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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. [ABSTRACT FROM AUTHOR]

This article addresses some general practices for the computation of CIE tristimulus values (TSVs), including different methods used for the interpolation, extrapolation, and truncation of data in the visible wavelength range. In each case, a quantitative analysis is presented on the basis of a dataset with 2365 spectral reflectances covering a wide color gamut, assuming six CIE illuminants and the two CIE standard colorimetric observers. For interpolation, it is found that among five tested methods, the (cubic) spline method is the best one when the spectral reflectance factors are uniformly sampled over the visible wavelength range. For extrapolation, it is found that the second-order extrapolation method gives better results than the use of nearest available data points or linear extrapolation methods. With respect to truncation, considering five different usual truncated ranges, it is found that the range from 360 to 780 nm provides more accurate results than the range from 380 to 780 nm currently recommended by CIE for nonfluorescent samples, and the use of the truncated range from 400 to 700 nm in place of the CIE-recommended range of 360 to 830 nm leads to TSVs with considerably high color differences of up to 0.9 CIELAB units. © 2016 Wiley Periodicals, Inc. Col Res Appl, 42, 10-18, 2017 [ABSTRACT FROM AUTHOR]

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 Δ λ 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 [ABSTRACT FROM AUTHOR]

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 [ABSTRACT FROM AUTHOR]