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

Zhang

Journal of Engineered Fibers and Fabrics

et al. 2019

Color is one of the most important appearance properties of objects. To digitize color, measuring and calculating tristimulus values are the most basic work besides obtaining reflectance spectrum. However, the accuracy of tristimulus values varies with instruments, measuring, and calculation methods. Textiles and some other application of color demand high color quality due to their special utilization. The series of our studies aim to analyze and evaluate some mathematical solutions in order to improve the accuracy of tristimulus values. The studies include two parts: (1) Part I concentrates on measurement bandpass and intervals and their corresponding improvement algorithms, (2) Part II focuses on the influence of measurement ranges and their truncation errors and some algorithms to overcome the truncation errors. In Part I (current article), measurement errors caused by bandpass and test intervals in the spectrophotometer are analyzed. Then, algorithms including two bandpass corrections (3-point correction and 5-point correction), three interpolations (third-order polynomial interpolation Lagrange and Spline, a fifth-order polynomial interpolation Sprague), two Oleari deconvolution methods (zero- and second-order), and three optimization weighting table methods (ASTM Table 6, Table LLR, and Table LWL) are studied systemically by programming MATLAB software and basing on measuring the spectral reflectance of 1301 chips in Munsell Color Book with Commission Internationale de L’Eclairage (CIE) 1964 color-matching functions and D65 standard illuminant. The results show that all algorithms mentioned above yield very positive effects, and among them, Table LWL performs best with reducing the bandpass error and intervals error to 7‰ of its original error and is recommended.

“…The spectral bandpass function. 10 the deficiencies of the instruments through mathematical methods so as to improve the accuracy of the TSVs.…”

Section: Methods For Higher Accuracy Of Tsvsmentioning

confidence: 99%

Section: Reduce Bandpass Error By Bandpass Correctionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Methods for improving the accuracy of Commission Internationale de L’Eclairage tristimulus values of object color by calculation – Part I: Improvement on measurement bandpass and intervals

Zhang

Journal of Engineered Fibers and Fabrics

et al. 2019

“…Coordinates u, v of the test light source (or illuminant) must also be computed from accurate TSVs using CIE recommendation (summations from 360 nm to 830 nm at 1 nm steps). Some methods have been recently proposed [24,25] for accurate TSVs computations in the case available spectral data are not as required by CIE. For the function f(T), the exact u(T) and v(T) are needed, which depend on the TSVs X(T), Y(T) and Z(T) (see Eqs. (5), (3), and (2)).…”

Section: The Proposed Methodsmentioning

confidence: 99%

Accurate method for computing correlated color temperature

Cui

Melgosa

et al. 2016

Opt. Express

Self Cite

For the correlated color temperature (CCT) of a light source to be estimated, a nonlinear optimization problem must be solved. In all previous methods available to compute CCT, the objective function has only been approximated, and their predictions have achieved limited accuracy. For example, different unacceptable CCT values have been predicted for light sources located on the same isotemperature line. In this paper, we propose to compute CCT using the Newton method, which requires the first and second derivatives of the objective function. Following the current recommendation by the International Commission on Illumination (CIE) for the computation of tristimulus values (summations at 1 nm steps from 360 nm to 830 nm), the objective function and its first and second derivatives are explicitly given and used in our computations. Comprehensive tests demonstrate that the proposed method, together with an initial estimation of CCT using Robertson's method [J. Opt. Soc. Am. 58, 1528-1535 (1968)], gives highly accurate predictions below 0.0012 K for light sources with CCTs ranging from 500 K to 10⁶ K.

Color Research & Application

“…Then, this set of reflectance functions was also extrapolated to cover the range from 360 to 830 nm. Thus, altogether, we constituted a dataset with 2365 SRFs at 1‐nm intervals from 360 to 830 nm, which provides a reasonable good coverage of the color gamut of real object colors and is referred to in this article as the standard dataset. For the purposes of the calculations to be described in this article, the accuracy of the measurements in our standard dataset is not of importance; it is enough that a set of realistic spectral data are available.…”

Section: Datasetmentioning

confidence: 99%

Interpolation, extrapolation, and truncation in computations of CIE tristimulus values

Wang

Zhao

Jiqiang

et al. 2016

Self Cite

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.