Investigation on the equi-depth of color depth formulas based on color discrimination threshold and acceptable tolerance

Accurate characterization of color depth is important for assessing a dye's relative strength, color fastness, and so on. There are several formulas for color depth, however, with evaluation effects that are quite different. In this study, we attempt to investigate the equi-depth properties of the color depth formulas so as to provide a reference for selection. One thousand two hundred and six color samples were dyed around six standard depths of three hues in SDC Standard Depth Scales. Sixteen observers were recruited for “Pass–Fail” psychophysical experiments. More than 30 000 experimental data points were obtained to calculate the values of discrimination thresholds and acceptable tolerances at six different standard depths for each formula. The equi-depth properties of five main color depth formulas were statistically analyzed through their coefficients of variation (CV)% values. Results show that the Yang3 formula is optimal for both color depth discrimination threshold and acceptable tolerance, and its average wrong decision is less than the minimum wrong decision of all observers, as well as those of the other four formulas. Overall, Yang3 formula shows the best equi-depth and highest relatively accuracy among the five formulas.