OSA's Digital Library

Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 27, Iss. 8 — Aug. 1, 1937
  • pp: 294–297

Projective Transformations of I. C. I. Color Specifications

DAVID L. MACADAM  »View Author Affiliations

JOSA, Vol. 27, Issue 8, pp. 294-297 (1937)

View Full Text Article

Acrobat PDF (627 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



The use of the I. C. I. 1931 Standard Observer and Coordinate System for Colorimetry for all general color specifications and calculations is urged for the elimination of confusion in the field of colorimetry. Methods for constructing other coordinate systems are exhibited, and interpretations are given for the eight independent constants in the equations for transformation from the I. C. 1. to other coordinate systems. Expressions are derived for the luminosity coefficients in terms of the constants of the equations for the transformation of coordinates. The possibility of assigning luminosity coefficients without restricting the shape of the spectrum locus is discussed, and an example is given. The assignment of luminosity coefficients interferes with the assignment of the shape of the spectrum locus only in the case of three equal luminosity coefficients. In general, two of the eight degrees of freedom which are available in the defining equations of a trichromatic coordinate system are eliminated by the assignment of the luminosity coefficients. Except in the case of three equal luminosity coefficients, four of the six remaining degrees of freedom are eliminated when the shape of the spectrum locus is established. One additional degree of freedom is eliminated when the size of the spectrum locus is assigned. The final degree of freedom is most profitably used for the purpose of simplifying the transformation equations. The entire discussion is based on well-known principles of transformation of color mixture data and projective geometry; no assumptions other than those underlying standard trichromatic color specification are made, and no conclusions of physiological or psychological import are justified.

DAVID L. MACADAM, "Projective Transformations of I. C. I. Color Specifications," J. Opt. Soc. Am. 27, 294-297 (1937)

Sort:  Author  |  Year  |  Journal  |  Reset


  1. D. B. Judd, "A Maxwell Triangle Yielding Uniform Chromaticity Scales," J. O. S. A. 25, 24 (1935).
  2. D. B. Judd, "Estimation of Chromaticity Differences and Nearest Color Temperature on the Standard 1931 I. C. I. Colorimetric Coordinate System," J. O. S. A. 26, 421 (1936).
  3. F. C. Breckenridge, and W. R. Schaub, "Rectangular Uniform-Chromaticity-Scale Coordinates," Abstract No. 14, J. O. S. A. 27, 226 (1937).
  4. R. H. Sinden, "Further Search for the Ideal Color System, I," J. O. S. A. 27, 124 (1937).
  5. H. E. Ives, "The Transformation of Color Mixture Equations from One System to Another," J. Frank. Inst. 180, 673 (1915); also "The Transformation of Color Mixture Equations from One System to Another, II. Graphical Aids," J. Frank. Inst. 195, 23 (1923).
  6. J. Guild, "The Transformation of Trichromatic Mixture Data: Algebraic Method," Trans. Opt. Soc. 26, 95 (1924); also "The Geometrical Solution of Color Mixture Problems," Trans. Opt. Soc. 26, 139 (1924).
  7. D. B. Judd, "Reduction of Data on Mixture of Color Stimuli," Nat. Bur. Stand. J. Research 4, 515 (1930).
  8. Proc. 8th Session, Commission International de l'Eclairage, Cambridge, 1931. Note that the initials, C. I. E., which refer to the French form of the title are sometimes used as an abbreviation instead of the initials, I. C. I. Also, T. Smith, and J. Guild, "The C. I. E. Colorimetric Standards and Their Use," Trans. Opt. Soc. 33, 73 (1931). Also, D. B. Judd, "The I. C. I. Standard Observer and Coordinate System for Colorimetry," J. O. S. A. 23, 359 (1933). The possibility of future changes in the international system of colorimetric specification cannot be denied. The fact that such changes would render obsolescent the tremendous mass of colorimetric data which is being accumulated by many laboratories in this country and abroad at an accelerating rate now totaling several hundred samples each working day appears to be creating an inertia which will tend to prevent any changes which are not necessitated by the discovery of extremely serious errors in the 1931 recommendations. Evidence of errors ofsuch a serious nature has not as yet been reported by any worker. The particular unitary stimuli in which the I. C. I. specifications are expressed have no peculiar merits, other than convenience for computation, which would lead to their adoption in preference to the ninefold infinity of other conceivable choices of unitary stimuli. They are peculiarly important only in that they are being used. widely as bases for colorimetric specifications.
  9. A. C. Hardy, Handbook of Colorimetry (Technology Press, Cambridge, Mass., 1936).
  10. D. L. MacAdam, "Theory of Maximum Visual Efficiency of Colored Materials," J. O. S. A. 25, 249 (1935).
  11. T. Smith, "The Color Triangle and Color Discrimination," Joint Discussion on Vision, Physical and Optical Societies, London, 1932. The special case of equal luminosity coefficients is discussed, beginning on page 217, with the correct statement that the alychne must be projected to infinity. This projection of the alychne to infinity interferes with the freedom to assign the shape of the spectrum locus. The complete discussion of this case would involve some rather annoying exercises in the evaluation of indeterminate ratios, and will be omitted from the present paper.

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited