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     

Spectral spaces and color spaces

It has long been known that color experiences under controlled conditions may be ordered into a color space based on three primary attributes. It is also known that the color of an object depends on its spectral reflectance function, among other factors. Using dimensionality reduction techniques applied to reflectance measurements (in our case a published set of 1 nm interval reflectance functions of Munsell color chips) it is possible to construct 3D spaces of various kinds. In this article we compare color spaces, perceptual or based on dimensionality reduction using color matching functions and additional operations (uniform color space), to spectral spaces derived with a variety of dimensionality reduction techniques. Most spectral spaces put object spectra into the ordinal order of a psychological color space, but so do many random continuous functions. In terms of interval scales there are large differences between color and spectral spaces. In spectral spaces psychophysical metamers are located in different places. © 2003 Wiley Periodicals, Inc. Col Res Appl, 29, 29–37, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.10211     

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。     

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     

Transferring the 45/0 spectral reflectance factor scale

The accuracy of spectrophotometric measurements is limited by the standards that are used to calibrate the instrument. Therefore, the procedure used in transferring the spectral reflectance factor scale from one material to another for use in calibration must induce the minimum amount of error. the Munsell Color Science Laboratory has been transferring the spectral reflectance factor scale to calibration materials using a statistical method to correct for the most pervasive systematic errors in the measurement process. This method is based on a statistical procedure in which a set of systematic spectrophotometric errors are estimated based on the measurement of seven NIST primary standards and corrected in subsequent measurements. the optimization of the spectral reflectance factor scale to NIST standards minimizes the induced error. the average reflectance factor error consistently found between the corrected measurements of the NIST standards and their certificate values have been 0.0006 and the average δ_ab has been on the order of 0.2.     

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     

Databases for spectral color science

In color science, spectral representation and analysis of colors have become a common approach to study color‐related problems, e.g., accurate industrial color measurement or analysis of color images. In developing algorithms for spectral color science, one often relies on existing databases of reflectance color spectra. Since a number of these databases are easily available, the same databases are commonly used by different research groups. During year 2003 the most popular one of our publicly available spectral reflectance databases was visited over 600 times. In the present article, we describe these color spectra databases and analyze their utility for spectral color science. However, the article does not take the complexity of fluorescent surfaces into account. The aim of this article is to set a solid ground for the comparisons of different methods in the spectral color science. The databases presented here include measured color spectra of natural and man‐made objects as well as spectra of some sets of standard colors. In addition to the commonly used data sets, some new data sets, including a set of standard calibrated colors and a set of natural colors, measured with 10 nm spectral resolution are introduced. © 2006 Wiley Periodicals, Inc. Col Res Appl, 31, 381–390, 2006; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.20244     

Improving color constancy of object colors

In a study of improving the color constancy of object colors, the spectral reflectances of the eight CIE color-rendering test samples (Munsell painted papers) were chosen as reference reflectance distributions. Many other distributions, more highly structured than those of the reference set, were synthesized by computer so as to be rendered by illuminant D₆₅ at the chromaticity at which one or another of the CIE-Munsell samples is rendered by D₆₅. The chromaticities, at which each of the synthesized reflectances is rendered by each of 30 additional illuminants, define both dominant wavelength and chroma vector for the resulting 50,000 illuminant–sample combinations. For most natural illuminants, and for present commercial lamplights, color constancy is maximized by synthesizing each sample reflectance from three relatively narrow components, 50–60 nm at half height, peaking at wavelengths near 450 nm, 530 nm, and 610 nm.     

Spectral‐reflectance‐factor deconvolution and colorimetric calculations by local‐power expansion

The experimental data of the spectral‐reflectance factor are considered as dependent on the instrument‐spectral‐bandwidth function in order to perform their deconvolution and to compute the tristimulus values. The deconvolution is performed by local‐power expansion. In the case that the spectral‐bandpass dependence regards only the spectral transmittance of the monochromator, the goodness of this technique is evaluated by simulation (1325 reflectance factors of the Munsell samples are considered as trial functions) and compared with other usual techniques: Stearns and Stearns method for bandpass error, ASTM‐weighting function interpolation, and Venable‐ASTM weighting function. The zero order of the deconvoluted spectral‐reflectance factor can be related to the Stearns and Stearns method for bandpass error. With respect to any other technique, the second‐order deconvolution, for the CIE standard illuminants, gives color differences lower by a factor 0.1 or more for a bandpass Δλ = 10 nm, color differences lower by a factor 0.3 or more for a bandpass Δλ = 20 nm and, for the CIE fluorescent illuminants, color differences generally lower. © 2000 John Wiley & Sons, Inc. Col Res Appl, 25, 176–185, 2000     

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.     

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.     

Spectral dependence of colorimetric characterisation of scanners

The spectral dependence of the colorimetric characterisation of a typical scanner was investigated. Different colour sets, including ColorChecker SG, Kodak Q‐60 colour input target, a set of plain woven coloured fabrics with a large colour gamut, and randomly selected samples of the Munsell Book of Color were used as training and testing sets in the colorimetric characterisation of a scanner by employing a non‐linear regression method. The coefficient matrices were optimised for each particular media in the training stage and used to predict the device‐independent colorimetric data, i.e. CIELab values of other media from their corresponding RGB values measured by the scanner. In order to extract the differences between the applied sets and determine the actual dimensions of their reflectance spectra, the principal component analysis technique was employed. As expected, it was observed that the different sets benefit from diverse dimensional properties and, in some cases, the spectral behaviours of the first few eigenvectors were apparently different. It was demonstrated that scanner colorimetric characterisation depended on the spectral properties of the applied colour set in the training stage and, consequently, the testing errors increased with increasing the spectral dissimilarity between the sets that were used in training and testing sequences. It was concluded that, to achieve better colour reproduction results, the scanner should be characterised for each media with specific spectral properties.     

A model of colour vision for predicting colour appearance

A set of possible cone spectral sensitivity functions has been used to obtain combinations of responses that provide good predictions for loci of constant hue, simple criteria for unique hues, and good approximations to the NCS and Munsell schemes for surface colours, and to data on the appearance of spectral colours.     

Colour category foci of Munsell colour spectra revealed by two computational methods

Colour names and psychophysical colour categories play an important role on human communication. For several application areas from computer vision to Internet shopping, it would be useful to manage colour information using methods of computational colour naming in a similar manner as people do in their everyday life. In this study, we applied two computational methods, the nonnegative matrix factorization and self‐organizing maps, to derive basic colours from a spectral database of Munsell colours, and a subset of it. The subset was generated to include only the most saturated samples of each Munsell Hue and Munsell Value pair of the original database. Using both the methods and both the databases, we calculated the sets of 3, 4, 6, and 8 basis vectors to represent the focal colours of colour categories. Colour names of the calculated focal colours were investigated using the results by Sturges and Whitfield as a reference. Nonnegative matrix factorization yields calculated colours more compatible with human basic colours, but the spectra generated by self‐organizing maps are more similar to natural spectra as their shape is smoother. © 2010 Wiley Periodicals, Inc. Col Res Appl, 2010     

Digitally reconstructing Van Gogh's Field with Irises near Arles. Part 2: Pigment concentration maps

Colors in many paintings of great art historical value have changed over time, due to the combined effects of natural ageing, accumulated surface grime, and materials added during later conservation treatments. The physical restoration of the colors in such paintings is not possible. This article describes one part of work done to digitally restore the colors of Van Gogh's painting Field with Irises near Arles, dating from May 1888. We have used multispectral reflectance data to estimate absorption K and backscattering S parameters of Kubelka‐Munk 2‐constant theory. This was done for all 13 pigments known to have been used by Van Gogh in this painting, and based on this the concentration maps for each of these pigments were calculated. We validated the calculated concentration maps in several ways. For some pigments, we were able to predict spots on the painting where the pigment is expected to occur in unmixed form based on visual examination. For several other pigments, the concentration maps could be shown to agree with XRF data. Finally, for some other pigments the concentration maps were supported by additional evidence from microscopic examinations, remarks in Van Gogh's letters and from early color reproductions. For the 1.7 million pixels for which multispectral data is available, the average color difference between the calculated and measured spectral reflectance curves is CIEDE2000 = 1.05. This further confirms that the Kubelka‐Munk calculations are well suited to describe the variety of spectral reflectance on the painting.     

A residual modified transformation formula from munsell to sRGB color system

A residual modified transformation formula from Munsell to sRGB color system is presented in this article. The development of the transformation formula is based on the 1625 Munsell color chips in the Munsell Renotation Data that could be displayed on the sRGB monitor. The developed transformation formula consists of two models, one is named as the corresponding matrix model and the other is the residual modified model. The corresponding matrix model was obtained using numerical analysis methods to map each chip color attribute values from Munsell to sRGB and then its corresponding matrix for each Hue was constructed. The residual modified model was obtained using the discrete cosine transform to construct a residual modified function, which was used to modify the transformation error of each chip after applying the corresponding matrix model. The transformed accuracy rate for the corresponding matrix model is 88.4% and for the residual modified model can be enhanced to 96.6% for all of the chips. The developed transformation formula can be applied to research in which Munsell colors are presented on the sRGB monitor. With the aid of these formulas, designers can show the advanced real‐time results on a sRGB monitor for the product's color planning based on Munsell color system. Therefore, this research has a great contribution on the practical application for color planning in product design. © 2014 Wiley Periodicals, Inc. Col Res Appl, 40, 243–255, 2015     

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     

Whiteness perception under different types of fluorescent lamps

The effects of correlated color temperature and the chromaticity of light sources on the perception of surface whiteness were investigated. For the experiment, a Munsell N9.25 chip and 11 nearly white chips (V = 9.25, Munsell chroma ≦ 1.0) were selected. The interval scale of the whiteness of these chips was determined from the results of pair comparisons under eight different fluorescent lamps with correlated color temperatures from 2800 to 6700 K. The Munsell 3PB, 10PB, 7P, and N chips gained high scores under 6700 K illumination, whereas the 3PB, 5B, 7BG, and 9G chips scored higher under the 2800 K illumination. The 12 chips were divided into two groups. In one group, the interval scale from the bottom was found to increase as the correlated color temperature increased, whereas in the other group, it decreased with the temperature. The Munsell 3PB/9.25/1.0 chips fell into the latter group but consistently exhibited the highest or at least high‐order scores for all the illuminations examined. In those cases in which the correlated color temperature was held constant, the chromaticity of the light source was found to have no significant effect on the whiteness interval scale. A high correlation was identified between the interval scale of the whiteness and the two metrics, the metric chroma of CIELAB, and CIECAM97s chroma C. © 2003 Wiley Periodicals, Inc. Col Res Appl, 28, 96–102, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.10129     

Color-rendering capacity of light

Two types of questions, both related to color-rendering properties of light, can be identified. Type A: Given a spectral reflectance chip under illumination of a certain spectral power distribution, What color can appear? Does the appearing color, in comparison with a reference one, look right or distorted? Type B: Given a great many chips of different spectral reflectance functions under illumination of a certain spectral power distribution, How many different colors, no matter what colors, can appear? Are there a great many different colors or just a few different colors appearing? Questions of type A reflect an important aspect of color-rendering properties and can be tackled with an established measure, the CIE color-rendering index. Questions of type B, related to quite another aspect of color-rendering properties, have particular relevance when illumination's function of making things visible is of most concern. This article discusses a new measure, the color-rendering capacity (CRC), developed for dealing with questions of type B, and explains the measure's derivation, calculation, and implications.     

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