Interpolation, extrapolation, and truncation in computations of <scp>CIE</scp> tristimulus values

Wang, Zhifeng; Zhao, Binghao; Jiqiang, Li; Luo, M. Ronnier; Pointer, Michael R.; Melgosa, Manuel; Li, Changjun

doi:10.1002/col.22016

Cited by 6 publications

(4 citation statements)

References 11 publications

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“…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

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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.

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Section: The Proposed Methodsmentioning

confidence: 99%

Accurate method for computing correlated color temperature

Cui

Melgosa

et al. 2016

Opt. Express

Self Cite

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“…When condition changes, the best extrapolation method may also vary. Taking Wang et al’s 14 research as an example, their result indicates the second-order method perform best.…”

Section: Experimental Study Of Extrapolationmentioning

confidence: 99%

“…Obviously, for the same reflectance data and the same number points of extrapolation, the optimal extrapolation algorithm may different. Besides, Wang et al 14 also imparts us that the extrapolation effect may also affect by the illuminants.…”

Section: Experimental Study Of Extrapolationmentioning

confidence: 99%

Methods for improving the accuracy of CIE tristimulus values of object color by calculation Part II: Improvement on measurement wavelength ranges

Yang

Zhang

Yang

et al. 2021

Journal of Engineered Fibers and Fabrics

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The previous paper (part I) analyzed test errors of the spectrophotometer and their reasons, then systematically investigated the algorithms to reduce measuring bandpass error and intervals error. This paper (part II) focuses on the influence of measurement wavelength ranges and their truncation errors, and some algorithms to overcome the truncation errors. CIE recommends that tristimulus values are calculated over a range of 360–830 nm. However, most spectrophotometers do not meet it. The reduction of measurement range will result in a measurement range error or a truncation error. In this study, five ranges commonly employed in practice are selected for investigating the truncation errors, and three extrapolation methods are used to extend the data to compensate for the measurement range loss. Results are obtained by employing 1301 Munsell color chips under illuminant D65 and CIE 1964 standard observer. For the standard 1-nm intervals, the narrower the range, the larger the truncation error. For the usual-measured 10-nm intervals, bandpass error and intervals error should be handled at the same time, 380–780 nm Table LWL gives the highest accurate outcomes, which even improve the accuracy of the range 360–750 nm to an acceptable level. Whereas, ranges of 360–700 nm and 400–700 nm still need extrapolation to reduce their truncation errors even with Table LWL. Three extrapolation methods of nearest, linear and second-order all reduce the truncation error, but for different ranges, algorithms and illuminants, the optimal method of extrapolation varies.

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“…In view of the non-spontaneous optical object color testing range without fluorescent lighting, it is recommended in 360-830 nm by CIE (International Illumination Committee), so, to ensure more accurate results, the visible light test range of from 360 nm to 750 nm was selected for test of jadeite-jade color green [20].…”

Section: Quantitative Analysis Of Color Greenmentioning

confidence: 99%

Feasibility study on color evaluation of jadeite based on GemDialogue color chip images

Guo

Zong²,

et al. 2018

J Image Video Proc.

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Through the calculation of gemological chromaticity, the green characters and range of chromaticity of 728 cabochon jadeite jade were determined, and then it studies and compares with GemDialogue color card images for jadeite-jade green quality evaluation. It is testified that the method is proved to be effective and the construction of emerald green quality grading system based on it is proved. First of all, with reference to China national standard GB/T 23885-2009 "Jadeite-jade Grading," the color appearance of jadeite-jade color green was analyzed contrastively with the help of three pieces of GemDialogue color chip images G, Y2G, and B2G where CIE recommended standard light sources D65, A, and CWF, and then it is proposed that the best light source of jadeite-jade color green measuring and evaluating is standard D65 based on quantitative analysis of samples' lightness L * , chroma C * , hue h 0. Secondly, according to samples color green and five pieces of GemDialogue color chip images G2Y, Y2G, G, B2G, and G2B, jadeite-jade color was graded in seven levels from the best end "Fancy Vivid" to the last end "Very Light" with the contribution of five different overlap modes of three color masks: black/gray transparent, brown transparent, and black/white opaque. Furthermore, the high accuracy of the method is verified by clustering analysis and Fisher's discrimination reversely. It draws conclusions that there are two evaluation methods of jadeite-jade color green; the first is the colorimetric way of GemDialogue color chip images, and the complementary is the way of Fisher functional method which sample parameters could be back substituted, and all these two methods could be extended to other green gem quality evaluation.

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

Cited by 6 publications

References 11 publications

Accurate method for computing correlated color temperature

Accurate method for computing correlated color temperature

Methods for improving the accuracy of CIE tristimulus values of object color by calculation Part II: Improvement on measurement wavelength ranges

Feasibility study on color evaluation of jadeite based on GemDialogue color chip images

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