Abstract

We have obtained two- and three-dimensional detection threshold contours in cone contrast space for sinusoidal gratings for three subjects at three spatiotemporal conditions (1 cycle/degree (c/deg), 0 Hz; 0.125 c/deg, 0 Hz; 1 c/deg, 24 Hz). These conditions were chosen to favor the response of each of the three postreceptoral mechanisms in turn. Contours were obtained from measurements in as many as 60 axes in (L, M, S) cone contrast space and were fitted by superellipses. Our technique permitted us to improve on earlier estimates of the cone weightings to the mechanisms. We found that the red–green mechanism has an input cone weighting of L−M with a 2% S-cone input; the luminance mechanism has a weighting of kL + M, where k varies between 3 and 5 at the high-temporal condition, with a 5% S-cone input in opposition to L- and M-cones; and the blue–yellow mechanism consists of S inputs in closely balanced opposition to L and M inputs. These cone weights were found to be consistent among our three subjects.

© 1996 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  12. 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).
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  13. P. E. King-Smith, A. J. Vingrys, S. C. Benes, “Visual thresholds measured with color video monitors,” Color Res. Appl. 12, 73–80 (1987).
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    [CrossRef] [PubMed]
  15. A. B. Poirson, B. A. Wandell, D. C. Varner, D. H. Brainard, “Surface characterizations of color thresholds,” J. Opt. Soc. Am. A 7, 783–789 (1990).
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  24. A. Bradley, L. Zhang, L. N. Thibos, “Failures of isoluminance caused by ocular chromatic aberration,” Appl. Opt. 31, 3657–3667 (1992).
    [CrossRef] [PubMed]
  25. D. G. Pelli, L. Zhang, “Accurate control of contrast on microcomputer displays,” Vision Res. 31, 1337–1350 (1991).
    [CrossRef] [PubMed]
  26. M. J. Sankeralli, “A quantitative analysis of normal postreceptoral chromatic mechanisms and its application to visual dysfunction,” Master’s thesis (McGill University, Montreal, Quebec, Canada, 1994).
  27. A. Chaparro, C. F. Stromeyer, G. Chen, R. E. Kronauer, “Human cones appear to adapt at low light levels: measurements on the red–green detection mechanism,” Vision Res. 35, 3103–3118 (1995).
    [CrossRef] [PubMed]
  28. R. F. Quick, “A vector-magnitude model for contrast detection,” Kybernetic 16, 65–67 (1974).
    [CrossRef]
  29. G. R. Cole, T. J. Hine, “Computation of cone contrasts for color vision research,” Behav. Res. Methods Instrum. Comp. 24, 22–27 (1992).
    [CrossRef]
  30. A. J. Vingrys, A. B. Metha, D. R. Badcock, “Modeling post receptoral mechanisms with cone contrast,” Invest. Ophthalmol. Vis. Sci. 34, 750 (1993).
  31. V. C. Smith, J. Pokorny, “Spectral sensitivity of the foveal photopigments between 400 and 500 nm,” Vision Res. 15, 161–171 (1975).
    [CrossRef] [PubMed]
  32. A. H. Barr, “Superquadrics and angle preserving transformations,” IEEE Comput. Graphics Appl. 1, 11–23 (1981).
    [CrossRef]
  33. P. Whaite, F. P. Ferrie, “From uncertainty to visual exploration,” IEEE Trans. PAMI 13, 1038–1049 (1991).
    [CrossRef]
  34. A. B. Metha, A. J. Vingrys, D. R. Badcock, “Detection and discrimination of moving stimuli: the effects of color, luminance, and eccentricity,” J. Opt. Soc. Am. A 11, 1697–1709 (1994).
    [CrossRef]
  35. A. Chaparro, C. F. Stromeyer, R. E. Kronauer, E. Hu, S. Klakadis, C. Rodgriguez, “Short wave cone input to the red–green detection mechanism,” Invest. Ophthalmol. Vis. Res. 36, S210 (1995).
  36. C. F. Stromeyer, A. Chaparro, A. Tolias, R. E. Kronauer, “Equiluminant settings change markedly with temporal frequency,” Invest. Ophthalmol. Vis. Sci. 36, S210 (1995).
  37. 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. 485, 221–243 (1995).
  38. L. T. Maloney, “The slopes of the psychometric function at different wavelengths,” Vision Res. 30, 129–136 (1990).
    [CrossRef]
  39. C. F. Stromeyer, J. Lee, R. T. Eskew, “Peripheral chromatic sensitivity for flashes: a post-receptoral red–green asymmetry,” Vision Res. 32, 1865–1873 (1992).
    [CrossRef] [PubMed]

1995 (4)

A. Chaparro, C. F. Stromeyer, G. Chen, R. E. Kronauer, “Human cones appear to adapt at low light levels: measurements on the red–green detection mechanism,” Vision Res. 35, 3103–3118 (1995).
[CrossRef] [PubMed]

A. Chaparro, C. F. Stromeyer, R. E. Kronauer, E. Hu, S. Klakadis, C. Rodgriguez, “Short wave cone input to the red–green detection mechanism,” Invest. Ophthalmol. Vis. Res. 36, S210 (1995).

C. F. Stromeyer, A. Chaparro, A. Tolias, R. E. Kronauer, “Equiluminant settings change markedly with temporal frequency,” Invest. Ophthalmol. Vis. Sci. 36, S210 (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. 485, 221–243 (1995).

1994 (2)

A. B. Metha, A. J. Vingrys, D. R. Badcock, “Detection and discrimination of moving stimuli: the effects of color, luminance, and eccentricity,” J. Opt. Soc. Am. A 11, 1697–1709 (1994).
[CrossRef]

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).
[CrossRef] [PubMed]

1993 (2)

A. J. Vingrys, A. B. Metha, D. R. Badcock, “Modeling post receptoral mechanisms with cone contrast,” Invest. Ophthalmol. Vis. Sci. 34, 750 (1993).

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]

1992 (4)

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

C. F. Stromeyer, J. Lee, R. T. Eskew, “Peripheral chromatic sensitivity for flashes: a post-receptoral red–green asymmetry,” Vision Res. 32, 1865–1873 (1992).
[CrossRef] [PubMed]

G. R. Cole, T. J. Hine, “Computation of cone contrasts for color vision research,” Behav. Res. Methods Instrum. Comp. 24, 22–27 (1992).
[CrossRef]

K. T. Mullen, J. C. Boulton, “Absence of smooth motion perception in color vision,” Vision Res. 32, 483–488 (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]

P. Whaite, F. P. Ferrie, “From uncertainty to visual exploration,” IEEE Trans. PAMI 13, 1038–1049 (1991).
[CrossRef]

1990 (3)

L. T. Maloney, “The slopes of the psychometric function at different wavelengths,” Vision Res. 30, 129–136 (1990).
[CrossRef]

A. B. Poirson, B. A. Wandell, “The ellipsoidal representation of spectral sensitivity,” Vision Res. 30, 647–652 (1990).
[CrossRef] [PubMed]

A. B. Poirson, B. A. Wandell, D. C. Varner, D. H. Brainard, “Surface characterizations of color thresholds,” J. Opt. Soc. Am. A 7, 783–789 (1990).
[CrossRef] [PubMed]

1989 (2)

J. Lee, C. F. Stromeyer, “Contribution of human short-wave cones to luminance and motion detection,” J. Physiol. 413, 563–593 (1989).
[PubMed]

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

1987 (3)

P. Cavanagh, D. I. A. MacLeod, S. M. Anstis, “Equiluminance: Spatial and temporal factors and the contribution of blue-sensitive cones,” J. Opt. Soc. Am. A 4, 1428–1438 (1987).
[CrossRef] [PubMed]

C. F. Stromeyer, G. R. Cole, R. E. Kronauer, “Chromatic suppression of cone inputs to the luminance flicker mechanism,” Vision Res. 27, 1113–1137 (1987).
[CrossRef] [PubMed]

P. E. King-Smith, A. J. Vingrys, S. C. Benes, “Visual thresholds measured with color video monitors,” Color Res. Appl. 12, 73–80 (1987).
[CrossRef]

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]

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

1983 (3)

1981 (2)

1980 (1)

1979 (1)

1975 (2)

V. C. Smith, J. Pokorny, “Spectral sensitivity of the foveal photopigments between 400 and 500 nm,” Vision Res. 15, 161–171 (1975).
[CrossRef] [PubMed]

C. R. Cavonius, O. Estevez, “Contrast sensitivity of individual colour mechanisms of human vision,” J. Physiol. 248, 649–662 (1975).
[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 sensitivity of primates,” Science 172, 180–184 (1971).
[CrossRef] [PubMed]

1968 (1)

D. G. Green, “Contrast sensitivity of colour mechanisms of the human eye,” J. Physiol. 196, 415–429 (1968).
[PubMed]

1966 (1)

Anstis, S. M.

Badcock, D. R.

A. B. Metha, A. J. Vingrys, D. R. Badcock, “Detection and discrimination of moving stimuli: the effects of color, luminance, and eccentricity,” J. Opt. Soc. Am. A 11, 1697–1709 (1994).
[CrossRef]

A. J. Vingrys, A. B. Metha, D. R. Badcock, “Modeling post receptoral mechanisms with cone contrast,” Invest. Ophthalmol. Vis. Sci. 34, 750 (1993).

Barr, A. H.

A. H. Barr, “Superquadrics and angle preserving transformations,” IEEE Comput. Graphics Appl. 1, 11–23 (1981).
[CrossRef]

Benes, S. C.

P. E. King-Smith, A. J. Vingrys, S. C. Benes, “Visual thresholds measured with color video monitors,” Color Res. Appl. 12, 73–80 (1987).
[CrossRef]

Boulton, J. C.

K. T. Mullen, J. C. Boulton, “Absence of smooth motion perception in color vision,” Vision Res. 32, 483–488 (1992).
[CrossRef] [PubMed]

Bradley, A.

Brainard, D. H.

Cavanagh, P.

Cavonius, C. R.

C. R. Cavonius, O. Estevez, “Contrast sensitivity of individual colour mechanisms of human vision,” J. Physiol. 248, 649–662 (1975).
[PubMed]

Chaparro, A.

A. Chaparro, C. F. Stromeyer, G. Chen, R. E. Kronauer, “Human cones appear to adapt at low light levels: measurements on the red–green detection mechanism,” Vision Res. 35, 3103–3118 (1995).
[CrossRef] [PubMed]

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. 485, 221–243 (1995).

A. Chaparro, C. F. Stromeyer, R. E. Kronauer, E. Hu, S. Klakadis, C. Rodgriguez, “Short wave cone input to the red–green detection mechanism,” Invest. Ophthalmol. Vis. Res. 36, S210 (1995).

C. F. Stromeyer, A. Chaparro, A. Tolias, R. E. Kronauer, “Equiluminant settings change markedly with temporal frequency,” Invest. Ophthalmol. Vis. Sci. 36, S210 (1995).

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).
[CrossRef] [PubMed]

Chen, G.

A. Chaparro, C. F. Stromeyer, G. Chen, R. E. Kronauer, “Human cones appear to adapt at low light levels: measurements on the red–green detection mechanism,” Vision Res. 35, 3103–3118 (1995).
[CrossRef] [PubMed]

Cole, G. R.

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, T. J. Hine, “Computation of cone contrasts for color vision research,” Behav. Res. Methods Instrum. Comp. 24, 22–27 (1992).
[CrossRef]

C. F. Stromeyer, G. R. Cole, R. E. Kronauer, “Chromatic suppression of cone inputs to the luminance flicker mechanism,” Vision Res. 27, 1113–1137 (1987).
[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]

Eisner, A.

Eskew, R. T.

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. 485, 221–243 (1995).

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).
[CrossRef] [PubMed]

C. F. Stromeyer, J. Lee, R. T. Eskew, “Peripheral chromatic sensitivity for flashes: a post-receptoral red–green asymmetry,” Vision Res. 32, 1865–1873 (1992).
[CrossRef] [PubMed]

Estevez, O.

C. R. Cavonius, O. Estevez, “Contrast sensitivity of individual colour mechanisms of human vision,” J. Physiol. 248, 649–662 (1975).
[PubMed]

Ferrie, F. P.

P. Whaite, F. P. Ferrie, “From uncertainty to visual exploration,” IEEE Trans. PAMI 13, 1038–1049 (1991).
[CrossRef]

Flitcroft, D. I.

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

Green, D. G.

D. G. Green, “Contrast sensitivity of colour mechanisms of the human eye,” J. Physiol. 196, 415–429 (1968).
[PubMed]

Harwerth, R. S.

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

Heuts, M. J. G.

Hine, T.

Hine, T. J.

G. R. Cole, T. J. Hine, “Computation of cone contrasts for color vision research,” Behav. Res. Methods Instrum. Comp. 24, 22–27 (1992).
[CrossRef]

Hu, E.

A. Chaparro, C. F. Stromeyer, R. E. Kronauer, E. Hu, S. Klakadis, C. Rodgriguez, “Short wave cone input to the red–green detection mechanism,” Invest. Ophthalmol. Vis. Res. 36, S210 (1995).

Kelly, D. H.

King-Smith, P. E.

P. E. King-Smith, A. J. Vingrys, S. C. Benes, “Visual thresholds measured with color video monitors,” Color Res. Appl. 12, 73–80 (1987).
[CrossRef]

Klakadis, S.

A. Chaparro, C. F. Stromeyer, R. E. Kronauer, E. Hu, S. Klakadis, C. Rodgriguez, “Short wave cone input to the red–green detection mechanism,” Invest. Ophthalmol. Vis. Res. 36, S210 (1995).

Koenderink, J. J.

Kronauer, R. E.

A. Chaparro, C. F. Stromeyer, R. E. Kronauer, E. Hu, S. Klakadis, C. Rodgriguez, “Short wave cone input to the red–green detection mechanism,” Invest. Ophthalmol. Vis. Res. 36, S210 (1995).

C. F. Stromeyer, A. Chaparro, A. Tolias, R. E. Kronauer, “Equiluminant settings change markedly with temporal frequency,” Invest. Ophthalmol. Vis. Sci. 36, S210 (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. 485, 221–243 (1995).

A. Chaparro, C. F. Stromeyer, G. Chen, R. E. Kronauer, “Human cones appear to adapt at low light levels: measurements on the red–green detection mechanism,” Vision Res. 35, 3103–3118 (1995).
[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).
[CrossRef] [PubMed]

C. F. Stromeyer, G. R. Cole, R. E. Kronauer, “Chromatic suppression of cone inputs to the luminance flicker mechanism,” Vision Res. 27, 1113–1137 (1987).
[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]

Lee, J.

C. F. Stromeyer, J. Lee, R. T. Eskew, “Peripheral chromatic sensitivity for flashes: a post-receptoral red–green asymmetry,” Vision Res. 32, 1865–1873 (1992).
[CrossRef] [PubMed]

J. Lee, C. F. Stromeyer, “Contribution of human short-wave cones to luminance and motion detection,” J. Physiol. 413, 563–593 (1989).
[PubMed]

MacLeod, D. I. A.

Maloney, L. T.

L. T. Maloney, “The slopes of the psychometric function at different wavelengths,” Vision Res. 30, 129–136 (1990).
[CrossRef]

McIlhagga, W.

Metha, A. B.

A. B. Metha, A. J. Vingrys, D. R. Badcock, “Detection and discrimination of moving stimuli: the effects of color, luminance, and eccentricity,” J. Opt. Soc. Am. A 11, 1697–1709 (1994).
[CrossRef]

A. J. Vingrys, A. B. Metha, D. R. Badcock, “Modeling post receptoral mechanisms with cone contrast,” Invest. Ophthalmol. Vis. Sci. 34, 750 (1993).

Mullen, K. T.

K. T. Mullen, J. C. Boulton, “Absence of smooth motion perception in color vision,” Vision Res. 32, 483–488 (1992).
[CrossRef] [PubMed]

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

Noorlander, C.

Pelli, D. G.

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

Poirson, A. B.

A. B. Poirson, B. A. Wandell, “The ellipsoidal representation of spectral sensitivity,” Vision Res. 30, 647–652 (1990).
[CrossRef] [PubMed]

A. B. Poirson, B. A. Wandell, D. C. Varner, D. H. Brainard, “Surface characterizations of color thresholds,” J. Opt. Soc. Am. A 7, 783–789 (1990).
[CrossRef] [PubMed]

Pokorny, J.

V. C. Smith, J. Pokorny, “Spectral sensitivity of the foveal photopigments between 400 and 500 nm,” Vision Res. 15, 161–171 (1975).
[CrossRef] [PubMed]

Pugh, E. N.

J. E. Thornton, E. N. Pugh, “Red/green color opponency at detection threshold,” Science 219, 191–193 (1983a).
[CrossRef] [PubMed]

J. E. Thornton, E. N. Pugh, “Relationship of opponent-colours cancellation measures to cone-antagonistic signals deduced from increment threshold data,” in Colour Vision: Physiology and Psychophysics, J. D. Mollon, L. T. Sharpe, eds. (Academic, London, 1983), pp. 362–373.

Quick, R. F.

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

Robson, J. G.

Rodgriguez, C.

A. Chaparro, C. F. Stromeyer, R. E. Kronauer, E. Hu, S. Klakadis, C. Rodgriguez, “Short wave cone input to the red–green detection mechanism,” Invest. Ophthalmol. Vis. Res. 36, S210 (1995).

Ryu, A.

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. 485, 221–243 (1995).

Sankeralli, M. J.

M. J. Sankeralli, “A quantitative analysis of normal postreceptoral chromatic mechanisms and its application to visual dysfunction,” Master’s thesis (McGill University, Montreal, Quebec, Canada, 1994).

Smith, V. C.

V. C. Smith, J. Pokorny, “Spectral sensitivity of the foveal photopigments between 400 and 500 nm,” Vision Res. 15, 161–171 (1975).
[CrossRef] [PubMed]

Sperling, H. G.

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

Stromeyer, C. F.

A. Chaparro, C. F. Stromeyer, G. Chen, R. E. Kronauer, “Human cones appear to adapt at low light levels: measurements on the red–green detection mechanism,” Vision Res. 35, 3103–3118 (1995).
[CrossRef] [PubMed]

A. Chaparro, C. F. Stromeyer, R. E. Kronauer, E. Hu, S. Klakadis, C. Rodgriguez, “Short wave cone input to the red–green detection mechanism,” Invest. Ophthalmol. Vis. Res. 36, S210 (1995).

C. F. Stromeyer, A. Chaparro, A. Tolias, R. E. Kronauer, “Equiluminant settings change markedly with temporal frequency,” Invest. Ophthalmol. Vis. Sci. 36, S210 (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. 485, 221–243 (1995).

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).
[CrossRef] [PubMed]

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M. J. Sankeralli, “A quantitative analysis of normal postreceptoral chromatic mechanisms and its application to visual dysfunction,” Master’s thesis (McGill University, Montreal, Quebec, Canada, 1994).

J. E. Thornton, E. N. Pugh, “Relationship of opponent-colours cancellation measures to cone-antagonistic signals deduced from increment threshold data,” in Colour Vision: Physiology and Psychophysics, J. D. Mollon, L. T. Sharpe, eds. (Academic, London, 1983), pp. 362–373.

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Figures (9)

Fig. 1
Fig. 1

Planes used for two-dimensional threshold contours in (L, M, S) space.

Fig. 2
Fig. 2

Superellipsoid parameters. a, θ, and ϕ parameters for each axis (x, y, z) of the three-dimensional superellipsoid fits.

Fig. 3
Fig. 3

Mechanism estimation from detection contours. (a) For two-dimensional contours the shorter axis approximates the vector representing the more-sensitive mechanism (solid arrow). The longer axis constrains the vector representing the less-sensitive vector (dashed arrows) to the contour tangent (dashed line). (b) In the three-dimensional case, the short axis again approximates the vector of the most-sensitive mechanism (solid arrow). The second-longest axis constrains the second-most-sensitive mechanism (thick dashed arrows) to a tangential line (horizontal thick dashed line). The longest axis constrains the least-sensitive mechanism (thin dashed arrows) to a tangential plane (thin dashed grid).

Fig. 4
Fig. 4

Two-dimensional contours for (1 c/deg, 0 Hz). Threshold contours in three planes (rows) for three subjects (columns). Axes are in units of cone contrast. Error bars represent standard deviations.

Fig. 5
Fig. 5

Three-dimensional contours for (1 c/deg, 0 Hz). Thresholds (top panels) and fit contours (bottom panels) for three subjects (columns). Axes are in units of cone contrast.

Fig. 6
Fig. 6

Same as Fig. 4 but for two-dimensional contours for (0.125 c/deg, 0 Hz).

Fig. 7
Fig. 7

Same as Fig. 5 but for three-dimensional contours for (0.125 c/deg, 0 Hz).

Fig. 8
Fig. 8

Same as Fig. 4 but for two-dimensional (L, M) contours for (1 c/deg, 24 Hz).

Tables (3)

Tables Icon

Table 1 Two-Dimensional Fit Parametersa

Tables Icon

Table 2 Three-Dimensional Fit Parametersa

Tables Icon

Table 3 Cone-Weight Estimatesa

Equations (14)

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I = I 0 [ 1 + C exp ( - y 2 / 2 σ y 2 ) sin 2 π f y y × exp ( - t 2 / 2 σ t 2 ) sin 2 π f t t ] ,
[ E L E M E S ] = [ r ( λ ) l ( λ ) d λ r ( λ ) p ( λ ) d λ g ( λ ) l ( λ ) d λ g ( λ ) p ( λ ) d λ b ( λ ) l ( λ ) d λ b ( λ ) p ( λ ) d λ r ( λ ) m ( λ ) d λ r ( λ ) p ( λ ) d λ g ( λ ) m ( λ ) d λ g ( λ ) p ( λ ) d λ b ( λ ) m ( λ ) d λ b ( λ ) p ( λ ) d λ r ( λ ) s ( λ ) d λ r ( λ ) p ( λ ) d λ g ( λ ) s ( λ ) d λ g ( λ ) p ( λ ) d λ b ( λ ) s ( λ ) d λ b ( λ ) p ( λ ) d λ ] × [ E R E G E B ] ,
f ( x , y ) = | x a x | β + | y a y | β = 1.
f ( x , y , z ) = ( | x a x | β 2 + | y a y | β 2 ) β 1 / β 2 + | z a z | β 1 = 1.
D = ( a x a y a z ) 1 / 2 [ f 1 ( x , y , z ) - 1 ] .
i m 1 p β = 1 ,
( m u , 1 u + m v , 1 v ) β + ( m u , 2 u + m v , 2 v ) β = 1 ,
( m u , 1 u ) β [ 1 + β ( m v , 1 v m u , 1 u ) + β ( β - 1 ) 2 ! ( m v , 1 v m u , 1 u ) 2 ] + ( m u , 2 u ) β [ 1 + β ( m v , 2 v m u , 2 u ) + β ( β - 1 ) 2 ! ( m v , 2 v m u , 2 u ) 2 ] = 1.
[ ( k x cos ϕ ) u + ( k x sin ϕ ) v ] β + [ ( k y sin ϕ ) u - ( k y cos ϕ ) v ] β = 1.
[ k x ( cos ϕ ) u ] β { 1 + β [ k x ( sin ϕ ) v k y ( cos ϕ ) u ] + β ( β - 1 ) 2 ! × [ k x ( sin ϕ ) v k x ( cos ϕ ) u ] 2 } + ( k y ( sin ϕ ) u ) β { 1 - β [ k y ( cos ϕ ) v k y ( sin ϕ ) u ] + β ( β - 1 ) 2 ! [ k y ( cos ϕ ) v k y ( sin ϕ ) u ] 2 } = 1 ,
m u , 1 β + m u , 2 β = ( k x cos ϕ ) β + ( k y sin ϕ ) β ,
m u , 1 β ( m v , 1 m u , 1 ) + m u , 2 β ( m v , 2 m u , 2 ) = ( k x cos ϕ ) β ( sin ϕ cos ϕ ) - ( k y sin ϕ ) β ( cos ϕ sin ϕ ) ,
m u , 1 β ( m v , 1 m u , 1 ) 2 + m u , 2 β ( m v , 2 m u , 2 ) 2 = ( k x cos ϕ ) β ( sin ϕ cos ϕ ) 2 + ( k y sin ϕ ) β ( cos ϕ sin ϕ ) 2 .
tan θ 1 = m v , 1 m u , 1 = ( k x cos ϕ ) β ( sin ϕ cos ϕ ) 2 + ( k y sin ϕ ) β ( cos ϕ sin ϕ ) 2 ( k x cos ϕ ) β ( sin ϕ cos ϕ ) - ( k y sin ϕ ) β ( cos ϕ sin ϕ ) .

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