Performance of recent advanced color-difference formulas using the standardized residual sum of squares index

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

OBJECTIVES

This multicenter study aimed to evaluate visual-instrumental agreement of six color measurement devices and optimize three color difference equations using a dataset of visual color differences (∆V) from expert observers.

METHODS

A total of 154 expert observers from 16 sites across 5 countries participated, providing visual scaling on 26 sample pairs of artificial teeth using magnitude estimation. Three color difference equations (ΔE*ab, ∆E00, and CAM16-UCS) were tested. Optimization of all three equations was performed using device-specific weights, and the standardized residual sum of squares (STRESS) index was used to evaluate visual-instrumental agreement.

RESULTS

The ΔE*ab formula exhibited STRESS values from 18 to 40, with visual-instrumental agreement between 60 % and 82 %. The ∆E00 formula showed STRESS values from 26 to 32, representing visual-instrumental agreement of 68 % to 74 %. CAM16-UCS demonstrated STRESS values from 32 - 39, with visual-instrumental agreement between 61-68 %. Following optimization, STRESS values decreased for all three formulas, with ΔE' demonstrating average visual-instrumental agreement of 79 % and ∆E00 of 78 %. CAM16-UCS showed average visual-instrumental agreement of 76 % post optimization.

SIGNIFICANCE

Optimization of color difference equations notably improved visual-instrumental agreement, overshadowing device performance. The optimzed ΔE' formula demonstrated the best overall performance combining computational simplicty with outstanding visual-instrumental agreement.

New Insights into Wine Color Analysis: A Comparison of Analytical Methods to Sensory Perception for Red and White Varietal Wines

The Glories method and CIE L*a*b* color space are poorly correlated in the light red high-saturation color area. Non-uniformities in the CIE L*a*b* color space have led to the CIEDE2000 formula, while the Euclidean color distance is still used in wine research. In this study, 112 white and red wines were examined to compare the Glories method, CIE L*a*b, and human perception using monovarietal wines from different grape varieties. The objective of this study was to investigate which of the two methods and which parameter of each method better aligned with human perception. The visual color threshold was re-evaluated with the CIEDE2000 formula and triangle testing. CIE L*a*b* more closely matched the human perception, elevating the use of CIE L*a*b* over the use of the Glories method. Visual color thresholds were better expressed with CIEDE2000 but still varied depending upon the color area in the CIE L*a*b* color space.

Accuracy of tooth color determination by dental students using daylight-calibrated dental operatory lighting sources

STATEMENT OF PROBLEM

Lighting conditions are an essential factor for accurately determining tooth color. However, the ideal lighting conditions for determining tooth shade are rarely met and are difficult to quantify. While the use of a standardized daylight lamp D55 can improve accuracy, its high cost limits its use in dental offices. The use of modern operatory treatment units for tooth color determination is promising, as they now allow for the adjustment of light source settings such as color temperature and intensity. However, studies are needed to determine whether they provide accurate color determination.

PURPOSE

The purpose of this study was to assess the accuracy of visual tooth shade determinations under the adjusted light sources of 2 different dental treatment units in comparison with a standardized daylight lamp D55.

MATERIAL AND METHODS

Dental treatment units from 2 manufacturers KaVoLUX 540 LED (LK) and LEDview Plus (LDS) were tested. The light sources of these units were adjusted to match daylight conditions. A daylight lamp (Dialite Color 7; Eickhorst & Co. KG) was used as a control (D55). A total of 49 participants (median age of 25 years, 30 women) underwent the Ishihara screening and received standardized training calibration. A total of 2205 clinical visual tooth shade determinations were performed with the Toothguide Training Box using the Vita 3D-Master shade guide under the 3 different lighting types. Each participant had 15 color determinations made under each of the 3 light settings. Color differences were analyzed by using the Kruskal-Wallis, Wilcoxon rank-sum, and chi-squared tests (α=.05).

RESULTS

The type of lighting used for tooth shade determination had no significant effect on the accuracy of selected shade based on the ΔE00 metric (P=.133). Perfect matches were achieved in 50.8% of the cases under LK, 49.8% under LDS, and 53.6% under D55 light, with no significant difference among percentages (P=.315). Although there was a significant difference in time elapsed for shade determination by light type (P=.004), this difference was not clinically relevant (20.8 seconds for LK, 23.9 seconds for LDS, 21.9 seconds for D55).

CONCLUSIONS

The accuracy of color determination for both examined dental operatory lamps was found to be comparable with that of the standard D55 daylight lamp when adjusted to specific settings.

Metrics of color-difference formula improvement

Metrics of color-difference formula improvement (i.e., standardized residual sum of squares and Pearson product moment correlation) are shown to convey the same information. Furthermore, each metric has two computational forms that assume different linear data models, specifically, with or without an ordinate intercept. It is essential to choose a computational form that matches the data model. We recommend explicitly declaring whether or not the data have been centered, i.e., by subtracting the mean value from each datum, to match the intercept-free data model. Statistical testing of the metrics assumes independent, normally distributed randomness of residuals from the data model, and homogeneous variance. Procedures consistent with these assumptions include robust statistical tests, homogenizing data transformations, and meta-analysis.

Visual and digital tooth shade selection methods, related effective factors and conditions, and their accuracy and precision: A literature review

OBJECTIVE

Despite developments of dental shade selection methods, shade selection is still a challenge affecting esthetic outcomes. The purpose of this review was to discuss visual and digital shade taking methods, related effective factors and conditions, and their accuracy and precision to find out the most accurate, precise shade selection method available in dentistry.

OVERVIEW

The key terms of accuracy, background, ceramic, color, colorimeter, color analysis, color science, color measurement, color measuring instrument, color matching, composite resin, dental/tooth shade guide, digital camera, esthetics, imaging, imaging application/program/ software, intraoral scanner, light source, photography, precision, shade, shade matching/ determination/prediction/reproduction/selection, shade taking device, spectrophotometer, spectrophotometry, tooth color measurement, tooth color/shade, and visual perception were used separately and jointly to detect related English-language articles published between January 1, 1985, and January 1, 2021. Electronic/non-electronic searches of Google Scholar/PubMed/Scopus/Web of Science were accomplished. Consequently, 249 articles were considered. Accordingly, the digital methods show higher accuracy and precision compared to the visual methods while requiring to be enhanced regarding accuracy to achieve ideal shade taking results.

CONCLUSIONS

Dental spectrophotometers provide the highest overall accuracy and precision among different shade selection methods while needing clinical setting to control related effective factors/conditions and technological improvement to perform optimally.

CLINICAL SIGNIFICANCE

Different factors can affect the accuracy and precision of tooth shade selection methods and devices. The understanding of these effective factors may lead to a standard shade taking protocol using accurate, precise methods and devices.

Fluctuating environmental light limits number of surfaces visually recognizable by colour

Small changes in daylight in the environment can produce large changes in reflected light, even over short intervals of time. Do these changes limit the visual recognition of surfaces by their colour? To address this question, information-theoretic methods were used to estimate computationally the maximum number of surfaces in a sample that can be identified as the same after an interval. Scene data were taken from successive hyperspectral radiance images. With no illumination change, the average number of surfaces distinguishable by colour was of the order of 10,000. But with an illumination change, the average number still identifiable declined rapidly with change duration. In one condition, the number after two minutes was around 600, after 10 min around 200, and after an hour around 70. These limits on identification are much lower than with spectral changes in daylight. No recoding of the colour signal is likely to recover surface identity lost in this uncertain environment.

Color changes of polyetheretherketone (PEEK) and polyoxymethelene (POM) denture resins on single and combined staining/cleansing action by CIELab and CIEDE2000 formulas

PURPOSE

The purpose of study was to investigate the long-term effect of staining and/or cleansing solutions on the color stability of two non-metal removable partial denture materials.

METHODS

One hundred disks (25×3mm) of polyoxymethylene (POM) and polyetheretherketone (PEEK) were immersed in water, wine, coffee, cleanser and combo bath, simulating normal daily use. Color parameters in the CIELAB system was measured every 30 cycles up to 240 using a contact colorimeter and color differences estimated using ΔE_ab and ΔE₀₀ formulas. Two-way repeated measures ANOVAs and regression analyses were performed at α=0.05.

RESULTS

Regression analysis indicated a strong R² between color changes and number of cycles, for both materials. Tests of within-subjects effects for the ΔE_ab revealed significant differences among cycles and between the materials in the wine and coffee baths (p<0.001). Significant materialXcycles interactions were also recorded with all staining baths. ΔE₀₀ values were lower than ΔE_ab up to 63.6%. Tests within and between-subjects effects for the ΔE₀₀ gave similar but not the same with ΔE_ab results.

CONCLUSIONS

ΔE₀₀ found to correlate well with ΔE_ab. Long term exposure of both materials showed a progressive discoloration in all except control baths. POM discolored more than PEEK in coffee, and combo baths but not in cleanser. Discoloration was smaller in combo bath (where a cleanser was also used) indicating the effectiveness of a cleanser to prevent long term discoloration of both materials.

Hyperspectral imaging in color vision research: tutorial

This tutorial offers an introduction to terrestrial and close-range hyperspectral imaging and some of its uses in human color vision research. The main types of hyperspectral cameras are described together with procedures for image acquisition, postprocessing, and calibration for either radiance or reflectance data. Image transformations are defined for colorimetric representations, color rendering, and cone receptor and postreceptor coding. Several example applications are also presented. These include calculating the color properties of scenes, such as gamut volume and metamerism, and analyzing the utility of color in observer tasks, such as identifying surfaces under illuminant changes. The effects of noise and uncertainty are considered in both image acquisition and color vision applications.

Comparison of two color-difference formulas using the Bland-Altman approach based on gingiva color space

The objectives of this study were to determine the relationship between the results provided by the classical CIELab (ΔE_ab*) and the CIEDE2000 (ΔE00) formulas and the gingival color space using the Bland and Altman limits of agreement, to use this relationship to establish the equivalences between the gingival color thresholds of perceptibility of both formulas, and to evaluate whether the relationship between ΔE_ab* and ΔE00 is modified depending on the axis in which the changes occur. The means of the L*, a*, and b* coordinates of the 21 gingiva porcelain samples (Heraceram, Heraeus Kulzer Mitsui Chemical Groups) were used and the differences in color were calculated in 210 pairs of samples using the CIELab (ΔE*ab) and CIEDE2000 (ΔE00) color-difference formulas. The results obtained with these formulas were compared and the limits of agreement after a logarithmic transformation of the data were obtained. The relationship between both formulas was ln ΔE₀₀ = - 0.22 + ln ΔE_ab*. The results obtained with the CIELab formula were between 1.01 (95% confidence interval 0.98-1.03) and 1.54 (95% confidence interval 1.52-1.59) times higher than those obtained with the CIEDE200 formula. In the gingiva color space, the scale factor between the CIEDE2000 and CIELab values changes from 0.63 to 1.02, such that providing an accurate scale factor between both values proves difficult. The pairs with the highest ratio were those where the difference in color was mainly due to changes in lightness, whereas the pairs with the smallest ratio were those where the difference in color was mainly due to changes in the blue-yellow or green-red axes.

The Verriest Lecture: Color vision in an uncertain world

The natural world is optically unconstrained. Surface properties may vary from one point to another, and reflected light may vary from one instant to the next. The aim of this work is to quantify some of the physical failures of color vision performance that result from uncertainty. In computational simulations with images of vegetated and nonvegetated outdoor scenes, it is shown that color provides an unreliable guide to surface identity. It is also shown that changes in illuminant may cause colors to no longer match and the relations between individual colors to vary. These failures are generally well described by a measure of the randomness of the colors in scenes, the Shannon entropy. Although uncertainty is intrinsic to the environment, its consequences for color vision can be predicted.

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.

How psychophysical methods influence optimizations of color difference formulas

For developing color difference formulas, there are several choices to be made on the psychophysical method used for gathering visual (observer) data. We tested three different psychophysical methods: gray scales, constant stimuli, and two-alternative forced choice (2AFC). Our results show that when using gray scales or constant stimuli, assessments of color differences are biased toward lightness differences. This bias is particularly strong in LCD monitor experiments, and also present when using physical paint samples. No such bias is found when using 2AFC. In that case, however, observer responses are affected by other factors that are not accounted for by current color difference formulas. For accurate prediction of relative color differences, our results show, in agreement with other works, that modern color difference formulas do not perform well. We also investigated if the use of digital images as presented on LCD displays is a good alternative to using physical samples. Our results indicate that there are systematic differences between these two media.

Power functions improving the performance of color-difference formulas

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.

Performance of select color-difference formulas in the blue region

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.

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.

Comparison of the performance of inverse transformation methods from OSA-UCS to CIEXYZ

The Optical Society of America's Uniform Color Scales (OSA-UCS) is one of the color spaces that most closely approximate a "true" uniform color space. Different techniques have been used to convert OSA-UCS-based color specification parameters, L, j, and g, to the CIE tristimulus values, X, Y, and Z. However, none of these methods provides a direct method of inverting OSA-UCS to CIEXYZ values. Thus, numerical algorithms, such as the Newton-Raphson method, have been employed to obtain the transformations. The relative low accuracy and long computation time of this method makes it undesirable for practical applications. An artificial neural network (ANN) was employed to convert OSA-UCS to CIEXYZ. Its performance was compared with that of numerical methods. After optimization, ANN gave a better performance with a mean error (ΔEXYZ) of 1.0×10(-4) and a conversion time of less than 1 s for 1891 samples.

Color-difference evaluation for digital images using a categorical judgment method

The CIELAB lightness and chroma values of pixels in five of the eight ISO SCID natural images were modified to produce sample images. Pairs of images were displayed on a calibrated monitor and assessed by a panel of 12 observers with normal color vision using a categorical judgment method. The experimental results showed that assuming the lightness parametric factor k(L)=1 to predict color differences in images, CIELAB performed better than CIEDE2000, CIE94, or CMC, which is a different result to the one found in color-difference literature for homogeneous color pairs. However, observers perceived CIELAB lightness and chroma differences in images in different ways. To fit current experimental data, a specific methodology is proposed to optimize k(L) in the color-difference formulas CIELAB, CIEDE2000, CIE94, and CMC. From the standardized residual sum of squares (STRESS) index, it was found that the optimized formulas, CIEDE2000(2.3:1), CIE94(3.0:1), and CMC(3.4:1), performed significantly better than their corresponding original forms with lightness parametric factor k(L)=1. Specifically, CIEDE2000(2.3:1) performed the best, with a satisfactory average STRESS value of 25.8, which is very similar to the 27.5 value that was found from the CIEDE2000(1:1) formula for the combined weighted dataset of homogeneous color samples employed at the development of this formula [J. Opt. Soc. Am. A25, 1828 (2008), Table 2]. However, fitting our experimental data, none of the four optimized formulas CIELAB(1.5:1), CIEDE2000(2.3:1), CIE94(3.0:1), and CMC(3.4:1) is significantly better than the others. Current results roughly agree with the recent CIE recommendation that color difference in images can be predicted by simply adopting a lightness parametric factor k(L)=2 in CIELAB or CIEDE2000 [CIE Publication 199:2011]. It was also found that the different contents of the five images have considerable influence on the performance of the tested color-difference formulas.

Evaluation of threshold color differences using printed samples

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.

Toward a unified color space for perception-based image processing

Image processing methods that utilize characteristics of the human visual system require color spaces with certain properties to operate effectively. After analyzing different types of perception-based image processing problems, we present a list of properties that a unified color space should have. Due to contradictory perceptual phenomena and geometric issues, a color space cannot incorporate all these properties. We therefore identify the most important properties and focus on creating opponent color spaces without cross contamination between color attributes (i.e., lightness, chroma, and hue) and with maximum perceptual uniformity induced by color-difference formulas. Color lookup tables define simple transformations from an initial color space to the new spaces. We calculate such tables using multigrid optimization considering the Hung and Berns data of constant perceived hue and the CMC, CIE94, and CIEDE2000 color-difference formulas. The resulting color spaces exhibit low cross contamination between color attributes and are only slightly less perceptually uniform than spaces optimized exclusively for perceptual uniformity. We compare the CIEDE2000-based space with commonly used color spaces in two examples of perception-based image processing. In both cases, standard methods show improved results if the new space is used. All color-space transformations and examples are provided as MATLAB codes on our website.

Visual search in natural scenes explained by local color properties

Success in visually searching for a small object or target in a natural scene depends on many factors, including the spatial structure of the scene and the pattern of observers' eye movements. The aim of this study was to determine to what extent local color properties of natural scenes can account for target-detection performance. A computer-controlled high-resolution color monitor was used to present images of natural scenes containing a small, randomly located, shaded gray sphere, which served as the target. Observers' gaze position was simultaneously monitored with an infrared video eye-tracker. About 60% of the adjusted variance in observers' detection performance was accounted for by local color properties, namely, lightness and the red-green and blue-yellow components of chroma. A similar level of variance was accounted for by observers' fixations. These results suggest that local color can be as influential as gaze position in determining observers' search performance in natural scenes.

Predicting frequency of metamerism in natural scenes by entropy of colors

Estimating the frequency of metameric surfaces in natural scenes usually requires many comparisons of surface colors to determine which are visually indistinguishable under one light but distinguishable-by a certain criterion degree-under another. The aim here was to test the predictive power of a simpler approach to estimation based on the entropy of colors. In simulations with 50 hyperspectral images of natural scenes, the logarithm of the observed relative frequency of metamerism in each scene under two successive daylights was regressed on combinations of the estimated Shannon differential entropies of the colors of the scene under the same two daylights. The regression was strong, and it remained so when restricted to the estimated differential entropy under just the first daylight, providing that the criterion degree of metamerism was limited. When the criterion degree was made more extreme, however, the restricted regression failed. A possible explanation of the predictive power of differential entropy is briefly considered.

Analyzing small suprathreshold differences of LCD-generated colors

Small suprathreshold color differences around five CIE color centers were investigated on a typical liquid crystal display (LCD) with fluorescent backlight using the method of constant stimuli. The results were evaluated using probit analysis and compared with surface-color differences of the RIT-DuPont dataset. We focused especially on the relationship between T50 distances obtained from LCD and surface-color stimuli and on the influence of the display's narrowband primaries and its relatively low luminance level on interobserver uncertainty. The low luminance level of the LCD decreases the perceived color differences. However, considering the visual uncertainty of the experimental data, we could not reject the hypothesis that T50 distances from the RIT-DuPont and our experiment agree up to a constant scaling factor. In addition, we found significantly higher interobserver variability in the estimation of small color differences if the colors are viewed on an LCD. There are some indications that color-difference perception might be influenced by individual color-matching functions and, thus, by the spectral power distribution of the stimuli. We provide the experimental data, including all spectral stimuli shown to the observers, on our website.

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.

Upgrading color-difference formulas

We propose a method to improve the prediction performance of existing color-difference formulas with additional visual data. The formula is treated as the mean function of a Gaussian process, which is trained with experimentally determined color-discrimination data. Color-difference predictions are calculated using Gaussian process regression (GPR) considering the uncertainty of the visual data. The prediction accuracy of the CIE94 formula is significantly improved with the GPR approach for the Leeds and the Witt datasets. By upgrading CIE94 with GPR we achieve a significantly lower STRESS value of 26.58 compared with that for CIEDE2000 (27.49) on a combined dataset. The method could serve to improve the prediction performance of existing color-difference equations around particular color centers without changing the equations themselves.

Comparison of naïve and expert subjects in the assessment of small color differences

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.

Euclidean color-difference formula for small-medium color differences in log-compressed OSA-UCS space

This work continues previous research by the same authors [J. Opt. Soc. Am. A23, 2077 (2006)], where empirical small-medium color differences were represented by an ellipsoidal equation DeltaEGP in the Uniform Color System of the Optical Society of America. Now logarithmic compressions on chroma and lightness are introduced to produce a new space with Euclidean color-difference formulas DeltaEE. The CIEDE2000, DeltaEGP, and DeltaEE formulas are found statistically equivalent in the prediction of many available empirical datasets. However, DeltaEE is the simplest formula providing relationships with visual processing. These analyses hold true for CIE 1964 Supplementary Standard Observer and D65 illuminant.