A hybrid adaptation strategy for reconstruction reflectance based on the given tristimulus values

Recently, Cao et al proposed an adaptive weighting method for the training samples for reflectance reconstruction according to both colorimetric and spectral reflectance similarities for a given vector defined by tristimulus values. It was shown the Cao et al method outperforms the other methods including the regression estimation method in terms of multiple evaluation criteria. In this article, motivated by the work of Cao et al, a hybrid weight is introduced, which results in the size of the training samples selected is half of that used by the Cao et al method. Simulation results showed that the proposed method performs equally well as or slightly better than the Cao et al method, but uses less central processing unit time than that used by the Cao et al method. It was also found that about 100 training samples selected is good enough for the proposed method.     

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     

A new method for computing optimum weights for calculating CIE tristimulus values

Weighing tables are widely used for calculating CIE tristimulus values. In this article, a direct method for computing optimum weighing tables for any illuminant and observer combination is developed. A comprehensive set of 1‐nm reflectance functions based upon Munsell samples is used to test various methods. Four types of weighing tables are compared. They are ASTM E308 Tables 5 and 6, ASTM E2022, and new tables proposed by this study. The results clearly show that the newly developed optimum tables outperform the other three types of tables. The new method is simple and avoids the iterative process used by Venable and adopted by ASTM for some of its tables. It may be used for calculating weighing tables for any combination of illuminant and observer. A detailed procedure and a worked example are given in the article. © 2004 Wiley Periodicals, Inc. Col Res Appl, 29, 91–103, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.10229     

Linear bases for spectral reflectance functions of acrylic paints

A linear model for representing reflectances has been developed from a group of 5574 samples of acrylic paint on paper. Using acrylic paints makes easy the generation of a large variety of samples by mixing, due to the high miscibility among these kinds of pigments: this point was the key to achieve a great spatial homogeneity in our samples. Besides, these kinds of paints keep their chromatic properties stable over time. The first 7 vectors of the so-called overall linear basis were sufficient for a more than adequate mathematical representation of the spectral-reflectance curves. A study by hue groups of the mathematical properties of these curves indicates that the use of a hue basis of representation implies, on the average, a reduction in 1 or 2 of the number of vectors needed in order to achieve results analogous to those of the overall basis. © 1998 John Wiley & Sons, Inc. Col Res Appl, 23, 39–45, 1998     

用改进的基向量法重建光谱反射比

如何从已知物体表面颜色的三刺激值及其照明条件和观察条件准确地重建其光谱反射比，是彩色图像研究领域尚待解决的一个重要课题．本文首先介绍了两种前人提出的方法，即“伪逆矩阵法”和“Wiener方法”，然后，分析了这两种方法的优缺点，指出了共同存在的问题，即所重建的光谱反射系数有可能超出实际可能的范围（0，1），进而提出了一种新的改进的基向量法．最后，文中还给出此改进的算法和上述两种算法的特性模拟仿真．从仿真的结果中可以看出，改进的算法不仅在精度上较上述两种算法更精确，而且能够保证所重建的光谱反射比能够满足其实际可能的范围（0，1）．因而，用本文中所给出的改进的基向量法重建物体表面的光谱反射比，较上述两种前人提出的算法更能满足工业实际需要．     

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.     

Testing the accuracy of methods for the computation of CIE tristimulus values using weighting tables

The least squares method for computing colorimetric weighting tables is presented and its connection with the optimum weights method is investigated. Each requires solving three linear systems of equations with the same coefficient matrix but three different right hand side vectors. It is shown that the two methods have nearly the same performance when the wavelength interval of the data is large. The two methods however, will perform differently when Δλ is small. Comparisons are also made between the least squares method, the optimum weights method, the zero‐ and second‐order weighting tables, and the ASTM weighting tables, both the original 1985 tables and the new 2013 Tables V and VI. The results show that the least squares method is the best for measurement intervals equal to or lower than 10 nm, and is competitive with the optimum weights method for 20 nm steps. The results presented in this article will contribute to the work of CIE Technical Committee TC1‐71 Tristimulus Integration as it seeks to make recommendations for the calculation of tristimulus values. © 2015 Wiley Periodicals, Inc. Col Res Appl, 41, 125–142, 2016     

Four‐transition 0‐1 functions for reflectance spectra

It is known that a reflectance spectrum for an optimal colour takes on the value 0 or 1 at every wavelength, with at most two transitions between those values. This article shows that any non‐optimal colour can be produced by a reflectance spectrum that takes on the value 0 or 1 at every wavelength, with at most four transitions. While the two‐transition optimal spectrum is unique, the four‐transition non‐optimal spectrum is not unique.     

A strategy toward spectral and colorimetric color reproduction using ordinary digital cameras

In this work, a methodology is introduced to use ordinary digital RGB cameras for the purpose of spectral and colorimetric color reproduction. First, it is attempted to recover the spectral reflectance from RGB camera response using different approaches, among which, it is shown that weighted nonlinear regression as performed better than other approaches. After analyzing the results, it is realized that although spectrally the results are satisfactory, there is still a significant colorimetric error left, that should be addressed. Therefore, in the second part of the article, different linear and nonlinear matrix transforms are used to change the RGB camera response to CIEXYZ tristimulus values under a specific condition. It is concluded that colorimetric error of the recovery can be reduced significantly when a separate path is used for colorimetric color reproduction.     

Reliability of the bromthymol blue method for color in virgin olive oils

The bromthymol blue (BTB) method is currently used for the assessment of color in olive and seed oils by visual comparison with standard solutions. Two BTB scales were prepared with 2 yr difference and compared, and the recent one was used to analyze 502 virgin olive oil samples, obtained by the Abencor® technique reproducing the industrial procedure. The temporal chromatic degradation of the BTB samples after 2 yr [3.93 Commission Internationale de l’Eclairage (CIE) 1976-(L*a*b*) (CIELAB) units, on the average], as well as the small percentage of virgin olive oils matching the colors of the samples provided by the BTB scales (13.1% with a suprathreshold color tolerance of 1.52 CIELAB units), indicates the limitations of the BTB method. Linear regression models are proposed in order to compute with acceptable accuracy the BTB indices from chromaticparameters. The use of CIELAB for the specification and future studies on color in virgin olive oils is recommended.     

Surface reflectance estimation by the dichromatic model

A method is described for estimating the surface-spectral reflectances of glossy objects when the color signal is a mixture of diffuse reflections, specular reflections, and interreflections. The objects are inhomogeneous dielectric materials, and the reflected light is measured using a spectroradiometer. We first describe the main idea; the color signals, reflected from two closely apposed surfaces with a single interreflection between them, can be expressed by a linear combination of the illuminant spectrum and two diffuse spectral reflection functions. We introduce a representation in which each of these three terms is projected onto a point on a unit sphere. Estimation of the diffuse reflection functions is then reduced to finding the vertices of the spherical triangle. Next, an algorithm is described to estimate the locations of the vertices of diffuse reflectance functions from the measured samples. The reliability of the algorithm is demonstrated in an experiment using two plastic objects with glossy surfaces. © 1996 John Wiley & Sons, Inc.     

Spectral power distributions for the CIE stimuli

The CIE reference colour stimuli, X, Y, and Z, were derived by constructing a triangle outside the R,G,B triangle and outside the area bounded by the spectrum locus and the purple line. By this means, all colours, including monochromatic ones, have positive tristimulus values. The colour‐matching functions are the relative quantities of these stimuli required to be mixed additively to match the equal energy monochromatic colours. The stimuli are not realizable as light sources, and the CIE has not specified their spectral power distributions. There is an infinite number of spectral power distributions whose properties meet the prerequisites for X (X = 100, Y = 0, Z = 0), Y (0, 100, 0), and Z (0, 0, 100), and two possible sets have been calculated by different methods. These curves could be used as primary red, green, and blue lights in additive mixing to produce synthetic reflectance curves, which are useful in the specification of on‐screen colours, and as a means of producing colour constant standards. © 2001 John Wiley & Sons, Inc. Col Res Appl, 26, 478–482, 2001     

Using weighted pseudo‐inverse method for reconstruction of reflectance spectra and analyzing the dataset in terms of normality

Most of spectral estimation methods are based on improving the learning‐based procedures which mainly modify the training sets used by the basic methods. In this article, a new method is developed for analyzing of superiority of these modified processes to the basic methods in terms of normality of datasets. Hence, two qualitative terms, named generality and similarity are introduced to interpret the recovery achievements of different databases and their roles as training and testing sets. Also, a simple technique based on dataset modification of pseudo‐inverse method is introduced for the recovery of reflectance spectra of samples from their corresponding colorimetric data. The method modifies the training dataset according to the color specifications of test sample. In fact, different weighting matrices are employed as dynamic modifiers to improve the pseudo‐inverse estimation as a simple recovery method. The employed datasets are examined in the self as well as cross test conditions and the results are spectrally and colorimetrically evaluated. The root mean square errors between the reconstructed and actual spectra along with the corresponding color difference values under different illuminants decrease by employing the suggested modification method in comparison to classical pseudo‐inverse technique as well as the recently improved version named optimized adaptive Wiener method. © 2010 Wiley Periodicals, Inc. Col Res Appl, 2010     

Results of the ASTM field test of tristimulus weighting functions

In 1993, the American Society for Testing and Materials carried out a field test of newly calculated tristimulus weighting factors. These weighting factors had been calculated by a method proposed by Venable. the test also included a method of correction for bandpass dependence put forth by Stearns. the purpose of the trial was to assess the possible reduction in bandpass dependence introduced by each of these sets of weights. A large number of sets of spectral data were gathered from the cooperators in the field test. Results of integration by the various sets of tristimulus weighting factors were calculated. A total of 15 120 color differences were calculated and statistics were derived to test the probable error resulting from each method of correction. Errors attributable to bandpass dependence were on the order of a few tenths to as much as one CIELAB unit when uncorrected weight sets were used. These errors could be reduced to a few hundreths of a CIELAB unit, and in some cases to a few thousandths of a unit, by employing one correcting strategy or the other. an overall mix of strategies was ultimately chosen to minimize the bandpass dependence over the entire range of weight sets. Utilizing this mixed strategy, the median error introduced into 10-nm integration by bandpass dependence was only 0.004 CIELAB units. © 1995 John Wiley & Sons, Inc.     

Mathematical approach for predicting non‐negative tristimulus values using the CAT02 chromatic adaptation transform

It has been reported that for certain colour samples, the chromatic adaptation transform CAT02 imbedded in the CIECAM02 colour appearance model predicts corresponding colours with negative tristimulus values (TSVs), which can cause problems in certain applications. To overcome this problem, a mathematical approach is proposed for modifying CAT02. This approach combines a non‐negativity constraint for the TSVs of corresponding colours with the minimization of the colour differences between those values for the corresponding colours obtained by visual observations and the TSVs of the corresponding colours predicted by the model, which is a constrained non‐linear optimization problem. By solving the non‐linear optimization problem, a new matrix is found. The performance of the CAT02 transform with various matrices including the original CAT02 matrix, and the new matrix are tested using visual datasets and the optimum colours. Test results show that the CAT02 with the new matrix predicted corresponding colours without negative TSVs for all optimum colours and the colour matching functions of the two CIE standard observers under the test illuminants considered. However, the accuracy with the new matrix for predicting the visual data is approximately 1 CIELAB colour difference unit worse compared with the original CAT02. This indicates that accuracy has to be sacrificed to achieve the non‐negativity constraint for the TSVs of the corresponding colours. © 2011 Wiley Periodicals, Inc. Col Res Appl, 2011     

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.     

Methods of selecting a small reflectance set as a transfer standard for correcting spectrophotometers

The present article concerns the use of software and transfer standards of reflectance to correct a fielded spectrophotometer so that it behaves closely like a reference instrument. A method is described to choose from a large set of reflectances the best subset of a few reflectances to act as a transfer standard. A reflectance set is generated from the algorithm using each of two alternative metrics for instrument closeness: CIELAB ΔE* and a weighted sum of absolute differences over wavelength. Both metrics yield transfer standards that conspicuously exclude BCRA reflectances and also show improvement over the BCRA reflectances currently used for this purpose. © 2005 Wiley Periodicals, Inc. Col Res Appl, 31, 13–17, 2006; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.20169     

感温变色建筑涂料的制备及光谱反射性能实验研究

感温变色建筑涂料在降低建筑冷热负荷、改善城市热环境方面具有很大的应用潜力。为了探究感温变色材料光学性能的影响因素,优化材料配方,首先制备了12种不同配方,变色温度为31℃的感温变色涂料,并分析了金红石型TiO₂质量百分含量对涂料光谱反射率和太阳光反射比的影响,研究表明涂料光谱反射率均随着TiO₂含量的增加而提高,感温变色粉最佳质量分数5%,TiO₂的最佳质量分数应在5%~10%之间,此时浅色态的反射比比深色态高0.2以上。同时探究了TiO₂粒径对涂料在不同波段反射率的影响,结果表明,在紫外和除红光外的可见光波段,感温变色涂料的反射率基本上随TiO₂粒径的增大而减小;在红光和近红外波段,感温变色涂料反射率基本上随TiO₂粒径的增大而增大。     

Study of the reconstruction of reflectance curves based on tristimulus values: Comparison of methods of optimization

This article presents and compares different methods applied to the reconstruction of reflectance curves. These are optimization methods such as the simplex method, simulated annealing, genetic algorithms, neural networks, and Hawkyard's method, which is specific to colorimetry. Improvements have been made to these methods to maximize their application, notably to ensure a convergence toward the global optimum by avoiding being trapped in local optima and to obtain physically viable reflectance curves. Objective and subjective criteria were used to compare these methods; the study used textile samples (cotton fibers), with a panel of 15 samples covering the CIELAB L*a*b* space. © 2002 Wiley Periodicals, Inc. Col Res Appl, 27, 88–99, 2002; DOI 10.1002/col.10031