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Journal of the Optical Society of America

  • Vol. 70, Iss. 2 — Feb. 1, 1980
  • pp: 197–212

Vector model for normal and dichromatic color vision

S. Lee Guth, Robert W. Massof, and Terry Benzschawel  »View Author Affiliations

JOSA, Vol. 70, Issue 2, pp. 197-212 (1980)

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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

S. Lee Guth, Robert W. Massof, and Terry Benzschawel, "Vector model for normal and dichromatic color vision," J. Opt. Soc. Am. 70, 197-212 (1980)

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  1. S. 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).
  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).
  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.
  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).
  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).
  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).
  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).
  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), are x′ = 1.0271 x - 0.00008 y - 0.00009/03845 x + 0.01496 y + 1, y′ =0.00376 x + 1.0072 y + 0.00764/0.03845 x + 0.01496 y + 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.
  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).
  15. R. M. Boynton and J. Gordon, "Bezold-Brücke hue shift measured by color-naming technique," J. Opt. Soc. Am. 55, 78–86 (1965).
  16. S. L. Guth, N. J. Donley, and R. T. Marrocco, "On luminance additivity and related topics," Vision Res. 9, 537–575 (1969).
  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).
  20. R. S. Harwerth and D. M. Levi, "Increment threshold spectral sensitivity in anisometropic amblyopia," Vision Res. 17, 585–590 (1977).
  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).
  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).
  25. R. W. Burnham, "The dependence of color upon area," Am. J. Psychol. 64, 521–533 (1951).
  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).
  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).
  28. S. L. Guth, "Nonadditivity and inhibition among chromatic luminances at threshold," Vision Res. 7, 319–328 (1967).
  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).
  30. G. Wyszecki, "Correlate for lightness in terms of CIE chromaticity coordinates and luminous reflectance," J. Opt. Soc. Am. 57, 254–257 (1967).
  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).
  32. D. L. MacAdam, "Visual sensitivities to color differences in daylight," J. Opt. Soc. Am. 32, 247–274 (1942).
  33. W. R. J. Brown, "The influence of luminance level on visual sensitivity to color differences," J. Opt. Soc. Am. 41, 684–688 (1951).
  34. L. T. Sharpe and G. Wyszecki, "Proximity factor in color-difference evaluations," J. Opt. Soc. Am. 66, 40–49 (1976).
  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).
  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).
  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).
  43. G. Trick, S. L. Guth, and R. Massof, "Wavelength discrimination in protanopes and deuteranopes," Mod. Probl. Ophthalmol. 17, 17–20 (1976).
  44. W. D. Wright, "The characteristics of tritanopia," J. Opt. Soc. Am. 42, 509–521 (1952).
  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).

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