Evaluation of uncertainties for CIELAB color coordinates

CIELAB color coordinates are characteristics of visible object's spectra widely used in color science, and a reliable evaluation of the uncertainty associated with measured color coordinates is desirable. The calculation of CIELAB color coordinates requires the application of a nonlinear transformation. We consider two ways to calculate the uncertainty of CIELAB color coordinates that originates from the uncertainty of the observed spectrum. The first approach is based on a linearization of the nonlinear transformation and a propagation of variances and covariances. The second approach is a Monte Carlo procedure that completely accounts for the nonlinearity of the transformation. While the approach based on linearization results in analytical formulas, the adequacy of linearization ought to be checked and the proposed Monte Carlo method can serve as a reference method for this purpose. We illustrate such proceeding in a large range of scenarios and explore those cases for which the method based on linearization may safely be applied.     

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     

Effect of chemico‐mineralogical composition on color of natural and calcined kaolins

A total of six washed French and Algerian kaolins were studied. Kaolinite, halloysite, muscovite, feldspars, anatase, rutile, gibbsite, goethite, and todorokite were present. The thermal behavior of the samples was studied and the transformation heats were determined and quantified by differential thermal analysis. Calcined samples from 900°C to 1400°C are studied by X‐ray diffraction, the results show that the crystallite sizes of mullite rises as the temperature rises. The calcined samples showed an inverse correlation of L* and the crystallite sizes of mullite due to the incorporation of chromophore elements (Fe³⁺, Ti⁴⁺, and Mn²⁺) in its structure. Muscovite and rutile phases decreased lightness and increased chromaticity. The reduction state of Fe³⁺/Fe²⁺ and Mn⁴⁺/Mn²⁺ at 1400°C enhanced lightness leading to the diminution of the b* parameter. The CIELAB color parameters were significantly affected with mineralogy and chemical compositions of the samples. Lightness of the natural kaolins is decreased (L* < 59) when organic matters beside manganese and iron oxides are present. L* was not affected when only iron (Fe²⁺) is present in the kaolin; however, the chromaticity is increased (b* > 22). Whiteness and tint indices (W₁₀, T_w,10) revealed that only one kaolin could be considered white (limits of CIE Colorimetry, 1986), though upon calcination, this number is enhanced to two. © 2013 Wiley Periodicals, Inc. Col Res Appl, 39, 499–505, 2014     

Reproducibility of the bromthymol blue standards used for color specification of virgin olive oil

Three replicates were prepared for each of 60 BTB (bromthymol blue) standards, which are usually employed to determine the color of virgin olive and seed oils, and their colors were measured by spectrophotometric and spectroradiometric techniques on a monthly basis over a year. Although in principle both techniques are valid, their results are weakly correlated. The major color change of the BTB standards occurred soon after sample preparation; after 5 mon, the color stabilized at approximately 3.0 Commission Internationale de l’éclairage 1976-(L^*a^*b^*) (CIELAB) units, with respect to the initial values. Therefore, after preparation, a certain waiting period would be advisable before using the BTB standards. The color of the BTB standards changes over time in the sense of becoming lighter, more saturated, and less greenish. In the monthly periods after the fifth month, the average color change of the BTB standards was negligible, being slightly lower than the average variability of the three replicates (which is around 1.5 CIELAB units).     

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     

Proposal of a uniform color scale for virgin olive oils

A new color scale was developed from a broad data set of 1700 virgin olive oil samples over four crop seasons, which can be considered highly representative of the whole color range of virgin olive oils available in Spain. This color scale provides a new set of 60 color standards, improving the results achieved by the old 60-color standards proposed by the bromthymol blue method. Seeking the greatest possibility of including a near match between colors of virgin olive oils and proposed standards, we developed our new color scale using a recent uniform color space, with standards placed in a regular rhombohedral lattice like the one employed by the Uniform Color Scales of the Optical Society of America. The average color difference between each of the 1700 virgin olive oils and its nearest standard is reduced from 8.17 CIELAB units, using the bromthymol blue standards, to 3.99 CIELAB units using the new standards. Within a color tolerance of 7.0 CIELAB units, 93.2% of our virgin olive oils can be classified with the new standards, but only 59.1% with the bromthymol blue ones. In the interest of future adoption, the performance of the new color standards should be tested by industry and researchers.     

Measuring linear density of threads in single‐system‐mélange color fabrics with FCM algorithm

According to the color yarns in the fabric, the fabrics can be divided into three categories: solid color fabrics, single‐system‐mélange color fabrics, and double‐system‐mélange color fabrics. The density of solid fabrics can be inspected with gray‐projection method or Fourier analysis method. But the methods cannot be applied to yarn‐dyed fabrics directly. A method for detecting the density of single‐system‐mélange color fabrics will be discussed in this article. By analyzing the pattern and color characters of single‐system‐mélange color fabrics, fuzzy C‐means algorithm is proposed to classify the colors in the fabric image based on CIELAB color space first. With the color segmentation results, the fabric can be divided into different blocks. The yarns can be located in different blocks with different average gray‐levels, and then the number of yarns can be counted in each block. The linear density of threads can be obtained by counting the yarns in a unit length finally. The experiment proved that the algorithm proposed in this study can inspect the density of single‐system‐mélange color fabric successfully. © 2012 Wiley Periodicals, Inc. Col Res Appl, 38, 456–462, 2013     

A statistical analysis for correlation approach to compensate the measured CIELAB colorimetric data for temperature alterations

The main focus of this work was to elucidate the further question of whether the color change correlated linearly with the surface temperature alteration or not. We selected and grouped the colored samples, which were in the form of textile, ceramic, plastic, paint, and ink. Those samples were first measured by IR Thermometer to record exact surface temperature, followed by an immediate color measurement using a spectrophotometer. The color variations of these samples were recorded from about 20°C to 60°C. The trend of CIELAB color coordinates was plotted against surface temperature. The dependency between each CIE colorimetric coordinate and the object's surface temperature was statistically evaluated using Pearson's r, R value, and R‐square analysis. A very strong correlation was observed for ceramic, paint, and ink samples tested, while the textile and plastic sample also exhibited a strong trend. The results added new information about the potential correlation between colorimetric data and temperature. Implications for the future research are discussed.     

The feasibility of establishing new color image scales using the magnitude estimation method

Color image is one of the most important factors in art and design. In general, artists and designers apply their own personal image meanings into their work. However, the image meaning for a specific work is frequently in conflict with those of the general observer. Thus it is necessary and important to derive one set of merit color image scales which can be utilized to predict the color image meanings of works in parallel with the average person's perception and which can also serve as a guide for artists and designers. In this study, the psychophysical method (magnitude estimation method), usually used in visual measurement of color appearance, was employed to attempt to establish new color image scales to evaluate the color image meanings of works matching those of the average person. The results show that new color image scales WIP are developed, and the relativity between the latest color image scales WIP and the color attributes (say Lightness L*, Hue h, and Chroma C*) of the CIELAB color space is also discussed. The total mean value of coefficient of variation for the results of visual assessment in the experiment of evaluating the color image meanings of the 207 color specimens used, in general, is about 36, similar to that for those experiments conducted using the psychological method. Also, a good relationship between the new color image scales and the color attributes of the CIELAB color space can be found. © 2007 Wiley Periodicals, Inc. Col Res Appl, 32, 463–468, 2007     

A qualitative description of thermochromism in color measurements

The color of an object depends on the temperature of the object. This phenomenon is known as the thermochromic effect, and it is already noticeable at room temperature if the temperature varies just a few centigrades. Red and orange samples are especially sensitive to temperature variation and may cause difficulties in precise color measurement. In this article we show how the phenomenon is based on physical processes and does not only reflect the instability of red color pigments. We derive simple formulas that are shown to be able to explain the published experimental data. © 2002 Wiley Periodicals, Inc. Col Res Appl, 27, 271–275, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.10062     

Experimental determination of the laws of color harmony. Part 4: Color preference and the color harmony content

In 1956, we decided at the Budapest University of Technology and Economics to start a large‐scale experiment on color harmony. The experiments and the processing of the experimental results have been completed in 2006. These experiments, described in this article, form a study of how much are people, participating in the experiment, influenced by their own personal color preference in judging the harmony content of a composition. These experiments have utilized the results of former (1958–1969) color preference experiments and the system of color preference indexes, which were developed by the generalization of those results. Within the framework of these experiments, conducted between 1998 and 2006 there were 24 compositions, shown to the participants, at first one by one, then in pairs and at last in groups of six. They had to assess the harmony content of the compositions and award a score on a scale between 0 and 10. Each composition possessed a specific amount of harmony content according to the rules of color space, based on the Coloroid harmony threshold and verified by former experiments. In these experiments the number of elementary observations were 135 568. The people participating in the experiment were approximately equal number of men and women, from the age group between 10 and 70 years. During processing, by using the color preference numerical indexing system, we compared the results of those experiments with the color preference of a similar age group, by using color compositions, identical to the ones used in the present experiment. We have found that the sensation of the color harmony and its intensity have a strong relation to how the observers relate to colors and also their color preferences. The sensation of color harmony is also influenced by the gender and the age of the observer. © 2009 Wiley Periodicals, Inc. Col Res Appl, 34, 210–224, 2009     

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     

Performance of two color scales for virgin olive oils: Influence of ripeness,variety, and harvest season

The purpose of this investigation was to compare the performance of the bromthymol blue (BTB) method and the Uniform Oil Color Scale (UOCS) method with different sets of virgin olive oil samples from Andalusia (Spain), namely, 1213 samples from olives at three stages of ripeness, 1008 samples from eight olive varieties, and 1700 samples from olives harvested in four different crop seasons. All oils were extracted in the laboratory by the same procedure. The performance of the two color scales was compared using CIELAB color differences between the oil samples and the nearest standard from each scale. The UOCS performed at least 2.0 times better than the BTB for each of the three stages of olive ripeness, and the difference between the two color scales was statistically significant (P<0.001). The UOCS performed at least 1.3 times better than the BTB for each of the eight olive varieties studied, and the differences between the two color scales were statistically significant (P<0.02). The UOCS also performed at least 1.6 times better than the BTB for each of the four harvests analyzed, and the differences between the two color scales were statistically significant (P<0.001). Using the current oil samples, we could discern no substantial improvements to the UOCS standards.     

A structural comparison of the Munsell renotation and the OSA–UCS uniform color systems

A structural comparison has been made of the lightness, chroma, and hue scales of the Munsell system, as expressed in the Munsell Renotations, and of the OSA‐UCS system. While the lightness scales are similar (except for the adjustment for the Helmholtz–Kohlrausch effect and the inclusion of a “crispening” effect in OSA–UCS), there are significant differences in the chroma scales along the major chromatic axes. Unlike in CIELAB, the increments in X and Z along these axes for equal chroma steps in both systems do not fall on a continuous function. In the two systems, as well as in CIELAB lines connecting colors of equal chroma differences at different Y values point to nonreal origins. These differ among the three systems. A major difference between Munsell and OSA–UCS is the size of the first chroma step away from gray. An experiment has been performed with the result that the OSA–UCS system is in much better agreement with the average observer in this respect than the Munsell system. OSA–UCS exhibits considerably more internal uniformity in terms of X and Z increments between steps than the Munsell system. © 2000 John Wiley & Sons, Inc. Col Res Appl, 25, 186–192, 2000     

Transferring the color imagery from an image: A color network model for assisting color combination

In order to transfer the color imagery from an image to another object to generate color schemes, a color network model is proposed. It consists of two subnets: source net for describing the color information of the reference image; target net for demonstrating the target object to be colored. Thus, the problem of reusing features of color patterns is translated into the mapping process from the source net to target net. Four indicators are designed to measure the conformity between the two nets: color sequence, adjacency, concentration, and the subspace size. In the meantime, a comprehensive aesthetic evaluation given by the designer is introduced to search the optimum combination of the four indicators to help generate imagery matching schemes. A prototype system is developed based on CorelDraw as a design tool. The feasibility of the color network model is then verified through a color combination of graphic design task.     

A general framework to study the price‐color relationship in paintings with an application to Mark Rothko rectangular series

We propose a general framework to study the relationship between the price of a painting and its color‐related attributes. To this end we focus on four key aspects: dominant colors, features of the color palette, color harmony, and color emotions. We demonstrate the usefulness of this approach with an example based on Mark Rothko's post‐1950 paintings (the “rectangular” series), and auction data from the 1994 to 2018 period. We identify two distinct price‐color regimes in Rothko's market: (a) [1994‐2005], a period in which prices are explained mainly by the growing popularity of the artist regardless of the color attributes of the paintings sold; and (b) [2006‐2018], a period in which color‐related attributes explain most of the prices. Furthermore, we find that in this second period, the dominant colors and the diversity of the color palette, are by far the most relevant attributes that influence the price; color harmony and color emotions hold almost no explanatory power during this period. Finally, we propose a new metric based on the Herfindahl Index to describe color diversity; this metric seems to be promising at characterizing the effect of the color palette on the price of a painting.     

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.     

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     

Reliability of the bromthymol blue method for color in virgin olive oils

The bromthymol blue (BTB) method is currently used for the assessment of color in olive and seed oils by visual comparison with standard solutions. Two BTB scales were prepared with 2 yr difference and compared, and the recent one was used to analyze 502 virgin olive oil samples, obtained by the Abencor® technique reproducing the industrial procedure. The temporal chromatic degradation of the BTB samples after 2 yr [3.93 Commission Internationale de l’Eclairage (CIE) 1976-(L*a*b*) (CIELAB) units, on the average], as well as the small percentage of virgin olive oils matching the colors of the samples provided by the BTB scales (13.1% with a suprathreshold color tolerance of 1.52 CIELAB units), indicates the limitations of the BTB method. Linear regression models are proposed in order to compute with acceptable accuracy the BTB indices from chromaticparameters. The use of CIELAB for the specification and future studies on color in virgin olive oils is recommended.