Uniform colour spaces based on the DIN99 colour‐difference formula

Several colour‐difference formulas such as CMC, CIE94, and CIEDE2000 have been developed by modifying CIELAB. These formulas give much better fits for experimental data based on small colour differences than does CIELAB. None of these has an associated uniform colour space (UCS). The need for a UCS is demonstrated by the widespread use of the a*b* diagram despite the lack of uniformity. This article describes the development of formulas, with the same basic structure as the DIN99 formula, that predict the experimental data sets better than do the CMC and CIE94 colour‐difference formulas and only slightly worse than CIEDE2000 (which was optimized on the experimental data). However, these formulas all have an associated UCS. The spaces are similar in form to L*a*b*. © 2002 Wiley Periodicals, Inc. Col Res Appl, 27, 282–290, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.10066     

A fallacy in the definition of ΔH*

When a color differs from the reference, it is desirable to ascribe the difference to differences in the perceptual attributes of hue, chroma, and/or lightness through psychometric correlates of these attributes. To this end, the CIE has recommended the quantity ΔH* as a psychometric correlate of hue as defined by ΔH* = [(ΔE*)² - (ΔL*)² - (ΔC*)²]^1/2, where the correlates correspond to either the 1976 CIELAB or CIELUV color spaces. Since ΔH* is defined as a “leftover,” this definition is valid only to the extent that ΔE* comprises exclusively ΔL*, ΔC*, and ΔH* and that ΔL*, ΔC*, and ΔH* are mutually independent compositionally, both psychophysically and psychometrically. It will be shown that as now defined ΔH* lacks psychometric independence of chroma and always leads to incorrect hue difference determination. Such a deficiency causes problems, especially in the halftone color printing industry, since it can suggest an incorrect adjustment for the hue of the inks. A revised definition herein of ΔH* provides a psychometric hue difference independent of chroma, valid for large and small psychometric color differences regardless of chroma. However, for small chromas, the seldom used metric ΔC might be a better color difference metric than ΔH* because complex appearance effects make the perceptual discrimination of lightness, chroma, and hue components more difficult than for high chromas.     

Comparison of the metrics between the CIELAB and the DIN99 uniform color spaces using dental resin composite material values

The sizes for the perceptible or acceptable color difference measured with instruments vary by factors such as instrument, material, and color‐difference formula. To compensate for disagreement of the CIELAB color difference (ΔE^*_ab) with the human observer, the CIEDE2000 formula was developed. However, since this formula has no uniform color space (UCS), DIN99 UCS may be an alternative UCS at present. The purpose of this study was to determine the correlation between the CIELAB UCS and DIN99 UCS using dental resin composites. Changes and correlations in color coordinates (CIE L*,a*, and b* versus L₉₉, a₉₉, and b₉₉ from DIN99) and color differences (ΔE^*_ab and ΔE₉₉) of dental resin composites after polymerization and thermocycling were determined. After transformation into DIN99 formula, the a value (red–green parameter) shifted to higher values, and the span of distribution was maintained after transformation. However, the span of distribution of b values (yellow–blue parameter) was reduced. Although color differences with the two formulas were correlated after polymerization and thermocycling (r = 0.77 and 0.68, respectively), the color coordinates and color differences with DIN99 were significantly different from those with CIELAB. New UCS (DIN99) was different from the present CIELAB UCS with respect to color coordinates (a and b) and color difference. Adaptation of a more observer‐response relevant uniform color space should be considered after visual confirmation with dental esthetic materials. © 2006 Wiley Periodicals, Inc. Col Res Appl, 31, 168–173, 2006     

The perception of static colored noise: Detection and masking described by CIE94

We present psychophysical data on the perception of static colored noise. In our experiments, we use the CIE94 color difference formula to quantify the noise strength and for describing our threshold data. In Experiment 1 we measure the visual detection thresholds for fixed pattern noise on a uniform background color. The noise was present in one of three perceptual color dimensions lightness (L*), chroma (C*), or hue (h). Results show that the average detection threshold for noise in L* is independent of hue angle and significantly lower than that for noise in C* or h. Thresholds for noise in C* and h depend on hue angle in an opponent fashion. The measured detection thresholds, expressed in terms of the components ΔL*/k_LS_L, ΔC*/k_CS_C, and ΔH*/k_HS_H that build up the CIE94 color difference formula are used to tune CIE94 to our experimental conditions by adjusting the parametric scaling factors k_L, k_C, and k_H. In Experiment 2, we measure thresholds for recognizing the orientation (left, right, up, down) of a test symbol that was incremental in L*, C*, or h, masked by supra‐threshold background noise levels in L*, C*, or h. On the basis of the CIE94 color difference formula we hypothesized (a) a constant ratio between recognition threshold and noise level when the test symbol and background noise are in the same perceptual dimension, and (b) a constant recognition threshold when in different dimensions. The first hypothesis was confirmed for each color dimension, the second however, was only confirmed for background noise in L*. The L*, C*, h recognition thresholds increase with increasing background noise in C* or h. On the basis of some 16,200 visual observations we conclude that the three perceptual dimensions L*, C*, and h require different scaling factors (hue dependent for C* and h) in the CIE94 color difference formula, to predict detection threshold data for color noise. In addition these dimensions are not independent for symbol recognition in color noise. © 2008 Wiley Periodicals, Inc. Col Res Appl, 33, 178–191, 2008     

A preliminary comparison of CIE color differences to textile color acceptability using average observers

Ninety‐six nylon pairs were prepared, including red, yellow, green, and blue standards, each at two lightness levels with CIE94 ΔE units ranging from 0.15 to 4.01. Visual assessments of acceptability were carried out by 21 females. Logistic regression compared visual results to four color‐difference equations, CIELAB, CMC, CIE94, and CIEDE2000. It was found that CMC most closely represented judgments of average observers. © 2005 Wiley Periodicals, Inc. Col Res Appl, 30, 288–294, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.20124     

Color‐difference formula performance for several datasets of small color differences based on visual uncertainty

Visual uncertainty, while reported, is not used routinely when evaluating color‐difference formula performance in comparison with visual data; rather, data are analyzed assuming no uncertainty; that is, repeating the experiment would result in the identical average results. Previously, Shen and Berns developed three methods to determine whether a color‐difference formula was well‐fitting, under‐fitting, or over‐fitting visual data when visual uncertainty was considered, the method dependent on how the uncertainty was reported and the colorimetric sampling of the color‐difference stimuli. The “nonellipsoid standard error method” was used in the current analyses. Three datasets were evaluated: BFD‐P, Leeds, and Witt. For the BFD‐P data, incorporating visual uncertainty led to the same performance results as the average results, that CIEDE2000 was an improvement over CIE94, which was an improvement over CIELAB. For the Witt data, incorporating visual uncertainty led to the same performance results as the average results, that CIEDE2000 and CIE94 had equivalent performance, both an improvement over CIELAB. However, both formulas under‐fitted the visual results; thus, neither formula was optimal. For the Leeds dataset, the visual uncertainty analysis did not support the improvement of CIEDE2000 over CIE94 that occurred when evaluating the average results. Both formulas well fit the visual data. These analyses also provided insight into the tradeoffs between the number of color‐difference pairs and the number of observations when fitting a local contour of equal perceived color difference: In particular, increasing the number of observations was more important than increasing the number of color‐difference pairs. Finally, average standard error could be used to approximate visual uncertainty defined using STRESS. © 2010 Wiley Periodicals, Inc. Col Res Appl, 2011     

A Euclidean color space in high agreement with the CIE94 color difference formula

Many consider it futile to try to create color spaces that are significantly more uniform than the CIELAB space, and, therefore, efforts concentrate on developing estimates of perceived color differences based on non‐Euclidean distances for this color space. A Euclidean color space is presented here, which is derived from the CIELAB by means of a simple adjustment of the a* and b* axes, and in which small Euclidean distances agree to within 10.5% with the non‐Euclidean distances given by the CIE94 formula. © 2000 John Wiley & Sons, Inc. Col Res Appl, 25, 64–65, 2000     

Visual evaluation at scale of threshold to suprathreshold color difference

Visual evaluation experiments of color discrimination threshold and suprathreshold color‐difference comparison were carried out using CRT colors based on the psychophysical methods of interleaved staircase and constant stimuli, respectively. A large set of experimental data was generated ranged from threshold to large suprathreshold color difference at the five CIE color centers. The visual data were analyzed in detail for every observer at each visual scale to show the effect of color‐difference magnitude on the observer precision. The chromaticity ellipses from this study were compared with four previous published data, of CRT colors by Cui and Luo, and of surface colors by RIT‐DuPont, Cheung and Rigg, and Guan and Luo, to report the reproducibility of this kind of experiment using CRT colors and the variations between CRT and surface data, respectively. The present threshold data were also compared against the different suprathreshold data to show the effect of color‐difference scales. The visual results were further used to test the three advance color‐difference formulae, CMC, CIE94, and CIEDE2000, together with the basic CIELAB equation. In their original forms or with optimized K_L values, the CIEDE2000 outperformed others, followed by CMC, and with the CIELAB and CIE94 the poorest for predicting the combined dataset of all color centers in the present study. © 2005 Wiley Periodicals, Inc. Col Res Appl, 30, 198–208, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.20106     

Three‐dimensional color prediction modeling of single‐ and double‐layered woven fabrics

In this research, the three‐dimensional structural and colorimetric modeling of three‐dimensional woven fabrics was conducted for accurate color predictions. One‐hundred forty single‐ and double‐layered woven samples in a wide range of colors were produced. With the consideration of their three‐dimensional structural parameters, three‐dimensional color prediction models, K/S‐, R‐, and L*a*b*‐based models, were developed through the optimization of previous two‐dimensional models which have been reported to be the three most accurate models for single‐layered woven structures. The accuracy of the new three‐dimensional models was evaluated by calculating the color differences ΔL*, ΔC*, Δh°, and ΔE_CMC(2:1) between the measured and the predicted colors of the samples, and then the error values were compared to those of the two‐dimensional models. As a result, there has been an overall improvement in color predictions of all models with a decrease in ΔE_CMC(2:1) from 10.30 to 5.25 units on average after the three‐dimensional modeling.     

Are chroma tolerances dependent on hue‐angle?

Relationships between suprathreshold chroma tolerances and CIELAB hue‐angles have been analyzed through the results of a new pair‐comparison experiment and the experimental combined data set employed by CIE TC 1–47 for the development of the latest CIE color‐difference formula, CIEDE2000. Chroma tolerances have been measured by 12 normal observers at 21 CRT‐generated color centers L*₁₀ = 40, C*_ab,10 = 20 and 40, and h_ab,10 at 30° regular steps). The results of this experiment lead to a chroma‐difference weighting function with hue‐angle dependence W_CH, which is in good agreement with the one proposed by the LCD color‐difference formula [Color Res Appl 2001;26:369–375]. This W_CH function is also consistent with the experimental results provided by the combined data set employed by CIE TC 1–47. For the whole CIE TC 1–47 data set, as well as for each one of its four independent subsets, the PF/3 performance factor [Color Res Appl 1999;24:331–343] was improved by adding to CIEDE2000 the W_CH function proposed by LCD, or the one derived by us using the results of our current experiment together with the combined data set employed by CIE TC 1–47. Nevertheless, unfortunately, from the current data, this PF/3 improvement is small (and statistically nonsignificant): 0.3 for the 3657 pairs provided by CIE TC 1–47 combined data set and 1.6 for a subset of 590 chromatic pairs (C*_ab,10>5.0) with color differences lower than 5.0 CIELAB units and due mainly to chroma. © 2004 Wiley Periodicals, Inc. Col Res Appl, 29, 420–427, 2004; Published online in Wiley Interscience (www.interscience.wiley.com). DOI 10.1002/col.20057     

Correlation between visual and colorimetric scales ranging from threshold to large color difference

Psychophysical experiments of color discrimination threshold and suprathreshold color‐difference comparison were carried out with CRT‐generated stimuli using the interleaved staircase and constant stimuli methods, respectively. The experimental results ranged from small (including threshold) to large color difference at the five CIE color centers, which were satisfactorily described by chromaticity ellipses as equal color‐difference contours in the CIELAB space. The comparisons of visual and colorimetric scales in CIELAB unit and threshold unit indicated that the colorimetric magnitudes typically were linear with the visual ones, though with different proportions in individual directions or color centers. In addition, color difference was generally underestimated by the Euclidean distance in the CIELAB space, whereas colorimetric magnitude was perceptually underestimated for threshold unit, implying the present color system is not a really linear uniform space. Furthermore, visual data were used to test the CIELAB‐based color‐difference formulas. In their original forms CIEDE2000 performed a little better than CMC, followed by CIELAB, and with CIE94 showing the worst performance for the combined data set under the viewing condition in this study. © 2002 Wiley Periodicals, Inc. Col Res Appl, 27, 349–359, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.10081     

Development of a comprehensive visual dataset based on a CIE blue color center: Assessment of color difference formulae using various statistical methods

The objectives of this work were to develop a comprehensive visual dataset around one CIE blue color center, NCSU‐B1, and to use the new dataset to test the performance of the major color difference formulae in this region of color space based on various statistical methods. The dataset comprised of 66 dyed polyester fabrics with small color differences ($\Delta E_{{\rm ab}}^* < 5$ ) around a CIE blue color center. The visual difference between each sample and the color center was assessed by 26 observers in three separate sittings using a modified AATCC gray scale and a total of 5148 assessments were obtained. The performance of CIELAB, CIE94, CMC(l:c), BFD(l:c), and CIEDE2000 (K_L:K_C:K_H) color difference formulae based on the blue dataset was evaluated at various K_L (or l) values using PF/3, conventional correlation coefficient (r), Spearman rank correlation coefficient (ρ) and the STRESS function. The optimum range for K_L (or l) was found to be 1–1.3 based on PF/3, 1.4–1.7 based on r, and 1–1.4 based on STRESS, and in these ranges the performances of CIEDE2000, CMC, BFD and CIE94 were not statistically different at the 95% confidence level. At K_L (or l) = 1, the performance of CIEDE2000 was statistically improved compared to CMC, CIE94 and CIELAB. Also, for NCSU‐B1, the difference in the performance of CMC (2:1) from the performance of CMC (1:1) was statistically insignificant at 95% confidence. The same result was obtained when the performance of all the weighted color difference formulae were compared for K_L (or l) 1 versus 2. © 2009 Wiley Periodicals, Inc. Col Res Appl, 2011     

Application of improved back propagation algorithm in color difference detection of fabric

Color is an indispensable indicator of product quality evaluation. To detect the color difference of fabrics, the Levenberg–Marquardt optimized back propagation (BP) algorithm is adopted to extract the color feature values of fabric images. First, RGB values are three inputs of BP neural network, and L*a*b* values measured by spectrophotometer are three outputs of the network. The trained network can obtain the corresponding L*a*b* values conveniently. Then the color difference can be calculated through color difference formula and the characteristic values obtained above. Finally, compared with the color difference calculated by the spectrophotometer, the most appropriate formula can be selected from the four formulas listed in the article (CIEDE2000, CMC, CIE94, and CIELAB) to acquire satisfying results. The experimental results reveal that the color difference of fabrics can be detected with a high accuracy and efficiency with this method. Plenty of duplication workloads and some complex conversion formulas can be avoided, making the acquirement of color difference more efficiently. © 2014 Wiley Periodicals, Inc. Col Res Appl, 40, 311–317, 2015     

Color errors of digital cameras

The mean color errors of a high‐quality digital camera are defined in CIELAB and CIEDE2000 ΔE units by using 16 ceramic color samples, whose accurate CIELAB values have been measured by a calibrated spectrophotometer. The bandwidths of CCD's color filters are evaluated by taking photographs of CRT‐display primaries. The lowest mean color errors were 13.1 CIELAB ΔE units and 8.1 CIEDE2000 ΔE units before corrections. Large color errors are decreased successfully by using three different methods: simple photoeditor, gamma correction, and multiple regression. © 2004 Wiley Periodicals, Inc. Col Res Appl, 29, 217–221, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.20007     

Prediction of optical efficacy of vital tooth bleaching using regression analysis

Establishing a colorimetric guideline to predict the effectiveness of tooth bleaching could produce a more reliable dental treatment. The purpose of this study was to evaluate the effectiveness of tooth bleaching and to test the predictability of tooth color changes. A 10% carbamide peroxide bleaching system was used in studies at Harvard University and at Iwate Medical University in Japan. L*, a*, and b* values (CIELAB) for pre‐ and postbleaching were obtained and color differences (ΔE) were calculated. The b* and L* values of the original tooth color indicated a relatively strong to moderate correlation with ΔE values, whereas a* showed a weak correlation. The multiple‐regression equation obtained from the color data of Harvard subjects performed better than the predictive model. The predicted ΔE correlated strongly with the observed ΔE (r = 0.78). The validation of this equation on data collected from Iwate confirmed the strong correlation (r = 0.74). © 2004 Wiley Periodicals, Inc. Col Res Appl, 29, 390–394, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.20048     

Some aspects of the visual scaling of large colour differences—II

In an earlier article the authors related visually‐ scaled large colour differences to ΔE* values calculated using four colour‐difference formulae. All four metrics yielded linear regressions from plots of visual colour difference against ΔE*, and ΔE gave the best linear fit, but the correlations were rather low. In an effort to clarify matters, the previous investigation is expanded to include data not hitherto examined. The link between visual colour difference and ΔE* colour metrics is further explored in terms of a power law relationship over a wide range of lightness, hue, and chroma variations within CIELAB colour space. It is shown that power‐law fits are superior to linear regressions in all cases, although correlations over large regions of the colour space are not very high. Partitioning of the experimental results to give reduced data sets in smaller regions is shown to improve correlations markedly, using power‐law fits. Conclusions are drawn concerning the uniformity of CIELAB space in the context of both linear and power‐law behavior. © 2000 John Wiley & Sons, Inc. Col Res Appl, 25, 116–122, 2000     

Color acceptance of direct dental restorative materials by human observers

The purposes of this study were to evaluate the CIELAB, CMC (2:1), and CMC (1:1) formulas to identify which provides the best indicator for acceptability of small color differences in the esthetic dental restorative materials, to determine if different groups of observers have different levels of acceptability, and to estimate the color difference that would indicate acceptability between a restoration and an adjacent tooth. The subject population of human observers was divided into four groups, each containing 12 subjects. The composition of the groups were: Group 1, dental auxiliaries and hygienists; Group 2, dentists; Group 3, dental materials scientists; and Group 4, patients. A color vision screening test was administered to each subject to ensure that only observers with normal color vision were evaluated. A composite resin color discrimination test was developed specifically for this study. This test was composed of six sets of discs fabricated from dental composite resin restorative materials. Each set consisted of one standard disc representing tooth color. In each set, six discs representing composite resin restorations were matched to the standard disc for a total of 36 pairings in the test. Color differences between the standard discs and the restoration discs were calculated in CIELAB, CMC (1:1), and CMC (2:1) color units. The subjects were asked to evaluate the composite resin materials as to acceptability of color differences between the disc pairs. The data were analyzed by logistic regression analysis for each observer and by each ΔE formula to generate receiver operating characteristics (ROC) curves. The areas under these ROC curves were calculated and ranked. ANOVA and Tukey's Studentized Range (HSD) Test were applied to the ranks. In regard to the acceptance of dental restorations based solely on color difference, the CMC (1:1) color difference formula gave better correlation than the CIELAB formula for small color differences in the esthetic dental restorative materials. There were significant differences found between the experiment groups in regard to acceptability of color differences using the CMC (1:1) and CIELAB formulas. The dental hygienist/auxiliaries group proved to be more discriminating in accepting differences between tooth and composite resin restorative material color than patients. The mean 50:50 ΔE replacement points for all subjects were 2.29 and 2.72 color units for the CMC (1:1) and CIELAB formulas, respectively. © 2000 John Wiley & Sons, Inc. Col Res Appl, 25, 278–285, 2000     

CIELAB color space boundaries under theoretical spectra and 99 test color samples

A color space is a three-dimensional representation of all the possible color percepts. The CIE 1976 L*a*b* is one of the most widely used object color spaces. In CIELAB, lightness L* is limited between 0 and 100, while a* and b* coordinates have no fixed boundaries. The outer boundaries of CIELAB have been previously calculated using theoretical object spectral reflectance functions and the CIE 1931 and 1964 observers under the CIE standard illuminants D50 and D65. However, natural and manufactured objects reflect light smoothly as opposed to theoretical spectral reflectance functions. Here, data generated from a linear optimization method are analyzed to re-evaluate the outer boundaries of the CIELAB. The color appearance of 99 test color samples under theoretical test spectra has been calculated in the CIELAB using CIE 1931 standard observer. The lightness L* boundary ranged between 6 and 97, redness-greenness a* boundary ranged between −199 and 270, and yellowness-blueness b* boundary ranged between −74 and 161. The boundary in the direction of positive b* (yellowness) was close to the previous findings. While the positive a* (redness) boundary exceeded previously known limits, the negative a* (greenness) and b* (blueness) boundaries were lower than the previously calculated CIELAB boundaries. The boundaries found here are dependent on the color samples used here and the spectral shape of the test light sources. Irregular spectral shapes and more saturated color samples can result in extended boundaries at the expense of computational time and power.     

A top down description of S‐CIELAB and CIEDE2000

Recent work in color difference has led to the recommendation of CIEDE2000 for use as an industrial color difference equation. While CIEDE2000 was designed for predicting the visual difference for large isolated patches, it is often desired to determine the perceived difference of color images. The CIE TC8‐02 has been formed to examine these differences. This paper presents an overview of spatial filtering combined with CIEDE2000, to assist TC8‐02 in the evaluation and implementation of an image color difference metric. Based on the S‐CIELAB spatial extension, the objective is to provide a single reference for researchers desiring to utilize this technique. A general overview of how S‐CIELAB functions, as well as a comparison between spatial domain and frequency domain filtering is provided. A reference comparison between three CIE recommended color difference formulae is also provided. © 2003 Wiley Periodicals, Inc. Col Res Appl, 28, 425–435, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.10195     

Do repeated firings affect the color properties of porcelain‐fused‐metal restorations that are fabricated differently?

Repeated firings can affect the quality of the porcelain color. The purpose of this study is to evaluate the effect of repeated firings on the color changes of porcelain‐fused‐metal restorations that are manufactured using different methods. A total of 60 cylindrical shaped cobalt–chromium alloys (Ø = 10 mm and h = 1.5 mm) were fabricated using casting (C), milling (M), direct metal laser sintering with and without annealing (EL+, EL‐), and selective laser melting with and without annealing (CL+, CL‐). The samples were veneered with A2 (as indicated by the Vita Shade Guide) dentin porcelain of 2 mm thickness. Then the samples subjected to the repeated firings (2nd, 4th, 6th, 8th, and 10th), and the color of each sample was recorded using a spectrophotometer. The CIEDE2000 (ΔE₀₀) formula was used to calculate color differences of the samples on repeated firings. Repeated measures analysis of variance (ANOVA ) and post‐hoc Tukey's test were utilized to analyze the results (a = 05). The L*, a*, and b* values of porcelain‐fused‐metal specimens were significantly affected by the number of firings (P < 0.001) and fabrication techniques (P < 0.001). The ΔE₀₀ values for C, M, CL‐, and EL‐ groups after 10th firing were above 0.8 unit, which indicates that visually perceivable color differences are clinically acceptable. On the other hand, the ΔE₀₀ values for CL+ and EL+ groups were above the PT value after 8th repeated firings. The color properties of porcelain‐fused‐metal restorations were affected by the fabrication techniques and the number of firings.