Paramerism and reliable parameric correction

In this article, the parameric decomposition method is considered as a technique for batch correction using three process primaries. It is proved that the parameric decomposition technique using optimal process primaries is a suitable method for reliable batch correction. Besides, the evaluation of parameric correction error for estimation of metamerism index is discussed. The creation of optimal spectral dataset to derive the appropriate process primaries is presented and the estimation of optimal statistical colorants for color reproduction of paint system is also developed. A set of pigments as primaries is used to generate three sets of batches using Kubelka–Munk theory; each set includes 10,000 paramer samples. Three sets of batches are generated to have different distributions around the match sample of target. The performance of process primaries derived from the Munsell dataset is compared with the optimal estimated statistical colorants for reliable parameric correction. To achieve greater success in estimation of appropriate metamerism index and make the estimated index more reliable, the statistical colorants used for parameric correction should be achieved from the spectral dataset generated by real primaries being used for matching of the target color. The outcome of parameric correction for pairs having miscellaneous mismatches is investigated to find out if it is sensible to just consider mismatch threshold for pairs being corrected. Finally, the conceptual subject of paramerism is developed to verify which spectral essence could be called as the paramer of an individual target color being matched. © 2010 Wiley Periodicals, Inc. Col Res Appl, 2010     

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     

Field trials for assessing the method of observer metamerism adopted by CIE

The following field trials are made for assessing the method of observer metamerism adopted by CIE. (1) The individual variation of metameric match was assessed between a fluorescent-lamp light and each of three different matching stimuli by the CIE method. The high precision of visual color match was confirmed for the 6-primary Donaldson colorimeter. The prediction was compared with experimental results for a similar fluorescent lamp. (2) The individual variation predicted by the CIE method was compared with that directly derived by using the Stiles original 20 color-matching functions. The effectiveness of the CIE method was confirmed. (3) It was clarified that the individual variation of colorimetric values on a single test stimulus corresponds to that for the metameric match between the test stimulus and a mixture of the CIE 10° r, g, b primaries. (4) The actual observer variation found by Stiles and Wyszecki in the field trial on the CIE 1964 color-matching functions was tested using the CIE method. The method is effective to assess the intrusion of other factors in actual color match, in addition to the individual variation of color-matching functions.     

Estimation of CIE tristimulus values under various illuminants

In this work, a procedure is described to estimate the CIE tristimulus values of Munsell color chips under new illuminants from CIE tristimulus values under specific illuminant. The estimation was performed by multiple linear regression (MLR) and principal component analysis (PCA) techniques. In addition, the effects of illuminants combination and Munsell hue, value and chroma on reconstruction of CIE tristimulus values were evaluated in both methods. The results obtained indicate that the performance of principal component method is better than multiple regression method. The accuracy of estimation depends on the initial and target illuminants and hue, chroma and value of samples. © 2009 Wiley Periodicals, Inc. Col Res Appl, 34, 100–107, 2009     

The metamerism potentiality of a color recipe

The weighted spectrophotometric color matching method with the optimum weighting to the spectrophotometric equations in each particular wavelength proportional to the viewing condition is applied for minimizing the color difference of instrumental color formulation of textile materials. The work is based on the one‐constant Kubelka–Munk theory. The sensitivity of a recipe to small perturbation of deviation between the reflectance of target and matched samples in the visible spectrum is determined as the metamerism potentiality of proposed recipe. Its correlation with metamerism index was also studied for some metameric pairs. Metamerism potentialities are also appraised under several light sources by using equilibrate matching strategy. The results show that the outputs of colorimetric color matching are exactly identical with the weighted spectrophotometic match under the same viewing condition. According to the numerical results for matching of 58 target samples, there is a good statistical correlation between metamerism indices and the metamerism potentialities of each recipe. Our results show that the quantitative value of the metamerism potentiality of each recipe can reasonably predict the metamerism indices of applied formulation. © 2006 Wiley Periodicals, Inc. Col Res Appl, 31, 483–490, 2006; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.20261     

Mathematical and empirical evaluation of accuracy of the Kubelka–Munk model for color match prediction of opaque and translucent surface coatings

Attempts were made to evaluate mathematically and empirically the accuracy of the Kubelka–Munk model for color match prediction of opaque and translucent surface coatings in the color using industries. To this end, an innovative inversed mathematical evaluation procedure was concocted which comprised of plotting the absorption and scattering constants of the Kubelka–Munk model or any of its various modified form or replacements theories against the intrinsic optical coefficients of the respective exact radiation transfer theories, namely Chandrasekhar for opaque and van de Hulst for translucent media. The results prove mathematically that the Kubelka–Munk model for opaque media is a sound theory and its various suggested modifications or replacements do not improve the color match prediction of opaque surface coating media. This mathematical conclusion was further confirmed by color match prediction of actual opaque paint samples. On the other hand, the mathematical prediction for translucent media illustrated a completely different picture, depicting nonlinearity between the optical constants and the respective concentrations of colorants. This implies that much further work has to be carried out to derive invertible new equations to enforce linearity to such situations or make use of alternative artificial intelligent procedures which are designed especially for nonlinearity.     

Spectral analysis of blacks

The spectral behavior of different black surfaces including papers and fabrics are investigated in this study. Several colored pigments are mixed with the blacks in different concentrations to prepare black surfaces with different shades while a series of black dyestuffs are applied on textile materials to increase the ranges of black objects. The principal component analysis technique is applied to determine the actual spectral size of the reflectance dataset. The technique simply extracts the principal directions of spectral data and organizes them in restricted spectral spaces. Three different spectral spaces, i.e., the reflectance spectra, the Kubelka‐Munk function of reflectance as well as the inverse of reflectance factor are selected to present the samples in the restricted spaces. Based on the results, it is found that, there are no significant differences between the employed spaces and far from the employed spectral domains, black surfaces could be adequately described in a three‐dimensional space. The three extracted statistical colorants are used for reconstruction of reflectance spectra of samples while the root mean square error percentage and the color difference values under the standard observing condition confirm the suitability of such virtual primaries. The work is extended to reconstruction of spectral data from colorimetric information and the adequacy of such three‐dimensional space is reconfirmed. © 2011 Wiley Periodicals, Inc. Col Res Appl, 2012     

Conversion between the reflectance spectra and the Munsell notations

A novel general transformation between reflectance spectra and the corresponding coordinates of the Munsell Color System is presented. The coefficient values of the transformation were experimentally determined by mapping the actual reflectance spectra of the chips in the Munsell Book of Color into the Munsell Color Order System and by minimizing the distance between calculated and actual coordinates. The experiment was repeated with a selected set of points of the Munsell Renotation System. Both the Smith–Pokorny functions and the CIE 1931 standard color‐matching functions were used as a basis of the transformation. There is a good correspondence between calculated and actual coordinates of the Munsell Color System. It is also shown that the linear part of the same transformation applied to the basis functions results in one achromatic response function and two chromatic response functions in accordance with the opponent‐colors theory. © 2005 Wiley Periodicals, Inc. Col Res Appl, 31, 57–66, 2006; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.20173     

A New matching strategy: Trial of the principal component coordinates

A new matching strategy based on the equalization of the first three principal component coordinates of sample and target in a 3D eigenvector space is stated. Two series of databases including 1269 specimens of Munsell Color Book and a virtual sample population of textile materials were selected. Their first three basis functions were extracted and considered as axes of eigenvector space. The principal component coordinates of two different collections of textile samples were determined in these spaces and considered as matching criteria. The performance of the proposed algorithm is evaluated by the color difference values under different light sources as well as the root mean square differences of reflectance curves. Results indicate some types of improvements in comparison with previous algorithms in terms of spectral as well as colorimetric accuracy. © 2007 Wiley Periodicals, Inc. Col Res Appl, 33, 10–18, 2008     

The usability of the CIE colour‐matching functions in the case of CRT monitors

During the past years, several papers have been published that question the use of the CIE colour‐matching functions in the case of metameric samples. Visually matching samples produced on CRT (Cathode Ray Tube) monitors are metameric to most colour stimuli created by illuminating reflecting materials. As CRT monitors are often used in colour design applications, it seemed important to check how well CIE colorimetry will predict such colour matches. To investigate this problem, we set up an experiment in which painted samples were matched with samples produced on a CRT monitor. The colour of incandescent lamp irradiated Munsell samples were visually matched to the mixture of the RGB primaries of a CRT monitor. Both the reflected colour stimuli of the Munsell samples and the emitted stimuli of the monitor were measured spectroradiometrically. Our results imply that there is an observer‐dependent variability among the matches, but we could not find a major difference between the tristimulus data of the hard copy and soft copy presentations that would indicate errors in the CIE colour‐matching functions. The measurement accuracy, quantization errors of the monitor, and the achieved accuracy of the colour matches are treated in this study. © 2001 John Wiley & Sons, Inc. Col Res Appl, 26, 436–441, 2001     

How strong metamerism disturbs color spaces

Systems for arranging and describing color include “color spaces” and “color order systems.” In a color space, tristimulus values R, G, and B are computable for every light (every point in the space). In familiar color spaces, such computation makes use of three functions of wavelength (the color-matching functions that define one of the CIE Standard Observers), one function corresponding to each of R, G, and B. In the presence of strong metamerism (marked spectral difference between the spectral power distributions of a pair of visually matching lights), the color-matching functions may report that one light of the pair has an entirely different color from that of the other member of the visually matching pair of lights. The CIE Standard Observer embodying those color-matching functions “sees” the two visually matching lights as entirely different in color, that is, it reports entirely different sets of R, G, and B for the two visually matching lights, and, thus, an entirely different chromaticity. In an example given here, each of the CIE Standard Observers assigns a strong green color to lights that are seen by normal human observers as a visual match to a hueless reference white. On the other hand, color order systems comprising sets of real objects in a specified illuminant, and which are assembled (visually arranged) by normal observers, as are the Munsell and OSA sets, do not suffer from the type of trouble discussed here. Color spaces depending on mathematical functions of R, G, and B are at risk: both Standard Observers are shown to plot visually identical lights at widely varying points in familiar color spaces (e.g., delta E*_ab = 40–50). © 1998 John Wiley & Sons, Inc. Col Res Appl, 23: 402–407, 1998     

A review of principal component analysis and its applications to color technology

Principal component analysis, abbreviated PCA, has been an important and useful mathematical tool in color technology since the 1960s. Its uses have included defining tolerance intervals and ellipsoidal regions, estimating colorant spectral properties from mixtures, deriving CIE daylight, data reduction for large ensembles of spectra, and spectral imaging. Although PCA is a common topic in many engineering disciplines, statistics, and mathematics, many color‐technology professionals and color‐science students come from disciplines where this technique is not part of their curricula. It is from this perspective that this review publication was written. The purpose of this publication is to describe PCA and present examples in its use for colorant estimation, spectral data reduction, and defining multidimensional confidence regions for colorimetric scatter data. © 2005 Wiley Periodicals, Inc. Col Res Appl, 30, 84–98, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.20086     

Study of the influence of various D65 simulators on colour matching

This study investigates the influence of various D65 simulators on visual colour matching. Spectroradiometric measurements of D65 simulators and visual assessments were obtained. The spectral power distributions of three D65 simulators were measured by spectroradiometer in a colour viewing cabinet. Based on the measured spectral power distributions, the quality of the D65 simulators were assessed using CIE No.51.2 and CIE No.13.3 methods. For visual assessment, the Davidson and Hemmendinger colour rule, which is composed of highly metameric pairs, was used in this study. The colorimetric match points and visual match points under three D65 simulators were determined. Pair-comparison t -tests were also used to examine the statistically significant differences among visual match points. The results show that various D65 simulators influence visual colour judgement of metameric pairs. The correlation between quality rating of D65 simulators under these two CIE methods and visual assessment was evaluated.     

Single‐constant simplification of Kubelka‐Munk turbid‐media theory for paint systems—A review

For opaque coloration systems, Kubelka‐Munk turbid media theory is used commonly to model optical mixing behavior. Most educational publications on the subject use opaque paint systems when describing the two‐constant approach and textile systems when describing the single‐constant simplification. Because of the differences in defining concentration for these systems and the corresponding degrees of freedom, the single‐constant simplification for paint and textile systems are not identical. The second edition of “Principles of Color Technology” showed a numerical example for an opaque paint system modeled using the textile equations. The third edition used the same example but modified the degrees of freedom, a hybrid of the paint and textile approaches. Recent research by Berns and Mohammadi has evaluated the single‐constant simplification for modeling artist paints; they have used both the hybrid and paint approaches. Thus, it was of interest to review these different approaches and determine whether these differences have practical importance and whether future printings and editions of Principles of Color Technology should be modified. The three approaches were tested for tints made from a mixture of cobalt blue and titanium white acrylic emulsion artist paints. The differences between the textile and hybrid approaches were inconsequential. The paint approach was superior and its use is recommended for opaque paint systems. The differences in the numerical example from Principles of Color Technology were very small. For future printings of the third edition, the example will remain unchanged. For future editions, including the numerical example remains an open question. © 2007 Wiley Periodicals, Inc. Col Res Appl, 32, 201–207, 2007     

Reconstruction of reflectance data by modification of Berns' Gaussian method

Berns' method for the synthesis of spectral reflectance curve from the tristimulus color coordinates is modified. Firstly, the Gaussian bell shape red primary is replaced with a sigmoidal one to solve the dissimilarity between the spectral curves at the end region of spectrum. Secondly, three predetermined Gaussian primaries used in the original Berns' method are replaced by the adaptive ones which their half‐height bandwidths vary with the tristimulus values of the desired color. The mentioned modifications are applied for the recovery of the reflectance curves of 1409 surface colors (including 1269 Munsell color chips and 140 samples of Colorchecker SG) and also 204 textile samples. Results of recovery are evaluated by the mean and the maximum color difference values under other standard light sources. The mean as well as the maximum of root mean squares between the reconstructed and the actual spectra are also calculated. The modifications are compared with the common principal component analysis (PCA) as well as Hawkyard's methods for recovery of reflectance factor. Although the PCA leads to the best results, the modifications significantly improve the recovery outcomes in comparison with the original Berns method. © 2008 Wiley Periodicals, Inc. Col Res Appl, 34, 26–32, 2009.     

Reconstruction of reflectance spectra using weighted principal component analysis

The weighted principal component analysis technique is employed for reconstruction of reflectance spectra of surface colors from the related tristimulus values. A dynamic eigenvector subspace based on applying certain weights to reflectance data of Munsell color chips has been formed for each particular sample and the color difference value between the target, and Munsell dataset is chosen as a criterion for determination of weighting factors. Implementation of this method enables one to increase the influence of samples which are closer to target on extracted principal eigenvectors and subsequently diminish the effect of those samples which benefit from higher amount of color difference. The performance of the suggested method is evaluated in spectral reflectance reconstruction of three different collections of colored samples by the use of the first three Munsell bases. The resulting spectra show considerable improvements in terms of root mean square error between the actual and reconstructed reflectance curves as well as CIELAB color difference under illuminant A in comparison to those obtained from the standard PCA method. © 2008 Wiley Periodicals, Inc. Col Res Appl, 33, 360–371, 2008     

Color discrimination capability under highly structured spectra

An experiment was performed to test the capability of measures of gamut area to predict the color discrimination capability of lamps with highly structured spectra. Sixteen subjects completed a Farnsworth Munsell 100 Hue Test under four different lighting conditions of similar chromaticity: light emitting diodes (LEDs) that used red, green, and blue primaries; two types of linear fluorescent; and tungsten halogen. Total Error Score (TES) was significantly worse under the LEDs than the other three conditions, which produced statistically equivalent scores. No measure considered in this work, including Color Rendering Index, Color‐Discrimination Index, or Farnsworth Munsell Gamut Area, was able to order correctly, let alone correlate with, the color discrimination capability of the four lamps, as characterized by TES. This calls into question the concept of using a measure of gamut area to characterize color discrimination as part of a multi‐index tool for quantifying color rendition, especially since lamps with highly structured spectral output are becoming more prevalent for general illumination. © 2011 Wiley Periodicals, Inc. Col Res Appl, 2011;     

Defining a practical method of ascertaining textile color acceptability

The relations between supplier and customer are today more important than they have ever been. However, conflicts do sometimes arise between them, deriving from differences in the judgment of color matchings. Colorimetry's role is precisely to avoid such conflicts through instrument measurements. A study was made on the pass/fail problems, based on 1,830 measurements and observations made in industrial textile firms, followed by 350 new tests. Human judgments are as liable to errors as instrument measurements, because the surface effects are often misleading for the observer. This study proposes a sorting method that combines the differences deriving from measurements by colorimetric instruments and by visual judgment. The Color Measurement Committee (CMC) equation, widely used in the textile field, has given excellent practical results. The CIE94 equation, which uses the same principle of ellipsoid tolerance, offers a mathematical simplification as well as further information on the sample observation conditions in order to determine color differences. Nevertheless, these two equations are different, and the CIE94 indexes must not be interpreted with the same tolerances as those of the CMC. Pending the CIE recommendations concerning textile samples, new acceptability tolerances should be redetermined for the CIE94. This article presents an innovative way of calculating metameric indexes that, when coupled with acceptability equations, allow the agreement rate between visual judgment and automatic selection to be increased.     

Evaluation of the performance of metameric indices

Forty three metameric pairs were obtained by comparison, shade-adjustment, and redyeing of 660 self shades dyed with direct, azoic, vat, and reactive dyes. The pairs were regrouped shadewise and ranked visually in increasing order of metamerism. Spearman's rank correlation coefficients were calculated between 11 measures of metamerism and the visual metameric ranking under three illuminants A, D65, and TL84 in pairs. The illuminant-independent general indices included the indices based on reflectance differences (Bridgeman), weighted reflectance differences (Nimeroff and Yurow), Cohen-Kappauf's residual differences (proposed) obtained from the spectral decompositions of the reflectance spectra of the metameric pair. Illuminant-specific special indices included color-differences under test illuminant, addition, subtraction, division, and multiplication of color-differences under test and reference illuminants, indices based on ΔL*, Δa*, Δb* differences under two illuminants, based on chromatic adapted ΔL*, Δa*, Δb* differences with multiplicative corrections for tristimulus differences under reference illuminant (Berns-Billmeyer), differences of the color constancy indices. The present work showed that indices based on ΔL*, Δa*, Δb* differences under two illuminants, both unmodified and modified by Berns-Billmeyer performed best among the existing indices. The differences of color constancy indices showed good correlation with the degree of metamerism in some cases, and this may be utilized for developing newer indices of metamerism. © 1996 John Wiley & Sons, Inc.