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     

Evaluating the 1931 CIE color‐matching functions

The use of colorimetry within industry has grown extensively in the last few decades. Central to many of today's instruments is the CIE system, established in 1931. Many have questioned the validity of the assumptions made by Wright¹ and Guild,² some suggesting that the 1931 color‐matching functions are not the best representation of the human visual system's cone responses. A computational analysis was performed using metameric data to evaluate the CIE 1931 color‐matching functions as compared to with other responsivity functions. The underlying assumption was that an optimal set of responsivity functions would yield minimal color‐difference error between pairs of visually matched metamers. The difference of average color differences found in the six chosen sets of responsivity functions was small. The CIE 1931 2° color‐matching functions on average yielded the largest color difference, 4.56 ΔE. The best performance came from the CIE 1964 10° color‐matching functions, which yielded an average color difference of 4.02 ΔE. An optimization was then performed to derive a new set of color‐matching functions that were visually matched using metameric pairs of spectral data. If all pairs were to be optimized to globally minimize the average color difference, it is expected that this would produce an optimal set of responsivity functions. The optimum solution was to use a weighted combination of each set of responsivity functions. The optimized set, called the Shaw and Fairchild responsivity functions, was able to reduce the average color difference to 3.92 ΔE. In the final part of this study a computer‐based simulation of the color differences between the sets of responsivity functions was built. This simulation allowed a user to load a spectral radiance or a spectral reflectance data file and display the tristimulus match predicted by each of the seven sets of responsivity functions. © 2002 Wiley Periodicals, Inc. Col Res Appl, 27, 316–329, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.10077     

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.     

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     

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     

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.     

Melt viscosity of acrylic copolymers

The melt flow behavior of methyl methacrylate (MMA) copolymerized with methyl acrylate (MA) was measured and analyzed in terms of the molecular structure of the copolymers. Measurement was done by using a capillary rheometer in the shear rate range from 6 × 10⁰ to 3 × 10³ s^?1 and in temperatures from 160°C to 280°C. The Newtonian flow pattern appeared in lower shear rate and higher temperature regions. However, with increasing shear rate at lower temperature, viscosity decreased to a constant slope on a logarithmic scale. The melt fracture arose at the critical shearing stress point S_c of 6 × 10⁶ dyn/cm². A die swell also appeared in the shear rate range larger than 1 × 10⁶ dyn/cm², and its maximum value was two times larger than that of the capillary diameter. The decrease in viscosity with increasing shear rate is explained in terms of the apparent energy of activation in flow E. E also decreases with increasing shear rate. The exponential relation of E to η is maintained in the higher shear rate. The lowering of viscosity in lower shear rate, however, is attributed to not only the change in E but also the change in the volume of flow unit. The melt viscosity increases in inverse proportion to the MA content in the copolymers which form more flexible chains. Syndiotactic form of MMA has increased viscosity, caused by the rigidifying of segmented chains, rather than the strengthening of intermolecular interaction.     

Determination of crystallinity ratio and some physicochemical properties of poly(4‐methyl‐1‐pentene)

It was determined that the thermal stability of poly(4‐methyl‐1‐pentene) (P4MP) was maintained up to 424°C in an inert atmosphere by thermogravimetric analysis. The retention diagrams of ethyl acetate, tert‐butyl acetate, and benzene on P4MP were plotted at temperatures between 30 and 280°C by inverse gas chromatography (IGC) technique. Melting temperature of the polymer was determined as 230 and 239.5°C by IGC and differential scanning calorimetry (DSC), respectively. The percent crystallinity of P4MP was obtained from the retention diagrams at temperatures below melting point. The percent crystallinity obtained by IGC is in good agreement with the ones obtained by DSC. Then, specific retention volume, V, weight fraction activity coefficient, Ω, Flory‐Huggins polymer‐solvent interaction parameter, χ, equation‐of‐state polymer‐solvent interaction parameter, χ, and effective exchange energy parameter, X_eff of octane, nonane, decane, undecane, dodecane, tridecane, n‐butyl acetate, isobutyl acetate, isoamyl acetate with P4MP, were determined between 240 and 280°C by IGC. © 2009 Wiley Periodicals, Inc. J Appl Polym Sci, 2009     

Structure development in biaxially stretched polystyrene film: Part I. Property-orientation correlation

A study of orientation development in polystyrene film by biaxial stretching is described. Stretch ratios up to 7.2 × 7.2 were used. Mechanical properties of polystyrene films were correlated with the level of molecular orientation developed by uniaxial or biaxial stretching. Sensitivity of the mechanical properties to change due to development of orientation varied as follows: Yield strength < Young's modulus < Tensile strength < Elongation to break. Brittle to ductile transition phenomena were observed at certain orientation values in the orientation triangle diagram. The transition occurs when f × f ～ 0.0025 for biaxially oriented and f ～ 0.015 in the machine direction for uniaxially oriented films. SEM photomicrographs show that the fracture surfaces of ductile failures exhibit many fibrils while brittle failures exhibit no fibrils.     

Effect of some anions of some nickel salts on the aqueous polymerization of methyl methacrylate

The aqueous polymerization of methyl methacrylate in the absence and in the presence of some anions of nickel salts was carried out at temperatures of 40°C, 50°C, and 60°C using sodium bisulfite as initiator. The nitrate anion (NO) was found to have the highest catalytic effect and resulted in polymers having the least average molecular weights, while the sulfate anion (SO) was found to have the least catalytic effect and resulted in polymers having the highest average molecular weights. The apparent activation energy for the polymerization process was found to be 4.3, 3.6, 3.8, and 4.8 × 10⁴ J/mol in the absence and in the presence of Ni(NO₃)₂, NiCl₂, and NiSO₄ containing the same amount of nickel (0.00587 g). ¹³C-NMR spectra for the polymers obtained in the absence and in the presence of different nickel anions were found to result in nearly the same tacticity.     

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     

Inverse gas chromatography of poly(n-butyl methacrylate): Effect of flow rate on specific retention volume and detection of glass transition temperature

Flow-rate effect on specific retention volume (V) was studied by eluting aliphatic, aromatic, and chlorinated aliphatic probes at infinite dilution on poly(n-butyl methacrylate) stationary phase at different temperatures from ?10 to 150°C, encompassing both the glass transition (T_g) and the softening temperatures of the polymer. The effect became pronounced as the temperature was reduced below 100°C. V decreased with an increase in the flow rate: first linearly at temperatures between 70 and 100°C, and then nonlinearly at all temperatures below 70°C. The retention diagrams of n-pentane, isooctane, and cyclohexane alone enabled the detection of glass transition. Dichloromethane gave a linear retention diagram through T_g without showing the flow-rate effect.     

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.     

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     

Contribution of polyalkyl(meth)acrylates to the design of PVC melt viscosity

The shear viscosity of poly(vinylchloride) (PVC) at 200°C can be decreased by at least one order of magnitude by the addition of as little as 5 wt% poly n-alkyl-(meth)acrylates (PMA) of a much lower dynamic viscosity than PVC. For this effect to be observed, the polymeric additive must be immiscible with PVC at 200°C. The average size of the dispersed phases is observed in the range of 0.5 to 5 μm; size fluctuation in this domain has no significant effect. When these conditions are met, there is a linear increase in the shear viscosity ratio η_blend/η_PVC from 0.2 to 1.0 with increasing logarithmic values of the dynamic viscosity ratio of the additive over PVC [(log(η/η)) from −4 to −1].     

Study on the structure and processibility of the iodinated poly(vinyl alcohol). I. Thermal analyses of iodinated poly(vinyl alcohol) films

To get more information on the structure of iodinated poly(vinyl alcohol) (PVA), thermal analyses of unoriented and oriented PVA films were conducted. Unoriented and oriented PVA films iodinated with aqueous solutions at selected concentrations were carried out by thermogravimetry (TG) and differential scanning calorimetry (DSC). The TG curves for the iodinated film shows four or five weight‐loss zones associated with degradation and evaporation of excess I₂ molecules and I₂ molecules from I, partial OH side groups on PVA, and I₂ from I, the remaining OH groups and the partial main chains, the remaining main chains, and a very small amount of residue from PVA. The char of KI salts remained. By investigating the TG results, it was identified that the amount of I ions increased with increasing I₂/KI up to 65%, but above that weight gain, the rate of increase diminished and the amount of I ions from the I ions increased. The TG curve for the oriented film was very similar to that for the unoriented film except for its greater weight loss at zone I due to narrow space in amorphous region. The DSC thermogram of iodinated films indicated two peaks at 145°C and 160–170°C, corresponding to the melting of crystals and the degradations of OH groups and main chains, respectively. The maximum temperatures of peaks were much lower than that of the untreated one. ©2003 Wiley Periodicals, Inc. J Appl Polym Sci 91: 2407‐2415, 2004     

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     

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     

Influence of anionic form on thermooxidation of TMAHP–cellulose

With the help of DTA, DTG elementary analysis of carbonized residues and ESR spectroscopy the influence of anionic form on thermooxidation of trimethylammoniumhydroxyprophyl (TMAHP)–cellulose was studied. At 300°C the percentage of carbon in carbonized residue thermolyzed in oxidative atmosphere is higher than for the sample degraded in inert atmosphere. The percentage of hydrogen decreases simultaneously. The concentration of free radicals in thermolyzed residue also increases due to the presence of oxygen. We propose that oxygen is abstracting the hydrogen atoms from polysaccharide and unpaired electrons on carbon atoms are produced. At 400°C the percentage of carbon in residues prepared at inert atmosphere is higher than for residue formed at oxidative atmosphere. Also the concentration of free radicals in thermolyzed residues obtained in inert atmosphere is greater than for those from oxidative ones. That is why suppose that at this temperature oxygen is bonded to polysaccharide residue and free radicals are terminated. From the semiquantitative DTA we can make the following sequence of samples according to their increasing thermooxidative effect: unmodified cellulose < A–HSO < A–Br^? < A–I^? < A–NO < A–H₂PO < A–CH₃COO^? < A–HCO < A–F^? < A–Cl^?1 < A–OH^p?.