The properties of multiple CMF determinations using alternative primary sets part I: Evidence and modeling
Authors: Oulton David P. 
Published: May 2004

This article concerns William Thornton's single‐observer colour matching functions (CMFs). Alternative “prime colour” (or PC), “non‐prime” (or NP), and “anti‐prime” (or AP) wavelengths were used, and the measurements appear to challenge the basis on which conventional colorimetry predicts metameric colour matches. An analysis of Thornton's visual match data for alternative‐primary CMFs is presented. Using conventional colorimetric calculations, Thornton's articles establish failures of linear transformability between experimental data sets, failures of tristimulus sum prediction, and differences in CIE chromaticity for a set of strongly metameric stimuli that all match the same neutral reference stimulus. Error analysis using an optimization model is first used to confirm that Thornton's data represent a significant challenge to the standard colorimetric model. Thornton's assertion is supported that spectral power appears to be visually subadditive at NP and AP wavelengths compared with spectral power at the PC wavelengths. It is next shown that each of the individual failures of prediction can be eliminated by relatively minor adjustments to the relevant CMFs. However, each instance of failure required a different adjustment. Multiple and significantly incompatible linear adjustments of the CMFs are apparently needed to explain Thornton's results. The implication is that the visually additive value of the spectral stimuli used in the matches varies not only with wavelength but also as a nonlinear function of stimulus power. The implied variations in visual additivity become significant only at certain wavelengths. Thus a small and specific subset of strongly metameric light‐source matches, such as those chosen by Thornton, are required to reveal significant variations. Such spectrally localized variations have a minimal overall effect in the tristimulus sum predictions for surface‐colour matches using broadband stimuli. A detailed analysis of the central assumptions concerning additive colour mixing is given. It suggests that any super and subadditive visual effects revealed by Thornton's measurements can be accommodated within the standard colorimetric model by extending the model rather than by modifying the CMFs. An extension is proposed in which any possible super‐ or subadditive phenomena are modeled by a redefinition of the units of visual additivity, using a spectral‐level precursor transform. Its intent is to equate the additive properties of all possible incident stimuli numerically, prior to manipulation using the Standard Model. An appropriate methodology is also described for confirming measuring and classifying any spectrally distinct super and subadditive effects. Under The Heading for Prediction Failures the methods described are applied to Thornton's data. They reveal consistent evidence of additivity differences that are both wavelength and stimulus power dependent. © 2004 Wiley Periodicals, Inc. Col Res Appl, 29, 273–284, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.20022