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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 47, Iss. 4 — Apr. 1, 1957
  • pp: 268–274

Analytical Approximations for Color Metric Coefficients

D. L. MACADAM  »View Author Affiliations


JOSA, Vol. 47, Issue 4, pp. 268-274 (1957)
http://dx.doi.org/10.1364/JOSA.47.000268


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Abstract

On the assumption of a color space of constant negative curvature, von Schelling has given simple formulas for the color metric coefficients. An attempt has been made to fit such formulas to newly available color-discrimination data for 12 normal observers. A least-squares analysis indicates that Y should be replaced with the quantity, Y′ = Y-0.085X+0.011Z, in the special role assigned to luminance by von Schelling. Corresponding to this change, coordinates x’=X/(X+ Y’+Z), y’= Y’/(X+ Y’+Z) yield the simplest formulas for the coefficients of the expression for color difference: ΔS=(g11Δx2+2g12Δx’Δy’+g22Δ′2+g33 Δy2/y2)½. Least-squares fitting of the experimental data to von Schelling’s formulas yielded: g11=g33/(10x’2-6.886x’+2.083+2.5y’-16.66xy’+19.6y2). g12=g11(0.3443-x’)/y’. g22=g11[0.09+(0.3443-x’)2]/y2. These formulas are the best approximations obtainable on the assumption of a color space of constant negative or zero curvature. However, they give such poor approximations to the experimental data that it is concluded that the assumption of a color space inherently more complicated than a space of constant curvature would be required to fit the data to a closeness commensurate with the experimental reproducibility.

Citation
D. L. MACADAM, "Analytical Approximations for Color Metric Coefficients," J. Opt. Soc. Am. 47, 268-274 (1957)
http://www.opticsinfobase.org/josa/abstract.cfm?URI=josa-47-4-268


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References

  1. D. L. MacAdam, J. Opt. Soc. Am. 32, 247–274 (1942).
  2. W. R. J. Brown and D. L. MacAdam, J. Opt. Soc. Am. 39, 808–834 (1949).
  3. W. R. J. Brown, J. Opt. Soc. Am. 47, 137–143 (1957).
  4. D. L. MacAdam, J. Opt. Soc. Am. 33, 18–26 (1943).
  5. H. von Schelling, J. Opt. Soc. Am. 45, 1072–1079 (1955).
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