Abstract

The inclusion of cone mechanisms in a slightly revised version of an earlier model allows accounts of phenomena that involve receptor effects as well as dichromatic color vision. Intensity-dependent parameters that simulate the adaptation of receptors and opponent and nonopponent mechanisms are varied to predict a wide range of data for both normals and dichromats, including: (i) color matching; (ii) the approximate apparent hue and saturation of the spectrum; (iii) foveal spectral sensitivities obtained by flicker photometry and by detection in the dark and under conditions of achromatic or chromatic adaptation; (iv) heterochromatic additivity failures in the dark-adapted and chromatically adapted eye; (v) approximate differences between brightness and luminance; and, (vi) color and wavelength discrimination under varying adaptation conditions.

© 1980 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. L. Guth, “A new color model,” in Color Metrics, edited by J. J. Vos, L. F. C. Friele, and P. L. Walraven (Association International de la Couleur, Soesterberg, 1972).
  2. S. L. Guth and H. R. Lodge, “Heterochromatic additivity, foveal spectral sensitivity, and a new color model,” J. Opt. Soc. Am. 63, 450–462 (1973).
    [CrossRef] [PubMed]
  3. D. B. Judd, “Response functions for types of vision according to the Müller theory,” J. Res. Natl. Bur. Stand. 42, 1–16 (1949); D. B. Judd and G. T. Yonemura, “CIE 1960 UCS diagram and the Müller theory of color vision,” J. Res. Natl. Bur. Stand. Sec. A 74, 23–30 (1970); G. T. Yonemura, “Opponent-color-theory treatment of the CIE 1960 (U.V.) diagram: Chromaticness difference and constant-hue loci,” J. Opt. Soc. Am. 60, 1407–1409 (1970).
    [CrossRef] [PubMed]
  4. Ingling and his colleagues [C. R. Ingling and B. Tsou, “Orthogonal combination of the three visual channels,” Vision Res. 17, 1075–1082 (1977); C. R. Ingling, ibid., 1083–1089 (1977)] have published a similar modification, which was first reported at the same ARVO meeting referred to in the title footnote.
    [CrossRef] [PubMed]
  5. R. W. Massof and J. F. Bird, “A general zone theory of color and brightness vision. I. Basic formulation,” J. Opt. Soc. Am. 68, 1465–1471 (1978); J. F. Bird and R. W. Massof, “A general zone theory of color and brightness vision. II. The space-time field,” ibid., 1471–1481 (1978).
    [CrossRef] [PubMed]
  6. P. L. Walraven, “On the Mechanisms of Colour Vision,” Ph.D. thesis, Utrecht, 1962 (unpublished).
  7. S. L. Guth, J. V. Alexander, J. I. Chumbly, C. B. Gillman, and M. M. Patterson, “Factors affecting luminance additivity at threshold among normal and color-blind subjects and elaborations of a trichromatic-opponent colors theory,” Vision Res. 8, 913–928 (1968).
    [CrossRef] [PubMed]
  8. V. C. Smith and J. Pokorny, “Spectral sensitivity of color-blind observers and the cone photopigments,” Vision Res. 12, 2059–2071 (1972); “Spectral sensitivity of the foveal cone photopigments between 400 and 500 nm,”  15, 161–171 (1975).
    [CrossRef] [PubMed]
  9. J. J. Vos and P. L. Walraven, “On the derivation of the foveal receptor primaries,” Vision Res. 11, 799–818 (1971); V. C. Smith, J. Pokorny, and S. J. Starr, “Variability of color mixture data. I. Interobserver variability in the unit coordinates,”  16, 1087–1094 (1976).
    [CrossRef] [PubMed]
  10. D. B. Judd, “Colorimetry and artificial daylight,” CIE Proc., Vol. I, Part 7, p. 11. See Table 5.8 in G. Wyszecki and W. S. Stiles, Color Science (Wiley, New York, 1967).
  11. For computational purposes, we actually used equations that transform CIE x, y, and z values to Judd’s x′, y′, and z′values. The equations, from J. J. Vos, Color Res. Applic. 3, 125–128 (1978), arex′=1.0271x−0.00008y−0.000090.03845x+0.01496y+1,y′=0.00376x+1.0072y+0.007640.03845x+0.01496y+1,z′=1−x′−y′. To convert the derived chromaticity coordinates to distribution coefficients, we scaled them to make y¯′equal to CIE y¯at 460 nm and above. Below 460 nm, we used Judd’s y¯′at 10-nm intervals and linearly interpolated between those points.
    [CrossRef]
  12. Given the R, G, and B receptors, the defining properties of these equations are: (i) A is Judd’s correction of y¯; (ii) T and D have cross points at 575 and 502 nm, respectively; and, (iii) the coefficients in the threshold level A, T, and D equations were scaled to optimize predictions of spectral sensitivity and heterochromatic additivity data as shown in Fig. 8 of Ref. 2 and Fig. 10 of this paper.
  13. D. B. Judd, “The Bezold-Brücke phenomenon and the Hering theory of vision,” J. Opt. Soc. Am. 38, 1095–1096 (1948).
  14. L. M. Hurvich and D. Jameson, “Some quantitative aspects of an opponent-colors theory. II. Brightness, saturation, and hue in normal and dichromatic vision,” J. Opt. Soc. Am. 45, 602–616 (1955).
    [CrossRef] [PubMed]
  15. R. M. Boynton and J. Gordon, “Bezold-Brücke hue shift measured by color-naming technique,” J. Opt. Soc. Am. 55, 78–86 (1965).
    [CrossRef]
  16. S. L. Guth, N. J. Donley, and R. T. Marrocco, “On luminance additivity and related topics,” Vision Res. 9, 537–575 (1969).
    [CrossRef] [PubMed]
  17. D. B. Judd, “Basic Correlates of the Visual Stimulus,” in Handbook of Experimental Psychology, edited by S. S. Stevens (Wiley, New York, 1951).
  18. CIE Technical Report No. 41, “Light as a true visual quantity: Principles of measurements,” Report of Technical Committee TC 1.4 (1979). Available from U.S. Natl. Committee, Natl. Bureau of Standards, Washington, DC (unpublished).
  19. H. G. Sperling and R. S. Harwerth, “Red-green cone interactions in the increment-threshold spectral sensitivity of primates,” Science 172, 180–184 (1972).
    [CrossRef]
  20. R. S. Harwerth and D. M. Levi, “Increment threshold spectral sensitivity in anisometropic amblyopia,” Vision Res. 17, 585–590 (1977).
    [CrossRef] [PubMed]
  21. G. Verriest and H. Kandemir, “Normal spectral increment thresholds on a white background,” Farbe 23, 3–16 (1974).
  22. P. E. King-Smith and D. Carden, “Luminance and opponent-color contributions to visual detection and adaptation and to temporal and spatial integration,” J. Opt. Soc. Am. 66, 709–717 (1976).
    [CrossRef] [PubMed]
  23. L. M. Hurvich, “The opponent-pairs scheme,” in Mechanisms of Colour Discrimination (Pergamon, London, 1960).
  24. A. Valberg, “Light adaptation and the saturation of colours,” Vision Res. 15, 401–404 (1975).
    [CrossRef] [PubMed]
  25. R. W. Burnham, “The dependence of color upon area,” Am. J. Psychol. 64, 521–533 (1951).
    [CrossRef] [PubMed]
  26. J. S. Kinney, “Changes in appearance of colored stimuli with exposure duration,” J. Opt. Soc. Am. 55, 738–739 (1965); R. W. Burnham, “Comparative effects of area and luminance on color,” Am. J. Psychol. 65, 27–38 (1952).
    [CrossRef] [PubMed]
  27. R. M. Boynton, G. Kandel, and J. W. Onley, “Rapid chromatic adaptation of normal and dichromatic observers,” J. Opt. Soc. Am. 49, 654–666 (1959).
    [CrossRef] [PubMed]
  28. S. L. Guth, “Nonadditivity and inhibition among chromatic luminances at threshold,” Vision Res. 7, 319–328 (1967).
    [CrossRef] [PubMed]
  29. R. M. Boynton, M. Ikeda, and W. S. Stiles, “Interactions among chromatic mechanisms as inferred from positive and negative increment thresholds,” Vision Res. 4, 87–117 (1964).
    [CrossRef] [PubMed]
  30. G. Wyszecki, “Correlate for lightness in terms of CIE chromaticity coordinates and luminous reflectance,” J. Opt. Soc. Am. 57, 254–257 (1967).
    [CrossRef] [PubMed]
  31. L. F. C. Friele, “Analysis of the Brown and Brown-MacAdam colour discrimination data,” Farbe 10, 193–224 (1961); L. F. C. Friele, “Color difference and color tolerance evaluation. Problems and outlook.” J. Mater. 6, 755–765 (1971); see also K. D. Chickering, “FMC color difference formulas: Clarification concerning usage,” J. Opt. Soc. Am. 61, 118–122 (1971).
    [CrossRef]
  32. D. L. MacAdam, “Visual sensitivities to color differences in daylight,” J. Opt. Soc. Am. 32, 247–274 (1942).
    [CrossRef]
  33. W. R. J. Brown, “The influence of luminance level on visual sensitivity to color differences,” J. Opt. Soc. Am. 41, 684–688 (1951).
    [CrossRef] [PubMed]
  34. L. T. Sharpe and G. Wyszecki, “Proximity factor in color-difference evaluations,” J. Opt. Soc. Am. 66, 40–49 (1976).
    [CrossRef] [PubMed]
  35. J. J. Vos and P. L. Walraven, “A zone-fluctuation line element describing colour discrimination,” in Color Metrics, edited by J. J. Vos, L. F. C. Friele, and P. L. Walraven (Association International de la Couleur, Soesterberg, 1972).
  36. R. W. Massof and J. E. Bailey, “Achromatic points in protanopes and deuteranopes,” Vision Res. 16, 53–57 (1966).
    [CrossRef]
  37. In the earlier description of the model, we incorrectly predicted the copunctal point for “loss” deuteranopes who lack the G receptor as well as the T system. The error was caused by a failure to remember that the defining equations were for observers who had all three receptors. That prediction would be correct only for “fusion” deuteranopes who also lack the T system, but who have normal R and G receptor inputs to the remaining A and D mechanisms. It may, of course, be that there exist both loss and fusion deuteranopes, but we here consider only the loss class. See D. B. Judd, “Fundamental studies of color vision from 1860 to 1960,” Proc. Natl. Acad. Sci. U.S.A. 55, 1313–1330 (1966).
  38. See second reference in Ref. 8.
  39. H. R. Lodge, “Implications of a zone color vision model for spectral sensitivity of normal, protanopic, and deuteranopic subjects as measured by several psychophysical techniques,” Ph.D. dissertation, Indiana University, 1971, University microfilm order number 72-15917 (unpublished).
  40. J. Pokorny and V. C. Smith, “Luminosity and CFF in deuteranopes and protanopes,” J. Opt. Soc. Am. 62, 111–117 (1972).
    [CrossRef] [PubMed]
  41. F. H. G. Pitt, “Characteristics of dichromatic vision,” Med. Res. Counc. Spec. Rep. Ser. 200, 1–58 (1935). Also see citations in Y. Hsia and C. H. Graham, “Color blindness,” in Vision and Visual Perception, edited by C. H. Graham (Wiley, New York, 1965).
  42. P. L. Walraven and M. A. Bouman, “Fluctuation theory of colour discrimination of normal trichromats,” Vision Res. 6, 567–586 (1966).
    [CrossRef] [PubMed]
  43. G. Trick, S. L. Guth, and R. Massof, “Wavelength discrimination in protanopes and deuteranopes,” Mod. Probl. Ophthalmol. 17, 17–20 (1976).
    [PubMed]
  44. W. D. Wright, “The characteristics of tritanopia,” J. Opt. Soc. Am. 42, 509–521 (1952).
    [CrossRef] [PubMed]
  45. F. P. Fischer, M. A. Bouman, and J. Ten Doesschate, “A case of tritanopy,” Doc. Ophthalmol. 5, 55–67 (1951).
  46. M. A. Bouman and P. L. Walraven, “Color discrimination data,” in Visual Psychophysics, edited by D. Jameson and L. Hurvich (Springer-Verlag, Berlin, 1972).
    [CrossRef]

1978 (2)

R. W. Massof and J. F. Bird, “A general zone theory of color and brightness vision. I. Basic formulation,” J. Opt. Soc. Am. 68, 1465–1471 (1978); J. F. Bird and R. W. Massof, “A general zone theory of color and brightness vision. II. The space-time field,” ibid., 1471–1481 (1978).
[CrossRef] [PubMed]

For computational purposes, we actually used equations that transform CIE x, y, and z values to Judd’s x′, y′, and z′values. The equations, from J. J. Vos, Color Res. Applic. 3, 125–128 (1978), arex′=1.0271x−0.00008y−0.000090.03845x+0.01496y+1,y′=0.00376x+1.0072y+0.007640.03845x+0.01496y+1,z′=1−x′−y′. To convert the derived chromaticity coordinates to distribution coefficients, we scaled them to make y¯′equal to CIE y¯at 460 nm and above. Below 460 nm, we used Judd’s y¯′at 10-nm intervals and linearly interpolated between those points.
[CrossRef]

1977 (2)

Ingling and his colleagues [C. R. Ingling and B. Tsou, “Orthogonal combination of the three visual channels,” Vision Res. 17, 1075–1082 (1977); C. R. Ingling, ibid., 1083–1089 (1977)] have published a similar modification, which was first reported at the same ARVO meeting referred to in the title footnote.
[CrossRef] [PubMed]

R. S. Harwerth and D. M. Levi, “Increment threshold spectral sensitivity in anisometropic amblyopia,” Vision Res. 17, 585–590 (1977).
[CrossRef] [PubMed]

1976 (3)

1975 (1)

A. Valberg, “Light adaptation and the saturation of colours,” Vision Res. 15, 401–404 (1975).
[CrossRef] [PubMed]

1974 (1)

G. Verriest and H. Kandemir, “Normal spectral increment thresholds on a white background,” Farbe 23, 3–16 (1974).

1973 (1)

1972 (3)

V. C. Smith and J. Pokorny, “Spectral sensitivity of color-blind observers and the cone photopigments,” Vision Res. 12, 2059–2071 (1972); “Spectral sensitivity of the foveal cone photopigments between 400 and 500 nm,”  15, 161–171 (1975).
[CrossRef] [PubMed]

J. Pokorny and V. C. Smith, “Luminosity and CFF in deuteranopes and protanopes,” J. Opt. Soc. Am. 62, 111–117 (1972).
[CrossRef] [PubMed]

H. G. Sperling and R. S. Harwerth, “Red-green cone interactions in the increment-threshold spectral sensitivity of primates,” Science 172, 180–184 (1972).
[CrossRef]

1971 (1)

J. J. Vos and P. L. Walraven, “On the derivation of the foveal receptor primaries,” Vision Res. 11, 799–818 (1971); V. C. Smith, J. Pokorny, and S. J. Starr, “Variability of color mixture data. I. Interobserver variability in the unit coordinates,”  16, 1087–1094 (1976).
[CrossRef] [PubMed]

1969 (1)

S. L. Guth, N. J. Donley, and R. T. Marrocco, “On luminance additivity and related topics,” Vision Res. 9, 537–575 (1969).
[CrossRef] [PubMed]

1968 (1)

S. L. Guth, J. V. Alexander, J. I. Chumbly, C. B. Gillman, and M. M. Patterson, “Factors affecting luminance additivity at threshold among normal and color-blind subjects and elaborations of a trichromatic-opponent colors theory,” Vision Res. 8, 913–928 (1968).
[CrossRef] [PubMed]

1967 (2)

1966 (3)

R. W. Massof and J. E. Bailey, “Achromatic points in protanopes and deuteranopes,” Vision Res. 16, 53–57 (1966).
[CrossRef]

In the earlier description of the model, we incorrectly predicted the copunctal point for “loss” deuteranopes who lack the G receptor as well as the T system. The error was caused by a failure to remember that the defining equations were for observers who had all three receptors. That prediction would be correct only for “fusion” deuteranopes who also lack the T system, but who have normal R and G receptor inputs to the remaining A and D mechanisms. It may, of course, be that there exist both loss and fusion deuteranopes, but we here consider only the loss class. See D. B. Judd, “Fundamental studies of color vision from 1860 to 1960,” Proc. Natl. Acad. Sci. U.S.A. 55, 1313–1330 (1966).

P. L. Walraven and M. A. Bouman, “Fluctuation theory of colour discrimination of normal trichromats,” Vision Res. 6, 567–586 (1966).
[CrossRef] [PubMed]

1965 (2)

1964 (1)

R. M. Boynton, M. Ikeda, and W. S. Stiles, “Interactions among chromatic mechanisms as inferred from positive and negative increment thresholds,” Vision Res. 4, 87–117 (1964).
[CrossRef] [PubMed]

1961 (1)

L. F. C. Friele, “Analysis of the Brown and Brown-MacAdam colour discrimination data,” Farbe 10, 193–224 (1961); L. F. C. Friele, “Color difference and color tolerance evaluation. Problems and outlook.” J. Mater. 6, 755–765 (1971); see also K. D. Chickering, “FMC color difference formulas: Clarification concerning usage,” J. Opt. Soc. Am. 61, 118–122 (1971).
[CrossRef]

1959 (1)

1955 (1)

1952 (1)

1951 (3)

F. P. Fischer, M. A. Bouman, and J. Ten Doesschate, “A case of tritanopy,” Doc. Ophthalmol. 5, 55–67 (1951).

W. R. J. Brown, “The influence of luminance level on visual sensitivity to color differences,” J. Opt. Soc. Am. 41, 684–688 (1951).
[CrossRef] [PubMed]

R. W. Burnham, “The dependence of color upon area,” Am. J. Psychol. 64, 521–533 (1951).
[CrossRef] [PubMed]

1949 (1)

D. B. Judd, “Response functions for types of vision according to the Müller theory,” J. Res. Natl. Bur. Stand. 42, 1–16 (1949); D. B. Judd and G. T. Yonemura, “CIE 1960 UCS diagram and the Müller theory of color vision,” J. Res. Natl. Bur. Stand. Sec. A 74, 23–30 (1970); G. T. Yonemura, “Opponent-color-theory treatment of the CIE 1960 (U.V.) diagram: Chromaticness difference and constant-hue loci,” J. Opt. Soc. Am. 60, 1407–1409 (1970).
[CrossRef] [PubMed]

1948 (1)

D. B. Judd, “The Bezold-Brücke phenomenon and the Hering theory of vision,” J. Opt. Soc. Am. 38, 1095–1096 (1948).

1942 (1)

1935 (1)

F. H. G. Pitt, “Characteristics of dichromatic vision,” Med. Res. Counc. Spec. Rep. Ser. 200, 1–58 (1935). Also see citations in Y. Hsia and C. H. Graham, “Color blindness,” in Vision and Visual Perception, edited by C. H. Graham (Wiley, New York, 1965).

Alexander, J. V.

S. L. Guth, J. V. Alexander, J. I. Chumbly, C. B. Gillman, and M. M. Patterson, “Factors affecting luminance additivity at threshold among normal and color-blind subjects and elaborations of a trichromatic-opponent colors theory,” Vision Res. 8, 913–928 (1968).
[CrossRef] [PubMed]

Bailey, J. E.

R. W. Massof and J. E. Bailey, “Achromatic points in protanopes and deuteranopes,” Vision Res. 16, 53–57 (1966).
[CrossRef]

Bird, J. F.

Bouman, M. A.

P. L. Walraven and M. A. Bouman, “Fluctuation theory of colour discrimination of normal trichromats,” Vision Res. 6, 567–586 (1966).
[CrossRef] [PubMed]

F. P. Fischer, M. A. Bouman, and J. Ten Doesschate, “A case of tritanopy,” Doc. Ophthalmol. 5, 55–67 (1951).

M. A. Bouman and P. L. Walraven, “Color discrimination data,” in Visual Psychophysics, edited by D. Jameson and L. Hurvich (Springer-Verlag, Berlin, 1972).
[CrossRef]

Boynton, R. M.

Brown, W. R. J.

Burnham, R. W.

R. W. Burnham, “The dependence of color upon area,” Am. J. Psychol. 64, 521–533 (1951).
[CrossRef] [PubMed]

Carden, D.

Chumbly, J. I.

S. L. Guth, J. V. Alexander, J. I. Chumbly, C. B. Gillman, and M. M. Patterson, “Factors affecting luminance additivity at threshold among normal and color-blind subjects and elaborations of a trichromatic-opponent colors theory,” Vision Res. 8, 913–928 (1968).
[CrossRef] [PubMed]

Donley, N. J.

S. L. Guth, N. J. Donley, and R. T. Marrocco, “On luminance additivity and related topics,” Vision Res. 9, 537–575 (1969).
[CrossRef] [PubMed]

Fischer, F. P.

F. P. Fischer, M. A. Bouman, and J. Ten Doesschate, “A case of tritanopy,” Doc. Ophthalmol. 5, 55–67 (1951).

Friele, L. F. C.

L. F. C. Friele, “Analysis of the Brown and Brown-MacAdam colour discrimination data,” Farbe 10, 193–224 (1961); L. F. C. Friele, “Color difference and color tolerance evaluation. Problems and outlook.” J. Mater. 6, 755–765 (1971); see also K. D. Chickering, “FMC color difference formulas: Clarification concerning usage,” J. Opt. Soc. Am. 61, 118–122 (1971).
[CrossRef]

Gillman, C. B.

S. L. Guth, J. V. Alexander, J. I. Chumbly, C. B. Gillman, and M. M. Patterson, “Factors affecting luminance additivity at threshold among normal and color-blind subjects and elaborations of a trichromatic-opponent colors theory,” Vision Res. 8, 913–928 (1968).
[CrossRef] [PubMed]

Gordon, J.

Guth, L.

L. Guth, “A new color model,” in Color Metrics, edited by J. J. Vos, L. F. C. Friele, and P. L. Walraven (Association International de la Couleur, Soesterberg, 1972).

Guth, S. L.

G. Trick, S. L. Guth, and R. Massof, “Wavelength discrimination in protanopes and deuteranopes,” Mod. Probl. Ophthalmol. 17, 17–20 (1976).
[PubMed]

S. L. Guth and H. R. Lodge, “Heterochromatic additivity, foveal spectral sensitivity, and a new color model,” J. Opt. Soc. Am. 63, 450–462 (1973).
[CrossRef] [PubMed]

S. L. Guth, N. J. Donley, and R. T. Marrocco, “On luminance additivity and related topics,” Vision Res. 9, 537–575 (1969).
[CrossRef] [PubMed]

S. L. Guth, J. V. Alexander, J. I. Chumbly, C. B. Gillman, and M. M. Patterson, “Factors affecting luminance additivity at threshold among normal and color-blind subjects and elaborations of a trichromatic-opponent colors theory,” Vision Res. 8, 913–928 (1968).
[CrossRef] [PubMed]

S. L. Guth, “Nonadditivity and inhibition among chromatic luminances at threshold,” Vision Res. 7, 319–328 (1967).
[CrossRef] [PubMed]

Harwerth, R. S.

R. S. Harwerth and D. M. Levi, “Increment threshold spectral sensitivity in anisometropic amblyopia,” Vision Res. 17, 585–590 (1977).
[CrossRef] [PubMed]

H. G. Sperling and R. S. Harwerth, “Red-green cone interactions in the increment-threshold spectral sensitivity of primates,” Science 172, 180–184 (1972).
[CrossRef]

Hurvich, L. M.

Ikeda, M.

R. M. Boynton, M. Ikeda, and W. S. Stiles, “Interactions among chromatic mechanisms as inferred from positive and negative increment thresholds,” Vision Res. 4, 87–117 (1964).
[CrossRef] [PubMed]

Ingling, C. R.

Ingling and his colleagues [C. R. Ingling and B. Tsou, “Orthogonal combination of the three visual channels,” Vision Res. 17, 1075–1082 (1977); C. R. Ingling, ibid., 1083–1089 (1977)] have published a similar modification, which was first reported at the same ARVO meeting referred to in the title footnote.
[CrossRef] [PubMed]

Jameson, D.

Judd, D. B.

In the earlier description of the model, we incorrectly predicted the copunctal point for “loss” deuteranopes who lack the G receptor as well as the T system. The error was caused by a failure to remember that the defining equations were for observers who had all three receptors. That prediction would be correct only for “fusion” deuteranopes who also lack the T system, but who have normal R and G receptor inputs to the remaining A and D mechanisms. It may, of course, be that there exist both loss and fusion deuteranopes, but we here consider only the loss class. See D. B. Judd, “Fundamental studies of color vision from 1860 to 1960,” Proc. Natl. Acad. Sci. U.S.A. 55, 1313–1330 (1966).

D. B. Judd, “Response functions for types of vision according to the Müller theory,” J. Res. Natl. Bur. Stand. 42, 1–16 (1949); D. B. Judd and G. T. Yonemura, “CIE 1960 UCS diagram and the Müller theory of color vision,” J. Res. Natl. Bur. Stand. Sec. A 74, 23–30 (1970); G. T. Yonemura, “Opponent-color-theory treatment of the CIE 1960 (U.V.) diagram: Chromaticness difference and constant-hue loci,” J. Opt. Soc. Am. 60, 1407–1409 (1970).
[CrossRef] [PubMed]

D. B. Judd, “The Bezold-Brücke phenomenon and the Hering theory of vision,” J. Opt. Soc. Am. 38, 1095–1096 (1948).

D. B. Judd, “Colorimetry and artificial daylight,” CIE Proc., Vol. I, Part 7, p. 11. See Table 5.8 in G. Wyszecki and W. S. Stiles, Color Science (Wiley, New York, 1967).

D. B. Judd, “Basic Correlates of the Visual Stimulus,” in Handbook of Experimental Psychology, edited by S. S. Stevens (Wiley, New York, 1951).

Kandel, G.

Kandemir, H.

G. Verriest and H. Kandemir, “Normal spectral increment thresholds on a white background,” Farbe 23, 3–16 (1974).

King-Smith, P. E.

Kinney, J. S.

Levi, D. M.

R. S. Harwerth and D. M. Levi, “Increment threshold spectral sensitivity in anisometropic amblyopia,” Vision Res. 17, 585–590 (1977).
[CrossRef] [PubMed]

Lodge, H. R.

S. L. Guth and H. R. Lodge, “Heterochromatic additivity, foveal spectral sensitivity, and a new color model,” J. Opt. Soc. Am. 63, 450–462 (1973).
[CrossRef] [PubMed]

H. R. Lodge, “Implications of a zone color vision model for spectral sensitivity of normal, protanopic, and deuteranopic subjects as measured by several psychophysical techniques,” Ph.D. dissertation, Indiana University, 1971, University microfilm order number 72-15917 (unpublished).

MacAdam, D. L.

Marrocco, R. T.

S. L. Guth, N. J. Donley, and R. T. Marrocco, “On luminance additivity and related topics,” Vision Res. 9, 537–575 (1969).
[CrossRef] [PubMed]

Massof, R.

G. Trick, S. L. Guth, and R. Massof, “Wavelength discrimination in protanopes and deuteranopes,” Mod. Probl. Ophthalmol. 17, 17–20 (1976).
[PubMed]

Massof, R. W.

Onley, J. W.

Patterson, M. M.

S. L. Guth, J. V. Alexander, J. I. Chumbly, C. B. Gillman, and M. M. Patterson, “Factors affecting luminance additivity at threshold among normal and color-blind subjects and elaborations of a trichromatic-opponent colors theory,” Vision Res. 8, 913–928 (1968).
[CrossRef] [PubMed]

Pitt, F. H. G.

F. H. G. Pitt, “Characteristics of dichromatic vision,” Med. Res. Counc. Spec. Rep. Ser. 200, 1–58 (1935). Also see citations in Y. Hsia and C. H. Graham, “Color blindness,” in Vision and Visual Perception, edited by C. H. Graham (Wiley, New York, 1965).

Pokorny, J.

J. Pokorny and V. C. Smith, “Luminosity and CFF in deuteranopes and protanopes,” J. Opt. Soc. Am. 62, 111–117 (1972).
[CrossRef] [PubMed]

V. C. Smith and J. Pokorny, “Spectral sensitivity of color-blind observers and the cone photopigments,” Vision Res. 12, 2059–2071 (1972); “Spectral sensitivity of the foveal cone photopigments between 400 and 500 nm,”  15, 161–171 (1975).
[CrossRef] [PubMed]

Sharpe, L. T.

Smith, V. C.

J. Pokorny and V. C. Smith, “Luminosity and CFF in deuteranopes and protanopes,” J. Opt. Soc. Am. 62, 111–117 (1972).
[CrossRef] [PubMed]

V. C. Smith and J. Pokorny, “Spectral sensitivity of color-blind observers and the cone photopigments,” Vision Res. 12, 2059–2071 (1972); “Spectral sensitivity of the foveal cone photopigments between 400 and 500 nm,”  15, 161–171 (1975).
[CrossRef] [PubMed]

Sperling, H. G.

H. G. Sperling and R. S. Harwerth, “Red-green cone interactions in the increment-threshold spectral sensitivity of primates,” Science 172, 180–184 (1972).
[CrossRef]

Stiles, W. S.

R. M. Boynton, M. Ikeda, and W. S. Stiles, “Interactions among chromatic mechanisms as inferred from positive and negative increment thresholds,” Vision Res. 4, 87–117 (1964).
[CrossRef] [PubMed]

Ten Doesschate, J.

F. P. Fischer, M. A. Bouman, and J. Ten Doesschate, “A case of tritanopy,” Doc. Ophthalmol. 5, 55–67 (1951).

Trick, G.

G. Trick, S. L. Guth, and R. Massof, “Wavelength discrimination in protanopes and deuteranopes,” Mod. Probl. Ophthalmol. 17, 17–20 (1976).
[PubMed]

Tsou, B.

Ingling and his colleagues [C. R. Ingling and B. Tsou, “Orthogonal combination of the three visual channels,” Vision Res. 17, 1075–1082 (1977); C. R. Ingling, ibid., 1083–1089 (1977)] have published a similar modification, which was first reported at the same ARVO meeting referred to in the title footnote.
[CrossRef] [PubMed]

Valberg, A.

A. Valberg, “Light adaptation and the saturation of colours,” Vision Res. 15, 401–404 (1975).
[CrossRef] [PubMed]

Verriest, G.

G. Verriest and H. Kandemir, “Normal spectral increment thresholds on a white background,” Farbe 23, 3–16 (1974).

Vos, J. J.

For computational purposes, we actually used equations that transform CIE x, y, and z values to Judd’s x′, y′, and z′values. The equations, from J. J. Vos, Color Res. Applic. 3, 125–128 (1978), arex′=1.0271x−0.00008y−0.000090.03845x+0.01496y+1,y′=0.00376x+1.0072y+0.007640.03845x+0.01496y+1,z′=1−x′−y′. To convert the derived chromaticity coordinates to distribution coefficients, we scaled them to make y¯′equal to CIE y¯at 460 nm and above. Below 460 nm, we used Judd’s y¯′at 10-nm intervals and linearly interpolated between those points.
[CrossRef]

J. J. Vos and P. L. Walraven, “On the derivation of the foveal receptor primaries,” Vision Res. 11, 799–818 (1971); V. C. Smith, J. Pokorny, and S. J. Starr, “Variability of color mixture data. I. Interobserver variability in the unit coordinates,”  16, 1087–1094 (1976).
[CrossRef] [PubMed]

J. J. Vos and P. L. Walraven, “A zone-fluctuation line element describing colour discrimination,” in Color Metrics, edited by J. J. Vos, L. F. C. Friele, and P. L. Walraven (Association International de la Couleur, Soesterberg, 1972).

Walraven, P. L.

J. J. Vos and P. L. Walraven, “On the derivation of the foveal receptor primaries,” Vision Res. 11, 799–818 (1971); V. C. Smith, J. Pokorny, and S. J. Starr, “Variability of color mixture data. I. Interobserver variability in the unit coordinates,”  16, 1087–1094 (1976).
[CrossRef] [PubMed]

P. L. Walraven and M. A. Bouman, “Fluctuation theory of colour discrimination of normal trichromats,” Vision Res. 6, 567–586 (1966).
[CrossRef] [PubMed]

M. A. Bouman and P. L. Walraven, “Color discrimination data,” in Visual Psychophysics, edited by D. Jameson and L. Hurvich (Springer-Verlag, Berlin, 1972).
[CrossRef]

P. L. Walraven, “On the Mechanisms of Colour Vision,” Ph.D. thesis, Utrecht, 1962 (unpublished).

J. J. Vos and P. L. Walraven, “A zone-fluctuation line element describing colour discrimination,” in Color Metrics, edited by J. J. Vos, L. F. C. Friele, and P. L. Walraven (Association International de la Couleur, Soesterberg, 1972).

Wright, W. D.

Wyszecki, G.

Am. J. Psychol. (1)

R. W. Burnham, “The dependence of color upon area,” Am. J. Psychol. 64, 521–533 (1951).
[CrossRef] [PubMed]

Color Res. Applic. (1)

For computational purposes, we actually used equations that transform CIE x, y, and z values to Judd’s x′, y′, and z′values. The equations, from J. J. Vos, Color Res. Applic. 3, 125–128 (1978), arex′=1.0271x−0.00008y−0.000090.03845x+0.01496y+1,y′=0.00376x+1.0072y+0.007640.03845x+0.01496y+1,z′=1−x′−y′. To convert the derived chromaticity coordinates to distribution coefficients, we scaled them to make y¯′equal to CIE y¯at 460 nm and above. Below 460 nm, we used Judd’s y¯′at 10-nm intervals and linearly interpolated between those points.
[CrossRef]

Doc. Ophthalmol. (1)

F. P. Fischer, M. A. Bouman, and J. Ten Doesschate, “A case of tritanopy,” Doc. Ophthalmol. 5, 55–67 (1951).

Farbe (2)

G. Verriest and H. Kandemir, “Normal spectral increment thresholds on a white background,” Farbe 23, 3–16 (1974).

L. F. C. Friele, “Analysis of the Brown and Brown-MacAdam colour discrimination data,” Farbe 10, 193–224 (1961); L. F. C. Friele, “Color difference and color tolerance evaluation. Problems and outlook.” J. Mater. 6, 755–765 (1971); see also K. D. Chickering, “FMC color difference formulas: Clarification concerning usage,” J. Opt. Soc. Am. 61, 118–122 (1971).
[CrossRef]

J. Opt. Soc. Am. (14)

D. L. MacAdam, “Visual sensitivities to color differences in daylight,” J. Opt. Soc. Am. 32, 247–274 (1942).
[CrossRef]

W. R. J. Brown, “The influence of luminance level on visual sensitivity to color differences,” J. Opt. Soc. Am. 41, 684–688 (1951).
[CrossRef] [PubMed]

L. T. Sharpe and G. Wyszecki, “Proximity factor in color-difference evaluations,” J. Opt. Soc. Am. 66, 40–49 (1976).
[CrossRef] [PubMed]

G. Wyszecki, “Correlate for lightness in terms of CIE chromaticity coordinates and luminous reflectance,” J. Opt. Soc. Am. 57, 254–257 (1967).
[CrossRef] [PubMed]

P. E. King-Smith and D. Carden, “Luminance and opponent-color contributions to visual detection and adaptation and to temporal and spatial integration,” J. Opt. Soc. Am. 66, 709–717 (1976).
[CrossRef] [PubMed]

J. S. Kinney, “Changes in appearance of colored stimuli with exposure duration,” J. Opt. Soc. Am. 55, 738–739 (1965); R. W. Burnham, “Comparative effects of area and luminance on color,” Am. J. Psychol. 65, 27–38 (1952).
[CrossRef] [PubMed]

R. M. Boynton, G. Kandel, and J. W. Onley, “Rapid chromatic adaptation of normal and dichromatic observers,” J. Opt. Soc. Am. 49, 654–666 (1959).
[CrossRef] [PubMed]

D. B. Judd, “The Bezold-Brücke phenomenon and the Hering theory of vision,” J. Opt. Soc. Am. 38, 1095–1096 (1948).

L. M. Hurvich and D. Jameson, “Some quantitative aspects of an opponent-colors theory. II. Brightness, saturation, and hue in normal and dichromatic vision,” J. Opt. Soc. Am. 45, 602–616 (1955).
[CrossRef] [PubMed]

R. M. Boynton and J. Gordon, “Bezold-Brücke hue shift measured by color-naming technique,” J. Opt. Soc. Am. 55, 78–86 (1965).
[CrossRef]

S. L. Guth and H. R. Lodge, “Heterochromatic additivity, foveal spectral sensitivity, and a new color model,” J. Opt. Soc. Am. 63, 450–462 (1973).
[CrossRef] [PubMed]

R. W. Massof and J. F. Bird, “A general zone theory of color and brightness vision. I. Basic formulation,” J. Opt. Soc. Am. 68, 1465–1471 (1978); J. F. Bird and R. W. Massof, “A general zone theory of color and brightness vision. II. The space-time field,” ibid., 1471–1481 (1978).
[CrossRef] [PubMed]

J. Pokorny and V. C. Smith, “Luminosity and CFF in deuteranopes and protanopes,” J. Opt. Soc. Am. 62, 111–117 (1972).
[CrossRef] [PubMed]

W. D. Wright, “The characteristics of tritanopia,” J. Opt. Soc. Am. 42, 509–521 (1952).
[CrossRef] [PubMed]

J. Res. Natl. Bur. Stand. (1)

D. B. Judd, “Response functions for types of vision according to the Müller theory,” J. Res. Natl. Bur. Stand. 42, 1–16 (1949); D. B. Judd and G. T. Yonemura, “CIE 1960 UCS diagram and the Müller theory of color vision,” J. Res. Natl. Bur. Stand. Sec. A 74, 23–30 (1970); G. T. Yonemura, “Opponent-color-theory treatment of the CIE 1960 (U.V.) diagram: Chromaticness difference and constant-hue loci,” J. Opt. Soc. Am. 60, 1407–1409 (1970).
[CrossRef] [PubMed]

Med. Res. Counc. Spec. Rep. Ser. (1)

F. H. G. Pitt, “Characteristics of dichromatic vision,” Med. Res. Counc. Spec. Rep. Ser. 200, 1–58 (1935). Also see citations in Y. Hsia and C. H. Graham, “Color blindness,” in Vision and Visual Perception, edited by C. H. Graham (Wiley, New York, 1965).

Mod. Probl. Ophthalmol. (1)

G. Trick, S. L. Guth, and R. Massof, “Wavelength discrimination in protanopes and deuteranopes,” Mod. Probl. Ophthalmol. 17, 17–20 (1976).
[PubMed]

Proc. Natl. Acad. Sci. U.S.A. (1)

In the earlier description of the model, we incorrectly predicted the copunctal point for “loss” deuteranopes who lack the G receptor as well as the T system. The error was caused by a failure to remember that the defining equations were for observers who had all three receptors. That prediction would be correct only for “fusion” deuteranopes who also lack the T system, but who have normal R and G receptor inputs to the remaining A and D mechanisms. It may, of course, be that there exist both loss and fusion deuteranopes, but we here consider only the loss class. See D. B. Judd, “Fundamental studies of color vision from 1860 to 1960,” Proc. Natl. Acad. Sci. U.S.A. 55, 1313–1330 (1966).

Science (1)

H. G. Sperling and R. S. Harwerth, “Red-green cone interactions in the increment-threshold spectral sensitivity of primates,” Science 172, 180–184 (1972).
[CrossRef]

Vision Res. (11)

R. S. Harwerth and D. M. Levi, “Increment threshold spectral sensitivity in anisometropic amblyopia,” Vision Res. 17, 585–590 (1977).
[CrossRef] [PubMed]

S. L. Guth, N. J. Donley, and R. T. Marrocco, “On luminance additivity and related topics,” Vision Res. 9, 537–575 (1969).
[CrossRef] [PubMed]

Ingling and his colleagues [C. R. Ingling and B. Tsou, “Orthogonal combination of the three visual channels,” Vision Res. 17, 1075–1082 (1977); C. R. Ingling, ibid., 1083–1089 (1977)] have published a similar modification, which was first reported at the same ARVO meeting referred to in the title footnote.
[CrossRef] [PubMed]

S. L. Guth, J. V. Alexander, J. I. Chumbly, C. B. Gillman, and M. M. Patterson, “Factors affecting luminance additivity at threshold among normal and color-blind subjects and elaborations of a trichromatic-opponent colors theory,” Vision Res. 8, 913–928 (1968).
[CrossRef] [PubMed]

V. C. Smith and J. Pokorny, “Spectral sensitivity of color-blind observers and the cone photopigments,” Vision Res. 12, 2059–2071 (1972); “Spectral sensitivity of the foveal cone photopigments between 400 and 500 nm,”  15, 161–171 (1975).
[CrossRef] [PubMed]

J. J. Vos and P. L. Walraven, “On the derivation of the foveal receptor primaries,” Vision Res. 11, 799–818 (1971); V. C. Smith, J. Pokorny, and S. J. Starr, “Variability of color mixture data. I. Interobserver variability in the unit coordinates,”  16, 1087–1094 (1976).
[CrossRef] [PubMed]

R. W. Massof and J. E. Bailey, “Achromatic points in protanopes and deuteranopes,” Vision Res. 16, 53–57 (1966).
[CrossRef]

S. L. Guth, “Nonadditivity and inhibition among chromatic luminances at threshold,” Vision Res. 7, 319–328 (1967).
[CrossRef] [PubMed]

R. M. Boynton, M. Ikeda, and W. S. Stiles, “Interactions among chromatic mechanisms as inferred from positive and negative increment thresholds,” Vision Res. 4, 87–117 (1964).
[CrossRef] [PubMed]

A. Valberg, “Light adaptation and the saturation of colours,” Vision Res. 15, 401–404 (1975).
[CrossRef] [PubMed]

P. L. Walraven and M. A. Bouman, “Fluctuation theory of colour discrimination of normal trichromats,” Vision Res. 6, 567–586 (1966).
[CrossRef] [PubMed]

Other (11)

M. A. Bouman and P. L. Walraven, “Color discrimination data,” in Visual Psychophysics, edited by D. Jameson and L. Hurvich (Springer-Verlag, Berlin, 1972).
[CrossRef]

L. Guth, “A new color model,” in Color Metrics, edited by J. J. Vos, L. F. C. Friele, and P. L. Walraven (Association International de la Couleur, Soesterberg, 1972).

L. M. Hurvich, “The opponent-pairs scheme,” in Mechanisms of Colour Discrimination (Pergamon, London, 1960).

See second reference in Ref. 8.

H. R. Lodge, “Implications of a zone color vision model for spectral sensitivity of normal, protanopic, and deuteranopic subjects as measured by several psychophysical techniques,” Ph.D. dissertation, Indiana University, 1971, University microfilm order number 72-15917 (unpublished).

J. J. Vos and P. L. Walraven, “A zone-fluctuation line element describing colour discrimination,” in Color Metrics, edited by J. J. Vos, L. F. C. Friele, and P. L. Walraven (Association International de la Couleur, Soesterberg, 1972).

D. B. Judd, “Colorimetry and artificial daylight,” CIE Proc., Vol. I, Part 7, p. 11. See Table 5.8 in G. Wyszecki and W. S. Stiles, Color Science (Wiley, New York, 1967).

P. L. Walraven, “On the Mechanisms of Colour Vision,” Ph.D. thesis, Utrecht, 1962 (unpublished).

D. B. Judd, “Basic Correlates of the Visual Stimulus,” in Handbook of Experimental Psychology, edited by S. S. Stevens (Wiley, New York, 1951).

CIE Technical Report No. 41, “Light as a true visual quantity: Principles of measurements,” Report of Technical Committee TC 1.4 (1979). Available from U.S. Natl. Committee, Natl. Bureau of Standards, Washington, DC (unpublished).

Given the R, G, and B receptors, the defining properties of these equations are: (i) A is Judd’s correction of y¯; (ii) T and D have cross points at 575 and 502 nm, respectively; and, (iii) the coefficients in the threshold level A, T, and D equations were scaled to optimize predictions of spectral sensitivity and heterochromatic additivity data as shown in Fig. 8 of Ref. 2 and Fig. 10 of this paper.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (26)

FIG. 1
FIG. 1

Schematic diagram of the ATD vector model.

FIG. 2
FIG. 2

Receptor absorption characteristics. Wavelengths of maximum absorption for R, G, and B are 566, 543, and 440 nm, respectively.

FIG. 3
FIG. 3

Threshold-level, equal-radiance response functions for A, the achromatic system (dots and dashes) T, the tritanopic system (short dashes), and D, the deuteranopic system (long dashes).

FIG. 4
FIG. 4

Threshold-level equal-detectability (equal-vector length) response functions for A (curve with maximum value), T (curve with most negative value), and D (remaining curve).

FIG. 5
FIG. 5

Apparent hue of the spectral colors for two levels according to data from Boynton and Gordon15 and according to the ATD vector model (right). Parameters for the low-intensity (t/d = 4.0) and high-intensity (t/d = 12.0) predictions are chosen for illustrative purposes and are not meant to yield optimal descriptions of the data.

FIG. 6
FIG. 6

Predicted apparent saturation of the spectrum according to several arbitrarily chosen variations of the ATD vector model.

FIG. 7
FIG. 7

Foveal spectral sensitivity based upon a literature review by Kaiser and Kinney18 (data points) and according to the ATD vector model (smooth curve).

FIG. 8
FIG. 8

Mean white-adapted (9000 td) incremental-threshold spectral sensitivities obtained by Harwerth and Levi20 from four subjects (solid line) and according to the vector model with a = 0.07, t = 0.19, and d = 0.74 (dashes).

FIG. 9
FIG. 9

Effects of chromatic adaptation on spectral sensitivities as obtained by Boynton, Kandel, and Onley27 (data points) and according to the ADT vector model with the indicated parameter values. Unspecified parameter values are unity.

FIG. 10
FIG. 10

Heterochromatic addivity data from Girth, Donley, and Marrocco16 (solid lines) and according to the normative threshold-level vector model, where a = t = d = 0.333 (dashes). The ordinate value for each point gives the angle (between the indicated wavelength and the abscissa wavelength) that predicts the detectability of the mixture of those wavelengths. Control data points, where wavelengths are added to themselves, are always at 0°. Several “superadditive” data points are presumed to be spurious and have been adjusted to 0°. This produces the apparent flatness in the 475, 500, 525, and 553 functions.

FIG. 11
FIG. 11

Transformed increment-threshold heterochromatic additivity data obtained with two intensities of greenish backgrounds by Boynton, Ikeda, and Stiles29 (solid lines) and as predicted by the vector model with the indicated parameters (dashes). One incremental component of each mixture was always 630 nm. The other incremental component is indicated on the abscissa.

FIG. 12
FIG. 12

Same as Fig. 11 (including parameters) except that one component was an increment and one a decrement.

FIG. 13
FIG. 13

Loci of constant brightness-to-luminance (vector luminance to achromatic luminance) ratios predicted (to a first approximation) by the vector model with a = t = d = 0.333.

FIG. 14
FIG. 14

Same as Fig. 13, except that a = 0.07, t = 0.19, and d = 0.74.

FIG. 15
FIG. 15

Left: unit achromatic luminance chromaticity diagrams for three variations (simulating three brightness levels) of the vector model. Right: JND circles in the high-brightness diagram. Centers of closed circles are MacAdam’s32 centers. Dashed circles would fall in extreme lower left corner of CE x, y space and illustrate the consequence of making the radius of the JND circle proportional to vector luminance or (to a first approximation) brightness.

FIG. 16
FIG. 16

Projections of closed circles from Fig. 15 into x, y space.

FIG. 17
FIG. 17

MacAdam’s ellipses.32

FIG. 18
FIG. 18

Projections of JND circles that could be drawn in the medium-size t/d chromaticity diagram of Fig. 15 into x, y chromaticity space. Center points are the same as in Figs. 16 and 17.

FIG. 19
FIG. 19

Arbitrarily positioned, equal-brightness (i.e., unit-vector length) wavelength discrimination functions as predicted by a representative selection of ATD models with the indicated parameters. Ordinate values are reciprocals of the mean distance from a given wavelength to its two neighbors, one 10 nm longer and one 10 nm shorter. Actual positioning of functions on the ordinate would “depend upon the Weber fraction that prevails.

FIG. 20
FIG. 20

Wavelength discrimination curves from various sources as collected by Vos and Walraven.35

FIG. 21
FIG. 21

Ratio of threshold spectral sensitivities to flicker-photometric sensitivities as determined by Lodge39 for eight deuteranopes (dashes) and according to the A, D vector model (solid line). Normalization is at 580 nm.

FIG. 22
FIG. 22

Same as Fig. 21 for five protanopes.

FIG. 23
FIG. 23

Mean relative vector luminances (threshold units) added to subthreshold fields of 635 (top), 435 (middle), or 500 nm (bottom) by normals (solid line), deuteranopes (open circles), and protanopes (dashes and filled circles). Same as Fig. 7 in Guth et al.7

FIG. 24
FIG. 24

Predictions of data shown in Fig. 23 as made by the normative, threshold-level vector model for subthreshold fields of 650 (top), 440 (middle), and 500 nm (bottom).

FIG. 25
FIG. 25

Same as Fig. 19, except that wavelength discrimination predictions are shown for deuteranopes (left) and protanopes (right).

FIG. 26
FIG. 26

Same as Fig. 19, except that wavelength discrimination predictions are shown for tritanopes.

Equations (14)

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

R = 0.2435 x ¯ + 0.8524 y ¯ 0.0516 z ¯ ,
G = 0.3954 x ¯ + 1.1642 y ¯ + 0.0837 z ¯ ,
B = 0.6225 z ¯ .
A = 1.0 ( 0.5967 R + 0.3654 G ) ,
T = 1.0 ( 0.9553 R 1.2836 G ) ,
D = 1.0 ( 0.0248 R + 0.0483 B ) .
A = 1.0 ( 0.9341 y ¯ )
T = 1.0 ( 0.7401 x ¯ 0.6801 y ¯ 0.1567 z ¯ )
D = 1.0 ( 0.0061 x ¯ 0.0212 y ¯ + 0.0314 z ¯ ) .
X = 1.1840 A + 1.4072 T + 7.0435 D , Y = 1.0698 A , Z = 0.9495 A + 0.2703 T + 33.2576 D .
X = 1.275 A + 1.137 T + 0.948 D , Y = 1.152 A , Z = 1.023 A + 0.218 T + 4.478 D .
A = 1.0 ( 0.9621 R ) , D = 1.0 ( 0.0400 R + 0.0483 B ) .
A = 1.0 ( 0.5967 R + 0.3654 G ) , T = 1.0 ( 0.9553 R 1.2836 G ) .
x=1.0271x0.00008y0.000090.03845x+0.01496y+1,y=0.00376x+1.0072y+0.007640.03845x+0.01496y+1,z=1xy.