Testing the differences between two color measurement probability distributions using Hotelling's T2 test and the permutation test

It is common practice in statistics to test the equality of two population means using, for example, the Student's t test, in the univariate case, or the Hotelling's T² Test in the multivariate case. However, tests on the equality of population means are not well developed for testing the difference between two populations of color measurements. Methods for analyzing populations of spectral reflectance and L*a*b* measurements have been described for applications such as analyzing inter-instrument agreement and repeatability. Methods have also been proposed for the analysis of color differences, but there are little written about techniques for testing whether two samples have the same probability distribution. This article focuses on testing the difference between color measurement probability distributions based on color difference. In addition, a metric is proposed called the threshold for color difference discrimination (TCDD, in units of ΔE), the color difference at which two populations can be considered to have different population distributions. A lower TCDD means smaller color differences between two samples can be resolved. Two parametric tests based on Hotelling's T² test and a nonparametric permutation test were used to determine the TCDD for populations of color measurements with different variances and sample sizes. The TCDD was found to be smaller by tests using the Hotelling's T² statistic, compared with a permutation test performed directly on color difference. It was also found, as expected, that larger sample sizes led to smaller TCDDs, as did smaller population variances.     

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     

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     

Effects of color on expectations of drug effects: A cross‐gender cross‐cultural study

To study the role of color in expectations of drug effects, 80 Chinese participants (40 females and 40 males) were asked to classify each of seven single colored capsules and six differently colored two‐piece capsules into one of four classifications of drug effects. The results from the Chinese sample were also compared with that from four other cultural groups studied elsewhere. The Chi‐square test results showed that all seven single colored capsules yielded non‐chance distributions in classifications of drug effects, with six showing specific effects; and that five two‐colored capsules had non‐chance distributions, with four significantly associated with specific effects. Notable gender differences were observed in the expectations of drug effects. While the cross‐group comparison revealed consistent red‐stimulant and blue‐depressant associations across the five cultural groups, disagreements existed for other colors among the groups. The findings emphasized the importance of color in drug design and administration in support of drug differentiation, medication adherence, and drug efficacy, and suggest gender and cultural implications on the basis of color to achieve better drug effects. © 2016 Wiley Periodicals, Inc. Col Res Appl, 42, 124–130, 2017     

A general form of color difference formula based on color discrimination ellipsoid parameters

A general color difference formula has been derived based on the parameters of color discrimination ellipsoids in the CIE 1976 L*a*b* color space. By using different orders of approximation, the general formula resembles the basic forms of the current formulae. The method described in this article suggests a framework for modifying the CIE 1976 L*a*b* color difference formula.     

Research on the detection of fabric color difference based on T‐S fuzzy neural network

T‐S fuzzy neural network algorithm is used to establish the mapping relationship from the RGB space to the L*a*b* space, which avoids the complex process of color space conversion. Meanwhile, the block method is adopted to detect color difference of dyed fabric that is wide format and wide viewing angle. Color differences in different regions can be calculated with Color Measurement Committee color difference formula based on T‐S fuzzy neural network. Experimental results are in accordance with the spectrophotometer measurement, which proves that T‐S fuzzy neural network algorithm used in real‐time color detection process is effective and feasible. Workers can make corresponding adjustment on‐line according to the deviation to ensure the quality of fabric color and reduce the loss.     

Influence of firing conditions and production methods on fracture strength of titanium-based metal ceramic crowns

Objectives: This study evaluated the effect of argon atmosphere compared with vacuum during porcelain firing on the fracture strength of crowns made of porcelain and electron beam melted (EBM) Ti-6Al-4 V, cast commercially pure titanium or milled commercially pure titanium. Methods: Sixty crown copings of c. p. titanium, Ti-6Al-4 V alloy and porcelain were fabricated using three production techniques. The copings were fired either under vacuum or in an argon gas atmosphere. Specimens were subdivided into groups of cast c. p. titanium, milled c. p. titanium and EBM Ti-6Al-4 V which were further subdivided according to firing modes employing either vacuum or argon gas. The 60 specimens were subjected to cyclic preloading and thermocycling, and were then individually loaded until interface fractured. Differences between the group mean values were calculated using the one-way ANOVA and Tukey’s range test. Two fractured samples from each group were cut with a diamond blade and examined using SEM and EDS for visualization and chemical composition analysis of the fractured interface. Results: The highest mean fracture strength values, though not significant, were recorded for the groups fired in argon atmosphere, and the lowest mean fracture strength values were recorded for the groups fired in vacuum, with one exception. Comparing the two main groups of firing atmosphere, no significant difference could be documented. SEM and EDS analysis indicated clear differences in composition and structure between the groups included in the study. Conclusions: Firing in argon atmosphere does not significantly improve the fracture strength of porcelain bonded to titanium.     

Canonical biplot statistical analysis to detect the magnitude of the effects of phosphates crystallization aging on the color in siliceous conglomerates

The Canonical Biplot method is used to determine the magnitude of the effects on the Δ chromatic coordinates (ΔL*, Δa*, Δb*) and the parameter ΔE*, where (ΔL*, Δa*, Δb*) are the difference in the values of the sample after each aging cycle and the value of the untreated sample and ΔE* = [(ΔL*)² + (Δa*)² + (Δb*)²]^1/2. We performed a study of the changes in color produced by two types of artificial aging procedures on four varieties of siliceous conglomerates from Zamora (Spain) that have traditionally been used in construction and later renovations in historical buildings in the zone. To accomplish this, 25 cycles of the following types of accelerated artificial aging were carried out: (a) freezing/thawing and cooling/heating (T1) and (b) combined freezing/thawing and cooling/heating + salt (phosphates) crystallization (T2). The results of the statistical study applied (Canonical Biplot) allowed us to differentiate the magnitude effect on the color of the surface brought about by T1 as compared with T2. These effects (p < 0.05) were observed in all but one (ochre conglomerate) of the varieties, but mainly in the variable governing red hue (Δa*) and yellow hue (Δb*). © 2012 Wiley Periodicals, Inc. Col Res Appl, 39, 82–87, 2014     

Investigation of metallic color perception using real‐world materials

Metallic colors have a unique appearance of glossiness with features such as highlights, contrast, and reflections on their surface, and therefore, metallic objects are very attractive to humans. Especially, gold, silver, and copper colors are familiar metals used as decorative materials, coins, and other furnishings. However, the mechanism and condition of metallic perception have not been fully investigated. There are a few studies for investigating metallic perception using rendered patches or images, but there is no study using real‐world objects. In our previous study, we developed a simple representation technique that made real objects appear to be made of gold by projecting a solid color onto a target nonmetallic object. By using the representation technique, in this study, we have further investigated the perception of metallic appearance such as gold, silver, and copper using real‐world materials, and analyzed the difference between these metallic perceptions. Our results indicate that the perception of the metallic object is different for gold, silver, and copper. Our new findings are as follows: the glitter required for the perception of gold and silver becomes an obstacle to the perception of copper; the metallic perception reveals that learning experience might be strongly affecting; and luminance adjustment is sensitive to the perception of metallic objects.     

Semantic interpretation of color differences and color‐rendering indices

A series of visual experiments were carried out to rate the similarity of color appearance of two color stimuli on categorical and continuous semantic rating scales. Pairs of color stimuli included two copies of the same colored real or artificial object illuminated by a test light source and a reference light source. A formula was developed to predict a category of color similarity (e.g., “moderate” or “good”) from an instrumentally measured color difference. Given a numeric value of a color difference between the two members of a pair of colors, for example, 2.07, the formula is able to predict a category of color similarity, for example, “good.” Because color‐rendering indices are based on color differences, the formula could be applied to interpret the values of the new color‐rendering index (n‐CRI or CRI2012) in terms of such semantic categories. This semantic interpretation enables nonexpert users of light sources to understand the color‐rendering properties of light sources and the differences on the numeric scale of the color‐rendering index in terms of regular language. For example, a numeric value of 87 can be interpreted as “good.” © 2013 Wiley Periodicals, Inc. Col Res Appl, 39, 252–262, 2014; Published online 14 March 2013 in Wiley Online Library ( wileyonlinelibrary.com ). DOI 10.1002/col.21798     

Multivariate Gaussian subspatial regression applied to predict the effect of phosphate crystallization aging on the color in silicious conglomerates

A new methodology has been applied to the experimental data obtained about a white siliceous conglomerate from Zamora (Spain), which was subjected to 25 cycles of 2 types of aging [freezing/thawing with cooling/heating (T1) and freezing/thawing with cooling/heating + phosphate crystallization (T2)]. Our model (multivariate Gaussian subspatial regression) allows the behavior and prediction of the chromatic coordinates (L*,a*,b*), including more than 25 cycles, to be analyzed. This model is much more flexible than classical models as it allows multiple variable combinations to be predicted in a dynamic way. The final result showed that the conglomerate experiences darkening, yellowing, and reddening, as the number of cycles increase and that the darkening is much less pronounced in T2 due to phosphate crystallization.     

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     

Optimization of color reproduction on CRT‐color monitors

In the present experimental study, we quantify the influence of the brightness and contrast levels of a CRT‐color monitor in the color reproduction of 60 Munsell chips distributed throughout the chromatic diagram. The images were captured by two CCD cameras, and the color differences were evaluated after reproducing the chips on a color monitor (the experiment was performed with 3 different monitors) for 9 combinations of brightness‐contrast levels. We evaluated the color differences with 3 different formulas: CIELAB, CIELUV, and CIE94. The results indicate that the optimal settings of a monitor, to minimize the color differences, is a medium or minimum brightness level in combination with a maximum contrast level. This combination ensures a more faithful color reproduction with respect to the original image. © 1999 John Wiley & Sons, Inc. Col Res Appl, 24, 207–213, 1999     

Dependence of the color appearance of some flowers on illumination

Seven flower colors perceived by five color experts using visual color measurement under 2800 K warm white fluorescent lamps, 3500 K plant growth lamps, and 6500 K light‐emitting diodes (LEDs) were compared with those under 6500 K fluorescent lamps, which represented illuminants in florist shops. Fluorescent lamps (6500 K, 1000 lx) were found to be effective for displaying flower colors and were used as the standard condition. The colors of flowers generally shifted in the same direction as those of the illuminants in CIELAB space. The color differences were highest under the 3500 K fluorescent lamp at both 500 and 2000 lx. At 500 lx, the ΔE values under the 6500 K LED were higher than those under the 2800 K lamp. The C* and ΔE values revealed that the 2800 K lamp was unsatisfactory for purple‐blue and purple flowers and was more suitable for floral displays at lower illuminance. Under the 3500 K lamp, the highest color distortion occurred in cool‐colored flowers, but C* increased for purple‐blue and purple flowers. The 6500 K LED tended to decrease C* for warm‐colored flowers under both illuminances, but it was effective for displaying purple‐blue and purple flowers with increased C*. © 2012 Wiley Periodicals, Inc. Col Res Appl, 39, 28–36, 2014     

Digital image‐color conversion between different illuminants by color‐constancy actuation in a color‐vision model based on the OSA‐UCS system

In digital image capture, the camera signals produced by the D65 illuminant, once translated into tristimulus values of the CIE 1931 standard colorimetric observer (assuming the Maxwell‐Ives‐Luther criterion is satisfied), are considered good to produce accurate color rendering. An image obtained under any illuminant other than D65 does not appear realistic and the tristimulus values of the camera must be transformed into the corresponding ones produced by the D65 illuminant. This transformation must satisfy color constancy. In this work, the transformation is obtained by a color‐vision model based on the Optical Society of America‐Uniform Color Scales system [Color Res Appl 2005; 30: 31–41] and is represented by a matrix dependent on the adaptation illuminant. This matrix is obtained by minimizing the distance between the pairs of the uniform scale chromatic responses related to the tristimulus values of the 99 different color samples of the SG Gretag‐Macbeth ColorChecker measured under a pair of different illuminants, one of which is the D65. Then any picture captured under a given light source can be translated into the picture of the same scene under the D65 illuminant. Metameric reason allows only approximate solutions. The transformations from Daylight and Planckian illuminants to the D65 illuminant have a very regular dependence on the color temperature, that appears to be the typical parameter for the color conversion. © 2012 Wiley Periodicals, Inc. Col Res Appl, 38, 412–422, 2013     

Chromaticity‐matched but spectrally different light source effects on simple and complex color judgments

As light‐emitting diode (LED) light sources mature, lighting designers will be able to deliver white light with a variety of spectral power distributions and a variety of color rendering properties. This experiment examined the effects of three spectral power distributions (SPDs) that were matched in illuminance and chromaticity on three measures of color perception: one objective (performance on the Farnsworth‐Munsell 100 hue test) and two subjective (judgments of the attractiveness of one's own skin, and preferences for the saturation of printed images). The three SPDs were a quartz‐halogen (QH) lamp and two LED sources that were matched to the QH lamp in terms of both illuminance and chromaticity; the three light sources were nominally CCT = 3500 K, x = 0.40, y = 0.39 and ～ 400 lx. LED A used three channels (red, green, blue), and had very poor color rendering (R_a = 18). LED B used four channels (red, amber, cyan, white) and had very good color rendering (R_a = 96, whereas the QH had R_a = 98). Secondary hypotheses addressed the effects of age and skin and eye color on the dependent measures. As expected, LED A delivered very different color perceptions on all measures when compared to QH; LED B did not differ from QH. The results show that it is possible for LED sources to match the familiar incandescent sources. However, although it is possible to deliver what appear to be millions of colors with a three‐chip (RGB) device, there is the risk of creating a very poor luminous environment. © 2013 National Research Council Canada and Wiley Periodicals, Inc. Col Res Appl, 39, 263–274, 2014; Published Online 12 April 2013 in Wiley Online Library ( wileyonlinelibrary.com ). DOI 10.1002/col.21811     

Characterization of basaltic tuffs and their applications for the production of ceramic and glass–ceramic materials

Alkaline basaltic tuffs, from Southern Turkey were characterized and employed to obtain ceramic and glass–ceramic materials by combined sintering and crystallization process. The chemical and mineralogical compositions were analyzed by X-ray fluorescence spectrometry and X-ray diffraction analyses, respectively. The phase formation and the sintering behaviour were investigated by DTA, differential dilatometer and hot-stage microscopy. The micro-structure and residual porosity of the sintered samples were observed by SEM and evaluated by pycnometric techniques. Ceramic material, based on 50% basaltic tuff and 50% clay, was obtained at 1150 °C with 13% total porosity and 4% water absorption. Glass–ceramic materials were synthesized directly using the milled basaltic tuff by mean of the sinter-crystallization technique, in the range 900–1150 °C. The investigation has showed that, due to the high porosity and low crystallinity, alkaline tuffs could be a suitable raw material for ceramic application.     

Performance of advanced color difference and CAM02‐based formulas in prediction of the Crispening effect for reflective samples

The Crispening effect is defined as an increase in the perceived color difference of the two stimuli, when their color (chromaticity or luminance) is close to the background on which the two stimuli are compared. In this study, the amount of the Crispening effect for three achromatic backgrounds and also the performance of six different color difference formulas (CDFs) for prediction of this effect have been investigated, by preparing 85 sample pairs in 9 CIE's recommended color centers. Regarding the results, the maximum (50%) and the minimum (4%) amount of the Crispening effect belong to the gray and the purple centers, respectively. According to the results of a comparative test, the Crispening intensifies when two stimuli have just lightness difference instead of just chromaticity difference. The highest variation was for the gray samples, in which the amount of the Crispening effect increased from 35% to 65%. By using PF/3 and STRESS index, it is also concluded that CMC and CIEDE2000 perform better than CAM02‐SCD and CAM02‐UCS in prediction of the Crispening effect on the dark gray and gray backgrounds. According to the results, the significant differences between the performances of the CDFs disappear when the luminance of the background increases. Huang's power functions also do not improve these results significantly. Furthermore, the results indicate that the traditional L* equation used in CIELAB performs similar to the Whittle's formula in prediction of the Crispening effect for reflective samples, and no significant difference was obtained.     

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.     

Polymer‐derived ceramic aerogels as sorbent materials for the removal of organic dyes from aqueous solutions

Polymer‐derived SiC and SiOC aerogels have been synthesized and characterized both from the microstructural point of view and as sorbent materials for removing organic dyes (Methylene Blue, MB, and Rhodamine B, RB) from water solutions. Their adsorbent behavior has been compared with a polymer‐derived SiC foam and a commercial mesoporous silica. The aerogels can efficiently remove MB and RB from water solution and their capacity is higher compared to the SiC foams due to the higher surface area. The SiOC aerogel remains monolithic after the water treatment (allowing for an easy removal without the need of a filtration step) and its maximum capacity for removing MB is 42.2 mg/g, which is higher compared to the studied mesoporous silica and many C‐based porous adsorbents reported in the literature. The reason for this high adsorption capacity has been related to the unique structure of the polymer‐derived SiOC, which consists of an amorphous silicon oxycarbide network and a free carbon phase.