Three numerical methods are presented for finding the smoothest reflectance curve associated with a given triplet of tristimulus values. The methods differ in how “smooth” is defined, and also differ in the domain of colors over which they are applicable. The first method is very quick and applies to any tristimulus values, but sometimes can yield reflectance curves with portions that fall outside the range 0 to 1. The second method applies to colors within the spectral locus (real colors) and guarantees that the reflectances produced are positive. The third method applies to colors within the object color solid (object colors) and guarantees that the reflectances fall within the range 0 to 1. The methods are shown to create reflectances that closely resemble those of real colors (natural and synthetic). Focus is given to implementing the numerical methods in very short MATLAB/Octave functions and to understanding the numerical behavior of the methods near the limits of their respective domains of applicability in terms of matrix conditioning and discretization artifacts.

中文翻译：

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最平滑反射率重建的数值方法

提出了三种数值方法来找到与给定的三刺激值三重态相关的最平滑的反射率曲线。这些方法在“平滑”的定义方式上有所不同，在适用颜色的范围方面也有所不同。第一种方法非常快速，适用于任何三色刺激值，但有时可以产生反射率曲线，其部分范围在0到1之外。第二种方法适用于光谱轨迹内的颜色（真实颜色），并保证产生的反射率是积极的。第三种方法适用于对象颜色纯色（对象颜色）内的颜色，并确保反射率在0到1的范围内。显示了这些方法可创建与真实颜色（天然和合成）的反射率非常相似的反射率。