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

Yang Hongying,Xie Wanzi,Cui Shizhong,Yang Zhihui,Zhang Jingjing,Zhou Jinli

doi:10.1177/1558925020985964

Yang Hongying, Xie Wanzi + Show 4 more

Open Access

https://doi.org/10.1177/1558925020985964

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Abstract

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.

Highlights

CIE 15: 20041 and CIE 167: 20052 defines that the tristimulus values (TSVs) are calculated over a wavelength range of [360–830] nm
The error caused by narrower measurement wavelength range is called measurement range error or truncation error
Measurement intervals and bandpass errors exist in the second case can be significantly reduced by Table LWL algorithms, so the truncation errors based on Table LWL are very worth to research

Summary

Introduction

CIE 15: 20041 and CIE 167: 20052 defines that the tristimulus values (TSVs) are calculated over a wavelength range of [360–830] nm. The reflectance data and calculate methods are the same as those in Part I of this series article Both relative error and color difference are employed to analyze the truncation error. If the optimization weighting table in Part I is used to improve the accuracy of the measured data with 10-nm intervals in range [400–700] nm, that is, the optimization algorithm is used to reduce the bandpass and the intervals error, the color differences will be significantly decreased. Median values of CIELAB color difference of all the 1128 possible truncation errors caused by ranges shorter than [360– 830] nm (shown at 10-nm intervals): (a) three-dimensional figure, (b) left view figure, (c) top view figure, and (d) right view figure. In addition to the large fluctuations at some ranges, the truncation error is basically reduced as the measurement range increases

Experimental study of truncation error

Experimental study of extrapolation

Findings

Conclusions and recommendations