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In additive color mixture, when more than two component tristimulus values are given then the mixture result is determined from a linear combination of the components. On the other hand, in subtractive color mixture, the resultant tristimulus values are not uniquely determined from component tristimulus values. Hence, analyses regarding the minimum and the maximum bounds are very important to understand the possible ranges of tristimulus values of subtractive color mixture. In our previous series of articles, several theorems have been proven related to the bounds. In addition to the values, the centroid of a possible range is very important and essential to the prediction of subtractive color mixture. In the present article, several theorems related to the centroid are provided and proven. © 2006 Wiley Periodicals, Inc. Col Res Appl, 31, 418–424, 2006; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.20247

Continuing our work to further understand the characteristics of stimulus values of a single tristimulus dimension in colors obtained by subtractive color mixture, discussions proceed related to realistic colorants. New theorems are intended to provide for the establishment of bounds for realistic colorants in mixtures when stimulus measurements of the constituent single-colorant samples and the illuminant are obtainable. Related to the new theorems, a formulation is derived for the calculation of the bounds of realistic colorants whose spectral transmittances are represented by weighted combinations of basic functions. By solving the formulation, numerical illustrations are provided for various conditions. The results contribute toward a comprehensive modeling of subtractive color mixture. © 2005 Wiley Periodicals, Inc. Col Res Appl, 30, 354–362, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.

Digital color-imaging systems require very large amounts of computer memory for the internal storage of images to be reproduced. Thus, although decreasing memory cost is an important factor in their recent success, techniques for reducing memory usage continue to be important. This article describes a method for assigning densities to quantized levels of reproduction primaries such that maximum perceptual uniformity is achieved. The result shows that the equal step division of psychometric lightness of gray scales obtainable in the system assures the maximum uniformity for all the other colors as well.

Two metameric color stimuli have spectral-power-distribution curves which, in general, intersect at three or more wavelengths within the visible spectrum. One of these wavelengths is located in the short-wavelength region, one in the middle-wavelength region, and one in the long-wavelength region. Recent work by Thornton puts these wavelengths at 448 ± 4 nm, 537 ± 3 nm, and 612 ± 8 nm, respectively. The rather precise locations of these nodes are examined in this paper. The method of generating metameric color stimuli is found to have a strong influence on the location as well as the frequency of occurrence of the nodes. Different methods will give different locations and frequency distributions, making it difficult to put much significance on Thornton's results.

By using the CIE color-matching functions, we describe a numerical method to derive new color-matching functions C(Λ) which satisfy the conditions (1) C(Λ) ≥ 0, (2) C(Λ) with a single peak, and (3) C(Λ)'s with the least overlaps.

A simplified method is proposed in an attempt to formulate spectral reflectance functions of actual object colors. The method is applied to evaluate the optimal color gamuts and chromaticity-mismatch limits for actual object colors.

A standard deviate observer (SDO) has been formulated that can predict the average color mismatches of metameric color pairs by 20 Stiles' observers. A nonlinear optimization technique, rather than a statistical analysis, has been employed to derive it. The colorimetric characteristics of the present SDO are compared with those of SDOs previously proposed.

Spectral curves of metameric colors intersect at least three times in the visible spectral range. Based on studies on the variation of intersection wavelengths with the degree of metamerism, it has been found that the intersections tend to converge more closely to three particular wavelengths as the object colors become more strongly metameric.