No abstract

This work continues previous research by the same authors [J. Opt. Soc. Am. A23, 2077 (2006)], where empirical small-medium color differences were represented by an ellipsoidal equation DeltaEGP in the Uniform Color System of the Optical Society of America. Now logarithmic compressions on chroma and lightness are introduced to produce a new space with Euclidean color-difference formulas DeltaEE. The CIEDE2000, DeltaEGP, and DeltaEE formulas are found statistically equivalent in the prediction of many available empirical datasets. However, DeltaEE is the simplest formula providing relationships with visual processing. These analyses hold true for CIE 1964 Supplementary Standard Observer and D65 illuminant.

An investigation of the color metrics and the complexity of the CIEDE2000 formula shows that CIELAB space is inadequate to represent small-medium color differences. The OSA-UCS (Uniform Color Space) Committee has shown that no space with uniform scale for large color differences exists. Therefore the practical way for color-difference specification is a color-difference formula in a nonuniform space. First, the BFD (Bradford University) ellipses are considered in the OSA-UCS space, and their very high regularity suggests a new and very simple color-difference formula at constant luminance. Then the COM (combined) data set used for the development of the CIEDE2000 formula is considered in the OSA-UCS space, and the color-difference formula is extended to sample pairs with a different luminance factor. The value of the performance factor PF/3 for the proposed OSA-UCS-based formula shows that the formula performs like the more complex CIEDE2000 formula for small-medium color differences.

We have used 13 experimental datasets (7420 colour pairs) to study the performance of the weighting function for lightness proposed by the CIEDE2000 colour‐difference formula, because it has been suggested that this function can be improved by using the weighting function for lightness SL = 1 adopted by the CIE94 colour‐difference formula. Using the standardised residual sum of squares (STRESS) index, it was found that: (i) replacing the SL in CIEDE2000 with SL = 1 improved the results for 7/13 datasets considered, but the improvement was statistically significant only for 1/13 datasets; (ii) a Whittle‐type lightness‐difference formula can be used to replace the term ∆L*/SL in CIEDE2000, which led to a new colour‐difference formula with no statistically significant difference with respect to CIEDE2000 for any of the 13 experimental datasets. A modification of the CIEDE2000 formula using a Whittle‐type lightness formula is proposed.

The most widely used color-difference formulas are based on color-difference data obtained under D65 illumination or similar and for a 10° visual field; i.e., these formulas hold true for the CIE 1964 observer adapted to D65 illuminant. This work considers the psychometric color-vision model based on the Optical Society of America-Uniform Color Scales (OSA-UCS) system previously published by the first author [J. Opt. Soc. Am. A 21, 677 (2004); Color Res. Appl. 30, 31 (2005)] with the additional hypothesis that complete illuminant adaptation with perfect color constancy exists in the visual evaluation of color differences. In this way a computational procedure is defined for color conversion between different illuminant adaptations, which is an alternative to the current chromatic adaptation transforms. This color conversion allows the passage between different observers, e.g., CIE 1964 and CIE 1931. An application of this color conversion is here made in the color-difference evaluation for any observer and in any illuminant adaptation: these transformations convert tristimulus values related to any observer and illuminant adaptation to those related to the observer and illuminant adaptation of the definition of the color-difference formulas, i.e., to the CIE 1964 observer adapted to the D65 illuminant, and then the known color-difference formulas can be applied. The adaptations to the illuminants A, C, F11, D50, Planckian and daylight at any color temperature and for CIE 1931 and CIE 1964 observers are considered as examples, and all the corresponding transformations are given for practical use.