Improving Color-Difference Formulas Using Visual Data

We propose a method to improve existing color-difference formulas with additional visual data from color discrimination experiments. Color-difference formulas are treated as mean functions of Gaussian processes, and the visual data are considered as observations of these processes. Gaussian process regression is applied to predict unknown color differences. The method was evaluated with a combination of the CIEDE2000 color-difference formula and the RIT-DuPont dataset. The standardized residual sum of squares (STRESS) index between visual and computed color differences was determined for several sets of visual data. The results show a STRESS index of 6.94 (CIEDE2000: 19.47) for the RIT-DuPont dataset. The prediction performance on other visual data (BFD, Leeds, Witt) is not significantly different from CIEDE2000 at a 95% confidence level. Introduction A perceptually uniform color space is required especially for quality control and various color technology applications. The CIELAB color space was designed for this purpose in 1976. It is used in many standards of the printing, graphic arts, coating, and automotive industries. Several drawbacks of CIELAB were discovered by now, including its lack of perceptual uniformity and hue linearity. Nevertheless, CIELAB could not be replaced by an improved color space (such as DIN99 [1, 2]) in everyday applications. Since changing common practice is difficult, this is unlikely to happen in the near future. Unfortunately, for some applications the perceptual uniformity of CIELAB is not sufficient, especially when color tolerances need to be defined. Data derived from color discrimination experiments (e.g., RIT-DuPont [3]) show the disagreement between perceived differences and Euclidean distances in CIELAB. Suprathreshold ellipsoids, which approximately define all colors with similar perceived distance to a color center, are of particular interest. Figure 1 shows four such ellipsoids derived from the RIT-DuPont data [4]. They differ significantly from spheres, which is a good indicator of perceptual non-uniformity of the underlying color space. To overcome the non-uniformity of CIELAB, various colordifference formulas were created (e.g., CMC [5], CIE94 [6], and CIEDE2000 [7]). Figure 1 shows that CIEDE2000 predictions differ not only from RIT-DuPont suprathreshold ellipsoids (which can be considered reliable [4]), but also from the corresponding color-difference vectors. A comparison of the entire RIT-DuPont dataset with corresponding CIEDE2000 predictions yields a PF/3 measure [8] of 19.56 and a standardized residual sum of squares (STRESS) index [9, 10] of 19.47. Color-difference formulas are designed by fitting parameters of predefined functions to visual data [11]. There are two main problems with this approach: 1. Visual data from a single experiment are usually sparsely distributed across CIELAB, and combining datasets obtained by different psychophysical methods (e.g., method of constant stimuli or gray-scale method [12]) is highly controversial. 2. The visual data might be overfitted, so that the resulting color-difference formula models noise and loses its generalization ability [13, 14]. The aim of this paper is not to create new color-difference formulas, but to improve existing formulas using visual data. A possible application is to enhance the prediction accuracy around particular color centers, e.g., a company’s corporate colors. Visual experiments at these color centers could improve the standardized global color-difference formula, provided that they were conducted under similar viewing conditions [15]. The proposed method is based on Gaussian process regression (GPR), a prediction approach often used in a geostatistical context (usually referred to as Kriging). It allows to incorporate the uncertainty of the visual data, which is important due to high interand intra-observer noise in experimental data [14, 16].