Using discrete optimization for designing dental shade guides

A key criterion in the design of dental shade guides used for matching tooth color is that the shade tabs cover the natural tooth color space as completely as possible with a manageable number of tabs. Earlier studies have designed hypothetical shade guides from a given population of tooth colors described in the CIELAB system using the goal of minimizing the mean coverage error. In this study, we investigate this topic using the goal of maximizing coverage, meaning that as many measured colors as possible were within a given color difference from the nearest shade tab of the guide. We use techniques of linear discrete optimization to determine the positions of the shade tabs and consider both color difference formulas, CIELAB and CIEDE2000, in an exemplary tooth color population. We obtain coverage error and coverage figures for hypothetical shade guides of various numbers of tabs designed with the goal of either minimizing coverage error or maximizing coverage. Results show that discrete optimization and the goal of maximizing coverage could be used to improve shade guide development. The described technique could be used not only for dental shade guides development, but also for any purpose requiring coverage of as many colors as possible while keeping the number of reference colors manageable. © 2009 Wiley Periodicals, Inc. Col Res Appl, 2010     

A novel Color Rendition Chart for digital tongue image calibration

Digital tongue images are usually acquired by a camera under specific illumination environments. In order to guarantee better color representation of the tongue body, we propose a novel tongue Color Rendition Chart acting as a color reference to be used in color calibration algorithms to standardize the captured tongue images. First, based on a large tongue image database captured with our digital tongue image acquisition system, we establish a statistical tongue color gamut. Then, from the first step, different quantities of colors in the Color Rendition Chart are determined via experimentation. Afterwards, results using X‐Rite's ColorChecker® Color Rendition Chart (a standard in the color calibration field) are compared with the proposed tongue Color Rendition Chart by applying the color difference calculation formula of CIELAB and CIEDE2000 as a reference for the mean color calibration error. The results show that the proposed tongue Color Rendition Chart, which has 24 colors, produces a much smaller error (CIELAB —8.0755/CIEDE 2000—6.3482) compared with X‐Rite's ColorChecker® Color Rendition Chart (CIELAB 1976—14.7836/CIEDE 2000—11.7686). This demonstrates the effectiveness of the novel tongue Color Rendition Chart.     

The CIELAB reversal in calibration and verification

A CIELAB anomaly, in which smaller spectrophotometric errors at all wavelengths lead to larger CIELAB differences, is identified. It is shown that the reversal can occur throughout tristimulus space and is colorimetrically important during calibration procedures. Three numerical examples of the reversal, using data from the BCRA tiles, are given. The reversal cannot be attributed entirely to metamerism, which itself may cause large spectrophotometric error leading to small CIELAB difference. The effect is compounded by the nonlinearity of CIELAB relative to tristimulus coordinates. A recommendation for avoiding the reversal is offered. © 2004 Wiley Periodicals, Inc. Col Res Appl, 30, 66–68, 2005; Published online in Wiley InterScience (www.interscience. wiley.com). DOI 10.1002/col.20076     

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     

Accuracy of approximations for CIELAB chroma and hue difference computation

The transformation in CIELAB from differences in the L^*, a^*, b^* coordinates to those in lightness, chroma, and hue, ΔL^*, ΔC_ab^*, ΔH_ab^*, can be approximated by a rotation in 3-space. Expressions for the error in the approximation of chroma and hue differences are developed. Significant errors are introduced if either the hue angle or chroma difference between reference and sample colors are large. A computed example illustrates the use of the analysis. © 1997 John Wiley & Sons, Inc. Col Res Appl, 22, 61–64, 1997.     

Suprathreshold color-difference ellipsoids for surface colors

The RIT-DuPont visual color-difference data [Color Res. Appl. 16, 297–316 (1991)] have been used to estimate contours of equal color-differences (ellipsoids) at 19 color centers, in CIELAB and x, y, Y/100 color spaces. The ellipsoid fits are better in the CIELAB space than in x, y, Y/100, since the design of the RIT-DuPont experiment emphasized directional balance in CIELAB. The ellipsoids estimated are hardly tilted with respect to L* or Y/100, and they appear to be in overall good agreement with those reported for object colors in recent publications. From the characteristics and accuracy of the RIT-DuPont experiment, the current ellipsoids can be considered highly reliable and representative of color discrimination under the observational conditions employed, these closely following the “reference conditions” recently suggested by the CIE for industrial color-difference evaluation [Color Res. Appl. 20, 399–403 (1995)]. © 1997 John Wiley & Sons, Inc. Col Res Appl, 22, 148–155, 1997     

Research on color harmony of building façades

In this study, the 28 primary colors and 11 complementary colors suggested by Chang et al in their investigation on building colors in Wanhua District of Taipei City were taken as color samples. The two-color combination mode was adopted to obtain 308 simulation photos, and two-color harmony was discussed from the perspective of visual evaluation using psychophysical tests. This study explored building façade color harmony in the CIELAB color space, and the relationship between the color attributes (hue, lightness, and chroma) and the color harmony, and between the differences of the color attributes and color harmony. It found that a high lightness of a building's primary color is associated with a high level of building color harmony, while the color harmony is reduced when the color falls in the green or blue sector in the CIELAB color space; a greater lightness difference between building façade colors is associated with a higher level of building color harmony, while the colors are disharmonized when they tend to the blue sector in the CIELAB color space. The contribution of this study is to summarize the principles for the application of building color harmony in urban renewal, and proposed suggestions on building color harmony in the urban renewal process.     

Precision and accuracy in the color specification of virgin olive oils from the bromthymol blue method

Twenty experienced observers with nondefective color vision judged 27 virgin olive oil samples within an acceptable color range, using the bromthymol blue (BTB) method, under controlled observation conditions (daylight source with a correlated color temperature of 6500 K, and standard gray back-ground). On the average, 44.8% of the observers agreed in their selections of the BTB standard solution matching a given oil sample, and this percentage increased to 88.2% considering ±one step in the two dimensions (pH and concentration) of the BTB scale. On the average, the lowest color difference between oil samples and available BTB solutions was 6.6 Commission Internationale de l'éclairage 1976-(L^*a^*b^*) (CIELAB) units, but this color difference was approximately two times greater for the color difference between oil samples and BTB solutions selected by our observers. The colors of the BTB standard solutions in the CIELAB space are not uniformly distributed, and thus one step in pH or concentration is equivalent to CIELAB color differences varying in a wide range (1.7–13.5 and 1.7–26.3 CIELAB units, respectively). From these values, indicating low precision, accuracy, and uniformity, some suggestions are made for future improvements of the current BTB method.     

Color memory matching: Time effect and other factors

The methods of simultaneous and successive, or memory, color matching have been compared for 10 color reference samples distributed in two groups each performed by 50 observers (25 men and 25 women). Our results, obtained with a total of two hundred Munsell color chips arrayed on ten gray cardboard panels, indicate that: (a) while by simultaneous matching the mean color differences obtained are, in most cases, lower than 1 CIELAB unit, those obtained by memory are generally higher; (b) the worst remembered colors are yellow, light green, blue, and pink, and the best remembered color is orange; (c) the influence of the delay time (15 s, 15 min, and 24 h) is significant for the remembered mean color (p < 0.03); (d) we find significant men-women differences for the remembered mean color (p < 0.05). © 1998 John Wiley & Sons, Inc. Col Res Appl, 23, 234–247, 1998     

The effect of gloss on color

A model was developed for the effect of gloss on reflected color, taking the measurement geometry of the color measuring device into account. It considers the total front surface reflectance of a given sample to be independent of gloss and determined only by its refractive index and the angle of the incident beam. Although the total front surface reflectance is fixed, its specular component increases (and the diffuse component decreases) with increasing sample gloss. Therefore, the diffuse reflectance factor measured by a spectrophotometer decreases with sample gloss. In this article, a defined curve was fitted to the measured reflectance factor of black xerographic print samples having a range of gloss values for the 0/45 and diffuse spectrophotometer geometries, and this curve was used to predict the CIELAB color values for samples of the other colors at various gloss levels. The predicted color was compared to the measured color for cyan, magenta, yellow, red, green, and blue images that spanned a wide range of gloss. The RMS color error between the predicted and measured color of all of these images was found to be about 3 CIELAB ΔE* units. © 1999 John Wiley & Sons, Inc. Col Res Appl, 24, 369–376, 1999     

Assessing the color of red wine like a taster's eye

Color of 33 commercial red wines and five‐color reference wines was measured in the same conditions in which visual color assessment is done by wine tasters. Measurements were performed in the two distinctive regions, center and rim, which are the regions assessed by wine tasters when the wine sampler is tilted. Commercial wines were classified into five color categories using the color specifications in their taste cards. The five color categories describe the spread of red hues found in red wines from the violet to brown nuances. The performance of CIELAB color coordinates in terms of their ability to reproduce the observed classification has been established using discriminant analysis. The CIELAB hue angle, h_ab, measured in the rim, where wine thickness is of the order of few millimeters, gives the best results classifying correctly 71.1% of the samples. Classification results are not significantly improved when additional color coordinates are considered. Moreover, ΔE* color differences with color reference wines do not provide good classification results. The analysis of reference and commercial wines supports the fact that hue is the main factor in the classification done by wine tasters. This is reinforced by the linear correlation found between h_ab in the rim and the wine age (R² = 0.795) in accordance with the fact that wines change their hues from violet to brown tints with ageing. © 2009 Wiley Periodicals, Inc. Col Res Appl, 34, 153–162, 2009     

Observer variability in metameric color matches using color reproduction media

Standard color-matching functions are designed to represent the mean color-matching response of the population of human observers with normal color vision. When using these functions, two questions arise. Are they an accurate representation of the population? And what is the uncertainty in color-match predictions? To address these questions in the dual context of human visual performance and cross-media reproduction, a color-matching experiment was undertaken in which twenty observers made matches between seven different colors presented in reflective and transmissive color reproduction media and a CRT display viewed through an optical apparatus that produced a simple split-field stimulus. In addition, a single observer repeated the experiment 20 times to estimate intra-observer variability. The results were used to evaluate the accuracy of three sets of color-matching functions, to quantify the magnitude of observer variability, and to compare intra- and inter-observer variability in color-matching. These results are compared with various techniques designed to predict the range of color mismatches. The magnitude of observer variability in this experiment also provides a quantitative estimate of the limit of cross-media color reproduction accuracy that need not be exceeded. On average, the differences between matches made by two different observers was approximately 2.5 CIELAB units. © 1997 John Wiley & Sons, Inc. Col Res Appl, 22, 174–188, 1997     

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     

彩色涤纶短纤维色差的控制

介绍了用于评定色差的CIELAB和CMC色差公式,并对2个公式在彩色涤纶短纤维色差控制中的实际运用做了对比实验。从对比结果和数据分析来看,CIELAB色差公式存在一定的局限性,CMC色差公式测试结果与目测具有更好的视觉一致性,完全可以在纺织行业色差控制上替代CIELAB色差公式并推广使用。     

Distance metrics for very large color differences

Small, supra-threshold color differences are typically described with Euclidean distance metrics, or dimension-weighted Euclidean metrics, in color appearance spaces such as CIELAB. This research examines the perception and modeling of very large color differences in the order of 10 CIELAB units or larger, with an aim of describing the salience of color differences between distinct objects in real-world scenes and images. A psychophysical experiment was completed to compare directly large color-difference pairs designed to probe various Euclidean and non-Euclidean distance metrics. The results indicate that very large color differences are best described by HyAB, a combination of a Euclidean metric in hue and chroma with a city-block metric to incorporate lightness differences.     

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     

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     

Determination of constant Hue Loci for a CRT gamut and their predictions using color appearance spaces

A colorimetrically characterized computer-controlled CRT display was used to determine 24 loci of constant perceived hue for pseudo-object related stimuli, sampling the display's interior color gamut at constant lightness and the edge of its gamut at variable lightness. Nine observers performed three replications generating matching data at 132 positions. the constant hue loci were used to evaluate the correlation between perceived hue and hue angle of CIELAB, CIELUV, Hunt, and Nayatani color appearance spaces. the CIELAB, CIELUV, and Hunt spaces exhibited large errors in the region of the blue CRT primary, while the Nayatani and CIELUV spaces produced large errors in the region of the red primary for constant lightness stimuli. Along the edge of the CRT's color gamut (variable lightness stimuli), all the spaces had a similar trend, large errors in the cyan region. the differences in performance between the four spaces were not statistically significant for the constant lightness stimuli. For the variable lightness stimuli, CIELAB and CIELUV had statistically superior performance in comparison with the Nayatani space and equal performance in comparison with the Hunt space. It was concluded that for imaging applications, a new color appearance space needs to be developed that will produce small hue error artifacts when used for gamut mapping along loci of constant hue angle. © 1995 John Wiley & Sons, Inc.     

A spectrophotometric color matching algorithm for precolored fiber blends

In this article, a spectrophotometric color matching algorithm based on Stearns‐Noechel model is proposed. This algorithm was run to predict recipes for 48 viscose blends. Color differences between the original blend samples and the calculated were expressed in CIELAB units (10°standard observer). M (the empirical constant in Stearns‐Noechel model) value was determined by median analysis. When M equals to 0.09, the best fit was obtained for three‐components fiber blends. In that case, the maximum color difference is 1.22 CIELAB units and the average computed color difference is 0.56 CIELAB units for 36 three‐components fiber blends under D65 illuminant. When M is from 0.03 to 0.06, the best fit was obtained for four‐components fiber blends. In that case, the maximum color difference is 4.48 CIELAB units and the average computed color difference is 1.02 CIELAB units for 12 four‐components fiber blends under D65 illuminant. It is demonstrated that the algorithm can be used in color matching of fiber blends. © 2009 Wiley Periodicals, Inc. Col Res Appl, 34, 108–114, 2009