OSA's Digital Library

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


View Full Text Article

Acrobat PDF (662 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

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

You do not have subscription access to this journal. Citation lists with outbound citation links are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Log in to access OSA Member Subscription

You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Log in to access OSA Member Subscription

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited