Comparison of two color-difference formulas using the Bland-Altman approach based on natural tooth color space

Statement of problem. Several formulas to measure color differences have been proposed to improve the correlation between color measurements and visual perception. Despite the progress obtained, equating between formulas is complex, rendering the exchange of information in scientific papers difficult. Purpose. The purpose of this study was to determine the relationship between the results provided by classic CIELab (Delta Eab*) and the CIEDE2000 (Delta E00) formulas in the natural tooth color space using the Bland and Altman limits of agreement, to use this relationship to establish the equivalences between the tooth color thresholds of acceptability and perceptibility of both formulas, and to evaluate whether the relationship between Delta Eab* and Delta E00 is modified depending on the axis on which the changes occur. Material and methods. The L*, a*, and b* means coordinates in the 26 shade tabs of the Tooth guide 3D Master were used, and color differences were calculated in 325 pairs of shade tabs using the CIELab (Delta E*ab) and CIEDE2000 (Delta E00) color difference formulas. The results obtained with these formulas were compared, and the limits of agreement after a logarithmic transformation of the data were obtained. Results. The linear relationship between both formulas was Delta E00=0.66 Delta E*ab. The results obtained with the CIELab formula were between 1.15 (95% confidence interval 1.11 to 1.18) and 2.09 (95% confidence interval 2.03 to 2.15) times higher than those obtained with the CIEDE2000 formula. Conclusions. In the natural tooth color space, the scale factor between CIEDE2000 and CIELab values changes from 0.46 to 0.90, such that providing an accurate scale factor between both values is difficult. Furthermore, the Delta E00/Delta E*ab ratio increases with the increase in Delta L* and the decrease in Delta b*. The pairs for which the ratio is highest are those in which the difference in color is mainly due to changes in lightness, whereas the pairs for which the ratio is the smallest are those in which the difference in color is mainly due to changes on the blue-yellow axis.