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CIE 217

2016 Edition, January 1, 2016

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Recommended Method for Evaluating the Performance of Colour-Difference Formulae

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For a pair of colour samples, the magnitude of the visually-perceived colour difference between such samples, usually designated as ΔV, can be considered as much as the computed colour difference from objective instrumental colour measurements of the colour samples, usually designated as ΔE. While ΔV is the result of a subjective answer from a human observer, ΔE is an objective measurement provided by what is known as a “colourdifference formula”. A colour-difference formula can be defined as a mathematical equation providing a non-negative number ΔE from the numerical colour specifications of two colour samples. Most recent colour-difference formulae also incorporate other parameters related to the illuminating and viewing conditions of the samples, which are usually known in the literature as “parametric factors” (CIE, 1993).

Obviously, the result given by the human visual system (ΔV) is the most important part in the binomial ΔV-ΔE, and the goal of colour scientists is to achieve a colour-difference formula providing an accurate prediction of colour differences perceived by average observers, for any pair of colour samples under any illuminating/viewing conditions. Certainly, this is an ambitious goal, bearing in mind that currently the human visual system is not fully understood. However, important advances have been made in recent years (Melgosa et al., 2008; M. Huang et al., 2015), as will be described in this report. Note that we can also speak about perceived (ΔV) and computed (ΔE) colour differences in more complex situations than just two homogeneous colour samples, as in the case of colour differences between two complex images (CIE, 2011). In fact, colour-difference formulae are currently used as part of colourquality control in many industries as well as in applications such as textiles (Kuo, 2010; P.-F. Li et al., 2014), printing (Liu et al., 2013; Z.J. Li and Meng, 2014), automobiles (Mirjalili et al., 2014; Melgosa et al., 2014), dentistry (Kim et al., 2009; Khashayar et al., 2014), food (Zhao et al., 2011; Salmerón et al., 2012), agriculture (Hauptmann et al., 2012; Gómez-Robledo et al., 2013), and medical imaging (Inoue et al., 2010; Jernigan, 2014).

This Technical Report mainly deals with methods to assess the performance or merit of different colour-difference formulae, proposing the use of the index known as the Standardized Residual Sum of Squares (STRESS) index. Among the main advantages of the STRESS index is that it can be used to test whether two colour-difference formulae are or are not statistically significantly different with respect to a given set of visual data, and also that it can be used to measure the intra- and inter-observer variability in the results from visual experiments (García et al., 2007; Melgosa et at., 2011). The results achieved by the most relevant colour-difference formulae currently employed in industrial applications are also provided, considering different visual datasets of object colours. Specifically, the structure of this Technical Report is as follows: in Clause 2, some background on the characteristics of visual colour-difference experiments, available colour-difference formulae, and reliable visual datasets is provided; Clause 3 considers how to measure the strength of the relationship between perceived and computed colour differences using indices proposed by different authors; Clause 4 proposes the use of the STRESS index in colour-difference evaluation; Clause 5 provides STRESS values for most relevant colour-difference formulae from the visual datasets adopted at the development of the last ISO/CIE recommended colourdifference formula, CIEDE2000 (Luo et al. 2001; CIE, 2001; ISO/CIE, 2014), and some other recent visual datasets proposed by different authors; and finally Clause 6 states the main conclusions, recommendations and suggestions for future work.