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, $\mathrm{\Delta }{E}_{ab}^{*}$. 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.

The commercialization of EnChroma glasses has generated great expectations for people to be able to see new colors or even correct color vision deficiency (CVD). We evaluate the effectiveness of these glasses using two complementary strategies for the first time. The first consists of using the three classical types of tests — recognition, arrangement and discrimination — with and without glasses, with a high number of individuals. In the second, we use the spectral transmittance of the glasses to simulate the appearance of stimuli in a set of scenes for normal observers and observers with CVD. The results show that the glasses introduce a variation of the perceived color, but neither improve results in the diagnosis tests nor allow the observers with CVD to have a more normal color vision.

This work continues previous research by the same authors [J. Opt. Soc. Am. A 23, 2077 (2006) ], where empirical small–medium color differences were represented by an ellipsoidal equation $\Delta E_{\mathit{GP}}$ 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 $\Delta E_E$. The CIEDE2000, $\Delta E_{\mathit{GP}}$, and $\Delta E_E$ formulas are found statistically equivalent in the prediction of many available empirical datasets. However, $\Delta E_E$ is the simplest formula providing relationships with visual processing. These analyses hold true for CIE 1964 Supplementary Standard Observer and D65 illuminant.

We have analyzed the way in which simulated textures made of random dots influence visual suprathreshold color tolerances. We considered 32 textures created by a systematic variation of the following variables: size, number, and color of the dots. Each texture was mapped on the five centers recommended by the International Commission on Illumination (CIE) in 1978 [Color Res. Appl. 3, 149 (1978) ]. A panel of five experienced observers determined the experimental tolerances using a CRT color monitor by the method of adjustment. At our observation distance, neither small differences in dot size (1 or $4\text{\hspace{0.17em} pixels}$) nor sparse number of dots (less than 20% of the surface of the sample) changed the tolerances found for homogeneous samples. For the textures that led to statistically significant differences with respect to homogeneous samples, the parametric factors of CIEDE2000 and CIE94 color-difference formulas were fitted. These simulated textures consistently reduced the color difference perceived in a pair or, equivalently, increased the tolerances, mainly (but not only) lightness tolerance. The results demonstrate that it is not simple to provide a unique set of parametric factors for all the potential textures.