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.     

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     

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     

Effect of classification by competitive neural network on reconstruction of reflectance spectra using principal component analysis

The best way to describe a color is to study its reflectance spectrum, which provide the most useful information. Different methods were purposed for reflectance spectra reconstruction from CIE tristimulus values such as principal components analysis. In this study, the training samples were first divided into 3, 6, 9, and 12 subgroups by creating a competitive neural network. To do that, L*a*b*, L*C*h or L*a*b*C*h were introduced to neural network as input elements. In order to investigate the performance of reflectance spectra reconstruction, the color difference and RMS between actual and reconstructed data were obtained. The reconstruction of reflectance spectra were improved by using a six or nine‐neuron layer with L*a*b* input elements. © 2016 Wiley Periodicals, Inc. Col Res Appl, 42, 182–188, 2017     

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     

Comparison of methods of parameric correction for evaluating metamerism

In practice, most metameric pairs do not achieve colorimetric equality for a set of reference conditions. These parameric pairs are composed of a residual color difference and a metameric difference. Three techniques have been used to correct this residual color difference: an additive correction in L*a*b*, a multiplicative correction in XYZ (recommended by the CIE), and parameric decomposition where the batch's spectrum is adjusted. Parameric decomposition can be viewed as batch correction using three “colorants” (process primaries) where the color‐mixing model is linear in reflectance. Most often, Cohen and Kappauf's Matrix R technique is used where the primaries are color matching functions. Alternative primaries were derived from a Munsell Book of Color and an automotive paint system using principal component analysis (PCA) and independent component analysis (ICA). 1,152 parameric pairs about 24 color centers were synthesized using the paint system and Kubelka–Munk turbid‐media theory. Each parameric pair was corrected to a metameric pair using these methods. Spectral accuracy was evaluated by comparing the corrected spectra to metameric reference spectra calculated using Kubelka–Munk batch correction. The Matrix R technique had the worst spectral accuracy under the reference conditions while both PCA and ICA had similar and reasonable accuracy. The special index of metamerism, change in illuminant, was calculated for each parameric pair using these various correction techniques to achieve colorimetric equality. The Matrix R and CIE‐recommended multiplicative techniques were statistically significantly worse than parameric decomposition using Munsell Book of Color PCA and ICA and automotive ICA process primaries. © 2007 Wiley Periodicals, Inc. Col Res Appl, 32, 293–303, 2007     

基于导函数层序聚类的光谱成分预测方法研究

多光谱成像技术通过增加颜色通道的维数,成功的实现了基于光谱的颜色复制。然而,由于其颜色信息维数较高,此方法在提高色度精度的同时引入了较大的计算及存储压力。为此,最常用的方法就是通过对光谱数据进行分组,并利用每组光谱数据集中的主成分向量来对各个光谱曲线进行线性表示,从而实现数据的降维处理。提出了1种新的针对光谱数据导函数曲线的聚类分析方法,并利用伪逆算法进行光谱重建;本研究采用孟塞尔光泽色卡及无光泽色卡作为实验数据集,并将提出的导函数聚类分析法与现有的主成分分析法、聚类分析法以及色相角分类法相比较,实验结果证明其颜色预测精度在色度匹配及光谱匹配方面均优于现有方法。     

Applying metamer sets to investigate data dependency of principal component analysis method in recovery of spectral data

Principal component analysis (PCA) has been widely studied for reconstruction of spectral reflectance of a color sample from its tristimulus values. One of the most important factors that influences the recovery performance is the characteristic of the data set used for obtaining principal vectors. In this article, we investigated the influence of color similarities or color differences between the recovered and principal component (PC) data sets on the reconstruction error. For this purpose, two metamer sets that have similar color differences with the recovered samples, are used. The results show that two metamer sets can make completely different performance in recovery of specific color samples. It was shown that the most important factor that influences the recovery of spectral reflectance by PCA method is the characteristics of the data set used for obtaining PC vectors independent of the recovered samples. Another factor that influences the performance of PCA for spectral recovery is the characteristic of the sample that would be recovered. Some spectral data cannot be recovered precisely even applying different PC data sets. © 2010 Wiley Periodicals, Inc. Col Res Appl, 2011     

Feasibility of using digital color imaging devices for the determination of cationic dyes compatibility

In the present research, the compatibility of dyes was evaluated using a scanner by the application of the method proposed by Khalili and Amirshahi, which had been proved as a novel and accurate method for evaluating the compatibility behavior of dye mixtures. A dip‐test method was employed to dye samples, compatibility panels, in binary combinations of cationic dyes on acrylic fibers. In order to use the scanner, first the device was colorimetrically characterized using a regression technique. The tristimulus values obtained from the scanner were, then, used for the reconstruction of the reflectance of the compatibility panels by principal component analysis. Next, the reconstructed reflectance of the panels were transferred to the corresponding K/S spectra and the Khalili and Amirshahi proposed method applied to the spectra in order to obtain the percentage variance (PV), which is the criterion of the dye compatibility. The comparison between the PVs obtained from the scanner and the corresponding one calculated by the spectrophotometrically measured reflectance of the compatibility panels showed a very significant correlation of the compatibility results regarding Pearson correlation coefficients and their K values. It was concluded that due to the smoothness of the reconstructed spectra and the performance of the PCA method of the reconstruction, which manifest itself in the good spectral reconstruction, the scanner method joined with the Khalili and Amirshahi proposed method can reliably be used for the determination of dye mixtures compatibility by a dip test. © 2016 Wiley Periodicals, Inc. Col Res Appl, 42, 337–345, 2017     

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     

Compression of spectral data using Box‐Cox transformation

The principal component analysis technique is used for the compression of different spectral databases including the reflectance spectra of nonfluorescent surfaces as well as the spiky spectra of the total radiance factors of fluorescent samples. Before extraction of principal directions, the Box‐Cox transformation technique is used in its original as well as modified version to improve the efficiency of employed compression technique by increasing the degree of normality in the datasets. The employed techniques are evaluated in terms of spectral dissimilarity between the reconstructed and the actual spectra and colorimetric differences by the value of CIELAB color differences of them under D65 and A illuminants and 1964 standard observer. The datasets departures from normal distribution are also investigated. The results confirm the effectiveness of the Box‐Cox modification technique for the reducing of spectral dimensions of samples. © 2012 Wiley Periodicals, Inc. Col Res Appl, 39, 136–142, 2014     

Representation and estimation of spectral reflectances using projection on PCA and wavelet bases

In this article, we deal with the problem of spectral reflectance function representation and estimation in the context of multispectral imaging. Because the reconstruction of such functions is an inverse problem, slight variations in input data completely skew the expected results. Therefore, stabilizing the reconstruction process is necessary. To do this, we propose to use wavelets as basis functions, and we compare those with Fourier and PCA bases. We present the idea and compare these three methods, which belong to the class of linear models. The PCA method is training‐set dependent and confirms its robustness when applied to reflectance estimation of the training sets. Fourier and wavelet bases allow good generalization; an advantage of wavelets is that they avoid boundary artifacts. The results are evaluated with the commonly used goodness‐of‐fit coefficient (GFC), and the reliability of the use of wavelets is proved. © 2008 Wiley Periodicals, Inc. Col Res Appl, 33, 485–493, 2008     

The principal components of reflectances

There are practical reasons to represent a set of reflectance spectra by a limited basis‐function expansion. Such an expansion is most tractable in color technology applications when it is homogenous. However, more often a true principal‐component analysis (PCA) is performed, which involves an offset of the expansion by a mean spectrum. In deference to custom, we discuss and exercise the traditional PCA on reflectances. We review the method of calculation and present tables of the principal components of 3,534 object‐color samples from three color‐order systems. Next, we describe two kinds of principal‐component coordinates of a measured reflectance spectrum, one obtained by least‐square best fit and the other by tristimulus match under one or more specified lights. Finally, we show illustrative examples, and propose some possible new uses for principal‐component analysis of reflectances. © 2004 Wiley Periodicals, Inc. Col Res Appl, 29, 104–110, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.10230     

Simplified measurement of virgin olive oil color by application of the characteristic vector method

There are several simplified methods to measure the color of virgin olive oils. However, their reliability is questionable, as they provide errors that sometimes can be considerable. A new method to calculate color coordinates and objective chromatic parameters in the color region of these olive oils is proposed with the aim of overcoming these objections. The method is a simplification of the original method proposed by the Commission Internationale de l'Eclairage (CIE), based on the measurement of the complete visible spectrum, from 380 to 770 nm. The characteristic vector analysis provides new equations to calculate tristimulus values as functions of these transmittance values based on a reconstruction of oil transmission spectra measuring from three to six wavelengths. The results show that color differences exist between the color coordinates of the experimental samples and those obtained by means of the proposed method. For more than 90% of the samples, the difference was smaller than three CIELAB units when equations based on four or more wavelengths were used.     

The munsell color system in fundamental color space

The Munsell color system is investigated as a structure in fundamental color space. The entire collection of samples from the 1929 Munsell Book of Color is mapped into fundamental color space and surfaces of constant hue, value, and chroma are identified. An algorithm, based on these surfaces, is presented for estimating the Munsell specification of an arbitrary reflectance curve.     

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     

Methods for generating spectral reflectance functions leading to color-constant properties

The Munsell color order system was rigorously defined for illuminant, observer, and surround. Using Nayatani's nonlinear model of chromatic adaptation, approximately colorconstant 1931 CIE tristimulus values for the notations of the Munsell Book of Color were calculated for a variety of continuous-spectrum illuminants between CIE A and 7600 K daylight. Several linear-programming models were devised for generating spectral reflectance functions that integrate to these tristimulus values. The most successful of these was a model based on an approximate-hue vector in tristimulus space, in which movement off and along this vector was restricted. Restrictions were also applied to the rate of change of reflectance with wavelength, following Ohta, and the model led to relatively smooth curves, comparable to those of real colorants. Indices of color constancy were devised to estimate the accuracy of the predictions. Comparisons with actual reflectance functions from physical samples revealed, in most cases, an improvement in color constancy and hue constancy.     

Measurement and Analysis of Object Reflectance Spectra

Recent algorithms developed in the field of color vision make assumptions based on the spectral reflectance curves of Munsell chips and natural materials. Some of them rely on data collected many years ago. which is partially incomplete in the visible spectrum. or contains many occurrences of the same material in it. In this article. we present a set of new measurements of different materials. In particular. we measured the spectral reflectance of Munsell chips, paints. and various natural materials in the 390–730-nm range. In addition, we have analyzed. through principal-component analysis, the possibility of representing the data collected with a set of basis functions. We show the implications of varying the number of principal components used (from 7 down to 3) on the errors introduced using this method.     

Munsell reflectance spectra represented in three‐dimensional Euclidean space

In this article we describe the results of an investigation into the extent to which the reflectance spectra of 1269 matt Munsell color chips are well represented in low dimensional Euclidean space. We find that a three dimensional Euclidean representation accounts for most of the variation in the Euclidean distances among the 1269 Munsell color spectra. We interpret the three dimensional Euclidean representation of the spectral data in terms of the Munsell color space. In addition, we analyzed a data set with a large number of natural objects and found that the spectral profiles required four basis factors for adequate representation in Euclidean space. We conclude that four basis factors are required in general but that in special cases, like the Munsell system, three basis factors are adequate for precise characterization. © 2003 Wiley Periodicals, Inc. Col Res Appl, 28, 182–196, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.10144     

Recovery of reflectance spectra from CIE tristimulus values using a progressive database selection technique

A procedure for creating efficient reflectance spectra from CIE tristimulus colour values is described using a modified linear model. By fixing certain criteria based on colour difference values, the proposed technique preliminarily selects a series of suitable samples from a main data set containing the reflectance values of a large number of different coloured samples, based on the colour specifications of a given sample. In this way, a series of different databases containing the reflectance values of confirmed samples relating to the particular samples are formed. Then, a well-known principal components linear model is applied using three basis functions. This operation yields higher cumulative variances in comparison with the original database, having the same number of basis vectors. The performance of the proposed method is evaluated using a different collection of samples and the resulting spectra show considerable improvements in terms of root mean square error as well as colour difference values under different illuminants.