Abstract

The existence of nonoriented cells but not of sustained orthogonal masking for achromatic stimuli led to an investigation of the spatial-frequency (SF) tuning of sustained nonoriented color units. For this purpose the Red–Green channel was isolated by the minimum flicker and hue cancellation techniques. Chromatic contrast sensitivity functions (CSF’s), threshold elevation (TE) curves, and contrast nonlinearities (TE-versus-mask-contrast curves) were measured with spatially localized vertical color tests and sinusoidal orthogonal color masks by the method of constant stimuli under Gaussian temporal presentation. Results show that (1) color CSF’s are a low-pass function of SF, whereas TE curves are a bandpass function of mask SF, and (2) a minimum of six SF-tuned color mechanisms (one low-pass and five bandpass functions of SF, with peak SF’s of 0.13, 0.5, 2, 4, and 8 cycles per degree and bandwidths of 3.9, 4.4, 2.9, 2.1, 1.1, and 1.2 octaves), similar to oblique-masking color mechanisms, are extracted by the multiple-mechanism model. These data imply that (1) most of the SF tuning of the broadly oriented color units is already present in the circularly symmetric units, and (2) the latter may be an input to the former.

© 1998 Optical Society of America

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References

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1997 (1)

1996 (2)

M. J. Sankeralli, K. T. Mullen, “Estimation of the L-, M-, and S-cone weights of the postreceptoral detection mechanisms,” J. Opt. Soc. Am. A 13, 906–915 (1996).
[CrossRef]

V. A. Billock, “Consequence of retinal color coding for cortical color decoding,” Science 274, 2118–2119 (1996) [also see the responses by D. M. Dacey, Science 274, 2119 (1996) and R. H. Masland, Science 274, 2119 (1996), and references therein]; D. M. Dacey, B. B. Lee, D. K. Stafford, J. Pokorny, V. C. Smith, “Horizontal cells of the primate retina: cone specificity without spectral opponency,” Science 271, 656 (1996); R. H. Masland, “Unscrambling color vision,” Science 271, 616 (1996); C. R. Ingling, E. Martinez-Uriegas, “The spatiotemporal properties of the r–g x-cell channel,” Vision Res. 25, 33–38 (1985).
[CrossRef] [PubMed]

1995 (1)

F. Crick, C. Koch, “Are we aware of neural activity in primary visual cortex?” Nature (London) 375, 121–123 (1995); M. Gur, M. Snodderly, “A dissociation between brain activity and perception: chromatically opponent cortical neurons signal chromatic flicker that is not perceived,” Vision Res. 37, 377–382 (1997).
[CrossRef] [PubMed]

1994 (5)

M. A. Webster, J. D. Mollon, “The influence of contrast adaptation on color appearance,” Vision Res. 34, 1993–2020 (1994).
[CrossRef] [PubMed]

A. Chaparro, C. F. Stromeyer, R. E. Kronauer, R. T. Eskew, “Separable Red–Green and luminance detectors for small flashes,” Vision Res. 34, 751–762 (1994), and the relevant references therein; C. F. Stromeyer, R. E. Kronauer, A. Ryu, A. Chaparro, R. T. Eskew, “Contribution of human long-wave and middle-wave cones to motion detection,” J. Physiol. (London) 485, 221–243 (1995); C. R. Cole, T. J. Hine, W. Mcilhagga, “Estimation of linear detection mechanisms for stimuli of medium spatial frequency,” Vision Res. 34, 1267-1278 (1994).
[CrossRef] [PubMed]

R. L. P. Vimal, R. Pandey, “Interaction between the spatial frequency tuned mechanisms of the Red–Green channel and those of the achromatic channel,” Invest. Ophthalmol. Visual Sci. Suppl. 35, 1370 (1994).

J. M. Foley, “Human luminance pattern-vision mechanisms: masking experiments require a new model,” J. Opt. Soc. Am. A 11, 1710–1719 (1994); A. B. Bonds, “Role of inhibition in the specification of orientation selectivity of cells in the cat striate cortex,” Visual Neurosci. 2, 41–55 (1989); D. J. Heeger, “Normalization of cell responses in cat visual cortex,” Visual Neurosci. 9, 181–197 (1992), and references therein.
[CrossRef]

K. T. Mullen, M. A. Losada, “Evidence for separate pathways for color and luminance detection mechanisms,” J. Opt. Soc. Am. A 11, 3136–3151 (1994); K. T. Mullen, S. J. Cropper, M. A. Losada, “Absence of linear subthreshold summation between Red–Green and luminance mechanisms over a wide range of spatio-temporal conditions,” Vision Res. 37, 1157–1165 (1997); M. A. Losada, K. T. Mullen, “The spatial tuning of chromatic mechanisms identified by simultaneous masking,” Vision Res. 34, 331–334 (1994).
[CrossRef] [PubMed]

1993 (5)

C. W. Tyler, L. Barghout, L. L. Kontsevich, “Surprises in analyzing the mechanisms underlying threshold elevation functions,” Invest. Ophthalmol. Visual Sci. Suppl. 34, 819 (1993); L. L. Kontsevich, C. W. Tyler, “A simple explanation of how contrast affects performance in detection and discrimination tasks below 3 c/deg,” Invest. Ophthalmol. Visual Sci. Suppl. 34, 782 (1993); J. Yang, Q. Xiaofeng, W. Makous, “Zero frequency masking and a model of contrast sensitivity,” Vision Res. 35, 1965–1978 (1995).
[CrossRef] [PubMed]

R. Pandey, R. L. P. Vimal, “Threshold elevation curves for the Red–Green channel estimated by oblique masking,” Invest. Ophthalmol. Visual Sci. Suppl. 34, 751 (1993); R. L. P. Vimal, R. Pandey, “Spatial frequency tuned mechanisms of the Red–Green channel estimated by oblique masking,” Soc. Neurosci. Abstr. 20 (Part 2), 1580 (1994). The MSC analysis for the oblique-masking color mechanisms is available from the author.

J. J. Atick, Z. Li, A. N. Redlich, “What does post-adaptation color appearance reveal about cortical color representation?,” Vision Res. 33, 123–129 (1993), and references therein.
[CrossRef] [PubMed]

R. Pandey, R. L. P. Vimal, “Contrast matching in the Red–Green channel: flattening effect and color-contrast-constancy,” Soc. Neurosci. Abstr. 19 (Part 3), 1802 (1993).

R. L. P. Vimal, R. Pandey, “Measurement of peak spatial frequency and bandwidth of threshold elevation curves of non-oriented units of the Red–Green channel by horizontal masking,” Invest. Ophthalmol. Visual Sci. Suppl. 34, 782 (1993).

1992 (1)

M. Gur, V. Akri, “Isoluminant stimuli may not expose the full contribution of color to visual functioning: spatial contrast sensitivity measurements indicate interaction between color and luminance processing,” Vision Res. 32, 1253–1262 (1992).
[CrossRef] [PubMed]

1991 (1)

R. T. Born, R. B. H. Tootell, “Spatial frequency tuning of single units in macaque supragranular striate cortex,” Proc. Natl. Acad. Sci. USA 88, 7066–7070 (1991).
[CrossRef] [PubMed]

1990 (3)

P. H. Schiller, N. K. Logothetis, E. R. Charles, “Functions of the colour-opponent and broad-band channels of the visual system,” Nature (London) 343, 68–70 (1990).
[CrossRef]

P. Flanagan, P. Cavanagh, O. E. Favreau, “Independent orientation-selective mechanisms for the cardinal direction of color space,” Vision Res. 30, 769–778 (1990).
[CrossRef]

P. Lennie, J. Krauskopf, G. Sclar, “Chromatic mechanisms in striate cortex of macaque,” J. Neurosci. 10, 649–669 (1990).
[PubMed]

1989 (2)

R. L. P. Vimal, J. M. Pokorny, V. C. Smith, S. K. Shevell, “Foveal cone thresholds,” Vision Res. 29, 61–78 (1989).
[CrossRef] [PubMed]

M. S. Silverman, D. H. Grosof, R. L. De Valois, S. D. Elfar, “Spatial-frequency organization in primate striate cortex,” Proc. Natl. Acad. Sci. USA 86, 711–715 (1989); D. P. Edwards, K. P. Purpura, E. Kaplan, “Contrast sensitivity and spatial frequency response of primate cortical neurons in and around the cytochrome oxidase blobs,” Vision Res. 35, 1501–1523 (1995).
[CrossRef] [PubMed]

1988 (4)

P. Lennie, M. D’Zmura, “Mechanisms of color vision,” Crit. Rev. Neurobiol. 3, 333–400 (1988).
[PubMed]

E. Switkes, A. Bradley, K. K. De Valois, “Contrast dependence and mechanisms of masking interactions among chromatic and luminance gratings,” J. Opt. Soc. Am. A 5, 1149–1162 (1988).
[CrossRef] [PubMed]

R. L. P. Vimal, “Spatial frequency discriminations: inphase and counter-phase photopic conditions compared,” Invest. Ophthalmol. Visual Sci. 29, 448 (1988); R. L. P. Vimal, R. Pandey, “Spatial frequency discrimination for inphase and counter-phase red–green stimuli: effect of apparent motion,” Soc. Neurosci. Abstr. 15 (Part 1), p. 625, No. 249.13 (1989).

D. Y. Ts’o, C. D. Gilbert, “The organization of chromatic and spatial interaction in the primate striate cortex,” J. Neurosci. 8, 1712–1727 (1988).

1987 (2)

M. A. Georgeson, J. M. Georgeson, “Facilitation and masking of briefly presented gratings: time-course and contrast dependence,” Vision Res. 27, 369–379 (1987).
[CrossRef] [PubMed]

M. S. Livingstone, D. H. Hubel, “Psychophysical evidence for separate channels for the perception of form, color, movement, and depth,” J. Neurosci. 7, 3416–3468 (1987) and references therein. The question mark (?) in the text (Section 1), presumably representing the uncertainty in the findings, was originally used by these authors.
[PubMed]

1986 (1)

H. R. Wilson, “Responses of spatial mechanisms can explain hyperacuity,” Vision Res. 26, 453–469 (1986).
[CrossRef] [PubMed]

1985 (4)

H. R. Wilson, “A model for direction selectivity in threshold motion perception,” Biol. Cybern. 51, 213–222 (1985).
[CrossRef] [PubMed]

V. P. Ferrera, H. R. Wilson, “Spatial frequency tuning of transient non-oriented units,” Vision Res. 25, 67–72 (1985); G. C. Phillips, H. R. Wilson, “Orientation bandwidths of spatial mechanisms measured by masking,” J. Opt. Soc. Am. A 1, 226–232 (1984).
[CrossRef] [PubMed]

C. R. Michael, “Laminar segregation of color cells in the monkey’s striate cortex,” Vision Res. 25, 415–423 (1985).
[CrossRef]

K. T. Mullen, “The contrast sensitivity of human colour vision to red/green and blue/yellow chromatic gratings,” J. Physiol. (London) 359, 381–400 (1985).

1984 (3)

H. R. Wilson, D. J. Gelb, “Modified line-element theory for spatial-frequency and width discrimination,” J. Opt. Soc. Am. A 1, 124–131 (1984).
[CrossRef] [PubMed]

L. G. Thorell, R. L. De Valois, D. G. Albrecht, “Spatial mapping of monkey V1 cells with pure color and luminance stimuli,” Vision Res. 24, 751–769 (1984).
[CrossRef] [PubMed]

W. H. Swanson, H. R. Wilson, S. C. Geise, “Contrast matching data predicted from contrast increment thresholds,” Vision Res. 24, 63–75 (1984); W. H. Swanson, M. A. Georgeson, H. R. Wilson, “Comparison of contrast responses across spatial mechanisms,” Vision Res. 28, 457–459 (1988) and references therein.
[CrossRef] [PubMed]

1983 (2)

S. M. Zeki, “The distribution of wavelength and orientation selectivity in different areas of monkey visual cortex,” Proc. R. Soc. London, Ser. B 207, 239–248 (1983).
[CrossRef]

H. R. Wilson, D. K. McFarlane, G. C. Phillips, “Spatial frequency tuning of orientation selective units estimated by oblique masking,” Vision Res. 23, 873–882 (1983), and references therein.
[CrossRef] [PubMed]

1982 (1)

J. Krauskopf, D. R. Williams, D. W. Heeley, “Cardinal directions of colour space,” Vision Res. 22, 1123–1131 (1982). For cone weightings see J. Krauskopf, H. J. Wu, B. Farell, “Coherence, cardinal directions and higher-order mechanisms,” Vision Res. 36, 1235–1245 (1996).
[CrossRef] [PubMed]

1981 (1)

1980 (3)

J. G. Daugman, “Two-dimensional spectral analysis of cortical receptive field profile,” Vision Res. 20, 847–856 (1980); M. A. Webster, R. L. De Valois, “Relationship between spatial-frequency and orientation tuning of striate-cortex cells,” J. Opt. Soc. Am. A 2, 1124–1132 (1985); R. L. De Valois, “Spatial processing of luminance and color information,” Invest. Ophthalmol. Visual Sci. 17, 834–835 (1978).
[CrossRef] [PubMed]

H. R. Wilson, “A transducer function for threshold and suprathreshold human vision,” Biol. Cybern. 38, 171–178 (1980).
[CrossRef] [PubMed]

A. M. Sillito, J. A. Kemp, J. A. Milson, N. Berardi, “A re-evaluation of the mechanism underlying simple cell orientation selectivity,” Brain Res. 194, 517–520 (1980); R. Hess, K. Negishi, O. Creutzfeldt, “The horizontal spread of intracortical inhibition in the visual cortex,” Exp. Brain Res. 22, 415–419 (1975); D. Allison, V. A. Casagrande, A. B. Bonds, “The influence of input from the lower cortical layers on the orientation tuning of upper layer V1 cells in a primate,” Visual Neurosci. 12, 309–320 (1995).
[CrossRef] [PubMed]

1976 (2)

V. C. Smith, J. M. Pokorny, S. Starr, “Variability of color mixture data. I. Interobserver variability in the unit coordinates,” Vision Res. 16, 1087–1094 (1976); J. M. Pokorny, V. C. Smith, S. Starr, “Variability of color mixture data. II. The effect of field size,” Vision Res. 16, 1087–1094 (1976).
[CrossRef]

stepit is a subroutine (the original method) in J. P. Chandler, “stept: direct research optimization solution of least-squares problems,” Indiana University, Chemistry Department, Quantum Chemistry Program Exchange (QCPE) 11, 307 (1976).

1974 (1)

H. Akaike, “A new look at statistical mode identification,” IEEE Trans. Autom. Control. 19, 716–723 (1974), and references therein. This is used by R. E. Fredericksen, P. J. Bex, F. A. J. Verstraten, “How big is a Gabor patch, and why should we care?” J. Opt. Soc. Am. A 14, 1–12 (1997).
[CrossRef]

1968 (2)

D. H. Hubel, T. N. Wiesel, “Receptive fields and functional architecture in the cat’s visual cortex,” J. Physiol. (London) 195, 215–243 (1968) and references therein.

F. W. Campbell, J. G. Robson, “Application of Fourier analysis to the visibility of gratings,” J. Physiol. (London) 197, 551–566 (1968); C. Blakemore, F. W. Campbell, “On the existence of neurons in the human visual system selectively sensitive to the orientation and size of retinal images,” J. Physiol. (London) 203, 237–260 (1969). For details see H. R. Wilson, “Psychophysical models of spatial vision and hyperacuity,” in Spatial Vision, Vol. 10 of Vision and Visual Dysfunction, D. Regan, ed. (Macmillan, London, 1991), pp. 64–86, and references therein.

1957 (1)

L. M. Hurvich, D. Jameson, “An opponent-process theory of color vision,” Psychol. Rev. 64, 384–404 (1957).
[CrossRef] [PubMed]

Akaike, H.

H. Akaike, “A new look at statistical mode identification,” IEEE Trans. Autom. Control. 19, 716–723 (1974), and references therein. This is used by R. E. Fredericksen, P. J. Bex, F. A. J. Verstraten, “How big is a Gabor patch, and why should we care?” J. Opt. Soc. Am. A 14, 1–12 (1997).
[CrossRef]

Akri, V.

M. Gur, V. Akri, “Isoluminant stimuli may not expose the full contribution of color to visual functioning: spatial contrast sensitivity measurements indicate interaction between color and luminance processing,” Vision Res. 32, 1253–1262 (1992).
[CrossRef] [PubMed]

Albrecht, D. G.

L. G. Thorell, R. L. De Valois, D. G. Albrecht, “Spatial mapping of monkey V1 cells with pure color and luminance stimuli,” Vision Res. 24, 751–769 (1984).
[CrossRef] [PubMed]

Atick, J. J.

J. J. Atick, Z. Li, A. N. Redlich, “What does post-adaptation color appearance reveal about cortical color representation?,” Vision Res. 33, 123–129 (1993), and references therein.
[CrossRef] [PubMed]

Barghout, L.

C. W. Tyler, L. Barghout, L. L. Kontsevich, “Surprises in analyzing the mechanisms underlying threshold elevation functions,” Invest. Ophthalmol. Visual Sci. Suppl. 34, 819 (1993); L. L. Kontsevich, C. W. Tyler, “A simple explanation of how contrast affects performance in detection and discrimination tasks below 3 c/deg,” Invest. Ophthalmol. Visual Sci. Suppl. 34, 782 (1993); J. Yang, Q. Xiaofeng, W. Makous, “Zero frequency masking and a model of contrast sensitivity,” Vision Res. 35, 1965–1978 (1995).
[CrossRef] [PubMed]

Beranek, L.

R. Bolt, L. Beranek, E. Newman, Curve Fitting Commands: RS/Explore User’s Guide (BBN Research System, Cambridge, Mass., 1986), Book 3, pp. 9-1–9-6.

Berardi, N.

A. M. Sillito, J. A. Kemp, J. A. Milson, N. Berardi, “A re-evaluation of the mechanism underlying simple cell orientation selectivity,” Brain Res. 194, 517–520 (1980); R. Hess, K. Negishi, O. Creutzfeldt, “The horizontal spread of intracortical inhibition in the visual cortex,” Exp. Brain Res. 22, 415–419 (1975); D. Allison, V. A. Casagrande, A. B. Bonds, “The influence of input from the lower cortical layers on the orientation tuning of upper layer V1 cells in a primate,” Visual Neurosci. 12, 309–320 (1995).
[CrossRef] [PubMed]

Billock, V. A.

V. A. Billock, “Consequence of retinal color coding for cortical color decoding,” Science 274, 2118–2119 (1996) [also see the responses by D. M. Dacey, Science 274, 2119 (1996) and R. H. Masland, Science 274, 2119 (1996), and references therein]; D. M. Dacey, B. B. Lee, D. K. Stafford, J. Pokorny, V. C. Smith, “Horizontal cells of the primate retina: cone specificity without spectral opponency,” Science 271, 656 (1996); R. H. Masland, “Unscrambling color vision,” Science 271, 616 (1996); C. R. Ingling, E. Martinez-Uriegas, “The spatiotemporal properties of the r–g x-cell channel,” Vision Res. 25, 33–38 (1985).
[CrossRef] [PubMed]

Bolt, R.

R. Bolt, L. Beranek, E. Newman, Curve Fitting Commands: RS/Explore User’s Guide (BBN Research System, Cambridge, Mass., 1986), Book 3, pp. 9-1–9-6.

Born, R. T.

R. T. Born, R. B. H. Tootell, “Spatial frequency tuning of single units in macaque supragranular striate cortex,” Proc. Natl. Acad. Sci. USA 88, 7066–7070 (1991).
[CrossRef] [PubMed]

Bradley, A.

E. Switkes, A. Bradley, K. K. De Valois, “Contrast dependence and mechanisms of masking interactions among chromatic and luminance gratings,” J. Opt. Soc. Am. A 5, 1149–1162 (1988).
[CrossRef] [PubMed]

A. Bradley, E. Switkes, K. K. De Valois, “Orientation and spatial frequency selectivity of adaptation to color and luminance gratings,” Vision Res.28, 841–856 (1988); R. L. De Valois, “Orientation and spatial frequency selectivity: properties and modular organization,” in From Pigments to Perception, A. Valberg, B. B. Lee, eds. (Plenum, New York, 1991), pp. 261–267.
[CrossRef] [PubMed]

Campbell, F. W.

F. W. Campbell, J. G. Robson, “Application of Fourier analysis to the visibility of gratings,” J. Physiol. (London) 197, 551–566 (1968); C. Blakemore, F. W. Campbell, “On the existence of neurons in the human visual system selectively sensitive to the orientation and size of retinal images,” J. Physiol. (London) 203, 237–260 (1969). For details see H. R. Wilson, “Psychophysical models of spatial vision and hyperacuity,” in Spatial Vision, Vol. 10 of Vision and Visual Dysfunction, D. Regan, ed. (Macmillan, London, 1991), pp. 64–86, and references therein.

Cavanagh, P.

P. Flanagan, P. Cavanagh, O. E. Favreau, “Independent orientation-selective mechanisms for the cardinal direction of color space,” Vision Res. 30, 769–778 (1990).
[CrossRef]

Chandler, J. P.

stepit is a subroutine (the original method) in J. P. Chandler, “stept: direct research optimization solution of least-squares problems,” Indiana University, Chemistry Department, Quantum Chemistry Program Exchange (QCPE) 11, 307 (1976).

Chaparro, A.

A. Chaparro, C. F. Stromeyer, R. E. Kronauer, R. T. Eskew, “Separable Red–Green and luminance detectors for small flashes,” Vision Res. 34, 751–762 (1994), and the relevant references therein; C. F. Stromeyer, R. E. Kronauer, A. Ryu, A. Chaparro, R. T. Eskew, “Contribution of human long-wave and middle-wave cones to motion detection,” J. Physiol. (London) 485, 221–243 (1995); C. R. Cole, T. J. Hine, W. Mcilhagga, “Estimation of linear detection mechanisms for stimuli of medium spatial frequency,” Vision Res. 34, 1267-1278 (1994).
[CrossRef] [PubMed]

Charles, E. R.

P. H. Schiller, N. K. Logothetis, E. R. Charles, “Functions of the colour-opponent and broad-band channels of the visual system,” Nature (London) 343, 68–70 (1990).
[CrossRef]

Cohen, J.

J. Welkowitz, R. B. Ewen, J. Cohen, Introductory Statistics for the Behavioral Sciences (Academic, New York, 1976); for standard deviation see pp. 51–58, for standard error see pp. 104–133, for chi-square see pp. 242–257, and for statistical tables see pp. 304–307.

Crick, F.

F. Crick, C. Koch, “Are we aware of neural activity in primary visual cortex?” Nature (London) 375, 121–123 (1995); M. Gur, M. Snodderly, “A dissociation between brain activity and perception: chromatically opponent cortical neurons signal chromatic flicker that is not perceived,” Vision Res. 37, 377–382 (1997).
[CrossRef] [PubMed]

D’Zmura, M.

P. Lennie, M. D’Zmura, “Mechanisms of color vision,” Crit. Rev. Neurobiol. 3, 333–400 (1988).
[PubMed]

Daugman, J. G.

J. G. Daugman, “Two-dimensional spectral analysis of cortical receptive field profile,” Vision Res. 20, 847–856 (1980); M. A. Webster, R. L. De Valois, “Relationship between spatial-frequency and orientation tuning of striate-cortex cells,” J. Opt. Soc. Am. A 2, 1124–1132 (1985); R. L. De Valois, “Spatial processing of luminance and color information,” Invest. Ophthalmol. Visual Sci. 17, 834–835 (1978).
[CrossRef] [PubMed]

De Valois, K. K.

E. Switkes, A. Bradley, K. K. De Valois, “Contrast dependence and mechanisms of masking interactions among chromatic and luminance gratings,” J. Opt. Soc. Am. A 5, 1149–1162 (1988).
[CrossRef] [PubMed]

A. Bradley, E. Switkes, K. K. De Valois, “Orientation and spatial frequency selectivity of adaptation to color and luminance gratings,” Vision Res.28, 841–856 (1988); R. L. De Valois, “Orientation and spatial frequency selectivity: properties and modular organization,” in From Pigments to Perception, A. Valberg, B. B. Lee, eds. (Plenum, New York, 1991), pp. 261–267.
[CrossRef] [PubMed]

De Valois, R. L.

M. S. Silverman, D. H. Grosof, R. L. De Valois, S. D. Elfar, “Spatial-frequency organization in primate striate cortex,” Proc. Natl. Acad. Sci. USA 86, 711–715 (1989); D. P. Edwards, K. P. Purpura, E. Kaplan, “Contrast sensitivity and spatial frequency response of primate cortical neurons in and around the cytochrome oxidase blobs,” Vision Res. 35, 1501–1523 (1995).
[CrossRef] [PubMed]

L. G. Thorell, R. L. De Valois, D. G. Albrecht, “Spatial mapping of monkey V1 cells with pure color and luminance stimuli,” Vision Res. 24, 751–769 (1984).
[CrossRef] [PubMed]

Elfar, S. D.

M. S. Silverman, D. H. Grosof, R. L. De Valois, S. D. Elfar, “Spatial-frequency organization in primate striate cortex,” Proc. Natl. Acad. Sci. USA 86, 711–715 (1989); D. P. Edwards, K. P. Purpura, E. Kaplan, “Contrast sensitivity and spatial frequency response of primate cortical neurons in and around the cytochrome oxidase blobs,” Vision Res. 35, 1501–1523 (1995).
[CrossRef] [PubMed]

Eskew, R. T.

A. Chaparro, C. F. Stromeyer, R. E. Kronauer, R. T. Eskew, “Separable Red–Green and luminance detectors for small flashes,” Vision Res. 34, 751–762 (1994), and the relevant references therein; C. F. Stromeyer, R. E. Kronauer, A. Ryu, A. Chaparro, R. T. Eskew, “Contribution of human long-wave and middle-wave cones to motion detection,” J. Physiol. (London) 485, 221–243 (1995); C. R. Cole, T. J. Hine, W. Mcilhagga, “Estimation of linear detection mechanisms for stimuli of medium spatial frequency,” Vision Res. 34, 1267-1278 (1994).
[CrossRef] [PubMed]

Ewen, R. B.

J. Welkowitz, R. B. Ewen, J. Cohen, Introductory Statistics for the Behavioral Sciences (Academic, New York, 1976); for standard deviation see pp. 51–58, for standard error see pp. 104–133, for chi-square see pp. 242–257, and for statistical tables see pp. 304–307.

Favreau, O. E.

P. Flanagan, P. Cavanagh, O. E. Favreau, “Independent orientation-selective mechanisms for the cardinal direction of color space,” Vision Res. 30, 769–778 (1990).
[CrossRef]

Ferrera, V. P.

V. P. Ferrera, H. R. Wilson, “Spatial frequency tuning of transient non-oriented units,” Vision Res. 25, 67–72 (1985); G. C. Phillips, H. R. Wilson, “Orientation bandwidths of spatial mechanisms measured by masking,” J. Opt. Soc. Am. A 1, 226–232 (1984).
[CrossRef] [PubMed]

Flanagan, P.

P. Flanagan, P. Cavanagh, O. E. Favreau, “Independent orientation-selective mechanisms for the cardinal direction of color space,” Vision Res. 30, 769–778 (1990).
[CrossRef]

Foley, J. M.

Geise, S. C.

W. H. Swanson, H. R. Wilson, S. C. Geise, “Contrast matching data predicted from contrast increment thresholds,” Vision Res. 24, 63–75 (1984); W. H. Swanson, M. A. Georgeson, H. R. Wilson, “Comparison of contrast responses across spatial mechanisms,” Vision Res. 28, 457–459 (1988) and references therein.
[CrossRef] [PubMed]

Gelb, D. J.

Georgeson, J. M.

M. A. Georgeson, J. M. Georgeson, “Facilitation and masking of briefly presented gratings: time-course and contrast dependence,” Vision Res. 27, 369–379 (1987).
[CrossRef] [PubMed]

Georgeson, M. A.

M. A. Georgeson, J. M. Georgeson, “Facilitation and masking of briefly presented gratings: time-course and contrast dependence,” Vision Res. 27, 369–379 (1987).
[CrossRef] [PubMed]

Gilbert, C. D.

D. Y. Ts’o, C. D. Gilbert, “The organization of chromatic and spatial interaction in the primate striate cortex,” J. Neurosci. 8, 1712–1727 (1988).

Grosof, D. H.

M. S. Silverman, D. H. Grosof, R. L. De Valois, S. D. Elfar, “Spatial-frequency organization in primate striate cortex,” Proc. Natl. Acad. Sci. USA 86, 711–715 (1989); D. P. Edwards, K. P. Purpura, E. Kaplan, “Contrast sensitivity and spatial frequency response of primate cortical neurons in and around the cytochrome oxidase blobs,” Vision Res. 35, 1501–1523 (1995).
[CrossRef] [PubMed]

Gur, M.

M. Gur, V. Akri, “Isoluminant stimuli may not expose the full contribution of color to visual functioning: spatial contrast sensitivity measurements indicate interaction between color and luminance processing,” Vision Res. 32, 1253–1262 (1992).
[CrossRef] [PubMed]

Heeley, D. W.

J. Krauskopf, D. R. Williams, D. W. Heeley, “Cardinal directions of colour space,” Vision Res. 22, 1123–1131 (1982). For cone weightings see J. Krauskopf, H. J. Wu, B. Farell, “Coherence, cardinal directions and higher-order mechanisms,” Vision Res. 36, 1235–1245 (1996).
[CrossRef] [PubMed]

Hubel, D. H.

M. S. Livingstone, D. H. Hubel, “Psychophysical evidence for separate channels for the perception of form, color, movement, and depth,” J. Neurosci. 7, 3416–3468 (1987) and references therein. The question mark (?) in the text (Section 1), presumably representing the uncertainty in the findings, was originally used by these authors.
[PubMed]

D. H. Hubel, T. N. Wiesel, “Receptive fields and functional architecture in the cat’s visual cortex,” J. Physiol. (London) 195, 215–243 (1968) and references therein.

Hurvich, L. M.

L. M. Hurvich, D. Jameson, “An opponent-process theory of color vision,” Psychol. Rev. 64, 384–404 (1957).
[CrossRef] [PubMed]

Jameson, D.

L. M. Hurvich, D. Jameson, “An opponent-process theory of color vision,” Psychol. Rev. 64, 384–404 (1957).
[CrossRef] [PubMed]

Kemp, J. A.

A. M. Sillito, J. A. Kemp, J. A. Milson, N. Berardi, “A re-evaluation of the mechanism underlying simple cell orientation selectivity,” Brain Res. 194, 517–520 (1980); R. Hess, K. Negishi, O. Creutzfeldt, “The horizontal spread of intracortical inhibition in the visual cortex,” Exp. Brain Res. 22, 415–419 (1975); D. Allison, V. A. Casagrande, A. B. Bonds, “The influence of input from the lower cortical layers on the orientation tuning of upper layer V1 cells in a primate,” Visual Neurosci. 12, 309–320 (1995).
[CrossRef] [PubMed]

Koch, C.

F. Crick, C. Koch, “Are we aware of neural activity in primary visual cortex?” Nature (London) 375, 121–123 (1995); M. Gur, M. Snodderly, “A dissociation between brain activity and perception: chromatically opponent cortical neurons signal chromatic flicker that is not perceived,” Vision Res. 37, 377–382 (1997).
[CrossRef] [PubMed]

Kontsevich, L. L.

C. W. Tyler, L. Barghout, L. L. Kontsevich, “Surprises in analyzing the mechanisms underlying threshold elevation functions,” Invest. Ophthalmol. Visual Sci. Suppl. 34, 819 (1993); L. L. Kontsevich, C. W. Tyler, “A simple explanation of how contrast affects performance in detection and discrimination tasks below 3 c/deg,” Invest. Ophthalmol. Visual Sci. Suppl. 34, 782 (1993); J. Yang, Q. Xiaofeng, W. Makous, “Zero frequency masking and a model of contrast sensitivity,” Vision Res. 35, 1965–1978 (1995).
[CrossRef] [PubMed]

Krauskopf, J.

P. Lennie, J. Krauskopf, G. Sclar, “Chromatic mechanisms in striate cortex of macaque,” J. Neurosci. 10, 649–669 (1990).
[PubMed]

J. Krauskopf, D. R. Williams, D. W. Heeley, “Cardinal directions of colour space,” Vision Res. 22, 1123–1131 (1982). For cone weightings see J. Krauskopf, H. J. Wu, B. Farell, “Coherence, cardinal directions and higher-order mechanisms,” Vision Res. 36, 1235–1245 (1996).
[CrossRef] [PubMed]

Kronauer, R. E.

A. Chaparro, C. F. Stromeyer, R. E. Kronauer, R. T. Eskew, “Separable Red–Green and luminance detectors for small flashes,” Vision Res. 34, 751–762 (1994), and the relevant references therein; C. F. Stromeyer, R. E. Kronauer, A. Ryu, A. Chaparro, R. T. Eskew, “Contribution of human long-wave and middle-wave cones to motion detection,” J. Physiol. (London) 485, 221–243 (1995); C. R. Cole, T. J. Hine, W. Mcilhagga, “Estimation of linear detection mechanisms for stimuli of medium spatial frequency,” Vision Res. 34, 1267-1278 (1994).
[CrossRef] [PubMed]

Kulikowski, J. J.

J. J. Kulikowski, “What really limits vision? Conceptual limitations to the assessments of visual functions and the role of interacting channels,” in Limits of Vision, Vol. 5 of Vision and Visual Dysfunctions, J. J. Kulikowski, V. Walsh, I. J. Murray, eds. (Macmillan, London, 1991), pp. 286–329.

Lennie, P.

P. Lennie, J. Krauskopf, G. Sclar, “Chromatic mechanisms in striate cortex of macaque,” J. Neurosci. 10, 649–669 (1990).
[PubMed]

P. Lennie, M. D’Zmura, “Mechanisms of color vision,” Crit. Rev. Neurobiol. 3, 333–400 (1988).
[PubMed]

Li, Z.

J. J. Atick, Z. Li, A. N. Redlich, “What does post-adaptation color appearance reveal about cortical color representation?,” Vision Res. 33, 123–129 (1993), and references therein.
[CrossRef] [PubMed]

Livingstone, M. S.

M. S. Livingstone, D. H. Hubel, “Psychophysical evidence for separate channels for the perception of form, color, movement, and depth,” J. Neurosci. 7, 3416–3468 (1987) and references therein. The question mark (?) in the text (Section 1), presumably representing the uncertainty in the findings, was originally used by these authors.
[PubMed]

Logothetis, N. K.

P. H. Schiller, N. K. Logothetis, E. R. Charles, “Functions of the colour-opponent and broad-band channels of the visual system,” Nature (London) 343, 68–70 (1990).
[CrossRef]

Losada, M. A.

McFarlane, D. K.

H. R. Wilson, D. K. McFarlane, G. C. Phillips, “Spatial frequency tuning of orientation selective units estimated by oblique masking,” Vision Res. 23, 873–882 (1983), and references therein.
[CrossRef] [PubMed]

Michael, C. R.

C. R. Michael, “Laminar segregation of color cells in the monkey’s striate cortex,” Vision Res. 25, 415–423 (1985).
[CrossRef]

Milson, J. A.

A. M. Sillito, J. A. Kemp, J. A. Milson, N. Berardi, “A re-evaluation of the mechanism underlying simple cell orientation selectivity,” Brain Res. 194, 517–520 (1980); R. Hess, K. Negishi, O. Creutzfeldt, “The horizontal spread of intracortical inhibition in the visual cortex,” Exp. Brain Res. 22, 415–419 (1975); D. Allison, V. A. Casagrande, A. B. Bonds, “The influence of input from the lower cortical layers on the orientation tuning of upper layer V1 cells in a primate,” Visual Neurosci. 12, 309–320 (1995).
[CrossRef] [PubMed]

Mollon, J. D.

M. A. Webster, J. D. Mollon, “The influence of contrast adaptation on color appearance,” Vision Res. 34, 1993–2020 (1994).
[CrossRef] [PubMed]

Mullen, K. T.

Newman, E.

R. Bolt, L. Beranek, E. Newman, Curve Fitting Commands: RS/Explore User’s Guide (BBN Research System, Cambridge, Mass., 1986), Book 3, pp. 9-1–9-6.

Pandey, R.

R. L. P. Vimal, R. Pandey, “Interaction between the spatial frequency tuned mechanisms of the Red–Green channel and those of the achromatic channel,” Invest. Ophthalmol. Visual Sci. Suppl. 35, 1370 (1994).

R. Pandey, R. L. P. Vimal, “Contrast matching in the Red–Green channel: flattening effect and color-contrast-constancy,” Soc. Neurosci. Abstr. 19 (Part 3), 1802 (1993).

R. L. P. Vimal, R. Pandey, “Measurement of peak spatial frequency and bandwidth of threshold elevation curves of non-oriented units of the Red–Green channel by horizontal masking,” Invest. Ophthalmol. Visual Sci. Suppl. 34, 782 (1993).

R. Pandey, R. L. P. Vimal, “Threshold elevation curves for the Red–Green channel estimated by oblique masking,” Invest. Ophthalmol. Visual Sci. Suppl. 34, 751 (1993); R. L. P. Vimal, R. Pandey, “Spatial frequency tuned mechanisms of the Red–Green channel estimated by oblique masking,” Soc. Neurosci. Abstr. 20 (Part 2), 1580 (1994). The MSC analysis for the oblique-masking color mechanisms is available from the author.

Phillips, G. C.

H. R. Wilson, D. K. McFarlane, G. C. Phillips, “Spatial frequency tuning of orientation selective units estimated by oblique masking,” Vision Res. 23, 873–882 (1983), and references therein.
[CrossRef] [PubMed]

Pokorny, J. M.

R. L. P. Vimal, J. M. Pokorny, V. C. Smith, S. K. Shevell, “Foveal cone thresholds,” Vision Res. 29, 61–78 (1989).
[CrossRef] [PubMed]

V. C. Smith, J. M. Pokorny, S. Starr, “Variability of color mixture data. I. Interobserver variability in the unit coordinates,” Vision Res. 16, 1087–1094 (1976); J. M. Pokorny, V. C. Smith, S. Starr, “Variability of color mixture data. II. The effect of field size,” Vision Res. 16, 1087–1094 (1976).
[CrossRef]

J. M. Pokorny, University of Chicago, Visual Science Center, 939 East 57th Street, Chicago, Illinois 60637 (personal communication, 1996).

Powell, I.

Redlich, A. N.

J. J. Atick, Z. Li, A. N. Redlich, “What does post-adaptation color appearance reveal about cortical color representation?,” Vision Res. 33, 123–129 (1993), and references therein.
[CrossRef] [PubMed]

Robson, J. G.

F. W. Campbell, J. G. Robson, “Application of Fourier analysis to the visibility of gratings,” J. Physiol. (London) 197, 551–566 (1968); C. Blakemore, F. W. Campbell, “On the existence of neurons in the human visual system selectively sensitive to the orientation and size of retinal images,” J. Physiol. (London) 203, 237–260 (1969). For details see H. R. Wilson, “Psychophysical models of spatial vision and hyperacuity,” in Spatial Vision, Vol. 10 of Vision and Visual Dysfunction, D. Regan, ed. (Macmillan, London, 1991), pp. 64–86, and references therein.

Sankeralli, M. J.

Schiller, P. H.

P. H. Schiller, N. K. Logothetis, E. R. Charles, “Functions of the colour-opponent and broad-band channels of the visual system,” Nature (London) 343, 68–70 (1990).
[CrossRef]

Sclar, G.

P. Lennie, J. Krauskopf, G. Sclar, “Chromatic mechanisms in striate cortex of macaque,” J. Neurosci. 10, 649–669 (1990).
[PubMed]

Shevell, S. K.

R. L. P. Vimal, J. M. Pokorny, V. C. Smith, S. K. Shevell, “Foveal cone thresholds,” Vision Res. 29, 61–78 (1989).
[CrossRef] [PubMed]

Sillito, A. M.

A. M. Sillito, J. A. Kemp, J. A. Milson, N. Berardi, “A re-evaluation of the mechanism underlying simple cell orientation selectivity,” Brain Res. 194, 517–520 (1980); R. Hess, K. Negishi, O. Creutzfeldt, “The horizontal spread of intracortical inhibition in the visual cortex,” Exp. Brain Res. 22, 415–419 (1975); D. Allison, V. A. Casagrande, A. B. Bonds, “The influence of input from the lower cortical layers on the orientation tuning of upper layer V1 cells in a primate,” Visual Neurosci. 12, 309–320 (1995).
[CrossRef] [PubMed]

Silverman, M. S.

M. S. Silverman, D. H. Grosof, R. L. De Valois, S. D. Elfar, “Spatial-frequency organization in primate striate cortex,” Proc. Natl. Acad. Sci. USA 86, 711–715 (1989); D. P. Edwards, K. P. Purpura, E. Kaplan, “Contrast sensitivity and spatial frequency response of primate cortical neurons in and around the cytochrome oxidase blobs,” Vision Res. 35, 1501–1523 (1995).
[CrossRef] [PubMed]

Smith, V. C.

R. L. P. Vimal, J. M. Pokorny, V. C. Smith, S. K. Shevell, “Foveal cone thresholds,” Vision Res. 29, 61–78 (1989).
[CrossRef] [PubMed]

V. C. Smith, J. M. Pokorny, S. Starr, “Variability of color mixture data. I. Interobserver variability in the unit coordinates,” Vision Res. 16, 1087–1094 (1976); J. M. Pokorny, V. C. Smith, S. Starr, “Variability of color mixture data. II. The effect of field size,” Vision Res. 16, 1087–1094 (1976).
[CrossRef]

Starr, S.

V. C. Smith, J. M. Pokorny, S. Starr, “Variability of color mixture data. I. Interobserver variability in the unit coordinates,” Vision Res. 16, 1087–1094 (1976); J. M. Pokorny, V. C. Smith, S. Starr, “Variability of color mixture data. II. The effect of field size,” Vision Res. 16, 1087–1094 (1976).
[CrossRef]

Stiles, W. S.

G. Wyszecki, W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulae, 2nd ed. (Wiley, New York, 1982), and references therein (for color vision models see pp. 582–689; for other topics see the index on pp. 935–950); R. M. Boynton, Human Color Vision (Holt, Rinehart & Winston, New York, 1979) (for an opponent color model, see pp. 211–215; for cone weightings see pp. 154 and 213).

Stromeyer, C. F.

A. Chaparro, C. F. Stromeyer, R. E. Kronauer, R. T. Eskew, “Separable Red–Green and luminance detectors for small flashes,” Vision Res. 34, 751–762 (1994), and the relevant references therein; C. F. Stromeyer, R. E. Kronauer, A. Ryu, A. Chaparro, R. T. Eskew, “Contribution of human long-wave and middle-wave cones to motion detection,” J. Physiol. (London) 485, 221–243 (1995); C. R. Cole, T. J. Hine, W. Mcilhagga, “Estimation of linear detection mechanisms for stimuli of medium spatial frequency,” Vision Res. 34, 1267-1278 (1994).
[CrossRef] [PubMed]

Swanson, W. H.

W. H. Swanson, H. R. Wilson, S. C. Geise, “Contrast matching data predicted from contrast increment thresholds,” Vision Res. 24, 63–75 (1984); W. H. Swanson, M. A. Georgeson, H. R. Wilson, “Comparison of contrast responses across spatial mechanisms,” Vision Res. 28, 457–459 (1988) and references therein.
[CrossRef] [PubMed]

Switkes, E.

E. Switkes, A. Bradley, K. K. De Valois, “Contrast dependence and mechanisms of masking interactions among chromatic and luminance gratings,” J. Opt. Soc. Am. A 5, 1149–1162 (1988).
[CrossRef] [PubMed]

A. Bradley, E. Switkes, K. K. De Valois, “Orientation and spatial frequency selectivity of adaptation to color and luminance gratings,” Vision Res.28, 841–856 (1988); R. L. De Valois, “Orientation and spatial frequency selectivity: properties and modular organization,” in From Pigments to Perception, A. Valberg, B. B. Lee, eds. (Plenum, New York, 1991), pp. 261–267.
[CrossRef] [PubMed]

Thorell, L. G.

L. G. Thorell, R. L. De Valois, D. G. Albrecht, “Spatial mapping of monkey V1 cells with pure color and luminance stimuli,” Vision Res. 24, 751–769 (1984).
[CrossRef] [PubMed]

Tootell, R. B. H.

R. T. Born, R. B. H. Tootell, “Spatial frequency tuning of single units in macaque supragranular striate cortex,” Proc. Natl. Acad. Sci. USA 88, 7066–7070 (1991).
[CrossRef] [PubMed]

Ts’o, D. Y.

D. Y. Ts’o, C. D. Gilbert, “The organization of chromatic and spatial interaction in the primate striate cortex,” J. Neurosci. 8, 1712–1727 (1988).

Tyler, C. W.

C. W. Tyler, L. Barghout, L. L. Kontsevich, “Surprises in analyzing the mechanisms underlying threshold elevation functions,” Invest. Ophthalmol. Visual Sci. Suppl. 34, 819 (1993); L. L. Kontsevich, C. W. Tyler, “A simple explanation of how contrast affects performance in detection and discrimination tasks below 3 c/deg,” Invest. Ophthalmol. Visual Sci. Suppl. 34, 782 (1993); J. Yang, Q. Xiaofeng, W. Makous, “Zero frequency masking and a model of contrast sensitivity,” Vision Res. 35, 1965–1978 (1995).
[CrossRef] [PubMed]

Vimal, R. L. P.

R. L. P. Vimal, “Orientation tuning of the spatial-frequency-tuned mechanisms of the Red–Green channel,” J. Opt. Soc. Am. A 14, 2622–2632 (1997). At 2 cpd the orientation bandwidth (Fig. 5 of the paper of Vimal in this reference) and also the SF bandwidth of the mechanism of the R–G chromatic channel are similar to those of the achromatic channel (compare the R–G mechanism C4 of Fig. 4 of the present paper with the achromatic mechanisms B and C of Fig. 10 of Wilson et al.7); the CSF for the achromatic channel peaks at approximately 2 cpd for the localized stimulus D6 (see Fig. 9 of Wilson et al.7). Therefore it appears that the spatial (SF and orientation) processing of color and luminance stimuli at 2 cpd is similar.
[CrossRef]

R. L. P. Vimal, R. Pandey, “Interaction between the spatial frequency tuned mechanisms of the Red–Green channel and those of the achromatic channel,” Invest. Ophthalmol. Visual Sci. Suppl. 35, 1370 (1994).

R. L. P. Vimal, R. Pandey, “Measurement of peak spatial frequency and bandwidth of threshold elevation curves of non-oriented units of the Red–Green channel by horizontal masking,” Invest. Ophthalmol. Visual Sci. Suppl. 34, 782 (1993).

R. Pandey, R. L. P. Vimal, “Contrast matching in the Red–Green channel: flattening effect and color-contrast-constancy,” Soc. Neurosci. Abstr. 19 (Part 3), 1802 (1993).

R. Pandey, R. L. P. Vimal, “Threshold elevation curves for the Red–Green channel estimated by oblique masking,” Invest. Ophthalmol. Visual Sci. Suppl. 34, 751 (1993); R. L. P. Vimal, R. Pandey, “Spatial frequency tuned mechanisms of the Red–Green channel estimated by oblique masking,” Soc. Neurosci. Abstr. 20 (Part 2), 1580 (1994). The MSC analysis for the oblique-masking color mechanisms is available from the author.

R. L. P. Vimal, J. M. Pokorny, V. C. Smith, S. K. Shevell, “Foveal cone thresholds,” Vision Res. 29, 61–78 (1989).
[CrossRef] [PubMed]

R. L. P. Vimal, “Spatial frequency discriminations: inphase and counter-phase photopic conditions compared,” Invest. Ophthalmol. Visual Sci. 29, 448 (1988); R. L. P. Vimal, R. Pandey, “Spatial frequency discrimination for inphase and counter-phase red–green stimuli: effect of apparent motion,” Soc. Neurosci. Abstr. 15 (Part 1), p. 625, No. 249.13 (1989).

Webster, M. A.

M. A. Webster, J. D. Mollon, “The influence of contrast adaptation on color appearance,” Vision Res. 34, 1993–2020 (1994).
[CrossRef] [PubMed]

Welkowitz, J.

J. Welkowitz, R. B. Ewen, J. Cohen, Introductory Statistics for the Behavioral Sciences (Academic, New York, 1976); for standard deviation see pp. 51–58, for standard error see pp. 104–133, for chi-square see pp. 242–257, and for statistical tables see pp. 304–307.

Wiesel, T. N.

D. H. Hubel, T. N. Wiesel, “Receptive fields and functional architecture in the cat’s visual cortex,” J. Physiol. (London) 195, 215–243 (1968) and references therein.

Williams, D. R.

J. Krauskopf, D. R. Williams, D. W. Heeley, “Cardinal directions of colour space,” Vision Res. 22, 1123–1131 (1982). For cone weightings see J. Krauskopf, H. J. Wu, B. Farell, “Coherence, cardinal directions and higher-order mechanisms,” Vision Res. 36, 1235–1245 (1996).
[CrossRef] [PubMed]

Wilson, H. R.

H. R. Wilson, “Responses of spatial mechanisms can explain hyperacuity,” Vision Res. 26, 453–469 (1986).
[CrossRef] [PubMed]

H. R. Wilson, “A model for direction selectivity in threshold motion perception,” Biol. Cybern. 51, 213–222 (1985).
[CrossRef] [PubMed]

V. P. Ferrera, H. R. Wilson, “Spatial frequency tuning of transient non-oriented units,” Vision Res. 25, 67–72 (1985); G. C. Phillips, H. R. Wilson, “Orientation bandwidths of spatial mechanisms measured by masking,” J. Opt. Soc. Am. A 1, 226–232 (1984).
[CrossRef] [PubMed]

W. H. Swanson, H. R. Wilson, S. C. Geise, “Contrast matching data predicted from contrast increment thresholds,” Vision Res. 24, 63–75 (1984); W. H. Swanson, M. A. Georgeson, H. R. Wilson, “Comparison of contrast responses across spatial mechanisms,” Vision Res. 28, 457–459 (1988) and references therein.
[CrossRef] [PubMed]

H. R. Wilson, D. J. Gelb, “Modified line-element theory for spatial-frequency and width discrimination,” J. Opt. Soc. Am. A 1, 124–131 (1984).
[CrossRef] [PubMed]

H. R. Wilson, D. K. McFarlane, G. C. Phillips, “Spatial frequency tuning of orientation selective units estimated by oblique masking,” Vision Res. 23, 873–882 (1983), and references therein.
[CrossRef] [PubMed]

H. R. Wilson, “A transducer function for threshold and suprathreshold human vision,” Biol. Cybern. 38, 171–178 (1980).
[CrossRef] [PubMed]

Wyszecki, G.

G. Wyszecki, W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulae, 2nd ed. (Wiley, New York, 1982), and references therein (for color vision models see pp. 582–689; for other topics see the index on pp. 935–950); R. M. Boynton, Human Color Vision (Holt, Rinehart & Winston, New York, 1979) (for an opponent color model, see pp. 211–215; for cone weightings see pp. 154 and 213).

Zeki, S. M.

S. M. Zeki, “The distribution of wavelength and orientation selectivity in different areas of monkey visual cortex,” Proc. R. Soc. London, Ser. B 207, 239–248 (1983).
[CrossRef]

Appl. Opt. (1)

Biol. Cybern. (2)

H. R. Wilson, “A model for direction selectivity in threshold motion perception,” Biol. Cybern. 51, 213–222 (1985).
[CrossRef] [PubMed]

H. R. Wilson, “A transducer function for threshold and suprathreshold human vision,” Biol. Cybern. 38, 171–178 (1980).
[CrossRef] [PubMed]

Brain Res. (1)

A. M. Sillito, J. A. Kemp, J. A. Milson, N. Berardi, “A re-evaluation of the mechanism underlying simple cell orientation selectivity,” Brain Res. 194, 517–520 (1980); R. Hess, K. Negishi, O. Creutzfeldt, “The horizontal spread of intracortical inhibition in the visual cortex,” Exp. Brain Res. 22, 415–419 (1975); D. Allison, V. A. Casagrande, A. B. Bonds, “The influence of input from the lower cortical layers on the orientation tuning of upper layer V1 cells in a primate,” Visual Neurosci. 12, 309–320 (1995).
[CrossRef] [PubMed]

Crit. Rev. Neurobiol. (1)

P. Lennie, M. D’Zmura, “Mechanisms of color vision,” Crit. Rev. Neurobiol. 3, 333–400 (1988).
[PubMed]

IEEE Trans. Autom. Control. (1)

H. Akaike, “A new look at statistical mode identification,” IEEE Trans. Autom. Control. 19, 716–723 (1974), and references therein. This is used by R. E. Fredericksen, P. J. Bex, F. A. J. Verstraten, “How big is a Gabor patch, and why should we care?” J. Opt. Soc. Am. A 14, 1–12 (1997).
[CrossRef]

Indiana University, Chemistry Department, Quantum Chemistry Program Exchange (QCPE) (1)

stepit is a subroutine (the original method) in J. P. Chandler, “stept: direct research optimization solution of least-squares problems,” Indiana University, Chemistry Department, Quantum Chemistry Program Exchange (QCPE) 11, 307 (1976).

Invest. Ophthalmol. Visual Sci. (1)

R. L. P. Vimal, “Spatial frequency discriminations: inphase and counter-phase photopic conditions compared,” Invest. Ophthalmol. Visual Sci. 29, 448 (1988); R. L. P. Vimal, R. Pandey, “Spatial frequency discrimination for inphase and counter-phase red–green stimuli: effect of apparent motion,” Soc. Neurosci. Abstr. 15 (Part 1), p. 625, No. 249.13 (1989).

Invest. Ophthalmol. Visual Sci. Suppl. (4)

C. W. Tyler, L. Barghout, L. L. Kontsevich, “Surprises in analyzing the mechanisms underlying threshold elevation functions,” Invest. Ophthalmol. Visual Sci. Suppl. 34, 819 (1993); L. L. Kontsevich, C. W. Tyler, “A simple explanation of how contrast affects performance in detection and discrimination tasks below 3 c/deg,” Invest. Ophthalmol. Visual Sci. Suppl. 34, 782 (1993); J. Yang, Q. Xiaofeng, W. Makous, “Zero frequency masking and a model of contrast sensitivity,” Vision Res. 35, 1965–1978 (1995).
[CrossRef] [PubMed]

R. L. P. Vimal, R. Pandey, “Measurement of peak spatial frequency and bandwidth of threshold elevation curves of non-oriented units of the Red–Green channel by horizontal masking,” Invest. Ophthalmol. Visual Sci. Suppl. 34, 782 (1993).

R. L. P. Vimal, R. Pandey, “Interaction between the spatial frequency tuned mechanisms of the Red–Green channel and those of the achromatic channel,” Invest. Ophthalmol. Visual Sci. Suppl. 35, 1370 (1994).

R. Pandey, R. L. P. Vimal, “Threshold elevation curves for the Red–Green channel estimated by oblique masking,” Invest. Ophthalmol. Visual Sci. Suppl. 34, 751 (1993); R. L. P. Vimal, R. Pandey, “Spatial frequency tuned mechanisms of the Red–Green channel estimated by oblique masking,” Soc. Neurosci. Abstr. 20 (Part 2), 1580 (1994). The MSC analysis for the oblique-masking color mechanisms is available from the author.

J. Neurosci. (3)

P. Lennie, J. Krauskopf, G. Sclar, “Chromatic mechanisms in striate cortex of macaque,” J. Neurosci. 10, 649–669 (1990).
[PubMed]

M. S. Livingstone, D. H. Hubel, “Psychophysical evidence for separate channels for the perception of form, color, movement, and depth,” J. Neurosci. 7, 3416–3468 (1987) and references therein. The question mark (?) in the text (Section 1), presumably representing the uncertainty in the findings, was originally used by these authors.
[PubMed]

D. Y. Ts’o, C. D. Gilbert, “The organization of chromatic and spatial interaction in the primate striate cortex,” J. Neurosci. 8, 1712–1727 (1988).

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

M. J. Sankeralli, K. T. Mullen, “Estimation of the L-, M-, and S-cone weights of the postreceptoral detection mechanisms,” J. Opt. Soc. Am. A 13, 906–915 (1996).
[CrossRef]

K. T. Mullen, M. A. Losada, “Evidence for separate pathways for color and luminance detection mechanisms,” J. Opt. Soc. Am. A 11, 3136–3151 (1994); K. T. Mullen, S. J. Cropper, M. A. Losada, “Absence of linear subthreshold summation between Red–Green and luminance mechanisms over a wide range of spatio-temporal conditions,” Vision Res. 37, 1157–1165 (1997); M. A. Losada, K. T. Mullen, “The spatial tuning of chromatic mechanisms identified by simultaneous masking,” Vision Res. 34, 331–334 (1994).
[CrossRef] [PubMed]

E. Switkes, A. Bradley, K. K. De Valois, “Contrast dependence and mechanisms of masking interactions among chromatic and luminance gratings,” J. Opt. Soc. Am. A 5, 1149–1162 (1988).
[CrossRef] [PubMed]

R. L. P. Vimal, “Orientation tuning of the spatial-frequency-tuned mechanisms of the Red–Green channel,” J. Opt. Soc. Am. A 14, 2622–2632 (1997). At 2 cpd the orientation bandwidth (Fig. 5 of the paper of Vimal in this reference) and also the SF bandwidth of the mechanism of the R–G chromatic channel are similar to those of the achromatic channel (compare the R–G mechanism C4 of Fig. 4 of the present paper with the achromatic mechanisms B and C of Fig. 10 of Wilson et al.7); the CSF for the achromatic channel peaks at approximately 2 cpd for the localized stimulus D6 (see Fig. 9 of Wilson et al.7). Therefore it appears that the spatial (SF and orientation) processing of color and luminance stimuli at 2 cpd is similar.
[CrossRef]

J. M. Foley, “Human luminance pattern-vision mechanisms: masking experiments require a new model,” J. Opt. Soc. Am. A 11, 1710–1719 (1994); A. B. Bonds, “Role of inhibition in the specification of orientation selectivity of cells in the cat striate cortex,” Visual Neurosci. 2, 41–55 (1989); D. J. Heeger, “Normalization of cell responses in cat visual cortex,” Visual Neurosci. 9, 181–197 (1992), and references therein.
[CrossRef]

H. R. Wilson, D. J. Gelb, “Modified line-element theory for spatial-frequency and width discrimination,” J. Opt. Soc. Am. A 1, 124–131 (1984).
[CrossRef] [PubMed]

J. Physiol. (London) (3)

K. T. Mullen, “The contrast sensitivity of human colour vision to red/green and blue/yellow chromatic gratings,” J. Physiol. (London) 359, 381–400 (1985).

D. H. Hubel, T. N. Wiesel, “Receptive fields and functional architecture in the cat’s visual cortex,” J. Physiol. (London) 195, 215–243 (1968) and references therein.

F. W. Campbell, J. G. Robson, “Application of Fourier analysis to the visibility of gratings,” J. Physiol. (London) 197, 551–566 (1968); C. Blakemore, F. W. Campbell, “On the existence of neurons in the human visual system selectively sensitive to the orientation and size of retinal images,” J. Physiol. (London) 203, 237–260 (1969). For details see H. R. Wilson, “Psychophysical models of spatial vision and hyperacuity,” in Spatial Vision, Vol. 10 of Vision and Visual Dysfunction, D. Regan, ed. (Macmillan, London, 1991), pp. 64–86, and references therein.

Nature (London) (2)

F. Crick, C. Koch, “Are we aware of neural activity in primary visual cortex?” Nature (London) 375, 121–123 (1995); M. Gur, M. Snodderly, “A dissociation between brain activity and perception: chromatically opponent cortical neurons signal chromatic flicker that is not perceived,” Vision Res. 37, 377–382 (1997).
[CrossRef] [PubMed]

P. H. Schiller, N. K. Logothetis, E. R. Charles, “Functions of the colour-opponent and broad-band channels of the visual system,” Nature (London) 343, 68–70 (1990).
[CrossRef]

Proc. Natl. Acad. Sci. USA (2)

M. S. Silverman, D. H. Grosof, R. L. De Valois, S. D. Elfar, “Spatial-frequency organization in primate striate cortex,” Proc. Natl. Acad. Sci. USA 86, 711–715 (1989); D. P. Edwards, K. P. Purpura, E. Kaplan, “Contrast sensitivity and spatial frequency response of primate cortical neurons in and around the cytochrome oxidase blobs,” Vision Res. 35, 1501–1523 (1995).
[CrossRef] [PubMed]

R. T. Born, R. B. H. Tootell, “Spatial frequency tuning of single units in macaque supragranular striate cortex,” Proc. Natl. Acad. Sci. USA 88, 7066–7070 (1991).
[CrossRef] [PubMed]

Proc. R. Soc. London, Ser. B (1)

S. M. Zeki, “The distribution of wavelength and orientation selectivity in different areas of monkey visual cortex,” Proc. R. Soc. London, Ser. B 207, 239–248 (1983).
[CrossRef]

Psychol. Rev. (1)

L. M. Hurvich, D. Jameson, “An opponent-process theory of color vision,” Psychol. Rev. 64, 384–404 (1957).
[CrossRef] [PubMed]

Science (1)

V. A. Billock, “Consequence of retinal color coding for cortical color decoding,” Science 274, 2118–2119 (1996) [also see the responses by D. M. Dacey, Science 274, 2119 (1996) and R. H. Masland, Science 274, 2119 (1996), and references therein]; D. M. Dacey, B. B. Lee, D. K. Stafford, J. Pokorny, V. C. Smith, “Horizontal cells of the primate retina: cone specificity without spectral opponency,” Science 271, 656 (1996); R. H. Masland, “Unscrambling color vision,” Science 271, 616 (1996); C. R. Ingling, E. Martinez-Uriegas, “The spatiotemporal properties of the r–g x-cell channel,” Vision Res. 25, 33–38 (1985).
[CrossRef] [PubMed]

Soc. Neurosci. Abstr. (1)

R. Pandey, R. L. P. Vimal, “Contrast matching in the Red–Green channel: flattening effect and color-contrast-constancy,” Soc. Neurosci. Abstr. 19 (Part 3), 1802 (1993).

Vision Res. (16)

V. C. Smith, J. M. Pokorny, S. Starr, “Variability of color mixture data. I. Interobserver variability in the unit coordinates,” Vision Res. 16, 1087–1094 (1976); J. M. Pokorny, V. C. Smith, S. Starr, “Variability of color mixture data. II. The effect of field size,” Vision Res. 16, 1087–1094 (1976).
[CrossRef]

W. H. Swanson, H. R. Wilson, S. C. Geise, “Contrast matching data predicted from contrast increment thresholds,” Vision Res. 24, 63–75 (1984); W. H. Swanson, M. A. Georgeson, H. R. Wilson, “Comparison of contrast responses across spatial mechanisms,” Vision Res. 28, 457–459 (1988) and references therein.
[CrossRef] [PubMed]

H. R. Wilson, “Responses of spatial mechanisms can explain hyperacuity,” Vision Res. 26, 453–469 (1986).
[CrossRef] [PubMed]

P. Flanagan, P. Cavanagh, O. E. Favreau, “Independent orientation-selective mechanisms for the cardinal direction of color space,” Vision Res. 30, 769–778 (1990).
[CrossRef]

R. L. P. Vimal, J. M. Pokorny, V. C. Smith, S. K. Shevell, “Foveal cone thresholds,” Vision Res. 29, 61–78 (1989).
[CrossRef] [PubMed]

J. Krauskopf, D. R. Williams, D. W. Heeley, “Cardinal directions of colour space,” Vision Res. 22, 1123–1131 (1982). For cone weightings see J. Krauskopf, H. J. Wu, B. Farell, “Coherence, cardinal directions and higher-order mechanisms,” Vision Res. 36, 1235–1245 (1996).
[CrossRef] [PubMed]

A. Chaparro, C. F. Stromeyer, R. E. Kronauer, R. T. Eskew, “Separable Red–Green and luminance detectors for small flashes,” Vision Res. 34, 751–762 (1994), and the relevant references therein; C. F. Stromeyer, R. E. Kronauer, A. Ryu, A. Chaparro, R. T. Eskew, “Contribution of human long-wave and middle-wave cones to motion detection,” J. Physiol. (London) 485, 221–243 (1995); C. R. Cole, T. J. Hine, W. Mcilhagga, “Estimation of linear detection mechanisms for stimuli of medium spatial frequency,” Vision Res. 34, 1267-1278 (1994).
[CrossRef] [PubMed]

J. G. Daugman, “Two-dimensional spectral analysis of cortical receptive field profile,” Vision Res. 20, 847–856 (1980); M. A. Webster, R. L. De Valois, “Relationship between spatial-frequency and orientation tuning of striate-cortex cells,” J. Opt. Soc. Am. A 2, 1124–1132 (1985); R. L. De Valois, “Spatial processing of luminance and color information,” Invest. Ophthalmol. Visual Sci. 17, 834–835 (1978).
[CrossRef] [PubMed]

L. G. Thorell, R. L. De Valois, D. G. Albrecht, “Spatial mapping of monkey V1 cells with pure color and luminance stimuli,” Vision Res. 24, 751–769 (1984).
[CrossRef] [PubMed]

C. R. Michael, “Laminar segregation of color cells in the monkey’s striate cortex,” Vision Res. 25, 415–423 (1985).
[CrossRef]

H. R. Wilson, D. K. McFarlane, G. C. Phillips, “Spatial frequency tuning of orientation selective units estimated by oblique masking,” Vision Res. 23, 873–882 (1983), and references therein.
[CrossRef] [PubMed]

V. P. Ferrera, H. R. Wilson, “Spatial frequency tuning of transient non-oriented units,” Vision Res. 25, 67–72 (1985); G. C. Phillips, H. R. Wilson, “Orientation bandwidths of spatial mechanisms measured by masking,” J. Opt. Soc. Am. A 1, 226–232 (1984).
[CrossRef] [PubMed]

M. Gur, V. Akri, “Isoluminant stimuli may not expose the full contribution of color to visual functioning: spatial contrast sensitivity measurements indicate interaction between color and luminance processing,” Vision Res. 32, 1253–1262 (1992).
[CrossRef] [PubMed]

M. A. Webster, J. D. Mollon, “The influence of contrast adaptation on color appearance,” Vision Res. 34, 1993–2020 (1994).
[CrossRef] [PubMed]

J. J. Atick, Z. Li, A. N. Redlich, “What does post-adaptation color appearance reveal about cortical color representation?,” Vision Res. 33, 123–129 (1993), and references therein.
[CrossRef] [PubMed]

M. A. Georgeson, J. M. Georgeson, “Facilitation and masking of briefly presented gratings: time-course and contrast dependence,” Vision Res. 27, 369–379 (1987).
[CrossRef] [PubMed]

Other (6)

G. Wyszecki, W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulae, 2nd ed. (Wiley, New York, 1982), and references therein (for color vision models see pp. 582–689; for other topics see the index on pp. 935–950); R. M. Boynton, Human Color Vision (Holt, Rinehart & Winston, New York, 1979) (for an opponent color model, see pp. 211–215; for cone weightings see pp. 154 and 213).

A. Bradley, E. Switkes, K. K. De Valois, “Orientation and spatial frequency selectivity of adaptation to color and luminance gratings,” Vision Res.28, 841–856 (1988); R. L. De Valois, “Orientation and spatial frequency selectivity: properties and modular organization,” in From Pigments to Perception, A. Valberg, B. B. Lee, eds. (Plenum, New York, 1991), pp. 261–267.
[CrossRef] [PubMed]

R. Bolt, L. Beranek, E. Newman, Curve Fitting Commands: RS/Explore User’s Guide (BBN Research System, Cambridge, Mass., 1986), Book 3, pp. 9-1–9-6.

J. Welkowitz, R. B. Ewen, J. Cohen, Introductory Statistics for the Behavioral Sciences (Academic, New York, 1976); for standard deviation see pp. 51–58, for standard error see pp. 104–133, for chi-square see pp. 242–257, and for statistical tables see pp. 304–307.

J. M. Pokorny, University of Chicago, Visual Science Center, 939 East 57th Street, Chicago, Illinois 60637 (personal communication, 1996).

J. J. Kulikowski, “What really limits vision? Conceptual limitations to the assessments of visual functions and the role of interacting channels,” in Limits of Vision, Vol. 5 of Vision and Visual Dysfunctions, J. J. Kulikowski, V. Walsh, I. J. Murray, eds. (Macmillan, London, 1991), pp. 286–329.

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Figures (5)

Fig. 1
Fig. 1

Color contrast sensitivity function (CSF) (contrast sensitivity versus test spatial frequency) for observers RV (open circles and dashed curve) and RP (filled circles and solid curve). Symbols represent data, and curves represent the best fits to the data by the multiple-mechanism model. Dotted lines (upper: RP; lower: RV) are drawn at half of the maximum of the data. For details see Subsections 3.A and 4.A.

Fig. 2
Fig. 2

TE curves [TE versus mask spatial frequency (SF)] for observers RV and RP at 60% mask contrast. Dashed, solid, and thick dotted–dashed curves represent the best fits to the data indicated by open circles, solid circles, and stars, respectively. Symbols with a downward arrow indicate the test SF’s, which are also placed onto the plots. For details see Subsections 2.C, 3.B, and 4.A.

Fig. 3
Fig. 3

TE versus mask contrast (TvC) curves on log–log coordinates for observers RV and RP. The mask contrasts were 6.25%, 12.5%, 25%, and 60% for all conditions; in addition, the mask contrast of 50% was also used at 0.0625 and 0.125 cpd for RV. However, mask contrasts are plotted in times threshold metric. Test SF=mask SF; they are placed onto the plots. Dashed and solid curves represent the best fits to the data indicated by open and solid circles, respectively. Dotted lines indicate no masking (TE=1).

Fig. 4
Fig. 4

SF tuned mechanisms of the Red–Green channel plotted as normalized sensitivity (to a peak value of unity) versus SF. The nonoriented SF-tuned color mechanisms (C1 is a low-pass function of SF, and in C2, C3, C4, C5, and C6 the filters peak at 0.13, 0.5, 2, 4, and 8 cpd, respectively) of observers RV and RP are shown by filled and open circles, respectively; the solid curves represent the geometrical mean over observers RV and RP; the bandwidths are listed in Table 2. The dashed curves represent the oblique-masking color mechanisms averaged over observers.6 The dotted lines are drawn at half-height for the data.

Fig. 5
Fig. 5

Statistics plotted as a function of the number of nonoriented mechanisms for observers RV (upper plots) and RP (lower plots). (a) Filled circles with solid curves indicate the increase of multiple R2 (“rel. R_sq.”), which represents the proportion of the total variation that is accounted for by the model, relative to max(data, fit), as the number of mechanisms increases. Open circles with dashed curves represent the increase of average correlation (“corr.”) of data and the best fit as the number of mechanisms increases. (b) Open circles with dashed curves represent absolute error (“abs. err.”) statistics, defined as 100 times the sum of the absolute value of (data-fit)/max(data, fit) divided by the total number of data points. Filled circles with solid curves indicate the decrease of the sum of the squares of relative error statistics (“sq. rel. err.”) with the increase of number of mechanisms; this is defined as the sum of the squares of (data-fit)/max(data, fit), plus the sum of the squares of (1-correlation) for CSF and TE data. A plateau is reached at approximately 6, which is taken as the minimum number of mechanisms.

Tables (2)

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Table 1 Parameters of the Mechanismsa

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Table 2 Bandwidths of Nonoriented and Oblique-Masking Mechanismsa

Equations (16)

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F=Eq+kEpIq+k,
E=SC,k=1/[H(1-)],p=q+1-,
I=SC.
ΔFi=|Fi(T+M)-Fi(M)|.
ΔF=ΔFiQ1/Q,
(SC)tm=S(M)Cm+ΔC(T, M)S(T).
S(T)=[Si(T)]Q1/Q,
Sni(T)=Si(T)/Smax,i,
TE=ΔC(T, M)S(T)=ΔC(T, M)/ΔC(T).
multipleR2=(regressionSS)/(regressionSS+residualSS)
=1-{[SSof(data-fit)]/(SSofdata)},
multipleR2=1-({SSof[(data-fit)/max(data,fit)]}/{SSof[data/max(data,fit)]}).
Fratio=(regressionSS)/(regressionDF)(residualSS)/(residualDF),
Fratio=[(Nd-Np)/(Np-1)][R2/(1-R2)],
χ2=[sumof(fit-data)2]/data.
MSC=ln(A/B)-(2Np/Nd),

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