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

Li, C. J.; Luo, M. Ronnier; Rigg, B.

doi:10.1002/col.10229

Cited by 14 publications

(33 citation statements)

References 5 publications

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“…7,8 standardized two sets of weighting tables of Table 5 and Table 6 and gave a procedure 9 for computing weighting tables of Table 5 and its Stearns correction tables using users' own spectral power distribution data, according to previous [10][11][12] and this studies, they (Table 5, Table 6, and Stearns weighting Tables) are not as accurate as the OP (or LS) weighting table. It is, therefore, we recommend that the OP method for calculating weighting tables should be considered for standardization.…”

Section: Resultsmentioning

confidence: 98%

“…In order to evaluate the performance of different methods for generating weighting tables, we adopt the approach used by Fairman 17 and Li et al [10][11][12] . The strategy used is to calculate CIELAB colour differences between the tristimulus values calculated from the standard 1-nm tables and those calculated using the corresponding table for a larger wavelength interval.…”

Section: Comparison Of Different Weighting Tablesmentioning

confidence: 99%

“…T5, OP, LS and DS stands for the tristimulus values computed using ASTM Intl. Table 5 7-9 , optimum [10][11][12] , least squares 13 , and direct selection methods respectively. Sometimes S, T5, OP, LS and DS also refer to the corresponding weighting tables or the methods for computing weighting tables.…”

Section: Introductionmentioning

confidence: 99%

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Recent progress in computing weighting tables for calculating CIE tristimulus values

Luo

Wang

2006

SPIE Proceedings

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In industrial practice, it is often required that weighting tables were prepared in advance and tristimulus values can then be directly computed using summation of the products of the weights and measured reflectance values. The CIE has never provided precise procedure to calculate the weighting tables, and various discrepant methods have been used. Hence it is possible to obtain significantly different tristimulus values from the same set of spectral data.

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Section: Resultsmentioning

confidence: 98%

Section: Comparison Of Different Weighting Tablesmentioning

confidence: 99%

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Recent progress in computing weighting tables for calculating CIE tristimulus values

Luo

Wang

2006

SPIE Proceedings

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“…In reality, a measurement recorded at a given (nominal) wavelength

λ_{j}^{}

is actually based on a signal collected over a narrow range of wavelengths evenly weighted about the nominal wavelength

λ_{j}^{}

. In mathematical terms, the measured SRF

{\overset{r}{true}}_{j}^{(Δ λ)}

is given by:

{\overset{r}{true}}_{j}^{(Δ λ)} = \int_{a}^{b} P_{j} false(λ false) R false(λ false) d λ

…”

Section: The Li–wang–luo Methodsmentioning

confidence: 99%

“…For the computation of TSVs, CIE also suggested that the ASTM weighting Tables V and VI, or the optimum weights method proposed by Li et al . can be used.…”

Section: Introductionmentioning

confidence: 99%

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

Luo

Melgosa

et al. 2015

Color Research & Application

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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

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Colorimetry and Colour Difference

Green

2023

Fundamentals and Applications of Colour Engineering

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

Cited by 14 publications

References 5 publications

Recent progress in computing weighting tables for calculating CIE tristimulus values

Recent progress in computing weighting tables for calculating CIE tristimulus values

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

Colorimetry and Colour Difference

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