Power functions improving the performance of color-difference formulas

Abstract

Color-difference formulas modified by power functions provide results in better agreement with visually perceived color differences. Each of the modified color-difference formulas proposed here adds only one relevant parameter to the corresponding original color-difference formula. Results from 16 visual data sets and 11 color-difference formulas indicate that the modified formulas achieve an average decrease of 5.7 STRESS (Standardized Residual Sum of Squares) units with respect to the original formulas, signifying an improvement of 17.3%. In particular, for these 16 visual data sets, the average decrease for the current CIE/ISO recommended color-difference formula CIEDE2000 modified by an exponent 0.70 was 5.4 STRESS units (17.5%). The improvements of all modified color-difference formulas with respect to the original ones held for each of the 16 visual data sets and were statistically significant in most cases, particularly for all data sets with color differences close to the threshold. Results for 2 additional data sets with color pairs in the blue and black regions of the color space confirmed the usefulness of the proposed power functions. The main reason of the improvements found for the modified color-difference formulas with respect to the original color-difference formulas seems to be the compression provided by power functions.

Method to determine the degrees of consistency in experimental datasets of perceptual color differences

“…In step 1, for practical purposes, the values α 1 1 and γ 1 5 have been reasonably well adopted [4,6,9] in Eq. (2), meaning that, in terms of nearness in color space, distances lower than or equal to 1 CIELAB unit are small (degree 1), and those higher than 5 CIELAB units are not at all considered small (degree 0).…”

“…In the antecedent of fuzzy rule 2.1, we need to model three vague terms, for which we will use the fuzzy sets described in Eqs. (8) and (9).…”

“…To date, several experimental datasets with limited accuracy have been proposed for developing and testing the merits of different color-difference formulas used in industrial applications [4][5][6][7][8][9]. Undoubtedly, a key point for successful future advances in this field would be to achieve a reliable and broad set of color pairs, distributed throughout all regions of color space, visually assessed by a high number of observers with normal color vision using an appropriate methodology.…”

“…However, it is well known that human perception behaves nonlinearly for different magnitudes of color differences [4,6,9,10,14]. Therefore, a color pair will now be compared only with near color pairs having similar visual color differences ΔV (which implies that there will be also similarity with respect to ΔE 00 ).…”

Measuring color differences in gonioapparent materials used in the automotive industry

“…Finally, from last row in Table 2 it is worth to mention that an exponent =0.65 in the original AUDI2000 color-difference formula produced a very important decrease of about 8.6 units in the STRESS value found in our current experiment. The use of this kind of power functions ( ' EE     ) in color-difference formulas was originally proposed by Attridge and Pointer [24], and it has been proved also useful in other previous experiments [25], including the one in [17] where the optimum value for the exponent α was 0.82. Interestingly, the value of 18.7 STRESS units found with =0.65 ( Table 2, last column) is very close value to the 18.2 STRESS units corresponding to the inter-observer variability in our current visual experiment.…”