Publications Sponsored by the Colour Measurement Committee—VIII

Abstract

Methods of describing the extent of agreement between the ΔE values calculated from a colour‐difference equation and the corresponding visual estimates of colour difference are discussed. Lack of agreement will be due to a combination of errors in the visual assessments, in the measurements, and in the colour‐difference equation itself. If there were no error in the instrumental measurements, the equation error for a particular colour difference would be the difference between the calculated ΔE value and the mean visual assessment of a very large number of observers (ΔVtrue). Experimental data in the form of acceptances (%) can be converted to ΔV values directly proportional to the observed colour differences. The overall equation error for n colour differences can be calculated from Eqn 1. The Davidson and Friede data are considered to be the most satisfactory of those presently available for testing the suitability of equations for industrial colour‐tolerance work and have been used to assess the accuracy of several well‐known equations. After allowing for errors in the visual assessment and in the instrumental measurements, σ(log ΔE) for the 1964 CIE equation was 0.22. Similar values (0.16‐0.23) were found for other equations. A lower a‐value was found for a very simple empirical equation essentially based on the x, y chromaticity diagram rather than on any transformation of it. The usual transformations tend to be based on data covering the whole chromaticity gamut, whereas real surface colours cover only a fraction of the possible area. This fact, together with the knowledge that most equations are based on data corresponding to small fields of view or large colour differences, could account for the relative failure of the standard equations.