Riemannian formulation and comparison of color difference formulas

Study of various color difference formulas by the Riemannian approach is useful. By this approach, it is possible to evaluate the performance of various color difference formulas having different color spaces for measuring visual color difference. In this article, the authors present mathematical formulations of CIELAB (ΔE), CIELUV (ΔE), OSA‐UCS (ΔE_E) and infinitesimal approximation of CIEDE2000 (ΔE₀₀) as Riemannian metric tensors in a color space. It is shown how such metrics are transformed in other color spaces by means of Jacobian matrices. The coefficients of such metrics give equi‐distance ellipsoids in three dimensions and ellipses in two dimensions. A method is also proposed for comparing the similarity between a pair of ellipses. The technique works by calculating the ratio of the area of intersection and the area of union of a pair of ellipses. The performance of these four color difference formulas is evaluated by comparing computed ellipses with experimentally observed ellipses in the xy chromaticity diagram. The result shows that there is no significant difference between the Riemannized ΔE₀₀ and the ΔE_E at small color difference, but they are both notably better than ΔE and ΔE. © 2011 Wiley Periodicals, Inc. Col Res Appl, 2011;     

Extending CIELAB: Vividness, , depth, , and clarity,

CIE L*, a*, b* is a rectangular coordinate system used extensively for numerical color communication and quality assurance. Often the a*, b* coordinates are rotated to cylindrical polar coordinates of (radial distance) and h_ab (angle measured counterclockwise from the a* axis), reasonably relating to chroma and hue. When each coordinate is considered independently, it is observed that colors in our daily experiences do not change in a similar independent fashion. Changes in concentration for mixtures of colorants result in changes in both chroma and lightness. Directly illuminated three‐dimensional colored objects change in both chroma and lightness between direct illumination and either shadow or highlight. Two new coordinates are defined for CIELAB: vividness, , and depth, . Each represents a Euclidean distance from a color defined by L* and to of 0 and either L* = 0 for vividness or L* = 100 for depth. Image‐based visualizations were made to demonstrate how changes in these variables led to color changes more representative of our daily experiences. For cases where a color and background had the same lightness, it was observed that colors became less distinct with a reduction in chroma. A third dimension was defined, clarity, , a Euclidean distance from a color defined by L*, a*, and b* to its background color, similarly defined. © 2013 Wiley Periodicals, Inc. Col Res Appl, 39, 322–330, 2014     

Equivalent lightness of elderlies investigated by cataract experiencing goggles

People get cataract in their eyes when they age. The color perceived by the senile cataract eyes desaturates because of the environment light that scatters in the eyes by the hazy crystalline lenses. We investigated the effect of the desaturation on brightness of objects in terms of the equivalent lightness , which is composed of the achromatic lightness and the chromatic lightness . If the color desaturates, becomes smaller and consequently becomes smaller in the cataract eyes. with and without cataract experiencing goggles at room illuminances to cover mesopic to photopic level was measured. Red, yellow, green, and blue patches of size 2° × 2° arc of the visual angle were investigated with the direct heterochromatic brightness matching between the color patches and a gray scale. Both took about the same value. with goggles was then transferred to the final where the matching gray scale was observed without goggles to express the equivalent lightness of cataract eyes by the gray scale perceived by normal eyes. with goggles was lower than without goggles by about 10 L* units in all the four colors. This reduction was almost equal to the reduction of L* by the reduced transmittance of the goggles showing that there was no effect of color desaturation. The color appearance in the color patches was measured by the elementary color naming method, and the results clearly showed the color desaturation with goggles implying decrease of . We concluded that the scattered environment light compensated the decrease of to keep the brightness of stimuli unchanged. © 2011 Wiley Periodicals, Inc. Col Res Appl, 38, 267–276, 2013     

Color variability for a wine sample poured into a standard glass wine sampler

Spectroradiometric color measurements were performed at 26 regularly spaced points of a standard wine sampler into which 100 cc of wine were poured. Our goal is to describe the color changes occurring in this system, but not to propose a new method for wine‐color measurement. Three samples of three different wines (red, rosé and white) were studied. From experimental measurements, lines of constant lightness (L), chroma (C_,10) and hue‐angle (h_ab,10) were plotted for each wine poured into the wine sampler, as well as lines of constant CIELAB color differences (ΔE_,10), with respect to a reference point placed at the axis of the wine sampler and at the zone with the greatest diameter. Considering different points of the wine sampler, the color attribute undergoing the greatest change was lightness (ΔL about 16.0, 15.0 and 11.0 for the red, rosé and white wines, respectively), followed by chroma (ΔC_,10 about 2.8, 3.8 and 2.6 for the red, rosé and white wines, respectively) and hue(ΔH_,10 lower than 1.0 for all the wines). Lightness variations were related mainly to the thickness differences between various zones of the wine sampler. Large color differences were found among the different points of the wine poured into the wine sampler (about 20.0, 21.0 and 14.0 CIELAB units, for the red, rosé and white wines, respectively). Panels should be aware of these large color variations when wine is visually assessed using standard wine samplers. It should be concluded that a single color specification for a wine poured into a wine sampler gives incomplete information, but hue, which is the main color attribute considered by observers, is nearly constant in the wine sampler. © 2003 Wiley Periodicals, Inc. Col Res Appl, 28, 473–479, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.10200     

3D Master Toothguide according to L*, C*, and h* coordinates

The purposes of this study are to describe the color coordinates of the 26 shade tabs of the 3D Master Toothguide according to their L*, C*, h* coordinates, and to calculate ΔE_ab*, ΔL*, ΔC*, and Δh* in the 26 shade tabs. The tooth color of 1361 maxillary central incisors was measured “in vivo” using a spectrophotometer. Tooth color was recorded following the 3D Master system and its corresponding L*, C*, h*color coordinates. Of the 325 shade tabs pairs compared a color difference ( ) of between 2.6 and 5.5 units was found in 9.54% (31 pairs). In 291 pairs (89.54%) there was color difference that exceeded the 5.5 units. Only 0.92% of the color differences () were less than 2.6 units. The minimum color difference ( ) found was 2.1 units and the maximum 45.0 units. The intervals in lightness, chroma, and hue groups between adjacent shade tabs were not uniform. In conclusion, this toothguide is clearly ordered regarding lightness or the L* coordinate. Most of the color differences between the 26 shade tabs of the 3D Master exceed the perceptible threshold of 2.6 units. Some clinical implications are as follows: the 26 shade tabs of the 3D Master Toothguide offer improvements as far as spatial arrangement is concerned. Thus, it is highly possible that the subjective visual color of the measurement would be correct. If there is a mistake when choosing the shade tab from the 3D Master guide there will quite probably be an unacceptable color difference from the clinical point of view. © 2014 Wiley Periodicals, Inc. Col Res Appl, 40, 518–524, 2015.     

Maximum number of discriminable colors in a region of uniform color space

Continuing a discussion by Kuehni, this note examines the problem of fitting as many as possible colors in a 1‐JND radius sphere such that each pair of colors is separated by at least 1 JND. Kuehni announced nine. A first estimate yields a maximum of 13, but this is too many because colors populating adjacent spheres will be too close to each other. Accordingly, I derive the maximum number, , of discriminable colors per unit volume of color space, and then formally compute from this number packing density a number of colors inside the unit sphere. That estimate, nearly 6, will undoubtedly erode when discrete color points are chosen within the unit sphere. Kuehni's estimate of 9 is too high. © 2016 Wiley Periodicals, Inc. Col Res Appl, 2016     

An optical model relating (L*a*b*) values for a scattering surface covered with a scattering layer to (L*a*b*) values for the uncovered surface and its application to tooth colour

The appearance of human dentition is important both psychologically and commercially. Many people perceive the lightness and chromaticity of their teeth as key factors in their overall appearance leading to large businesses in materials for colour‐matched fillings and crowns and in tooth whitening products. The human eye is very sensitive to small colour differences, recognizing a row of highly colour‐matched crowns as unnatural yet seeing excessive colour variation or darkness as unattractive. One cause of tooth discolouration is a darkening of the dentine, visible through the enamel. This has lead the authors to develop a model capable of relating ( ) measurements on a scattering surface, in our case dentine, to ( ) measurements when overlaid by a translucent scattering layer, in our case tooth enamel. The model can be used when any scattering layer is superimposed on a coloured surface. In contrast to existing models, no spectral measurements are necessary allowing the use of colourimeters rather than spectrophotometers. However, there are limitations on the degree of colour saturation for both the coloured surface and the scattering layer as the model uses an approximation valid only for weakly saturated colours. As neither the enamel nor the dentine have strongly saturated colouration, the limitation is entirely acceptable for our work. The use of ( ) measurements directly rather than having to measure the spectrum of reflected light is of practical importance as such measurements in a dental surgery are impossible in all but exceptional cases whilst ( ) measurements in the surgery are routine. © 2014 Wiley Periodicals, Inc. Col Res Appl, 40, 504–517, 2015     

Dancheong colors used for Korean cultural heritage architecture restoration

Dancheong is Korean traditional decorative coloring on special wooden buildings, and it has been preserved by Danjeongjang as a national intangible cultural heritage—a craftman with a special skill to paint dancheong. All dancheong in the national heritage have been managed by the Cultural Heritage Administration following the standard procedure. However, there is no available information about final colors. In this study, a total of six different dancheong color paletts were prepared by six different apprentices of the living national treasures. In total, there were 20 different colors and 12 colors were shown in all six palettes. The color measurement result showed that well trained dancheong painter can reproduce the same colors repeatedly with fairly high precision with 1.8 on average except two colors—Ju‐hong and Yang‐cheong—showing high chroma differences, but with very similar lightness and hue angle indicating that hue of dancheong colors is the most important factor to judge the correctness of the color preproduction. The dancheong colors show large variations depending on the painters but the painters trained by the same teacher have the similar color palettes. Further in‐depth dancheong color investigation is needed to fully understand the contemporary dancheong colors.     

The influence of thermal treatment on color response of wood materials

In this study, the influence of thermal treatment on color changes of six different wood materials was investigated. Test specimens were subjected to three different temperatures (160, 180, and 200°C) and durations (3, 5, and 7 h). The data obtained were analyzed using variance analysis, and then the statistical analysis of Tukey's test was conducted. After this treatment, the results showed that the color values of the six wood materials changed significantly. It was determined that L* (lightness) values decreased; the minimum change in L* was ～4% for Juniper wood, and the maximum change in L* was ～64% for Beech wood. The values of a* (red coordinate) and b* (yellow coordinate) showed varying levels of increase when the heat treatment conditions were 160°C for 3 to 7 h (not including Cherry wood), but the values began to decrease slowly after treatment at 160°C for 5 h. The ratios of the minimum and maximum color change in a* and b* were determined at 180°C for 3 h in Plane wood, 200°C for 5 h in Hazelnut wood, and 160°C for 3 h and 200°C for 7 h in Beech wood. As temperature and duration were increased, the minimum total color change (ΔE) was ～3.5% for 160°C at 3 h in Cypress wood, and the maximum total color change (ΔE) was ～50% for 200°C at 7 h in Cypress wood. © 2010 Wiley Periodicals, Inc. Col Res Appl, 2010     

Standard color liquid crystal displays by a dimming technology

Dimming technologies have been used in liquid crystal display (LCD) products, especially for mobile applications, to reduce power consumption. It is widely known that dimming technologies tend to degrade the color accuracy. This article, however, presents that color performance of a dimmed LCD is better than a conventional one. We show a max method, one of dimming methods, converting an input digital data into higher values that have less color shift phenomenon. We propose how to compare the color performance of original and dimmed colors based on a modified standard. The average value of measured Δu′v′ of 25 dimmed colors was 0.0040, whereas that of the original colors was 0.0190. In addition, the average value of measured Δ of 25 dimmed colors was 2.40, whereas that of the original colors was 9.24. The measured results prove that the dimming technology can make LCD better in not only power consumption but also color performance. This article is the world's first report that breaks the usual stereotype on dimming technologies. This work proposes a dimmed LCD as a standard color display. © 2013 Wiley Periodicals, Inc. Col Res Appl, 39, 480–485, 2014     

Image quality evaluation for high dynamic range and wide color gamut applications using visual spatial processing of color differences

High dynamic range (HDR) and wide color gamut imagery has an established video ecosystem, spanning image capture to encoding and display. This drives the need for evaluating how image quality is affected by the multitudes of ecosystem parameters. The simplest quality metrics evaluate color differences on a pixel‐by‐pixel basis. In this article, we evaluate a series of these color difference metrics on four HDR and three standard dynamic range publicly available distortion databases consisting of natural images and subjective scores. We compare the performance of the well‐established CIE L*a*b* metrics (ΔE₀₀ , ΔE₉₄ ) alongside two HDR‐specific metrics (ΔE_Z [J_za_zb_z], ΔE_ITP [IC_TC_P]) and a spatial CIE L*a*b* extension (). We also present a novel spatial extension to ΔE_ITP derived by optimizing the opponent color contrast sensitivity functions. We observe that this advanced metric, , outperforms the other color difference metrics, and we quantify the improved performance with the steps of metric advancement.     

Correlation and modeling between color variation and quality of the surface between accelerated and natural tropical weathering in Acacia mangium,Cedrela odorata and Tectona grandis wood with two coating

To prevent the photodegradation process, a wide range of coatings have been developed. This study evaluated wood color change (ΔE*) and the surface quality index (SQI) generated by ASTM D‐660 standards in wood protected with polyurethane and varnish finishes of three tropical species (Acacia mangium, Cedrela odorata and Tectona grandis) in two weathering conditions (natural and accelerated condition). In addition, a model was developed to predict ΔE* and SQI in natural weathering based on ΔE* and SQI from accelerated weathering. The results showed that the application of these finishes generated variations in the color parameters of wood before being exposed to the elements. Additionally, it was found that finishes generated increases in ΔE*, especially the varnish type finish, and decreasing of SQI. Finally, models were found to predict color changes or surface quality in natural weathering based on color changes or surface quality in accelerated weathering. The model algorithm was expressed by ΔE* or SQI measured (X) and time exposure (t) in accelerated weathering by equation . With these models, it is possible to predict the equivalence of exposure times in natural weathering in tropical conditions for different kinds of finishes in three tropical species. © 2013 Wiley Periodicals, Inc. Col Res Appl, 39, 519–529, 2014     

Comparing large colour‐difference data sets

This study investigated the differences between different large colour‐difference (LCD) data sets (with a mean ΔE value about 10). Six data sets were studied. For each data set, various CIELAB based colour difference models were derived to fit the data. These models were compared to shed light on the difference between the different data sets. It was found that all data sets have very similar characteristics except for the Munsell data. Detailed investigation showed that the discrepancy is mainly due to the balance between the lightness and chromatic differences used previously for the Munsell data set. It was found that one unit of Munsell Value appears to be three times as large colour difference as one unit of Munsell Chroma at least under the experimental conditions for the data sets studied here. © 2010 Wiley Periodicals, Inc. Col Res Appl, 2011     

Effect of ceramic veneer thickness and cement shade on the CIELAB system after bonding—an in vitro study

In restoration dentistry clinicians need to control the effect of the ceramic thickness and cement shade to achieve successful colorimetric results when all‐ceramic veneers are bonded. The purpose of this study was to evaluate the in vitro effects of cement color and the thickness of the final shade on porcelain discs. The study sample comprised 120 e.max Press HT A‐2 ceramic discs of two thicknesses (60 of 1 mm thick and 60 of 0.5 mm thick). Three different lightnesses of Variolink Veneer cement were used (?3, 0, and +3) for the cementation process. An Easyshade spectrophotometer was used to measure color coordinates (L*, C*, h, a*, and b*) on the discs both before and after cementation. To a large extent, color changes (ΔE ) after the cementation process were found to depend on cement thickness, ceramic thickness, and cement lightness. This model predicted 52% of the observed variability. The most marked change in color appeared on discs 0.5 mm thick and a cement lightness of ?3 (ΔE = 12.0 units). By contrast, color was more stable (minor changes) on discs with a cement lightness of +3 (ΔE = 2.3 units). All color coordinates were significantly modified after bonding, both on thin and thick discs and in all three cement color groups (?3, 0, and +3). However the difference in color (ΔE ) is significantly greater in discs 0.5 mm thick as compared with ceramic discs 1 mm thick. The most prominent change after bonding was found in the h (hue) coordinate. © 2015 Wiley Periodicals, Inc. Col Res Appl, 41, 642–648, 2016     

Counterion-Induced Cationic Flexible Nanoparticle Catalytic of Piperidinolysis of Phenyl Salicylate

The removal of PSa^? from bulk aqueous phase to the pseudo‐micellar phase by halobenzoate counterion X is responsible for the monotonic increase in k_obs (pseudo first‐order rate constants) with the increase in the values of [MX] where MX = sodium salts of 2‐, and 4‐halobenzoic acids. The values of ion exchange constants, or for X = 2‐ and 4‐halobenzoate ions in the presence of tetradecyltrimethylammonium bromide (TTABr) were calculated from the apparent catalytic rate constants, ^Xk_cat which represent the catalytic effect of CFN. Larger values of or were observed for X = 4‐halobenzoate ions than that for X = 2‐halobenzoate ions due to isomeric factors. The values of or determined in the presence of TTABr were compared with previously determined or values in the presence of cetyltrimethylammonium bromide (CTABr). The values of or are nearly 8 ~ 9‐fold larger for 4‐IBz^?, 4‐BrBz^? and 4‐ClBz^? compared to the respective values of X = 2‐IBz^?, 2‐BrBz^? and 2‐ClBz^?. The values of or for X = 4‐FBz^? is nearly 3‐fold larger than that for X = 2‐FBz^?. The values of or for X = 2‐ and 4‐halobenzoates are significantly smaller in the presence of TTABr than these in the presence of CTABr nanoparticles.     

Effect of Surface Concentration of Lu on Oxygen Permeation of Polycrystalline Alumina at High Temperatures

The effect of Lu surface concentration on oxygen permeation in polycrystalline α‐alumina wafers was determined at 1773 K under limited oxygen potential gradients (Δ), where the two surfaces of the wafer were deliberately subjected to different oxygen partial pressures [ (I) ?  (II)]. When oxygen permeation occurred mainly by oxygen GB diffusion under a Δ generated by a combination of low values, the Lu‐coating on the (I) [ (II)] surface decreased [increased] the oxygen permeability constants. When Δ was the result of a combination of high values, where oxygen permeation proceeded mainly by aluminum GB diffusion, the oxygen permeability constants were decreased only by the Lu‐coating on the (I) surface. The analysis of mass transfer parameters, such as the chemical potentials, GB diffusion coefficients, and fluxes of aluminum and oxygen in the wafers, suggested that ambient oxygen molecules were effectively attracted toward Lu‐coated surfaces exposed to low‐ environments, leading to a change in oxygen permeability.     

Mass transfer coefficient of tubular ultrafiltration membranes under high‐flux conditions

The effect of suction flow on the mass transfer coefficient of tubular ultrafiltration membranes, in particular that under a high‐flux condition, was studied. We pointed out that is proportional to under turbulent conditions, and that the proportional constant, b, exceeds 0.023 when the effect of suction flow is not negligible. We conducted the velocity variation method using ultrafiltration membranes with MWCOs of 20k and 100k and dextrans having molecular weights of 40,000 and 70,000 at the conditions, where exceeded . We demonstrated that the effect of suction flow includes not only flux but also the diffusion coefficient of solute, and that the ratio of the flux to the diffusion coefficient, expressed as , is an important index. Finally, we concluded that , when is smaller than , giving the Deissler equation itself, and that , when exceeds . © 2017 American Institute of Chemical Engineers AIChE J, 64: 1778–1782, 2018     

NMR spectroscopic study of chemical equilibria in solutions of formaldehyde,water, and butynediol

Liquid mixtures of formaldehyde, water, and butynediol are complex reacting multicomponent systems in which formaldehyde forms oligomers both with water and butynediol. ‐ and ‐NMR spectra of these mixtures are elucidated. The species distribution of the oligomers is quantitatively determined by ‐NMR spectroscopy. The measurements cover temperatures from 293 to 366 K, overall formaldehyde mass fractions from to , and overall butynediol mass fractions from to . A mole fraction‐based and an activity‐based model of the chemical equilibrium in the studied system are developed and chemical equilibrium constants are reported. © 2017 American Institute of Chemical Engineers AIChE J, 63: 4442–4450, 2017     

The role of wettability of nonideal nozzle plate: From drop‐on‐demand droplet jetting to impact on solid substrate

The dynamics of drop‐on‐demand (DoD) droplet formation and subsequently impact on the solid substrate are investigated using a three‐dimensional (3‐D) multirelaxation‐time (MRT) pseudopotential lattice Boltzmann (LB) model. The wettability of nonideal nozzle plate and solid substrate is modeled by a geometric scheme within the LB framework. The dynamics of droplet formation are explored in a range of the inverse of Ohnesorge number , , and , and the Reynolds number , , and . For , no satellite droplet is observed and the wettability of nozzle plate greatly influences the velocity and length of jetting fluids. For , the filament breakup and recombination are observed. The moment of filament breakup is delayed with advancing contact angle increasing. For with , the primary and satellite droplets could not be recombined with and which agree with the literature. Whereas with , the recombination occurs. The dynamics of subsequent oscillating droplet impact on the substrate are similar to that of equilibrium droplet which could obtain high‐resolution printed features. Consequently, considering with large and numbers, the printable range could be extended which could help increase the printing frequency and boost the production outputs of inkjet printing. © 2018 American Institute of Chemical Engineers AIChE J, 64: 2837–2850, 2018     

Color naming for the Persian language

According to Berlin and Kay, there is a set of 11 universal basic color terms: White, Black, Red, Green, Yellow, Blue, Brown, Purple, Pink, Orange, and Gray. To approve this, a world survey (WCS) was begun to gather data on color categorization through the world, although, despite many languages, Persian language has not been studied so far. We report a study of color naming in Iran. A study was carried out in six major cities including: Tehran, Isfahan, Mashhad, Yazd, Rasht, and Shiraz to investigate the color naming for Persian language and also the effect of local culture. The main purpose of this study was to describe the basic color terms of Persian language and to verify Berlin and Kay's theory. In total, 200 subjects were studied from all the six cities. Our results showed that there were the same basic color terms (as Berlin and Kay's theory) in Persian language overall including:“ (White) ”,“ (Black) ”, “ (Red) ”, “ (Green) ”, “ (Yellow) ”, “ (Blue) ”, “ (Brown) ”, “ (Purple) ”, “ (Pink) ”, “ (Orange), ” and “ (Gray) ”. However, this was not valid for all the cities when they were investigated individually. There were 10 basic terms in Mashhad and Shiraz while the other cities had 11 basic terms. Also, the set of the used terms would differ by the city. © 2014 Wiley Periodicals, Inc. Col Res Appl, 40, 352–360, 2015