Linearity of the Relationship between the Tristimulus Values of Corresponding Colours Seen under Different Conditions of Chromatic Adaptation

Abstract

The hypothesis that the tristimulus values of the corresponding colours are linearly related is tested in three cases of chromatic adaptation. Test colours illuminated by yellow, magenta and green lights are matched against Munsell samples under the illuminant C in a binocular viewer of improved design, and the elements of the transformation matrices are calculated by the method of least squares. Scrutiny of the discrepancies between the values of the observed and the computed matches indicates that the hypothesis of linearity holds in these cases as it did in the previously investigated cases of adaptation to illuminants of continuous energy distributions. On the strength of this evidence the invariant colours are calculated in each case using the geometrical properties of the affine transformation. The red and the blue invariants differ but little from the earlier determinations. The third invariant still shows no inclination to any particular region of the colour chart.