Abstract

We used a noise masking technique to test the hypothesis that detection is subserved by only two chromatic postreceptoral mechanisms (red–green and blue–yellow) and one achromatic (luminance) mechanism. The task was to detect a 1-c/deg Gaussian enveloped grating presented in a mask of static, spatially low-passed binary or Gaussian distributed noise. In the main experiment, the direction of the test stimulus (termed the signal) was constant in cone contrast space, and the direction of the noise was sampled in equally spaced directions within a plane (the noise plane) in the space. The signal was chosen to coincide with one of the three cardinal directions of three postulated mechanisms. The noise plane was selected to span two of the cardinal directions, including that chosen as the signal direction. As the noise direction was sampled around the noise plane, the signal detection threshold was found to vary in accordance with a linear cosine model, which predicted noise directions yielding maximum and minimum masking of the signal. In the direction of minimum masking (termed a null direction), the noise was found to have no masking effect on the signal. Moreover, the null was not orthogonal to the signal direction but lay instead in one of the cardinal directions. Our findings suggest that detection is mediated by only three mechanisms. In a further experiment we found little or no cross masking between each pair of cardinal directions up to the limit of our noise mask contrasts. This further supports the presence of no more than three independent postreceptoral mechanisms.

© 1997 Optical Society of America

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  19. K. Knoblauch, L. T. Maloney, “Testing the indeterminacy of linear color mechanisms from color discriminationdata,” Vision Res. 36, 295–306 (1996).
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  23. W. P. Tanner, T. G. Birdsall, “Definitions of d′ and h as psychometric measures,” J. Acoust. Soc. Am. 30, 922–928 (1958).
    [CrossRef]
  24. D. M. Green, J. A. Swets, Signal Detection Theory and Psychophysics (Wiley, New York, 1966).
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    [CrossRef] [PubMed]
  27. D. G. Pelli, L. Zhang, “Accurate control of contrast on microcomputer displays,” Vision Res. 31, 1337–1350 (1991).
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  28. W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing, 2nd ed. (Cambridge U. Press, Cambridge, 1992).
  29. D. I. Flitcroft, “The interactions between chromatic aberration, defocus and stimuluschromaticity: implications for visual physiology and colorimetry,” Vision Res. 29, 349–360 (1989).
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  30. A. Bradley, L. Zhang, L. N. Thibos, “Failures of isoluminance caused by ocular chromatic aberration,” Appl. Opt. 31, 3657–3667 (1992).
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    [CrossRef] [PubMed]
  33. A. B. Watson, D. G. Pelli, “QUEST: a Bayesian adaptive psychometric method,” Percept. Psychophys. 33, 113–120 (1983).
    [CrossRef] [PubMed]
  34. A. Chaparro, R. Thabet, C. F. Stromeyer, R. E. Kronauer, “Spatial masking: mechanisms jointly tuned to color and luminance?” Invest. Ophthalmol. Visual Sci. Suppl. 37, 3 (1996).
  35. A. Li, P. Lennie, “Mechanisms underlying segmentation of colored textures,” Vision Res. 37, 83–97 (1997).
    [CrossRef] [PubMed]
  36. A. M. Derrington, J. Krauskopf, P. Lennie, “Chromatic mechanisms in lateral geniculate nucleus of macaque,” J. Physiol. (London) 357, 241–265 (1984).
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  38. G. R. Cole, C. F. Stromeyer, R. E. Kronauer, “Visual interactions with luminance and chromatic stimuli,” J. Opt. Soc. Am. A 7, 128–140 (1990).
    [CrossRef] [PubMed]
  39. M. D'Zmura, “Color in visual search,” Vision Res. 13, 951–966 (1991).
    [CrossRef]
  40. K. T. Mullen, S. J. Cropper, M. A. Losada, “Absence of linear subthreshold summation between red–green andluminance mechanisms over a wide range of spatio-temporal conditions,” Vision Res. 37, 1157–1165 (1997).
    [CrossRef] [PubMed]
  41. CIE coordinates provided were as follows: mean white point, (0.32, 0.33); one unit on red axis, (0.337, 0.323); one unit on green axis, (0.303, 0.339); one unit on luminance axis, 0.138 contrast unit. These were converted to cone excitations with the CIE/Smith–Pokorny conversion equations [see P. K. Kaiser, R. M. Boynton, Human Color Vision, 2nd ed. (Optical Society of America, Washington D.C., 1996), p. 557] and then to cone contrast units by normalizing by the cone excitations at the mean white point. In our (r, θ, ϕ) cone contrast representation, Gegenfurtner and Kiper's6 luminance and red–green axes were found, respectively, to be (45°, 35.3°), as in our study, and (83.0°, 21.6°), differing somewhat from ours. Using these two axes, we converted intermediate directions by linear transforms.
  42. J. Rovamo, H. Kukkonen, “The effect of noise check size and shape on grating delectability,” Vision Res. 36, 271–279 (1996).
    [CrossRef] [PubMed]

1997 (2)

A. Li, P. Lennie, “Mechanisms underlying segmentation of colored textures,” Vision Res. 37, 83–97 (1997).
[CrossRef] [PubMed]

K. T. Mullen, S. J. Cropper, M. A. Losada, “Absence of linear subthreshold summation between red–green andluminance mechanisms over a wide range of spatio-temporal conditions,” Vision Res. 37, 1157–1165 (1997).
[CrossRef] [PubMed]

1996 (5)

J. Rovamo, H. Kukkonen, “The effect of noise check size and shape on grating delectability,” Vision Res. 36, 271–279 (1996).
[CrossRef] [PubMed]

A. Chaparro, R. Thabet, C. F. Stromeyer, R. E. Kronauer, “Spatial masking: mechanisms jointly tuned to color and luminance?” Invest. Ophthalmol. Visual Sci. Suppl. 37, 3 (1996).

K. Knoblauch, L. T. Maloney, “Testing the indeterminacy of linear color mechanisms from color discriminationdata,” Vision Res. 36, 295–306 (1996).
[CrossRef] [PubMed]

F. Giulianini, W. Lee, R. T. Eskew, “Chromatic noise masking of gabor patches in contrast space,” Invest. Ophthalmol. Visual Sci. Suppl. 37, 427 (1996).

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

1995 (2)

C. F. Stromeyer, R. E. Kronauer, A. Ryu, A. Chaparro, R. T. Eskew, “Contributions of human long-wave and middle-wave cones to motion detection,” J. Physiol. (London) 485, 211–243 (1995).

F. Giulianini, R. T. Eskew, “Noise masking of chromatic and achromatic detection mechanisms,” Invest. Ophthalmol. Visual Sci. Suppl. 36, 663 (1995).

1994 (3)

1993 (1)

1992 (4)

J. Krauskopf, K. Gegenfurtner, “Color discrimination and adaptation,” Vision Res. 32, 2165–2175 (1992).
[CrossRef] [PubMed]

K. R. Gegenfurtner, D. C. Kiper, “Contrast detection in luminance and chromatic noise,” J. Opt. Soc. Am. A 9, 1880–1888 (1992).
[CrossRef] [PubMed]

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

A. Bradley, L. Zhang, L. N. Thibos, “Failures of isoluminance caused by ocular chromatic aberration,” Appl. Opt. 31, 3657–3667 (1992).
[CrossRef] [PubMed]

1991 (2)

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

M. D'Zmura, “Color in visual search,” Vision Res. 13, 951–966 (1991).
[CrossRef]

1990 (2)

1989 (1)

D. I. Flitcroft, “The interactions between chromatic aberration, defocus and stimuluschromaticity: implications for visual physiology and colorimetry,” Vision Res. 29, 349–360 (1989).
[CrossRef]

1988 (1)

1986 (1)

J. Krauskopf, D. R. Williams, M. B. Mandler, A. M. Brown, “Higher order color mechanisms,” Vision Res. 26, 23–32 (1986).
[CrossRef] [PubMed]

1985 (2)

C. F. Stromeyer, G. R. Cole, R. E. Kronauer, “Second-site adaptation in the red–green chromatic pathways,” Vision Res. 25, 219–237 (1985).
[CrossRef]

B. A. Wandell, “Color measurement and discrimination,” J. Opt. Soc. Am. A 2, 62–71 (1985).
[CrossRef] [PubMed]

1984 (1)

A. M. Derrington, J. Krauskopf, P. Lennie, “Chromatic mechanisms in lateral geniculate nucleus of macaque,” J. Physiol. (London) 357, 241–265 (1984).

1983 (2)

A. B. Watson, D. G. Pelli, “QUEST: a Bayesian adaptive psychometric method,” Percept. Psychophys. 33, 113–120 (1983).
[CrossRef] [PubMed]

C. Noorlander, J. J. Koenderink, “Spatial and temporal discrimination ellipsoids in color space,” J. Opt. Soc. Am. 73, 1533–1543 (1983).
[CrossRef] [PubMed]

1982 (1)

J. Krauskopf, D. R. Williams, D. W. Heeley, “Cardinal directions of colour space,” Vision Res. 22, 1123–1131 (1982).
[CrossRef]

1981 (1)

A. E. Burgess, R. F. Wagner, R. J. Jennings, H. B. Barlow, “Efficiency of human visual signal discrimination,” Science 214, 93–94 (1981).
[CrossRef] [PubMed]

1979 (2)

D. I. A. Macleod, R. M. Boynton, “Chromaticity diagram showing cone excitation by stimuli by equal luminance,” J. Opt. Soc. Am. 69, 1183–1186 (1979).
[CrossRef] [PubMed]

K. Kranda, P. E. King-Smith, “Detection of coloured stimuli by independent linear systems,” Vision Res. 19, 733–745 (1979).
[CrossRef] [PubMed]

1974 (1)

R. F. Quick, “A vector-magnitude model for contrast detection,” Kybernetic 16, 65–67 (1974).
[CrossRef]

1971 (1)

H. G. Sperling, R. S. Harwerth, “Red-green cone interactions in the increment threshold spectral sensitivityof primates,” Science 172, 180–184 (1971).
[CrossRef] [PubMed]

1958 (1)

W. P. Tanner, T. G. Birdsall, “Definitions of d′ and h as psychometric measures,” J. Acoust. Soc. Am. 30, 922–928 (1958).
[CrossRef]

Akri, V.

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

Badcock, D. R.

Barlow, H. B.

A. E. Burgess, R. F. Wagner, R. J. Jennings, H. B. Barlow, “Efficiency of human visual signal discrimination,” Science 214, 93–94 (1981).
[CrossRef] [PubMed]

Birdsall, T. G.

W. P. Tanner, T. G. Birdsall, “Definitions of d′ and h as psychometric measures,” J. Acoust. Soc. Am. 30, 922–928 (1958).
[CrossRef]

Boynton, R. M.

D. I. A. Macleod, R. M. Boynton, “Chromaticity diagram showing cone excitation by stimuli by equal luminance,” J. Opt. Soc. Am. 69, 1183–1186 (1979).
[CrossRef] [PubMed]

CIE coordinates provided were as follows: mean white point, (0.32, 0.33); one unit on red axis, (0.337, 0.323); one unit on green axis, (0.303, 0.339); one unit on luminance axis, 0.138 contrast unit. These were converted to cone excitations with the CIE/Smith–Pokorny conversion equations [see P. K. Kaiser, R. M. Boynton, Human Color Vision, 2nd ed. (Optical Society of America, Washington D.C., 1996), p. 557] and then to cone contrast units by normalizing by the cone excitations at the mean white point. In our (r, θ, ϕ) cone contrast representation, Gegenfurtner and Kiper's6 luminance and red–green axes were found, respectively, to be (45°, 35.3°), as in our study, and (83.0°, 21.6°), differing somewhat from ours. Using these two axes, we converted intermediate directions by linear transforms.

Bradley, A.

Brainard, D. H.

Brown, A. M.

J. Krauskopf, D. R. Williams, M. B. Mandler, A. M. Brown, “Higher order color mechanisms,” Vision Res. 26, 23–32 (1986).
[CrossRef] [PubMed]

Burgess, A. E.

A. E. Burgess, R. F. Wagner, R. J. Jennings, H. B. Barlow, “Efficiency of human visual signal discrimination,” Science 214, 93–94 (1981).
[CrossRef] [PubMed]

Chaparro, A.

A. Chaparro, R. Thabet, C. F. Stromeyer, R. E. Kronauer, “Spatial masking: mechanisms jointly tuned to color and luminance?” Invest. Ophthalmol. Visual Sci. Suppl. 37, 3 (1996).

C. F. Stromeyer, R. E. Kronauer, A. Ryu, A. Chaparro, R. T. Eskew, “Contributions of human long-wave and middle-wave cones to motion detection,” J. Physiol. (London) 485, 211–243 (1995).

Cole, G. R.

G. R. Cole, T. J. Hine, W. McIlhagga, “Estimation of linear detection mechanisms for stimuli of medium spatialfrequency,” Vision Res. 34, 1267–1278 (1994).
[CrossRef] [PubMed]

G. R. Cole, T. Hine, W. McIlhagga, “Detection mechanisms in L-, M-, and S-cone contrast space,” J. Opt. Soc. Am. A 10, 38–51 (1993).
[CrossRef] [PubMed]

G. R. Cole, C. F. Stromeyer, R. E. Kronauer, “Visual interactions with luminance and chromatic stimuli,” J. Opt. Soc. Am. A 7, 128–140 (1990).
[CrossRef] [PubMed]

C. F. Stromeyer, G. R. Cole, R. E. Kronauer, “Second-site adaptation in the red–green chromatic pathways,” Vision Res. 25, 219–237 (1985).
[CrossRef]

Cropper, S. J.

K. T. Mullen, S. J. Cropper, M. A. Losada, “Absence of linear subthreshold summation between red–green andluminance mechanisms over a wide range of spatio-temporal conditions,” Vision Res. 37, 1157–1165 (1997).
[CrossRef] [PubMed]

De Valois, K. K.

Derrington, A. M.

A. M. Derrington, J. Krauskopf, P. Lennie, “Chromatic mechanisms in lateral geniculate nucleus of macaque,” J. Physiol. (London) 357, 241–265 (1984).

D'Zmura, M.

M. D'Zmura, “Color in visual search,” Vision Res. 13, 951–966 (1991).
[CrossRef]

M. D'Zmura, “Surface color psychophysics,” Ph.D. dissertation (University of Rochester, Rochester, N.Y., 1990).

Eskew, R. T.

F. Giulianini, W. Lee, R. T. Eskew, “Chromatic noise masking of gabor patches in contrast space,” Invest. Ophthalmol. Visual Sci. Suppl. 37, 427 (1996).

F. Giulianini, R. T. Eskew, “Noise masking of chromatic and achromatic detection mechanisms,” Invest. Ophthalmol. Visual Sci. Suppl. 36, 663 (1995).

C. F. Stromeyer, R. E. Kronauer, A. Ryu, A. Chaparro, R. T. Eskew, “Contributions of human long-wave and middle-wave cones to motion detection,” J. Physiol. (London) 485, 211–243 (1995).

Flannery, B. P.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing, 2nd ed. (Cambridge U. Press, Cambridge, 1992).

Flitcroft, D. I.

D. I. Flitcroft, “The interactions between chromatic aberration, defocus and stimuluschromaticity: implications for visual physiology and colorimetry,” Vision Res. 29, 349–360 (1989).
[CrossRef]

Gegenfurtner, K.

J. Krauskopf, K. Gegenfurtner, “Color discrimination and adaptation,” Vision Res. 32, 2165–2175 (1992).
[CrossRef] [PubMed]

Gegenfurtner, K. R.

Giulianini, F.

F. Giulianini, W. Lee, R. T. Eskew, “Chromatic noise masking of gabor patches in contrast space,” Invest. Ophthalmol. Visual Sci. Suppl. 37, 427 (1996).

F. Giulianini, R. T. Eskew, “Noise masking of chromatic and achromatic detection mechanisms,” Invest. Ophthalmol. Visual Sci. Suppl. 36, 663 (1995).

Green, D. M.

D. M. Green, J. A. Swets, Signal Detection Theory and Psychophysics (Wiley, New York, 1966).

Gur, M.

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

Harwerth, R. S.

H. G. Sperling, R. S. Harwerth, “Red-green cone interactions in the increment threshold spectral sensitivityof primates,” Science 172, 180–184 (1971).
[CrossRef] [PubMed]

Heeley, D. W.

J. Krauskopf, D. R. Williams, D. W. Heeley, “Cardinal directions of colour space,” Vision Res. 22, 1123–1131 (1982).
[CrossRef]

Hine, T.

Hine, T. J.

G. R. Cole, T. J. Hine, W. McIlhagga, “Estimation of linear detection mechanisms for stimuli of medium spatialfrequency,” Vision Res. 34, 1267–1278 (1994).
[CrossRef] [PubMed]

Jennings, R. J.

A. E. Burgess, R. F. Wagner, R. J. Jennings, H. B. Barlow, “Efficiency of human visual signal discrimination,” Science 214, 93–94 (1981).
[CrossRef] [PubMed]

Kaiser, P. K.

CIE coordinates provided were as follows: mean white point, (0.32, 0.33); one unit on red axis, (0.337, 0.323); one unit on green axis, (0.303, 0.339); one unit on luminance axis, 0.138 contrast unit. These were converted to cone excitations with the CIE/Smith–Pokorny conversion equations [see P. K. Kaiser, R. M. Boynton, Human Color Vision, 2nd ed. (Optical Society of America, Washington D.C., 1996), p. 557] and then to cone contrast units by normalizing by the cone excitations at the mean white point. In our (r, θ, ϕ) cone contrast representation, Gegenfurtner and Kiper's6 luminance and red–green axes were found, respectively, to be (45°, 35.3°), as in our study, and (83.0°, 21.6°), differing somewhat from ours. Using these two axes, we converted intermediate directions by linear transforms.

King-Smith, P. E.

K. Kranda, P. E. King-Smith, “Detection of coloured stimuli by independent linear systems,” Vision Res. 19, 733–745 (1979).
[CrossRef] [PubMed]

Kiper, D. C.

Knoblauch, K.

K. Knoblauch, L. T. Maloney, “Testing the indeterminacy of linear color mechanisms from color discriminationdata,” Vision Res. 36, 295–306 (1996).
[CrossRef] [PubMed]

Koenderink, J. J.

Kranda, K.

K. Kranda, P. E. King-Smith, “Detection of coloured stimuli by independent linear systems,” Vision Res. 19, 733–745 (1979).
[CrossRef] [PubMed]

Krauskopf, J.

J. Krauskopf, K. Gegenfurtner, “Color discrimination and adaptation,” Vision Res. 32, 2165–2175 (1992).
[CrossRef] [PubMed]

J. Krauskopf, D. R. Williams, M. B. Mandler, A. M. Brown, “Higher order color mechanisms,” Vision Res. 26, 23–32 (1986).
[CrossRef] [PubMed]

A. M. Derrington, J. Krauskopf, P. Lennie, “Chromatic mechanisms in lateral geniculate nucleus of macaque,” J. Physiol. (London) 357, 241–265 (1984).

J. Krauskopf, D. R. Williams, D. W. Heeley, “Cardinal directions of colour space,” Vision Res. 22, 1123–1131 (1982).
[CrossRef]

Kronauer, R. E.

A. Chaparro, R. Thabet, C. F. Stromeyer, R. E. Kronauer, “Spatial masking: mechanisms jointly tuned to color and luminance?” Invest. Ophthalmol. Visual Sci. Suppl. 37, 3 (1996).

C. F. Stromeyer, R. E. Kronauer, A. Ryu, A. Chaparro, R. T. Eskew, “Contributions of human long-wave and middle-wave cones to motion detection,” J. Physiol. (London) 485, 211–243 (1995).

G. R. Cole, C. F. Stromeyer, R. E. Kronauer, “Visual interactions with luminance and chromatic stimuli,” J. Opt. Soc. Am. A 7, 128–140 (1990).
[CrossRef] [PubMed]

C. F. Stromeyer, G. R. Cole, R. E. Kronauer, “Second-site adaptation in the red–green chromatic pathways,” Vision Res. 25, 219–237 (1985).
[CrossRef]

Kukkonen, H.

J. Rovamo, H. Kukkonen, “The effect of noise check size and shape on grating delectability,” Vision Res. 36, 271–279 (1996).
[CrossRef] [PubMed]

Lee, W.

F. Giulianini, W. Lee, R. T. Eskew, “Chromatic noise masking of gabor patches in contrast space,” Invest. Ophthalmol. Visual Sci. Suppl. 37, 427 (1996).

Lennie, P.

A. Li, P. Lennie, “Mechanisms underlying segmentation of colored textures,” Vision Res. 37, 83–97 (1997).
[CrossRef] [PubMed]

A. M. Derrington, J. Krauskopf, P. Lennie, “Chromatic mechanisms in lateral geniculate nucleus of macaque,” J. Physiol. (London) 357, 241–265 (1984).

Li, A.

A. Li, P. Lennie, “Mechanisms underlying segmentation of colored textures,” Vision Res. 37, 83–97 (1997).
[CrossRef] [PubMed]

Losada, M. A.

K. T. Mullen, S. J. Cropper, M. A. Losada, “Absence of linear subthreshold summation between red–green andluminance mechanisms over a wide range of spatio-temporal conditions,” Vision Res. 37, 1157–1165 (1997).
[CrossRef] [PubMed]

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).
[CrossRef]

Macleod, D. I. A.

Maloney, L. T.

K. Knoblauch, L. T. Maloney, “Testing the indeterminacy of linear color mechanisms from color discriminationdata,” Vision Res. 36, 295–306 (1996).
[CrossRef] [PubMed]

Mandler, M. B.

J. Krauskopf, D. R. Williams, M. B. Mandler, A. M. Brown, “Higher order color mechanisms,” Vision Res. 26, 23–32 (1986).
[CrossRef] [PubMed]

McIlhagga, W.

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Other (6)

CIE coordinates provided were as follows: mean white point, (0.32, 0.33); one unit on red axis, (0.337, 0.323); one unit on green axis, (0.303, 0.339); one unit on luminance axis, 0.138 contrast unit. These were converted to cone excitations with the CIE/Smith–Pokorny conversion equations [see P. K. Kaiser, R. M. Boynton, Human Color Vision, 2nd ed. (Optical Society of America, Washington D.C., 1996), p. 557] and then to cone contrast units by normalizing by the cone excitations at the mean white point. In our (r, θ, ϕ) cone contrast representation, Gegenfurtner and Kiper's6 luminance and red–green axes were found, respectively, to be (45°, 35.3°), as in our study, and (83.0°, 21.6°), differing somewhat from ours. Using these two axes, we converted intermediate directions by linear transforms.

D. M. Green, J. A. Swets, Signal Detection Theory and Psychophysics (Wiley, New York, 1966).

D. G. Pelli, “The effects of visual noise,” Ph.D. dissertation (Cambridge University, Cambridge, 1981).

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing, 2nd ed. (Cambridge U. Press, Cambridge, 1992).

A. V. Oppenheim, R. W. Schafer, Discrete-Time Signal Processing (Prentice-Hall, Englewood Cliffs, N.J., 1989).

M. D'Zmura, “Surface color psychophysics,” Ph.D. dissertation (University of Rochester, Rochester, N.Y., 1990).

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Figures (12)

Fig. 1
Fig. 1

Signal threshold versus noise contrast: self condition. Signal versus noise functions plotted for four signal directions in the (L, M) plane (legend), with noise fixed in same direction as signal. Curves represent fits to linear model (Table 1). Standard errors in signal threshold squared are approximately 0.1 log unit.

Fig. 2
Fig. 2

Signal threshold versus noise contrast: cross condition. Signal versus noise functions plotted for four signal directions in the (L, M) plane (legend), with noise fixed in the direction orthogonal to that of the signal. Curves represent fit to the linear model (Table 1). Standard errors in signal threshold squared are approximately 0.1 log unit.

Fig. 3
Fig. 3

Masking functions in cardinal directions. Signal versus noise-masking functions obtained for signal and noise placed in each of our three cardinal directions (legend). Masking of signal and noise in different cardinal directions is much less than for signal and noise in the same direction. A small facilitation is observed for near-threshold luminance noise.

Fig. 4
Fig. 4

rg signal in rg/by noise. Top left, fixed signal direction (thick arrow) and noise plane (circle) in (L, M, S) cone contrast space. Bold italic labels represent the cardinal directions spanning the plane; large solid labels represent the reference axes in the plane. Remaining panels, detection threshold of fixed signal (thick arrow) in the absence of noise (radius of inner circle) and as a function of noise direction in the plane (diamond data points). The direction of data points from the origin represents applied noise direction in the plane; distance from the origin represents cone contrast threshold. The average standard error for each data point is approximately one tenth of its radial distance from the origin. Maximum (thin solid arrow) and minimum (thin dashed arrow) signal thresholds are obtained by cosine fit (solid curve). The minimum threshold predicted from the three-mechanism model lies along one of the cardinal directions (dashed lines). Noise contrast is fixed at 10%. A null is found when noise is placed in the blue–yellow cardinal direction, confirming signal detection by the red–green mechanism and showing little S-cone input to this mechanism. Data points at null are obscured in the figure.

Fig. 5
Fig. 5

rg signal in rg/lum noise. See caption for Fig. 4. Noise contrast is fixed at 10%. The direction of maximum masking confirms that the red–green mechanism lies in the L-M direction. Data points at null are obscured in the figure.

Fig. 6
Fig. 6

lum signal in by/lum noise. See caption for Fig. 4. Noise contrast is fixed at 40%. Null in the blue–yellow cardinal direction confirms signal detection by the luminance mechanism. Deviation of the maximum masking direction from the L+M axis for two subjects, with small S-cone input to the luminance mechanism.

Fig. 7
Fig. 7

lum signal in rg/lum noise. See caption for Fig. 4. Noise contrast is fixed at 10%.

Fig. 8
Fig. 8

by signal in by/lum noise. See caption for Fig. 4. Noise contrast is fixed at 40%. Null in the luminance cardinal direction confirms detection by the blue–yellow mechanism. The inward deviation of the data relative to the cosine model near the L+M axis suggests facilitation by luminance noise (Fig. 3).

Fig. 9
Fig. 9

Intermediate (L-cone) signal in rg/lum noise. See caption for Fig. 4. Noise contrast is fixed at 10%. For subject PJM, signal thresholds were measured by the QUEST procedure. Nulls lie in the luminance cardinal direction, indicating primary detection by the red–green mechanism (data points at null for subject MJS are obscured). However, systematic distortion with respect to the cosine model suggests the influence of the luminance mechanism (compare with Fig. 12).

Fig. 10
Fig. 10

Estimation of L- and M-cone weights to the blue–yellow mechanism. See caption for Fig. 4. Variable component of noise is fixed at 10% contrast. Noise components are fixed in the L+M+S direction (10% contrast) and in the L-M direction (1.8% contrast). Maximum masking in S-(L+M)/2 direction suggests this as the cone input weights to this mechanism.  

Fig. 11
Fig. 11

Replot in cone contrast space of results from Gegenfurtner and Kiper6: replot of results for subjects AB and KG in Fig. 6 of that study, using calibration information provided by the authors. Signal contrast threshold (diamonds) shown as function of noise direction in cone contrast space for luminance (upper panels), intermediate (middle panels), and red–green (lower panels) signals (signal direction is denoted by thick bars). Minimum contrast threshold is predicted by the three-mechanism model to lie along one or more of the cardinal axes (dashed lines: vertical=luminance; sloping=redgreen). Nulls appear to lie in cardinal directions, in agreement with the three-mechanism model.

Fig. 12
Fig. 12

Replication of results from Gegenfurtner and Kiper 6: results for subject MJS in our study replicating the method for results shown in Fig. 11. See caption for Fig. 11. Thin dashed curve represents the fit to the cosine model. Differences between Fig. 11 and 12 are due mainly to differing constraints on the contrast of noise as its direction varied (see text). The cosine model is obeyed only for the luminance signal. The nominal red–green signal (thick arrow, bottom panel) does not lie in our proposed cardinal direction (sloping dashed line).  

Tables (1)

Tables Icon

Table 1 Fitted Values of Scaled Efficiency J and Signal Contrast Threshold C0 for Self and Cross Conditions a

Equations (8)

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

R=(L2+M2+S2)1/2;
θ=sin-1M(L2+M2)1/2;
ϕ=sin-1S(L2+M2+S2)1/2.
E=kN+E0,
k=d2η,
Cs2=1J Cn2+C02,
Cs1J Cn.
R=R0+A cos|θ-θ0|,

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