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

Abstract

AbstractThis 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