Using simulated data sets, we have analyzed some mathematical properties of different statistical measurements that have been employed in previous literature to test the performance of different color-difference formulas. Specifically, the properties of the combined index PF/3 (performance factor obtained as average of three terms), widely employed in current literature, have been considered. A new index named standardized residual sum of squares (STRESS), employed in multidimensional scaling techniques, is recommended. The main difference between PF/3 and STRESS is that the latter is simpler and allows inferences on the statistical significance of two color-difference formulas with respect to a given set of visual data.

The standardized residual sum of squares (STRESS) index was used to reevaluate four experimental datasets employed during the development of CIEDE2000, the current CIE recommended color-difference formula. This index enables statistical inferences not achievable by other metrics used commonly for performance evaluation. It was found that CIEDE2000 was statistically superior at a 95% confidence level to either CIE94, the previous recommended equation by the CIE, or the simple Euclidean distance in CIELAB, DeltaE*ab. Recent formulas based on the CIECAM02 color-appearance space and chroma-compressed variants of CIELAB were also evaluated and found to have only slightly reduced performance compared with CIEDE2000. These formulas have the advantage of simplicity and easier interpretation when used for quantifying color accuracy. Finally, each experimental dataset was evaluated separately rather than weight averaged as used during the development of CIEDE2000. Significant differences were found between datasets, suggesting that combining datasets may obscure important differences and that the practice of parameter optimization during formula development using combined data is likely suboptimal.

Psychophysical experiments were conducted in the UK, Taiwan, France, Germany, Spain, Sweden, Argentina, and Iran to assess colour emotion for two-colour combinations using semantic scales warm/cool, heavy/ light, active/passive, and like/dislike. A total of 223 observers participated, each presented with 190 colour pairs as the stimuli, shown individually on a cathode ray tube display. The results show consistent responses across cultures only for warm/cool, heavy/light, and active/passive. The like/dislike scale, however, showed some differences between the observer groups, in particular between the Argentinian responses and those obtained from the other observers. Factor analysis reveals that the Argentinian observers preferred passive colour pairs to active ones more than the other observers. In addition to the cultural difference in like/dislike, the experimental results show some effects of gender, professional background (design vs. nondesign), and age. Female observers were found to prefer colour pairs with high-lightness or lowchroma values more than their male counterparts. Observers with a design background liked low-chroma This article was published online on 12 November 2010. An error was subsequently identified in Table II. This notice is included in the online and print version to indicate that both have been corrected. *Correspondence to: Li-Chen Ou (e-mail: l.ou@leeds.ac.uk).Volume 37, Number 1, February 2012 23 colour pairs or those containing colours of similar hue more than nondesign observers. Older observers liked colour pairs with high-lightness or high-chroma values more than young observers did. Based on the findings, a two-level theory of colour emotion is proposed, in which warm/cool, heavy/light, and active/passive are identified as the reactive-level responses and like/dislike the reflective-level response.

A new set of quantitative models of colour emotion and colour harmony were developed in this study using psychophysical data collected from 12 regions in the world, and the UK. These data have previously been published in journals or conferences (for details see Tables 1 and 2). For colour emotion, three new models were derived, showing satisfactory predictive performance in terms of an average correlation coefficient of 0.78 for "warm/cool", 0.80 for "heavy/light" and 0.81 for "active/passive". The new colour harmony model also had satisfactory predictive performance, with an average correlation coefficient of 0.72. Principal component analysis shows that the common colour harmony principles, including hue similarity, chroma similarity, lightness difference and high lightness principles, were partly agreed by observers of the same region. The findings suggest that it is feasible to develop universal models of colour emotion and colour harmony, and that the former was found to be relatively more culture-independent than the latter. K E Y W O R D Scolour emotion, colour harmony, cross-cultural study, universal model

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