Perceived Lightness Differences in Complex Scenes

For evaluating the performance of color-difference equations, several goodness-of-fit measures were proposed in the past, such as Pearson’s correlation coefficient (r), the performance factor PF/3, and the recently proposed standardized residual sum of squares (STRESS) measure. The STRESS shares its main advantage, which is the possibility to statistically test performance differences, with the correlation coefficient. We show, by mathematical analysis supported by instructive numerical examples, that the STRESS has no meaningful interpretation in this regression analysis context. In addition, we present objections to the use of the STRESS for evaluating color-difference equations. Therefore, we recommend using the correlation coefficient in combination with a graphical and diagnostics analysis to ensure proper application as with any statistical technique.

The standardized residual sum of squares (STRESS) index has been employed to determine the goodness of fit between sensory and measured datasets. It has also been applied to determine inter- and intra-individual variability in repeated sensory evaluations. The primary goal of this work is to demonstrate the application of STRESS in the perceptual evaluation of textile products. Using case studies, the suitability of STRESS for evaluation of observer preferences of clothing colors was demonstrated. It was shown that the metric is a useful analytical tool for quantifying observer variability in perceptual assessments within the textile and apparel domains.

The standardized residual sum of squares (STRESS) index was used to reevaluate four experimental datasets employed during the development of CIEDE2000, the current CIE recommended color-difference formula. This index enables statistical inferences not achievable by other metrics used commonly for performance evaluation. It was found that CIEDE2000 was statistically superior at a 95% confidence level to either CIE94, the previous recommended equation by the CIE, or the simple Euclidean distance in CIELAB, DeltaE*ab. Recent formulas based on the CIECAM02 color-appearance space and chroma-compressed variants of CIELAB were also evaluated and found to have only slightly reduced performance compared with CIEDE2000. These formulas have the advantage of simplicity and easier interpretation when used for quantifying color accuracy. Finally, each experimental dataset was evaluated separately rather than weight averaged as used during the development of CIEDE2000. Significant differences were found between datasets, suggesting that combining datasets may obscure important differences and that the practice of parameter optimization during formula development using combined data is likely suboptimal.

This study compares two designs of psychophysical used for colour difference experiments for two classes of observers, those with normal colour vision and those with a colour vision deficiency. A grey scale pair experiment was conducted on a computer display including two groups of observers; 15 deutan type colour vision deficient observers and a reference group of 15 observers with normal colour vision. Here, the participants assessed 194 colour pairs from 8 colour centers. Each colour center had variations in lightness, chroma and hue relative to a reference colour. Each colour pair consisted of a reference colour and a variation, and the subjects compared the colour difference in this pair against the differences in a set of 6 neutral grey scale pairs. Additionally, based on the same colour centers and variations, a Two-Alternative Forced Choice (2AFC) experiment was conducted where observers selected the largest difference between a reference colour and the two alternative sample colours, and subsequently scaled the perceived difference from a category scale. The STandardized Residual Sum of Squares (STRESS) was used to evaluate the coherence between the visual and the computed colour difference. Intra-observer and inter-observer variations are used to describe the variation and repeatability. A comparison of the visual and computed colour difference for the observer groups shows a lower visual score and a higher dispersion for the CVD observer group. There are also higher inter-observer variability, which is expected as the severeness of the conditions varies from nearly normal to strongly affected. However, the STRESS results are at the level of normal performance for some of the selected colour centers. The 2AFC method give better STRESS results for both observer groups.

In this paper, the influence of neutral backgrounds with different lightness on color appearance was studied, five color centers and nine neutral backgrounds with different lightness based on printed samples were prepared. 20 observers were organized to carry out visual experiment with the method of paired comparison. The obtained experimental results indicate that the color appearance of color center is more affected by higher lightness backgrounds than the lower, which is quite different with the results computed by color appearance models (CAM). Furthermore, the factor of Standardized Residual Sum of Squares (STRESS) was used to evaluate the performance of CAM16 and CAM02 model. The STRESS values show that CAM16 (37.22) predicted more close to the visual results and performed well comparing with CAM02 (44.00).

Using simulated data sets, we have analyzed some mathematical properties of different statistical measurements that have been employed in previous literature to test the performance of different color-difference formulas. Specifically, the properties of the combined index PF/3 (performance factor obtained as average of three terms), widely employed in current literature, have been considered. A new index named standardized residual sum of squares (STRESS), employed in multidimensional scaling techniques, is recommended. The main difference between PF/3 and STRESS is that the latter is simpler and allows inferences on the statistical significance of two color-difference formulas with respect to a given set of visual data.

Mapping soil particle-size fractions: A comparison of compositional kriging and log-ratio kriging

Based on previous visual assessments of 440 color pairs of 3D-printed samples, we tested the performance of eight color-difference formulas (CIELAB, CIEDE2000, CAM02-LCD, CAM02-SCD, CAM02-UCS, CAM16-LCD, CAM16-SCD, and CAM16-UCS) using the standardized residual sum of squares (STRESS) index. For the whole set of 440 color pairs, the introduction of kL (lightness parametric factor), b (exponent in total color difference), and kL + b produced an average STRESS decrease of 2.6%, 26.9%, and 29.6%, respectively. In most cases, the CIELAB formula was significantly worse statistically than the remaining seven formulas, for which no statistically significant differences were found. Therefore, based on visual results using 3D-object colors with the specific shape, size, gloss, and magnitude of color differences considered here, we concluded that the CIEDE2000, CAM02-, and CAM16-based formulas were equivalent and thus cannot recommend only one of them. Disregarding CIELAB, the average STRESS decreases in the kL + b-optimized formulas from changes in each one of the four analyzed parametric factors were not statistically significant and had the following values: 6.2 units changing from color pairs with less to more than 5.0 CIELAB units; 2.9 units changing the shape of the samples (lowest STRESS values for cylinders); 0.7 units changing from nearly-matte to high-gloss samples; and 0.5 units changing from 4 cm to 2 cm samples.

Determination of the role of subject experience in the development of accurate color difference formulas is of potentially critical concern. As part of a larger multivariable experiment investigating the minimum inter- and intra-subject variability possible among a set of subjects, a study was conducted to compare the performance of 25 novice versus 25 expert visual assessors for a set of 27 pairs of colored textile samples using a controlled psychophysical method and several statistical techniques including t-test, ANOVA, and Standardized Residual Sum of Squares (STRESS) functions. Experts exhibited approximately 43% higher visual difference ratings than novice subjects when assessing sample pairs having small color differences. In addition, a statistically significant difference at the 95% confidence level was found between the judgments made by novice and expert assessors. According to the STRESS function, however, CMC(1:1) and CIEDE2000(1:1) color difference formulas do not show a significant difference in performance when the visual data from either group of subjects are compared.

In order to test the performances of different color matching functions (CMFs), a total of 80 pairs of neutral metamerism printed samples based on five lightness levels were prepared. 26 observers with normal color vision were organized to carry out the visual experiments with the gray scale method. Four CMFs, including CIE1964, CIE2006, Sarkar 2 and BIGC 17 were compared with the calculated color difference (∆E) and the visual color differences (∆V) by the Standardized Residual Sum of Squares (STRESS) values. The results indicated that amongst the four CMFs, Sarkar 2 with the smallest STRESS value of 26.8 and the maximum number (equal to 46) of observers from 52 judgements, it’s outperformed others and secondly by BIGC17 CMFs. CIE recommended CMFs, CIE1964 and CIE2006 have no advantages over Sarkar 2 and BIGC17 CMFs when viewing printed materials illuminated by the fluorescent light sources in the field size larger than 10°.KeywordsColor matching functionsGray scale methodMetamerism neutral printed samples STRESS

The performances of uniform color spaces and color-difference formulae for predicting threshold color differences were investigated based on visual assessments of 893 pairs of printed color patches under a D65 source. The average ΔE(ab,10)* of the pairs was 1.1 units. A threshold psychophysical experiment was repeated three times by a panel of 16 observers with normal color vision. The experimental data were used to evaluate nine color-difference formulae and uniform color spaces using the standardized residual sum of squares (STRESS) measure. The results indicated that all formulae and spaces performed very similarly to each other, and outperformed CIELAB for threshold color differences. The chromaticity-discrimination ellipses were used to compare with previous results from small color differences [Color Res. Appl. (2011), doi:10.1002/col.20689], and they agreed with each other, except for the purple color center.

Color difference used to test the quality of printing products is one of the most important factors in the printing industry. Many new color difference formulae such as CIEDE2000, CIEDE94, CMC(l:c) etc were developed to improve the uniformity. In this paper the color difference formulae have been compared throughout their weighting functions SL, SC, and SH to the CIELAB components , , . In order to test which color difference formula has the better performance in the printing industry they are evaluated by our own data sets. First of all, we developed a printing data set for evaluating color difference with psychophysical methods. And the visual color differences of every pairs were obtained. After that the color difference formula mentioned before were evaluated using the data set with the standardized residual sum of squares (STRESS) methods which has better mathematical properties to evaluate the performance of color difference formulae using ΔV and ΔE than PF/3 that cannot indicate the statistical significance of the difference between two color-difference formulae. The result shows that CIEDE2000 and CIE94 color difference formulae are better than CIELAB and CMC. Finally we recommend that the national standards and occupation standards should be updated and CIEDE2000 should be popularized in the printing industry.

The main objective of this work was to test the performance of major formulas for assessment of small suprathreshold color differences in the blue region. The models examined include CIELAB color space based equations, including CIELAB, CIE94, CIEDE2000, CMC (l:c), BFD (l:c), and formulas based on more uniform color spaces, such as DIN99d, CAM02-SCD, CAM02-UCS, OSA-GP, and OSA-Eu in comparison against data obtained via visual assessments. For this purpose, a dataset around the CIE high-chroma blue color center, hereafter called NCSU-B2, was developed. The NCSU-B2 dataset comprised 65 textile substrates and a standard, with a mean ΔE(ab)* color difference of 2.72, ranging from 0.54-5.72. Samples were visually assessed by 26 subjects against the reference gray scale in three separate trials with at least 24 h between assessments. A total of 5070 assessments were obtained. The standardized residual sum of squares (STRESS) index was used to examine the performance of various formulas for this dataset, as well as a previously developed NCSU-B1 low-chroma blue dataset [Color Res. Appl. 36, 27, 2011], and blue centers from other established visual datasets. Results show that formulas based on more recent uniform color spaces provide better agreement with perceptual data compared with models based on CIELAB space.

In this work, a machine learning methodology is proposed for the issue of color space Euclidization. Given a color difference formula as reference distance law, the Euclidization task consists in finding an injective transformation from the original color space into a real vector space and the corresponding inverse transformation, such that the Euclidean distances in the embedded color space align with the reference color distances. For this, artificial neural networks are devised as function approximators for the color space transformations being sought. Training these neural networks is accomplished through unsupervised learning, making use of random sampling and gradient descent. As key disagreement measure, either the (symmetric) relative isometric disagreement or the standardized residual sum of squares (STRESS) index is considered at a time and incorporated as part of the optimization criterion into the objective function. Comparative evaluation is carried out on well‐established color distance laws, including the CIELAB‐based DE2000 color difference formula. The evaluation results indicate significant performance advantages of the proposed approach over previous contributions.

Bridging instrumental and visual perception with improved color difference equations: A multi-center study