Abstract

A brief summary is given of the paper by Stiles. The line-element suggested by Stiles is shown to be the sum of the squares of total differentials of three magnitudes. Therefore, the corresponding color threefold is Euclidean. For the same reason, the line-element originally proposed by Helmholtz also defined a Euclidean color space. The customary parameters of colorimetry correspond to curvilinear coordinates in the color space of both Helmholtz and Stiles. In both of those spaces, constant luminosity is represented by curved surfaces. The forms of the line-elements of both Helmholtz and Stiles imply that geodesics, representing series of colors which exhibit the least number of just-perceptible differences between any two colors, are straight lines in the Euclidean spaces defined by those line-elements. They also imply that ordinary length measured along these lines is proportional to the number of just-perceptible differences between the colors represented by the terminal points. No direct tests of these implications are known. MacAdam’s data on the discrimination of equiluminous colors determine a surface of constant luminosity in the color discrimination space for at least one observer (PGN). This surface exhibits such severe (and irreducible) curvature that the straight lines drawn between most pairs of considerably different equiluminous colors are, at their midpoints, far from the surface of constant luminosity. The line-elements of both Stiles and Helmholtz, therefore, imply that the series of colors exhibiting the least number of just-perceptible differences between two equiluminous colors includes many colors of very different luminosity. Although no observational tests are known, it seems unreasonable to expect that considerable departures from the common luminosity of the terminal colors will reduce the number of differences perceptible in any series between them. Attention is called to the criterion of probability of errors in color matching as an alternative to just-perceptible differences for investigations of visual sensitivities to color differences. This concept leads to a definition of the line-element independently of any assumption of the applicability to color discrimination of Fechner’s law or its modifications.

© 1947 Optical Society of America

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References

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Equations (13)

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