Abstract

We investigated sensitivity to orientation modulation using visual stimuli with bandpass filtered noise carriers. We characterized the relationship between the spatial parameters of the modulator and the carrier using a 2-AFC detection task. The relationship between these two parameters is potentially informative of the underlying coupling between first- and second-stage filtering mechanisms, which, in turn, may bear on the interrelationship between striate and extrastriate cortical processing. Our previous experiments on analogous motion stimuli found an optimum sensitivity when the ratio of the carrier and modulator spatial frequency parameters (r) was approximately ten. The current results do not exhibit an optimum sensitivity at a given value of the ratio r. Previous experiments involving second-order modulation sensitivity show an inconsistent range of estimates of optimum sensitivity at values of r between 5 and 50. Our results, using a complementary approach, confirm these discrepancies, demonstrating that the coupling between carrier and modulator frequency parameters depends on a number of stimulus-specific factors, such as contrast sensitivity, stimulus eccentricity, and absolute values of the carrier and modulator spatial frequency parameters. We show that these observations are true for a stimulus limited in eccentricity and that this orientation-modulated stimulus does not exhibit scale invariance. Such processing can not be modeled by a generic filter–rectify–filter model.

© 2011 Optical Society of America

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    [CrossRef] [PubMed]
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  24. F. A. A. Kingdom and D. R. T. Keeble, “On the mechanism for scale invariance in orientation-defined textures,” Vision Res. 39, 1477–1489 (1999).
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  27. D. C. V. Essen and J. H. R. Maunsell, “Hierarchical organization and functional streams in the visual cortex,” Trends Neurosci. 6, 370–375 (1983).
    [CrossRef]
  28. J. H. Jamar and J. J. Koenderink, “Contrast detection and detection of contrast modulation for noise gratings,” Vision Res. 25, 511–521 (1985).
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    [CrossRef]
  32. R. J. Snowden, “Orientation bandwidth: the effect of spatial and temporal frequency,” Vision Res. 32, 1965–1974 (1992).
    [CrossRef] [PubMed]
  33. J. P. Thomas and J. Gille, “Bandwidths of orientation channels in human vision,” J. Opt. Soc. Am. 69, 652–660 (1979).
    [CrossRef] [PubMed]
  34. N. Graham, “Non-linearities in texture segregation,” Ciba Found. Symp. 184, 309–322; discussion, 323-338 (1994).
    [CrossRef] [PubMed]
  35. J. R. Bergen and M. S. Landy, “Computational modeling of visual texture segregation,” in Computational Models of Visual Processing, M.S.Landy and J.A.Movshon, eds. (MIT, 1991), pp. 253–271.
  36. D. Sagi, “Detection of an orientation singularity in Gabor textures: effect of signal density and spatial-frequency,” Vision Res. 30, 1377–1388 (1990).
    [CrossRef] [PubMed]
  37. F. A. Kingdom and D. R. Keeble, “Luminance spatial frequency differences facilitate the segmentation of superimposed textures,” Vision Res. 40, 1077–1087 (2000).
    [CrossRef] [PubMed]
  38. S. C. Dakin, C. B. Williams, and R. F. Hess, “The interaction of first- and second-order cues to orientation,” Vision Res. 39, 2867–2884 (1999).
    [CrossRef] [PubMed]
  39. I. Motoyoshi and S. Y. Nishida, “Cross-orientation summation in texture segregation,” Vision Res. 44, 2567–2576 (2004).
    [CrossRef] [PubMed]
  40. F. A. A. Kingdom and D. R. T. Keeble, “A linear systems approach to the detection of both abrupt and smooth spatial variations in orientation-defined textures,” Vision Res. 36, 409–420 (1996).
    [CrossRef] [PubMed]

2010 (1)

A. I. Meso and R. F. Hess, “Visual motion gradient sensitivity shows scale invariant spatial frequency and speed tuning properties,” Vision Res. 50, 1475–1485 (2010).
[CrossRef] [PubMed]

2004 (1)

I. Motoyoshi and S. Y. Nishida, “Cross-orientation summation in texture segregation,” Vision Res. 44, 2567–2576 (2004).
[CrossRef] [PubMed]

2003 (1)

A. J. Schofield and M. A. Georgeson, “Sensitivity to contrast modulation: the spatial frequency dependence of second-order vision,” Vision Res. 43, 243–259 (2003).
[CrossRef] [PubMed]

2002 (1)

M. S. Landy and I. Oruc, “Properties of second-order spatial frequency channels,” Vision Res. 42, 2311–2329 (2002).
[CrossRef] [PubMed]

2001 (1)

C. L. Baker, Jr., and I. Mareschal, “Processing of second-order stimuli in the visual cortex,” Prog. Brain Res. 134, 171–191(2001).
[CrossRef] [PubMed]

2000 (2)

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

F. A. Kingdom and D. R. Keeble, “Luminance spatial frequency differences facilitate the segmentation of superimposed textures,” Vision Res. 40, 1077–1087 (2000).
[CrossRef] [PubMed]

1999 (3)

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

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

A. J. Schofield and 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]

1996 (3)

Y. X. Zhou and 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]

F. A. A. Kingdom and D. R. T. Keeble, “A linear systems approach to the detection of both abrupt and smooth spatial variations in orientation-defined textures,” Vision Res. 36, 409–420 (1996).
[CrossRef] [PubMed]

F. A. Kingdom and D. R. Keeble, “A linear systems approach to the detection of both abrupt and smooth spatial variations in orientation-defined textures,” Vision Res. 36, 409–420 (1996).
[CrossRef] [PubMed]

1995 (2)

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

F. A. Kingdom, D. Keeble, and B. Moulden, “Sensitivity to orientation modulation in micropattern-based textures,” Vision Res. 35, 79–91 (1995).
[CrossRef] [PubMed]

1994 (4)

T. Ledgeway and A. T. Smith, “Evidence for separate motion-detecting mechanisms for first- and second-order motion in human vision,” Vision Res. 34, 2727–2740 (1994).
[CrossRef] [PubMed]

A. B. Watson and M. P. Eckert, “Motion-contrast sensitivity: visibility of motion gradients of various spatial frequencies,” J. Opt. Soc. Am. A 11, 496–505 (1994).
[CrossRef]

R. F. Hess and L. M. Wilcox, “Linear and nonlinear filtering in stereopsis,” Vision Res. 34, 2431–2438 (1994).
[CrossRef] [PubMed]

N. Graham, “Non-linearities in texture segregation,” Ciba Found. Symp. 184, 309–322; discussion, 323-338 (1994).
[CrossRef] [PubMed]

1992 (2)

R. J. Snowden, “Orientation bandwidth: the effect of spatial and temporal frequency,” Vision Res. 32, 1965–1974 (1992).
[CrossRef] [PubMed]

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

1991 (1)

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

1990 (1)

D. Sagi, “Detection of an orientation singularity in Gabor textures: effect of signal density and spatial-frequency,” Vision Res. 30, 1377–1388 (1990).
[CrossRef] [PubMed]

1989 (2)

A. Sutter, J. Beck, and N. Graham, “Contrast and spatial variables in texture segregation: testing a simple spatial-frequency channels model,” Percept. Psychophys. 46, 312–332(1989).
[CrossRef] [PubMed]

C. Chubb and G. Sperling, “Two motion perception mechanisms revealed through distance-driven reversal of apparent motion,” Proc. Natl. Acad. Sci. USA 86, 2985–2989 (1989).
[CrossRef] [PubMed]

1988 (1)

J. R. Bergen and E. H. Adelson, “Early vision and texture perception,” Nature 333, 363–364 (1988).
[CrossRef] [PubMed]

1986 (1)

M. R. Turner, “Texture discrimination by Gabor functions,” Biol. Cybern. 55, 71–82 (1986).
[PubMed]

1985 (2)

1983 (2)

D. C. V. Essen and J. H. R. Maunsell, “Hierarchical organization and functional streams in the visual cortex,” Trends Neurosci. 6, 370–375 (1983).
[CrossRef]

J. H. Jamar and J. J. Koenderink, “Sine-wave gratings: scale invariance and spatial integration at suprathreshold contrast,” Vision Res. 23, 805–810 (1983).
[CrossRef] [PubMed]

1980 (1)

D. Marr and E.-C. Hildreth, “Theory of edge detection,” Proc. R. Soc. B 207, 187–217 (1980).
[CrossRef]

1979 (1)

1974 (1)

R. L. Devalois, H. Morgan, and D. M. Snodderly, “Psychophysical studies of monkey vision. 3. Spatial luminance contrast sensitivity tests of macaque and human observers,” Vision Res. 14, 75–81 (1974).
[CrossRef]

1968 (1)

F. W. Campbell and J. R. Robson, “Application of Fourier analysis to the visibility of gratings,” J. Physiol. 197, 551–566 (1968).
[PubMed]

1946 (1)

D. Gabor, “Theory of communication. Part 1: The analysis of information,” J. Inst. Elect. Eng. 93, 429–441 (1946).
[CrossRef]

Adelson, E. H.

J. R. Bergen and E. H. Adelson, “Early vision and texture perception,” Nature 333, 363–364 (1988).
[CrossRef] [PubMed]

Baker, C. L.

C. L. Baker, Jr., and I. Mareschal, “Processing of second-order stimuli in the visual cortex,” Prog. Brain Res. 134, 171–191(2001).
[CrossRef] [PubMed]

Y. X. Zhou and 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]

Beck, J.

A. Sutter, J. Beck, and N. Graham, “Contrast and spatial variables in texture segregation: testing a simple spatial-frequency channels model,” Percept. Psychophys. 46, 312–332(1989).
[CrossRef] [PubMed]

Bergen, J. R.

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

J. R. Bergen and E. H. Adelson, “Early vision and texture perception,” Nature 333, 363–364 (1988).
[CrossRef] [PubMed]

J. R. Bergen and M. S. Landy, “Computational modeling of visual texture segregation,” in Computational Models of Visual Processing, M.S.Landy and J.A.Movshon, eds. (MIT, 1991), pp. 253–271.

Campbell, F. W.

F. W. Campbell and J. R. Robson, “Application of Fourier analysis to the visibility of gratings,” J. Physiol. 197, 551–566 (1968).
[PubMed]

Chubb, C.

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

C. Chubb and G. Sperling, “Two motion perception mechanisms revealed through distance-driven reversal of apparent motion,” Proc. Natl. Acad. Sci. USA 86, 2985–2989 (1989).
[CrossRef] [PubMed]

Dakin, S. C.

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

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

Daugman, J. G.

DeValois, K. K.

R. L. DeValois and K. K. DeValois, Spatial Vision (Oxford Univ. Press, 1988).

Devalois, R. L.

R. L. Devalois, H. Morgan, and D. M. Snodderly, “Psychophysical studies of monkey vision. 3. Spatial luminance contrast sensitivity tests of macaque and human observers,” Vision Res. 14, 75–81 (1974).
[CrossRef]

R. L. DeValois and K. K. DeValois, Spatial Vision (Oxford Univ. Press, 1988).

Eckert, M. P.

Essen, D. C. V.

D. C. V. Essen and J. H. R. Maunsell, “Hierarchical organization and functional streams in the visual cortex,” Trends Neurosci. 6, 370–375 (1983).
[CrossRef]

Ferrera, V. P.

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

Gabor, D.

D. Gabor, “Theory of communication. Part 1: The analysis of information,” J. Inst. Elect. Eng. 93, 429–441 (1946).
[CrossRef]

Georgeson, M. A.

A. J. Schofield and M. A. Georgeson, “Sensitivity to contrast modulation: the spatial frequency dependence of second-order vision,” Vision Res. 43, 243–259 (2003).
[CrossRef] [PubMed]

A. J. Schofield and 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]

Gille, J.

Graham, N.

N. Graham, “Non-linearities in texture segregation,” Ciba Found. Symp. 184, 309–322; discussion, 323-338 (1994).
[CrossRef] [PubMed]

A. Sutter, J. Beck, and N. Graham, “Contrast and spatial variables in texture segregation: testing a simple spatial-frequency channels model,” Percept. Psychophys. 46, 312–332(1989).
[CrossRef] [PubMed]

Graham, N. V. S.

N. V. S. Graham, Visual Pattern Analyzers (Oxford Univ. Press, 1989).
[CrossRef]

Hess, R. F.

A. I. Meso and R. F. Hess, “Visual motion gradient sensitivity shows scale invariant spatial frequency and speed tuning properties,” Vision Res. 50, 1475–1485 (2010).
[CrossRef] [PubMed]

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

R. F. Hess and L. M. Wilcox, “Linear and nonlinear filtering in stereopsis,” Vision Res. 34, 2431–2438 (1994).
[CrossRef] [PubMed]

Hildreth, E.-C.

D. Marr and E.-C. Hildreth, “Theory of edge detection,” Proc. R. Soc. B 207, 187–217 (1980).
[CrossRef]

Jamar, J. H.

J. H. Jamar and J. J. Koenderink, “Contrast detection and detection of contrast modulation for noise gratings,” Vision Res. 25, 511–521 (1985).
[CrossRef] [PubMed]

J. H. Jamar and J. J. Koenderink, “Sine-wave gratings: scale invariance and spatial integration at suprathreshold contrast,” Vision Res. 23, 805–810 (1983).
[CrossRef] [PubMed]

Keeble, D.

F. A. Kingdom, D. Keeble, and B. Moulden, “Sensitivity to orientation modulation in micropattern-based textures,” Vision Res. 35, 79–91 (1995).
[CrossRef] [PubMed]

Keeble, D. R.

F. A. Kingdom and D. R. Keeble, “Luminance spatial frequency differences facilitate the segmentation of superimposed textures,” Vision Res. 40, 1077–1087 (2000).
[CrossRef] [PubMed]

F. A. Kingdom and D. R. Keeble, “A linear systems approach to the detection of both abrupt and smooth spatial variations in orientation-defined textures,” Vision Res. 36, 409–420 (1996).
[CrossRef] [PubMed]

Keeble, D. R. T.

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

F. A. A. Kingdom and D. R. T. Keeble, “A linear systems approach to the detection of both abrupt and smooth spatial variations in orientation-defined textures,” Vision Res. 36, 409–420 (1996).
[CrossRef] [PubMed]

Kingdom, F. A.

F. A. Kingdom and D. R. Keeble, “Luminance spatial frequency differences facilitate the segmentation of superimposed textures,” Vision Res. 40, 1077–1087 (2000).
[CrossRef] [PubMed]

F. A. Kingdom and D. R. Keeble, “A linear systems approach to the detection of both abrupt and smooth spatial variations in orientation-defined textures,” Vision Res. 36, 409–420 (1996).
[CrossRef] [PubMed]

F. A. Kingdom, D. Keeble, and B. Moulden, “Sensitivity to orientation modulation in micropattern-based textures,” Vision Res. 35, 79–91 (1995).
[CrossRef] [PubMed]

Kingdom, F. A. A.

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

F. A. A. Kingdom and D. R. T. Keeble, “A linear systems approach to the detection of both abrupt and smooth spatial variations in orientation-defined textures,” Vision Res. 36, 409–420 (1996).
[CrossRef] [PubMed]

Koenderink, J. J.

J. H. Jamar and J. J. Koenderink, “Contrast detection and detection of contrast modulation for noise gratings,” Vision Res. 25, 511–521 (1985).
[CrossRef] [PubMed]

J. H. Jamar and J. J. Koenderink, “Sine-wave gratings: scale invariance and spatial integration at suprathreshold contrast,” Vision Res. 23, 805–810 (1983).
[CrossRef] [PubMed]

Landy, M. S.

M. S. Landy and I. Oruc, “Properties of second-order spatial frequency channels,” Vision Res. 42, 2311–2329 (2002).
[CrossRef] [PubMed]

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

J. R. Bergen and M. S. Landy, “Computational modeling of visual texture segregation,” in Computational Models of Visual Processing, M.S.Landy and J.A.Movshon, eds. (MIT, 1991), pp. 253–271.

Ledgeway, T.

T. Ledgeway and A. T. Smith, “Evidence for separate motion-detecting mechanisms for first- and second-order motion in human vision,” Vision Res. 34, 2727–2740 (1994).
[CrossRef] [PubMed]

Mareschal, I.

C. L. Baker, Jr., and I. Mareschal, “Processing of second-order stimuli in the visual cortex,” Prog. Brain Res. 134, 171–191(2001).
[CrossRef] [PubMed]

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

Marr, D.

D. Marr and E.-C. Hildreth, “Theory of edge detection,” Proc. R. Soc. B 207, 187–217 (1980).
[CrossRef]

D. Marr, Vision: A Computational Investigation into the Human Representation and Processing of Visual Information (Freeman, 1982).
[PubMed]

Maunsell, J. H. R.

D. C. V. Essen and J. H. R. Maunsell, “Hierarchical organization and functional streams in the visual cortex,” Trends Neurosci. 6, 370–375 (1983).
[CrossRef]

Meso, A. I.

A. I. Meso and R. F. Hess, “Visual motion gradient sensitivity shows scale invariant spatial frequency and speed tuning properties,” Vision Res. 50, 1475–1485 (2010).
[CrossRef] [PubMed]

Morgan, H.

R. L. Devalois, H. Morgan, and D. M. Snodderly, “Psychophysical studies of monkey vision. 3. Spatial luminance contrast sensitivity tests of macaque and human observers,” Vision Res. 14, 75–81 (1974).
[CrossRef]

Motoyoshi, I.

I. Motoyoshi and S. Y. Nishida, “Cross-orientation summation in texture segregation,” Vision Res. 44, 2567–2576 (2004).
[CrossRef] [PubMed]

Moulden, B.

F. A. Kingdom, D. Keeble, and B. Moulden, “Sensitivity to orientation modulation in micropattern-based textures,” Vision Res. 35, 79–91 (1995).
[CrossRef] [PubMed]

Nishida, S. Y.

I. Motoyoshi and S. Y. Nishida, “Cross-orientation summation in texture segregation,” Vision Res. 44, 2567–2576 (2004).
[CrossRef] [PubMed]

Oruc, I.

M. S. Landy and I. Oruc, “Properties of second-order spatial frequency channels,” Vision Res. 42, 2311–2329 (2002).
[CrossRef] [PubMed]

Robson, J. R.

F. W. Campbell and J. R. Robson, “Application of Fourier analysis to the visibility of gratings,” J. Physiol. 197, 551–566 (1968).
[PubMed]

Sagi, D.

D. Sagi, “Detection of an orientation singularity in Gabor textures: effect of signal density and spatial-frequency,” Vision Res. 30, 1377–1388 (1990).
[CrossRef] [PubMed]

Schofield, A. J.

A. J. Schofield and M. A. Georgeson, “Sensitivity to contrast modulation: the spatial frequency dependence of second-order vision,” Vision Res. 43, 243–259 (2003).
[CrossRef] [PubMed]

A. J. Schofield and 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]

Smith, A. T.

T. Ledgeway and A. T. Smith, “Evidence for separate motion-detecting mechanisms for first- and second-order motion in human vision,” Vision Res. 34, 2727–2740 (1994).
[CrossRef] [PubMed]

Snodderly, D. M.

R. L. Devalois, H. Morgan, and D. M. Snodderly, “Psychophysical studies of monkey vision. 3. Spatial luminance contrast sensitivity tests of macaque and human observers,” Vision Res. 14, 75–81 (1974).
[CrossRef]

Snowden, R. J.

R. J. Snowden, “Orientation bandwidth: the effect of spatial and temporal frequency,” Vision Res. 32, 1965–1974 (1992).
[CrossRef] [PubMed]

Sperling, G.

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

C. Chubb and G. Sperling, “Two motion perception mechanisms revealed through distance-driven reversal of apparent motion,” Proc. Natl. Acad. Sci. USA 86, 2985–2989 (1989).
[CrossRef] [PubMed]

Sutter, A.

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Figures (8)

Fig. 1
Fig. 1

Three example stimulus intervals. (a) Full-field high-carrier-contrast (L) image with f m = 4   cyc / im , f c = 0.17   cyc / pix with horizontal modulators. (b) Full-field low-carrier-contrast image with no modulators ( m = 0 ) and f c = 0.17   cyc / pix , which serves as the reference interval. (c) Ring stimulus with horizontal modulators of f m = 8   cyc / im and a carrier frequency of f c = 0.25   cyc / pix . Image centered spatial units are given rather than retinal units because stimuli were tested over a range of viewing distances.

Fig. 2
Fig. 2

Thresholds of luminance contrast (L) at which participants can just detect the modulation in the stimulus plotted against the ratio r of carrier-to-modulator frequencies ( f c / f m ) for three participants for condition A plotted with black circles and condition B plotted with white circles. In (a)–(c), for each participant, the plots show the averaged results following four experimental blocks, each fitted with a logistic function to find a threshold. The error bars indicate the standard deviation. (a) Threshold functions for author participant AM. Curves show separate functions, with a low optimal ratio of r for condition A and a flat tuning for condition B. (b) Thresholds for naïve participant AY showing separable functions with lower ratios of r showing higher sensitivity under condition A compared with condition B. (c) Thresholds for naïve participant PC showing separable functions with a bandpass tuning to low ratios under condition A compared with a largely flat tuning function under condition B. (d) Group data showing the mean and standard error (SE as error bars) calculated from the individual data shown in (a)–(c). The group data for both conditions show separate functions with shapes that seem to be modulated by different mechanisms. Condition A shows much higher sensitivity than condition B at the point corresponding to low ratios of f c / f m around 2   cyc / deg . Condition B shows a broadly bandpass function.

Fig. 3
Fig. 3

Thresholds of both luminance (L) and modulator (m) contrasts at which participants can just detect the modulation in the stimulus plotted against orientation bandwidth tested as a control. Data shown are the means from three participants (AM, AY, and PC) with the SE used for the error bars. Standard stimulus parameters were used, defined in Subsection 3A of the text, with Eq. (2) used to set the bandwidth. (a) Luminance contrast (L) thresholds and (b) modulator contrast (m) thresholds; both appear flat within the range of 10 60 ° of orientation bandwidth tested.

Fig. 4
Fig. 4

Threshold modulator contrasts (m) at which participants can just detect the modulation in the stimulus plotted against the ratio, r ( f c / f m ), for three participants showing both condition A (black circles), in which f c was varied while f m was fixed, and condition B (white circles) in which f m was varied while f c was fixed. In (a)–(c), plots show the individual participant averaged results from repeated experimental blocks each fitted with a logistic function estimate of the threshold. Error bars indicate the standard deviation. (a) Author participant AM shows no difference between the conditions. (b) Naïve participant JB shows a broad bandpass-shaped function for condition B but a flat function for condition A. (c) Naïve participant PC shows little difference between the conditions. (d) Group data showing the mean and SE calculated from individual data in (a)–(c). Data show no measurable difference between conditions and almost flat functions over the range tested.

Fig. 5
Fig. 5

Luminance contrast (L) thresholds at which participants can just detect the modulation in the stimulus plotted against the carrier-to-modulator frequency ratio, r ( f c / f m ) for three participants for condition A, plotted with black circles, and condition B, with white circles for all plots, using a stimulus presented within a limited eccentricity outside of the fovea. In (a)–(c), plots show the individual participant averaged results from experimental blocks each fitted with a logistic function estimate of the threshold. Error bars indicate the standard deviation. (a) Participant AM showed a slight difference between the conditions with an optimum that appeared only under condition A at a ratio of about 6. (b) For participant AY, condition A showed an optimum sensitivity shifted toward lower ratios while condition B showed an optimum shifted toward higher ratios. (c) Similarly, for participant PC, condition A showed an optimum sensitivity shifted toward lower ratios than condition B. (d) Group data showing the mean and SE calculated from individual data in (a)–(c). Data for condition A found maximum sensitivity at a low ratio r ( f c / f m < 8 ), corresponding to a carrier frequency of around 2   cyc / deg . Condition B showed more of a low-pass tuning (with respect to f m ) to higher ratios ( f c / f m > 16 ), corresponding to spatial frequency of less than 0.2   cyc / deg .

Fig. 6
Fig. 6

Modulator contrast (m) thresholds at which participants can just detect the modulation in the stimulus as a function of the ratio r ( f c / f m ) for the ring stimuli presented at a limited eccentricity to three participants. Two conditions were tested, condition A (black circles) and condition B (white circles). In (a)–(c), plots show the individual participant-averaged results from experimental blocks each fitted with a logistic function estimate of the threshold. Error bars indicate the standard deviation. (a) Participant AM, threshold functions showing a flat curve for condition B, which does not overlap with that of condition A. (b) Participant JB shows a broadly bandpass function for condition B, which does not fully overlap with the curve from condition A. (c) Participant PC shows a largely flat function under condition B and different from condition A. (d) Group data showing the mean and SE calculated from individual data in (a)–(c). For all observers, the two conditions showed differences from each other, evident in the group average. Condition A consistently showed a dip corresponding to reduced sensitivity for all participants at r = 10 .

Fig. 7
Fig. 7

Modulation contrast (m) thresholds at which participants can just detect the modulation in the stimulus plotted against the ratio, r ( f c / f m ) , compared for three viewing distances (28, 57, and 230 cm ), corresponding to retinal image sizes of 36, 18, and 4.6 ° plotted for three participants. In (a)–(c), plots show the individual participant-averaged results from experimental blocks each fitted with a logistic function estimate of the threshold. Error bars indicate the standard deviation. (a) Participant AM shows differences between all three curves. (b) Participant JB showed differences between all three functions, although the 28 and 57 cm are nearly superimposed. (c) Participant PC shows differences between the tuning functions for 28 and 57 cm from those measured at 230 cm . (d) Group data showing the mean and SE calculated from individual data in (a)–(c). For the group results, the tuning functions at different distances are not found to have the same basic shape.

Fig. 8
Fig. 8

Curve fits for the psychophysically obtained threshold functions against r. The circles show the mean threshold value for three participants measured psychophysically and the error bars are standard errors. The white circles in (a)–(d) show data collected under condition A, where f c was varied, while the filled circles show data collected under condition B, where f m was varied (see Appendix A and Subsection 2B2 for explanation). (e) Data in which the viewing distance was varied. (f) A summary table of the values of R 2 for the various fits, with best fits highlighted in gray where they were obtained. A description of the fitting procedure and the details of the fitted cases can be found in the text of Appendix A.

Equations (5)

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DoG ( x , y ) = 1 2 π σ a 2 exp ( x 2 + y 2 2 σ a 2 ) 1 2 π k 2 σ a 2 exp ( x 2 + y 2 2 k 2 σ a 2 ) .
Gs ( r ) = 1 σ b 2 π exp ( r 2 2 σ b 2 ) .
C n ( x , y ) = c n ( x , y ) * DoG ( x , y ) [ ISOTROPIC:BANDPASS ] , d n ( x , y ) = r = C n ( x r × cos θ n , y r × sin θ n ) × Gs ( r ) r [ ORIENTATION ] .
m 1 ( y ) = [ 0.5 × ( 1 + m × sin ( 2 π f m y ) ) ] 0.5 , m 2 ( y ) = [ 0.5 × ( 1 m × sin ( 2 π f m y ) ) ] 0.5 .
L S ( x , y ) = L O ( 1 + L × w s ( x , y ) × [ m 1 ( y ) d 1 ( x , y ) + m 2 ( y ) d 2 ( x , y ) ] ) .

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