev. 1, 205–214 (1981).
[CrossRef]

R. J. Watt, Understanding Vision (Academic Press, London, UK, 1991).

Wiesel, T. N.

D. H. Hubel, T. N. Wiesel, “Receptive fields, binocular interaction and function architecture in the cat’s visual cortex,” J. Physiol. 160, 106–154 (1962).
[PubMed]

Wijesundra, S. A.

D. C. Burr, S. A. Wijesundra, “Orientation discrimination depends on spatial frequency,” Vision Res. 31, 1449–1452 (1991).
[CrossRef] [PubMed]

Williams, C. B.

T. S. Meese, C. B. Williams, “Probability summation for multiple patches of luminance modulation,” Vision Res. 40, 2101–2113 (2000).
[CrossRef] [PubMed]

Wilson, H. R.

H. R. Wilson, P. Ferrera, C. Yo, “A psychophysically motivated model for two-dimensional motion perception,” Vision Res. 9, 79–97 (1992).

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, p. 235–242 (1997).
[CrossRef]

Yo, C.

H. R. Wilson, P. Ferrera, C. Yo, “A psychophysically motivated model for two-dimensional motion perception,” Vision Res. 9, 79–97 (1992).

Zeevi, Y. Y.

Y. Y. Zeevi, S. S. Mangoubi, “Vernier acuity with noisy lines: estimation of relative position uncertainty,” Biol. Cybern. 50, 371–376 (1984).
[CrossRef] [PubMed]

Zhang, L.

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

Biol. Cybern. (2)

I. Fogel, D. Sagi, “Gabor filters as texture discriminator,” Biol. Cybern. 61, 103–113 (1989).
[CrossRef]

Y. Y. Zeevi, S. S. Mangoubi, “Vernier acuity with noisy lines: estimation of relative position uncertainty,” Biol. Cybern. 50, 371–376 (1984).
[CrossRef] [PubMed]

Current Psychol. Rev. (1)

R. J. Watt, D. Andrews, “APE: Adaptive probit estimation of psychometric functions,” Current Psychol. Rev. 1, 205–214 (1981).
[CrossRef]

IEEE Trans. Pattern Anal. Mach. Intell. (1)

A. Bovik, M. Clark, W. Geisler, “Multi-channel texture analysis using localised spatial filters,” IEEE Trans. Pattern Anal. Mach. Intell. 12, 55–73 (1990).
[CrossRef]

J. Neurophysiol. (1)

J. J. Knierim, D. C. van Essen, “Neuronal responses to static texture patterns in area V1 of the alert macaque monkey,” J. Neurophysiol. 67, 961–980 (1992).
[PubMed]

J. Opt. Soc. Am. A (6)

J. Physiol. (1)

D. H. Hubel, T. N. Wiesel, “Receptive fields, binocular interaction and function architecture in the cat’s visual cortex,” J. Physiol. 160, 106–154 (1962).
[PubMed]

J. Physiol. (London) (1)

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

Nature (3)

P. Verghese, L. S. Stone, “Perceived visual speed constrained by image segmentation,” Nature 381, 161–163 (1996).
[CrossRef] [PubMed]

S. He, P. Cavanagh, J. Intriligator, “Attentional resolution and the locus of visual awareness,” Nature 383, 334–347 (1996).
[CrossRef] [PubMed]

J. S. Joseph, M. M. Chun, K. Nakayama, “Attentional requirements in a ‘preattentive’ feature search task,” Nature 387, 805–807 (1997).
[CrossRef] [PubMed]

Nature (London) (1)

R. F. Hess, S. C. Dakin, “Absence of contour linking in peripheral vision,” Nature (London) 390, 602–604 (1997).
[CrossRef]

Q. J. Exp. Psychology A (1)

M. J. Morgan, R. M. Ward, E. Castet, “Visual search for a tilted target: tests of spatial uncertainty models,” Q. J. Exp. Psychology A 51, 347–370 (1998).
[CrossRef]

Spatial Vision (5)

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

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

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. Sagi, B. Julesz, “Short-range limitation on detection of feature differences,” Spatial Vision 2, 39–49 (1987).
[CrossRef] [PubMed]

D. W. Heeley, “Spatial frequency discrimination for sinewave gratings with random, bandpass frequency modulation: evidence for averaging in spatial acuity,” Spatial Vision 2, 317–335 (1987).
[CrossRef] [PubMed]

Vision Res. (24)

H. R. Wilson, P. Ferrera, C. Yo, “A psychophysically motivated model for two-dimensional motion perception,” Vision Res. 9, 79–97 (1992).

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. J. Watt, R. F. Hess, “Spatial information and uncertainty in anisometropic amblyopia,” Vision Res. 27, 661–674 (1987).
[CrossRef] [PubMed]

R. J. Watt, M. J. Morgan, “The recognition and representation of edge blur: evidence for spatial primitives in human vision,” Vision Res. 23, 1465–1477 (1983).
[CrossRef] [PubMed]

T. S. Meese, C. B. Williams, “Probability summation for multiple patches of luminance modulation,” Vision Res. 40, 2101–2113 (2000).
[CrossRef] [PubMed]

E. R. Howell, R. F. Hess, “The functional area for summation to threshold for sinusoidal gratings,” Vision Res. 18, 369–374 (1978).
[CrossRef] [PubMed]

J. G. Robson, N. Graham, “Probability summation and regional variation in contrast sensitivity across the visual field,” Vision Res. 21, 409–418 (1981).
[CrossRef] [PubMed]

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

F. A. Kingdom, D. R. Keeble, “On the mechanism for scale invariance in orientation-defined textures,” Vision Res. 39, 1477–1489 (1999).
[CrossRef] [PubMed]

H. C. Nothdurft, “Sensitivity for structure gradient in texture discrimination tasks,” Vision Res. 25, 1957–1968 (1985).
[CrossRef] [PubMed]

M. S. Landy, J. R. Bergen, “Texture segregation and orientation gradient,” Vision Res. 31, 679–691 (1991).
[CrossRef] [PubMed]

U. Polat, C. W. Tyler, “What pattern the eye sees best,” Vision Res. 39, 887–895 (1999).
[CrossRef] [PubMed]

P. Verghese, S. N. J. Watnmaniuk, S. P. McKee, N. M. Grzywacz, “Local motion detectors cannot account for the detectability of an extended trajectory in noise,” Vision Res. 39, 19–30 (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]

A. B. Watson, “Summation of grating patches indicates many types of detectors at one retinal location,” Vision Res. 22, 17–25 (1982).
[CrossRef]

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

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

S. J. M. Rainville, F. A. A. Kingdom, “The functional role of oriented spatial filters in the perception of mirror symmetry,” Vision Res. 40, 2621–2644 (2000).
[CrossRef]

P. Verghese, D. G. Pelli, “The information capacity of visual attention,” Vision Res. 32, 983–995 (1992).
[CrossRef] [PubMed]

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

D. W. Heeley, H. M. Buchanan-Smith, “Recognition of stimulus orientation,” Vision Res. 32, 719–743 (1990).

D. C. Burr, S. A. Wijesundra, “Orientation discrimination depends on spatial frequency,” Vision Res. 31, 1449–1452 (1991).
[CrossRef] [PubMed]

H. C. Nothdurft, C. Y. Li, “Texture discrimination: representation of orientation and luminance differences in cells of the cat striate cortex,” Vision Res. 25, 99–113 (1985).
[CrossRef] [PubMed]

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

Visual Neurosci. (1)

I. Mareschal, C. L. Baker, “Cortical processing of second-order motion,” Visual Neurosci., 3, 527–540 (1999).

Other (4)

D. G. Pelli, “The quantum efficiency of vision,” in Vision Coding and Efficiency, C. Blakemore, ed. (Cambridge U. Press, Cambridge, UK, 1990).

R. J. Watt, Understanding Vision (Academic Press, London, UK, 1991).

J. R. Bergen, M. S. Landy, “Computational modeling of visual texture segmentation,” in Computational Models of Visual Processing, M. S. Landy, J. A. Movshon, eds. (MIT Press, Cambridge, Mass., 1991).

N. V. S. Graham, Visual Pattern Analyzers (Oxford U. Press, New York, 1989).

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Figures (8)

Fig. 1
Fig. 1

(a) Texture composed of 16 Gabor micropatterns with orientations drawn from a Gaussian random distribution with a mean of 92° (2° clockwise from vertical) and a standard deviation of 4°. Observers’ ability to accurately discriminate mean orientation in the presence of considerable orientation variance necessitates pooling of multiple orientation estimates. (b) A “pop-out” stimulus. A single element, tilted 15° from vertical, is embedded in a field of vertical distractors. The presence of the discrepant element could be signaled by a simple local orientation statistic (such as the mean). (c–e) Examples of the stimuli used in the experiments (contrast enhanced for the purpose of reproduction). Each is composed of 64 Gabor elements randomly distributed within a circular region with orientations drawn from a Gaussian distribution with a mean of 90° and a standard deviation equal to (c) 0.5°, (d) 4°, and (e) 23°. Subjects’ ability to estimate mean orientation deteriorates with increasing orientation variance, allowing one to estimate the effective internal noise and the number of orientation samples being employed. The textures shown in (c–e) fall in the midrange of the patch sizes, densities, and numerosities tested.

Fig. 2
Fig. 2

Examples of the stimuli; the orientation of elements is Gaussian distributed with a mean of 90° and a standard deviation of 4°. (a, b) Examples from the fixed radius condition. Textures are composed of (a) 16 elements and (b) 256 elements falling within a circular region with a radius of 3.5°. (c, d) Examples from the fixed density condition. Textures are composed of (c) 16 elements with a 1.7° radius and (d) 256 elements with a 7.0° radius. Thus density is fixed at 5.1 elements per degree squared. (e, f) Examples from the fixed number condition. Textures are composed of 256 elements falling in a region of radius (e) 1.7° and (f) 7.0°.

Fig. 3
Fig. 3

Texture density (measured in elements per square degree of visual angle) as a function of the patch radius and the number of elements. The boxed cells give the spatial parameters of the textures used in the 13 subconditions tested.

Fig. 4
Fig. 4

Data from the fixed-size experiment (experiment 1). Each graph shows the effect of orientation variability (bandwidth) on one subject’s judgment of the mean orientation of a texture patch as a function of the number of Gabor microelements constituting the texture. For subjects AM and SCD, Gabor elements were uniformly randomly distributed within a circular window with a radius of 3.5°. For subject JS, Gabors were distributed with a two-dimensional Gaussian spatial distribution. Density covaried with numerosity in this condition. The fits shown are for the variance model described by Eq. 1 Notice that the parameters derived from the fit (shown in the legend) indicate that both the number of orientation samples used and the internal noise increase with the numerosity and density, although efficiency drops.

Fig. 5
Fig. 5

Data from the fixed-density experiment (experiment 2). Each graph shows the effect of orientation variability on an observer’s orientation thresholds measured with textures composed of various numbers of elements. In this condition the size of patches was covaried with numerosity so that the densities of all patches tested were similar. Note that texture density was uniform for subjects AM and SCD but that subject JS was tested with Gaussian-distributed elements. Parameters derived from the variance-summation model are given in the legend to each graph and indicate that, as for the fixed patch-radius condition, progressively more samples are employed as the numerosity and patch size increase. However, there appears to be much less variation in the estimated internal noise across subconditions, compared with experiment 1.

Fig. 6
Fig. 6

Data from the fixed-numerosity experiment (experiment 3). Graphs show the effect of orientation variability on a mean orientation judgment as a function of the size of the texture patch. Because the number of texture elements was fixed, patch density covaried with patch size. Unlike previous conditions, parameters derived from fitting the variance model indicate that subjects are now employing a broadly similar number of orientation samples over approximately eight octaves of densities and patch sizes. This suggests that it is the number of samples presented to subjects that determines their sampling strategy regardless of size or density.

Fig. 7
Fig. 7

Summary of parameters derived from the model fits. The top row shows estimates of the number of samples employed by observer, and the bottom row shows the associated internal noise parameter. (a) and (d) fixed size condition, (b) and (e) fixed density-condition, and (c) and (f) the fixed-numerosity condition. Notice in (c) that there is little change in the number of samples employed for a fixed number of elements, and in (e) that there is little change in estimated internal noise for a fixed texture density.

Fig. 8
Fig. 8

Orientation bandwidth of the textures used (standard deviation of best-fitting Gaussian fit to Fourier power spectra) as a function of the orientation standard deviation and the number of elements (2–2048) constituting each texture. Note that bandwidth is largely constant as a function of the number of elements, except for the lowest density/highest orientation standard deviation combinations.

Equations (1)

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σobs=σint2+σext2/n1/2,

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