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;     

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     

Investigation on vermilion,gingiva, and tooth color of young Uygur and Han populations in Xinjiang,China

This study examines oral tissue color in Uygur and Han Chinese populations. The color of oral tissues is of great significance in dental field. It remains uncertain whether there is any difference in the color of oral tissues between different nationalities or ethnicities. Little is known about the color of oral tissues in different Chinese populations. The study included 263 Uygur and Han students aged 18–22 years. The color of anterior teeth, vermilion, and attached gingiva in the subjects was measured by spectrophotometry and expressed through the CIELCh system. The t test and ANOVA was used to analyze color difference between groups. Distribution ranges for L (lightness), C (chroma) and h (hue angle) of anterior teeth, vermilion, and attached gingiva in these two ethnicities were obtained. Significant differences in color of oral tissues between Uygur and Han Ethnicities were found out. The Uygur and Han populations have similar spatial distribution ranges for the color of oral tissues, with slight differences that displayed strong regularities, suggesting that the color of oral tissues was associated with race. In addition, there was a trend of decreasing lightness (especially for maxillary anterior teeth), increasing chroma and redder hue from the center of teeth toward the sides in both ethnicities. There were differences in the color of teeth and attached gingiva between sexes in the Uygur and Han populations. The color of the upper vermilion differed significantly from that of the lower vermilion. © 2010 Wiley Periodicals, Inc. Col Res Appl, 2010     

Color distribution of maxillary primary incisors in Korean children

The purpose of this study was to investigate the color distribution of maxillary primary incisors measured with a colorimeter. The subjects were 100 Korean children aged 2–5 with total number of 400 teeth. A spot measurement intraoral colorimeter was used to determine the color of maxillary primary central and lateral incisors at labial central area. The CIE L*, a*, b* value of each tooth and color difference (ΔE) among each other were calculated and analyzed. The range of L*, a*, and b* values, regardless of the type of teeth, was 72.7–84.9, ?0.6 to 4.9, and 4.7–15.0, respectively. Mean value (SD) of L*, a*, and b* for maxillary primary incisors was 78.6 (2.3), 1.2 (0.9), and 9.6 (1.8), respectively. Boys showed more red (higher a* value) and less yellow (lower b* value) hue than girls in the central incisors (P < 0.05). Mean color difference (ΔE) (SD) between two values which selected from overall 400 L*, a*, b* values measured (n = ₄₀₀C₂) was 3.9 (1.8) with 95% confidence interval range of 3.86–3.89, and most of them were found to be present around the previously reported clinical acceptability thresholds (ΔE = 2.7–6.8). Because mean intraperson ΔE (SD) was 3.0 (1.6) with 95% confidence interval range of 2.86–3.12, most colors among primary incisors in the same person were presumably difficult to discern by naked eye (ΔE < 3.7). Age influenced L* and b* values significantly, but the correlation coefficients were not high (r = ?0.182 for L* of central incisors, P < 0.01; r = 0.188 for b* of central incisors, P < 0.01; and r = 0.143 for b* of lateral incisors, P < 0.05). The present study showed somewhat higher color coordinates than the previous reports which based on primary anterior teeth in other ethnic groups. The results of this study could be used for the color modification of esthetic materials for primary teeth. © 2009 Wiley Periodicals, Inc., Col Res Appl, 2010.     

Testing uniform colour spaces and colour‐difference formulae using printed samples

A grey‐scale psychophysical experiment was carried out for evaluating colour differences using printed colour patches. In total, 446 pairs of printed samples were prepared surrounding 17 colour centers recommended by the CIE with an average δE of 3 units. Each pair was assessed 27 times by nine observers. The visual results were used to test some selected more advanced colour‐difference formulae and uniform colour spaces. The results showed that CIELAB and OSA performed the worst, and the advanced formulae and spaces gave quite satisfactory performance such as CIEDE2000, CIE94, DIN99d, CAM02‐UCS, and OSA‐GP‐Eu. The colour discrimination ellipses were used to compare with those of the earlier studies. The results showed that they agreed well with each other. © 2011 Wiley Periodicals, Inc. Col Res Appl, 2012     

Estimation of hue discrimination thresholds using a computer interactive method

An experimental approach is described for measuring colour discrimination thresholds of human observers. Special software was developed for the accurate display of colour pairs on a high resolution CRT, using serial feedback from a spectroradiometer. Discrimination thresholds between a test and a target colour are determined by repeatedly showing an observer a circle composed of four separate quadrants, one of which has a different colour from the other three. Three quadrants are of the test colour and one of the target colour, or vice versa. Observers are asked to select the quadrant that differs from the others. An experiment is described where hue‐dependent effects affecting hue discrimination are investigated. Eighteen hue threshold values around the hue circle, at constant L = 51 and C = 25, were measured for three observers. Hue thresholds were found to vary around the hue circle, exhibiting an abrupt change in the blue to purple region (240° ≤ h_ab,10 = 300°) This change is not fully accounted for by any CIELAB‐based colour difference formula, including the most recent CIEDE2000 formula. © 2005 Wiley Periodicals, Inc. Col Res Appl, 30, 410–415, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.20153     

The shifting gamma perception

True to life, color display and color management depend on a proper technical model of the display used. Current gamma models and fitting procedures are not accurate in modeling the lower part of the tone reproduction curve. The GOG‐ and GOGO‐model used in color management standards tend to clip the luminance to zero for digital values were luminance can be seen and measured. Two improvements to the models are suggested. First, the models should be fitted by optimizing the root mean square error (RMSE) of the CIE lightness instead of the luminance. Second, a shifting gamma model is adopted, with gamma increasing in value for lower voltages. Results show that the adapted models correspond better with the luminance measurements. The clipping values are nearer to the measured zero luminance threshold, and the average RMSE and ΔE over the whole scale are smaller. © 2005 Wiley Periodicals, Inc. Col Res Appl, 30, 332–340, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.     

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     

Evaluation of colour‐difference formulae for different colour‐difference magnitudes

Most of the colour‐difference formulae were developed to fit data sets having a limited range of colour‐difference magnitudes. Hence, their performances are uncertain when applying them to a range of colour differences from very small to very large colour differences. This article describes an experiment including three parts according to the colour‐difference magnitudes: large colour difference (LCD), small colour difference (SCD), and threshold colour difference (TCD) corresponding to mean ΔE values of 50.3, 3.5, and 0.6, respectively. Three visual assessment techniques were used: ratio judgement, pair comparison, and threshold for LCD, SCD, and TCD experiments, respectively. Three data sets were used to test six colour‐difference formulae and uniform colour spaces (CIELAB, CIE94, CIEDE2000, CAM02‐SCD, CAM02‐UCS, and CAM02‐LCD). The results showed that all formulae predicted visual results with great accuracy except CIELAB. CIEDE2000 worked effectively for the full range of colour differences, i.e., it performed the best for the TCD and SCD data and reasonably well for the LCD data. The three CIECAM02 based colour spaces gave quite satisfactory performance. © Wiley Periodicals, Inc. Col Res Appl, 2012     

Visual color matching under various viewing conditions

In this article, we provide colorimetry data for which it was judged that the colors between different media matched under various viewing conditions. Painted color patches, a monitor, and printed color patches were used in the color matching experiments, in which we compared the appearances of the painted color patch and the monitor, or the monitor and the printed color patch, using the method of constant stimuli. The nine types of viewing conditions we used could be envisaged to occur when comparing different device outputs indoors. The experimental data obtained were compared with corresponding colors predicted with the use of five types of color appearance model, including color appearance formulae. We found that when the viewing conditions were the same for the different media, there was good agreement between the experimental data and the CIECAT94 model. And by adjusting the brightness induction and the chromatic induction factors, it was possible to improve conformity for the lightness and the chromaticity. Moreover, it was possible to improve the white point shift, which cannot be adjusted with the use of optimized parameters by introducing incomplete adaptation. By optimizing the parameters and introducing incomplete adaptation, it is possible to make the mean color difference ΔE between the corresponding color and the color matching point less than 10 CIELAB units for all of the viewing conditions.     

Color managing the third edition of Billmeyer and Saltzman's Principles of Color Technology

Commercial ICC‐compliant color‐management software was used to produce color‐managed CMYK‐encoded images for the third edition of Principles of Color Technology. Custom profiles were created for a Scitex Eversmart Pro flatbed scanner and a Kodak Approval proofing device. This enabled objects such as color‐order systems and colorimetric‐encoded, computer‐generated graphical images to be reproduced with reasonable colorimetric accuracy. The GretagMacbeth ColorChecker Color Rendition Chart was used as an independent verification target. Its printed reproduction had an average error of 4.2 ΔE (6.4 ΔE^*_ab). Colorimetric‐rendering device profiles enabled the visualization of the book's color gamut and of a calibrated visible spectrum. © 2002 Wiley Periodicals, Inc. Col Res Appl, 27, 360–373, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.10083     

The proper use of indices of metamerism

General (spectral) and special (colorimetric) indices of metamerism have been developed to evaluate match quality for metameric and parameric specimens. For a parameric pair, in which there is not an exact colorimetric match for a reference observer and illuminant, various corrections can be used to adjust one of the stimuli such that an exact match is achieved. These adjustments can be spectral or colorimetric. In cases where the mismatch is large, the resultant metameric index may be misleading. A small index of metamerism and a large color difference under the reference conditions has a different interpretation than its converse. This is demonstrated for blue, yellow, magenta artist paints matching a spectrally nonselective gray. The implication is that special indices of metamerism should be calculated only for a limited range of color differences under the reference condition. It is suggested that metameric indices should not be calculated for pairs having a mismatch beyond a threshold value, for example, 5 ΔE. © 2008 Wiley Periodicals, Inc. Col Res Appl, 33, 509–512, 2008     

Tearing mode interlaminar fracture toughness of composite materials

The Simplified Split Cantilever Beam (SSCB) is proposed in this work and compared with the Split Cantilever Beam (SCB) to obtain the tearing mode interlaminar fracture toughness. The materials considered are single‐fiber system composites and interply hybrid composites. For interply hybrid composites, three different types of stacking sequence for SSCB specimens, which are [0/0//0],[0/0//0]. and [0/0//0], are tested to compare their suitability. Finite element analysis combined with a modified crack closure integral has been applied to separate the different components of the strain‐energy release rate. In addition, the method of compliance calibration was used to calculate Gc values. The effects of crack growth, initial crack length, specimen width, and number of glass fiber plies were also studied. The results show that SSCB testing has a more dominant Mode III component and more stable Gc values than SCB testing. For SSCB testing, the crack growth and the specimen width for the range considered have no clear effects on the interlaminar fracture toughness, but the initial crack length should be carefully selected to obtain corrected values. The tearing mode interlaminar fracture toughness of interply hybrid composites is higher than that of carbon/epoxy composites, and the three different types of stacking sequence considered are all suitable to approximate the Mode III interlaminar fracture toughness for interply hybrid composites.     

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     

Solution and diffusion properties of cyclohexane,cyclohexanol, and cyclohexanone in poly(ethylene glycol) by inverse gas chromatography

The solution and diffusion properties of cyclohexane, cyclohexanol, and cyclohexanone in poly(ethylene glycol) (PEG) and crosslinked PEG have been studied in the temperature range of 368.15 to 403.15 K using inverse gas chromatography (IGC) technique. The infinite dilute activity coefficient (Ω) and diffusion coefficient (D) have been determined for the above solvent/polymer systems. Accordingly, several thermodynamic functions, the diffusion pre‐exponential factor, and activation energy have been attained. The results showed a decrease in Ω and an increase in D with rising temperature. The order of the relative magnitude of Ω and D of the solvents were explained by comparing their interactions with the polymer and their collision diameters, respectively. Moreover, Ω and D in crosslinked PEG were smaller than those in PEG at various temperatures. The analysis of Ω, the infinite dilute selectivity and capacity showed the possibility of using crosslinked PEG as an appropriate membrane material for the separation of cyclohexane, cyclohexanol, and cyclohexanone mixture. A thermodynamic study also implied that the solvent sorptions in the polymers were all enthalpically driven in the experimental range. © 2011 Wiley Periodicals, Inc. J Appl Polym Sci, 2011.     

Intrinsic birefringence of nylon 6

Different values are reported in the literature for the intrinsic birefringence of the crystalline (Δn) and the amorphous (Δn) phases in nylon 6. Mostly, these values have either been determined by extrapolation (and then it is assumed that Δn = Δn) or calculated theoretically. In this study, intrinsic birefringence values Δn and Δn for nylon 6 were determined using the Samuels two-phase model which correlates sonic modulus with structural parameters. Three series of fiber samples were used: (1) isotropic samples of different degrees of crystallinity for estimation of E and E moduli at two temperatures. The following modulus values were obtained: 1.62 × 10⁹ and 6.66 × 10⁹ N/m² for 28.5°C, and 1.81 × 10⁹ and 6.71 × 10⁹ N/m² for ?20°C; (2) anisotropic, amorphous fiber samples for estimation of Δn = 0.076 and E = 1.63 × 10⁹ N/m² at 28.5°C; (3) semicrystalline samples of various draw ratios for estimations of Δn = 0.089 and Δn = 0.078. All measurements were carried out with carefully dried samples to avoid erroneous results caused by moisture.     

Competitive adsorption of uranyl ions in the presence of Pb(II) and Cd(II) ions by poly(glycidyl methacrylate) microbeads carrying amidoxime groups and polarographic determination

The adsorption capacity of UO in the presence of Pb(II) and Cd(II) ions was investigated with amidoximated poly(glycidyl methacrylate) (PGMA) microbeads with an average size of 135 μm packed in a glass column (0.5‐cm i.d. and 20‐cm length, flow rate = 3 mL/min) under competitive conditions. A differential pulse polarography technique was used for the determination of trace quantities of uptaken elements by the measurement of the reduction peak currents at ?200/?950, ?400, and ?600 mV (vs a saturated calomel electrode) for UO, Pb(II), and Cd(II) ions, respectively. When only UO was found in the eluate, its adsorption was 85.3% from a 50 μM initial solution. However, when there was UO with binary systems of Pb(II) or Cd(II), it was 78.2 and 76.3%, respectively. On the other hand, in a ternary mixture of UO with Pb(II) and Cd(II), the adsorption was found to be 75.2% with the same initial concentration. According to the results, the competitive adsorption studies showed that these amidoximated PGMA microbeads had good adsorption selectivity for UO with the coexistence of Pb(II) and Cd(II) ions. The ionic strength of the solution also influenced the UO adsorption capacity of the amidoximated PGMA microbeads. © 2007 Wiley Periodicals, Inc. J Appl Polym Sci 104: 4168–4172, 2007     

Mass transport process for the adsorption of Cr(VI) onto water‐insoluble cationic starch synthetic polymers in aqueous systems

Dynamic adsorption behaviors between Cr(VI) ion and water‐insoluble amphoteric starches was investigated. It was found that the HCrO ion predominates over the initial pH ∼ 2–4, the CrO ion predominates over the initial pH ∼ 10–12, and both ions coexist over the initial pH ∼ 6–8. The sorption process occurs in two stages: the external mass transport process occurs in the early stage and the intraparticle diffusion process occurs in the long‐term stage. The diffusion coefficient of the early stage (D₁) is larger than that of the long‐term stage (D₂) for the initial pH 4 and pH 10. The diffusion rate of HCrO ion is faster than that of CrO ion for both processes. The D₁ and D₂ values are ∼ 1.38 × 10⁻⁷–10.1 × 10⁻⁷ and ∼ 0.41 × 10⁻⁷–1.60 × 10⁻⁷ cm² s⁻¹, respectively. The ion diffusion rate in both processes is concentration dependent and decreases with increasing initial concentration. The diffusion rate of HCrO ion is more concentration dependent than that of CrO ion for the external mass transport process. In the intraparticle diffusion process, the concentration dependence of the diffusion rate of HCrO and CrO ions is about the same. The external mass transport and intraparticle diffusion processes are endothermic and exothermic, respectively, for the initial pH 4 and pH 10. The k_d values of the external mass transport and intraparticle diffusion processes are ∼ 15.20–30.45 and ∼ −3.53 to −12.67 kJ mol⁻¹, respectively. The diffusion rate of HCrO ion is more temperature dependent than that of CrO ion for both processes. © 1999 John Wiley & Sons, Inc. J Appl Polym Sci 71: 2409–2418, 1999     

Nonlinear programming methods to determine surface free energy components of polymers using harmonic mean approximation

The dispersion and polar surface free energy components, γ and γ, and the critical surface free energy, γ_c, of polymers were determined from contact angle data by the application of a nonlinear programming method using harmonic mean approximation. The surface free energy components of the probe liquids, γ and γ, which reflect the conditions of the maximized interaction parameter, Φ, were also simultaneously determined by this method.     

Study on the thermal stability of heterogeneous nucleation effect of polypropylene nucleated by different nucleating agents

The thermal stability of the heterogeneous nucleation effect of polypropylene (PP) nucleated with an organic phosphate (A) and two kinds of sorbitol derivatives (B and D) was investigated by DSC multiscanning. For pure PP, the peak temperature of crystallization (T) was little changed with an increasing number of DSC scans, indicating that nucleation of PP is thermally stable. For the PP nucleated with an organic phosphate (PPA), the temperatures at the onset of crystallization (T) and at the completion of crystallization (T); the peak temperature of crystallization (T) and melting (T); and the heat of crystallization (ΔH_c) and fusion (ΔH_m) of PP are higher than those of pure PP and were little influenced with an increasing number of DSC scans. For PP nucleated with the sorbitol derivatives (PPB and PPD), the T, T, T, and T decreased with an increasing the number of scans. These results indicated that the thermal stability of heterogeneous nucleation effect of the nucleating agent A is higher than that of nucleating agents B and D. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 83: 1643–1650, 2002