Luis Gómez-Robledo

Notes on the application of the standardized residual sum of squares index for the assessment of intra- and inter-observer variability in color-difference experiments

The standardized residual sum of squares index was proposed to examine the significant merit of a given color-difference formula over another with respect to a given set of visual color-difference data [J. Opt. Soc. Am. A 24, 1823-1829, 2007]. This index can also be employed to determine intra- and inter-observer variability, although the full complexity of this variability cannot be described by just one number. Appropriate utilization of the standardized residual sum of squares index for the assessment of observer variability is described with a view to encourage its use in future color-difference research. The main goal of this paper is to demonstrate that setting the F parameters of the standardized residual sum of squares index to 1 results in a loss of essential properties of the index (for example, symmetry), and is therefore strongly discouraged.

Measuring color differences in automotive samples with lightness flop: A test of the AUDI2000 color-difference formula

From a set of gonioapparent automotive samples from different manufacturers we selected 28 low-chroma color pairs with relatively small color differences predominantly in lightness. These color pairs were visually assessed with a gray scale at six different viewing angles by a panel of 10 observers. Using the Standardized Residual Sum of Squares (STRESS) index, the results of our visual experiment were tested against predictions made by 12 modern color-difference formulas. From a weighted STRESS index accounting for the uncertainty in visual assessments, the best prediction of our whole experiment was achieved using AUDI2000, CAM02-SCD, CAM02-UCS and OSA-GP-Euclidean color-difference formulas, which were no statistically significant different among them. A two-step optimization of the original AUDI2000 color-difference formula resulted in a modified AUDI2000 formula which performed both, significantly better than the original formula and below the experimental inter-observer variability. Nevertheless the proposal of a new revised AUDI2000 color-difference formula requires additional experimental data.

Fuzzy analysis for detection of inconsistent data in experimental datasets employed at the development of the CIEDE2000 colour-difference formula

Relating instrumental measurements to visually perceived colour-differences, under specific illuminating and viewing conditions, is one of the challenges of advanced colorimetry. Experimental data are used to devise new colour-difference formulas as well as to assess the performance of other colour-difference formulas. In this paper, we analyse the consistency of experimental data employed at the development of the last CIE recommended colour-difference formula, CIEDE2000. Because of the subjective and imprecise nature of these data, we adopt a fuzzy approach, so that finally, for each experimental datum, we establish the fuzzy degree to which it can be considered consistent with the remaining data. The results of our analyses show that only a few data are associated with a rather low degree of consistency. These data in many cases correspond to colour pairs with a very small colour-difference for which visual assessments seem to be overestimated.

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

We propose a fuzzy method to analyze datasets of perceptual color differences with two main objectives: to detect inconsistencies between couples of color pairs and to assign a degree of consistency to each color pair in a dataset. This method can be thought as the outcome of a previous one developed for a similar purpose [J. Mod. Opt.56, 1447 (2009)JMOPEW0950-034010.1080/09500340902944038], whose performance is compared with the proposed one. In this work, we present the results achieved using the dataset employed to develop the current CIE/ISO color-difference formula, CIEDE2000, but the method could be applied to any dataset. Specifically, in the mentioned dataset, we find that some couples of color pairs have contradictory information, which can interfere in the successful development of future color-difference formulas as well as in checking the performance of current ones.

Testing the AUDI2000 colour-difference formula for solid colours using some visual datasets with usefulness to automotive industry

Colour-difference formulas are tools employed in colour industries for objective pass/fail decisions of manufactured products. These objective decisions are based on instrumental colour measurements which must reliably predict the subjective colour-difference evaluations performed by observers’ panels. In a previous paper we have tested the performance of different colour-difference formulas using the datasets employed at the development of the last CIErecommended colour-difference formula CIEDE2000, and we found that the AUDI2000 colour-difference formula for solid (homogeneous) colours performed reasonably well, despite the colour pairs in these datasets were not similar to those typically employed in the automotive industry (CIE Publication x038:2013, 465-469). Here we have tested again AUDI2000 together with 11 advanced colour-difference formulas (CIELUV, CIELAB, CMC, BFD, CIE94, CIEDE2000, CAM02-UCS, CAM02-SCD, DIN99d, DIN99b, OSA-GP-Euclidean) for three visual datasets we may consider particularly useful to the automotive industry because of different reasons: 1) 828 metallic colour pairs used to develop the highly reliable RIT-DuPont dataset (Color Res. Appl. 35, 274-283, 2010); 2) printed samples conforming 893 colour pairs with threshold colour differences (J. Opt. Soc. Am. A 29, 883-891, 2012); 3) 150 colour pairs in a tolerance dataset proposed by AUDI. To measure the relative merits of the different tested colour-difference formulas, we employed the STRESS index (J. Opt. Soc. Am. A 24, 1823-1829, 2007), assuming a 95% confidence level. For datasets 1) and 2), AUDI2000 was in the group of the best colour-difference formulas with no significant differences with respect to CIE94, CIEDE2000, CAM02-UCS, DIN99b and DIN99d formulas. For dataset 3) AUDI2000 provided the best results, being statistically significantly better than all other tested colour-difference formulas.

Color-quality control using color-difference formulas: progress and problems

We report on some recent advances in industrial color-difference evaluation focused in three main fields: Development of reliable experimental visual datasets; proposal of new color spaces and color-difference formulas; tools to evaluate the merits of color-difference formulas. The use of fuzzy techniques to assign consistency degrees to color pairs in combined visual datasets is described. The CIE/ISO joint proposal of the CIEDE2000 color-difference formula as a standard will facilitate the communication among companies and users. The CIE recommendation of the STRESS index to assess observers’ variability and relative merits of different color-difference formulas is reported. Power functions are an efficient method to improve the performance of modern color-difference formulas. We need of advanced color-difference formulas accounting for new materials with different kind of textures and gonioapparent effects.

Measuring color differences in gonioapparent materials used in the automotive industry

This paper illustrates how to design a visual experiment to measure color differences in gonioapparent materials and how to assess the merits of different advanced color-difference formulas trying to predict the results of such experiment. Successful color-difference formulas are necessary for industrial quality control and artificial color-vision applications. A color- difference formula must be accurate under a wide variety of experimental conditions including the use of challenging materials like, for example, gonioapparent samples. Improving the experimental design in a previous paper [Melgosaet al., Optics Express 22, 3458-3467 (2014)], we have tested 11 advanced color-difference formulas from visual assessments performed by a panel of 11 observers with normal colorvision using a set of 56 nearly achromatic colorpairs of automotive gonioapparent samples. Best predictions of our experimental results were found for the AUDI2000 color-difference formula, followed by color-difference formulas based on the color appearance model CIECAM02. Parameters in the original weighting function for lightness in the AUDI2000 formula were optimized obtaining small improvements. However, a power function from results provided by the AUDI2000 formula considerably improved results, producing values close to the inter-observer variability in our visual experiment. Additional research is required to obtain a modified AUDI2000 color-difference formula significantly better than the current one.