Theoretical analysis of subtractive color mixture characteristics II—General colorants and single tristimulus dimension

To further understand the characteristics of the stimulus values in colors obtained via subtractive color mixture, new theorems are provided. The theorems aim to establish bounds on mixtures of colorants given stimulus measurements of the constituent single‐colorant samples and the illuminant. Previously we only proved theorems for the ideal color. In the present article, new theorems related to the removal of the restriction of the ideal color are provided and establish bounds for all cases of spectral transmittances. The results of this article contributes to a systematization of subtractive color mixture. © 2004 Wiley Periodicals, Inc. Col Res Appl, 29, 354–359, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.20043     

Theoretical analysis of subtractive color mixture characteristics III—Realistic colorants and single tristimulus dimension

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.     

Theoretical analysis of subtractive color mixture characteristics IV—Theorems on ideal color and tristimulus dimension

Giving a continuation to our work to understand the characteristics of the tristimulus values in colors obtained by subtractive color mixture, we extend several theorems provided in our previous articles. Previously, we started proving theorems for a single dimension, considering only individual tristimulus values. In the present article, the one‐dimensional discussion is extended to the three‐dimensional discussions of the tristimulus space. These theorems establish the absolute lower and upper bounds for tristimulus values of subtractive color mixtures of the ideal color. The results contribute toward a comprehensive modeling of subtractive color mixture. © 2005 Wiley Periodicals, Inc. Col Res Appl, 30, 427–437, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.     

Theoretical analysis of subtractive color mixture characteristics V—Centroid of subtractive tristimulus values

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     

Color science applications of the Binet–Cauchy theorem

The Binet–Cauchy theorem, an expansion of the determinant of the product of two nonsquare matrices, is quite useful in deriving theorems about ordering relations in color science. The theorem is first described in a special case that proved suitable to color. Then an application of the theorem is described that finds the conditions among reflectance factors in a color atlas such that their chromaticity ordering is illuminant invariant. Finally, an application is described that finds local pathologies in the color gamuts of subtractive and complex‐subtractive colorant systems. These applications should be useful for the design of color atlases. © 2002 Wiley Periodicals, Inc. Col Res Appl, 27, 310–315, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.10080     

Examples of interference and the color pigment mixtures green with red and red with green

In industrial paint formulations, interference pigments are usually mixed with color pigments. Transparent interference pigments mix together according to the laws of additive mixing and color pigments to the laws of subtractive mixing. The behavior of both types differs depending on whether similar colors such as pearl green and green or contrasting colors such as pearl green and red are mixed. In this article examples of these differences for color measurement are discussed, along with showing the resulting charts. © 2001 Wiley Periodicals, Inc. Col Res Appl, 27, 276–281, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.10063     

Complementary colors theory of color vision: Physiology,color mixture,color constancy and color perception

I describe complementary colors' physiology and functional roles in color vision, in a three‐stage theory (receptor, opponent color, and complementary color stages). 40 specific roles include the complementary structuring of: S and L cones, opponent single cells, cardinal directions, hue cycle structure, hue constancy, trichromatic color mixture, additive/subtractive primaries, two unique hues, color mixture space, uniform hue difference, lightness‐, saturation‐, and wavelength/hue‐discrimination, spectral sensitivity, chromatic adaptation, metamerism, chromatic induction, Helson‐Judd effect, colored shadows, color rendering, warm‐cool colors, brilliance, color harmony, Aristotle's flight of colors, white‐black responsivity, Helmholtz‐Kohlrausch effect, rainbows/halos/glories, dichromatism, spectral‐sharpening, and trimodality of functions (RGB peaks, CMY troughs whose complementarism adapts functions to illuminant). The 40 specific roles fall into 3 general roles: color mixture, color constancy, and color perception. Complementarism evidently structures much of the visual process. Its physiology is evident in complementarism of cones, and opponent single cells in retina, LGN, and cortex. Genetics show our first cones were S and L, which are complementary in daylight D65, giving a standard white to aid chromatic adaptation. M cone later split from L to oppose the nonspectral (red and purple) hues mixed from S+L. Response curves and wavelength peaks of cones L, S, and (S+L), M, closely resemble, and lead to, those of opponent‐color chromatic responses y, b, and r, g, a bimodal system whose summation gives spectral‐sharpened trimodal complementarism (RGB peaks, CMY troughs). Spectral sharpening demands a post‐receptoral, post‐opponent‐colors location, hence a third stage. © 2011 Wiley Periodicals, Inc. Col Res Appl, 2011     

Changes in hue and saturation of chromatic lights presented in the peripheral visual field

The perception of ten different colors on a CRT display presented across the horizontal meridian of the visual field were measured to determine the range of relevant test stimuli for color zone map measurement. Hue and saturation judgments were used based on the opponent‐colors theory. The changes of the unique hue components for eccentric displays of red, yellow, green, and blue fall within the distribution range of previous results obtained using monochromatic lights. Chromatic displays of nearly unique hues with high saturation would be significant as test colors for measurement for a color zone map. © 2003 Wiley Periodicals, Inc. Col Res Appl, 28, 413–424, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.10194     

Databases for spectral color science

In color science, spectral representation and analysis of colors have become a common approach to study color‐related problems, e.g., accurate industrial color measurement or analysis of color images. In developing algorithms for spectral color science, one often relies on existing databases of reflectance color spectra. Since a number of these databases are easily available, the same databases are commonly used by different research groups. During year 2003 the most popular one of our publicly available spectral reflectance databases was visited over 600 times. In the present article, we describe these color spectra databases and analyze their utility for spectral color science. However, the article does not take the complexity of fluorescent surfaces into account. The aim of this article is to set a solid ground for the comparisons of different methods in the spectral color science. The databases presented here include measured color spectra of natural and man‐made objects as well as spectra of some sets of standard colors. In addition to the commonly used data sets, some new data sets, including a set of standard calibrated colors and a set of natural colors, measured with 10 nm spectral resolution are introduced. © 2006 Wiley Periodicals, Inc. Col Res Appl, 31, 381–390, 2006; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.20244     

Adequateness of a newly modified opponent‐colors theory

Two features of a newly modified opponent‐colors theory are examined for correctness: (1) The perceived chroma of pure color is different for different hues. This was confirmed by using Ikeda's UCS (Uniform Color Scales) formula and also by the maximum Munsell Chroma Values for different hues. (2) Chromatic colors with the same values of whiteness, blackness, grayness, and perceived chroma have the same perceived lightness and chromatic tone regardless of hue. This was confirmed by a theoretical analysis and observations of the color samples in the Practical Color Co‐ordinate System (PCCS) developed in Japan. Chromatic tone, a complex concept of object colors, is clarified. The structure of the newly modified theory and its corresponding color space were confirmed by observation of object colors. Furthermore, it was found effective for developing a color‐order system and its corresponding standard color charts to the modified theory. © 2003 Wiley Periodicals, Inc. Col Res Appl, 28, 298–307, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.10164     

How many object colors can we distinguish?

The question of how many different colors humans can perceive has been of interest to philosophers, psychologists and color scientists for centuries. In recent years the question of the number of distinguishable object color stimuli has been addressed by color scientists by defining a distinguishable color as a given stimulus surrounded by the contour of stimuli just noticeably different from the central stimulus. For a particular set of conditions the number of distinguishable object color stimuli assessed in this manner has recently been found to be slightly larger than 2 million. In this article an argument is made that the related rules are arbitrary and unnecessarily limiting. Based on logical arguments and experimental just noticeable difference data it is shown that, for the conditions involved, a more realistic if conservative number of distinguishable object color stimuli is ～40 million. © 2015 Wiley Periodicals, Inc. Col Res Appl, 41, 439–444, 2016     

Individual differences of unique hue loci and their relation to color preferences

Loci of the four unique hues (red, green, blue, and yellow) on the equiluminant plane on the color display and three preferred colors were obtained from 115 normal trichromats. We sought possible correlations between these measures. Different unique hue loci were not correlated with each other. The three preferred colors were not correlated with each other. We found five combinations of significant correlation between a preferred color and unique hue settings, yet the overall tendency is not very clear. We conclude that individual differences in color appearance measured by unique hues and color preferences measured by asking for favorite colors may not be predicted from each other or even within a category because the differences in the earlier visual mechanisms can be compensated for and these high‐level measures can be influenced by learning and experience. © 2004 Wiley Periodicals, Inc. Col Res Appl, 29, 285–291, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.20023     

Cognitive color

This report surveys cognitive aspects of color in terms of behavioral, neuropsychological, and neurophysiological data. Color is usually defined as a color stimulus or as perceived color. In this article, a definition of the concept of cognitive color is formulated. To elucidate this concept, those visual tasks are described where it is relevant: in color categorization, color coding, color naming, the Stroop effect, spatial organization of colored visual objects, visual search, and color memory. © 2003 Wiley Periodicals, Inc. Col Res Appl, 29, 7–19, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.10209     

Influence of basic color categories on color memory discrimination

Two color-memory experiments were performed to investigate whether observers tended to confuse colors with a smaller color difference in memory or colors in a same color-category region. We made color stimuli on a color CRT. Color difference was determined by a simultaneous color discrimination experiment. Color-category regions were obtained by a categorical color-naming experiment using the 11 basic color names: white, black, red, green, yellow, blue, brown, orange, purple, pink, and gray. The results show that two colors with a certain color difference can be confused more easily when they are in a same color category than in different color categories, and that colors identified with memory tend to distribute within their own color-category regions or their neighbor color-category regions, depending on their positions in a color space. These findings indicate that color memory is characterized by the color categories, suggesting a color-category mechanism in a higher level of color vision. © 1996 John Wiley & Sons, Inc.     

Complementary colors: The structure of wavelength discrimination,uniform hue,spectral sensitivity,saturation, chromatic adaptation,and chromatic induction

Complementary colors have long been thought important to color vision due to their ability (as admixed pairs) to extinguish all chromaticity, and to adapt automatically (i.e., wavelength pairs and radiant power ratios) to illuminant. Their role in color mixture and chromatic induction is well documented but other roles have not been demonstrated. This article studies the structure of complementary colors in the wavelength and radiance dimensions over the hue cycle (the nonspectrals are represented by a nominal‐wavelength metric). In the wavelength dimension, the basic structure of complementary colors is the complementary intervals ratio (ratio of a wavelength interval to its complementary interval of 1 nm). The ratio has RGB peaks, complementary CMY troughs, and provides models of chromatic induction, wavelength discrimination, and uniform hue difference in good agreement with data. Novel analyses of six color order/UCS hue circles indicate essential characteristics of a uniform hue scale. In the radiance dimension, basic structure is the complementary powers ratio (power of a stimulus required to neutralize its complementary of 1 Watt). The inverse structure has RGB peaks, complementary CMY troughs, and provides models of saturation, spectral sensitivity, and chromatic adaptation to illuminant. The RGB peaks demonstrate spectral sharpening, implying a postreceptoral location in the physiology. The models indicate that complementary colors have a significant role in color appearance besides their well known role in color mixture. © 2009 Wiley Periodicals, Inc. Col Res Appl, 34, 233–252, 2009     

A test of uniformities in the OSA‐UCS and the NCS

In the OSA‐UCS (Optical Society of America–Uniform Color Scales), except for colors on the boundary of the three‐dimensional solid (L, j, g), each color is surrounded by the 12 nearest neighboring colors that are supposed to be perceptually equally different (local uniformity). In the Swedish NCS (Natural Color System), colors are arranged so as to gradually vary in each of the three perceptual attributes: hue, ?; blackness, s; and chromaticness, c. The gradual change in an attribute may correspond to change of color difference from one to the next with a constant step (local uniformity). In each of these color‐order systems, the uniformity was tested by a color‐difference formula d? based on color‐component differences. When a coordinate is fixed (e.g., j in OSA‐UCS, or c in NCS), d? for neighboring pairs turned out fairly constant. However, systematic differences were found between d? in one coordinate and d? in another coordinate. © 2003 Wiley Periodicals, Inc. Col Res Appl, 28, 277–283, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.10162     

Color appearance and color connotation models for unrelated colors

The purpose of this research is to investigate the color appearance and color connotation of unrelated colors. To investigate color appearance (i.e., brightness, colorfulness, and hue) for unrelated colors, 22 observers have answered their color appearance for 50 unrelated color stimuli using the magnitude estimation method. Perceptual data obtained by the experiment is compared with the color attributes data estimated by unrelated‐color appearance models, CAM97u and CAM02u. It is found that both models perform reasonably well but the performance of CAM02u is better than that of CAM97u. For investigating color connotation for unrelated colors, 32 observers have judged their color connotation for the 50 unrelated color stimuli using the 10 color connotation scales (i.e., “Warm – Cool,” “Heavy – Light,” “Modern – Classical,” “Clean – Dirty,” “Active – Passive,” “Hard – Soft,” Tense – Relaxed,” “Fresh – Stale,” “Masculine – feminine,” and “like – Dislike”), and semantic differential method is used for measurement. It is found that the color connotation models developed for related colors perform poorly for unrelated colors. Experimental results indicate that brightness attribute is confusing to estimate and does not affect color connotation significantly for unrelated colors. Based on the psychophysical data, new models for “Warm‐Cool”, “Heavy‐Light”, “Active‐Passive” and “Hard‐Soft” were proposed using CAM02u hue, brightness, and colorfulness. Color connotations for unrelated colors are classified into three categories, which “Color solidity,” “Color heat,” and “Color purity.” © 2013 Wiley Periodicals, Inc. Col Res Appl, 40, 40–49, 2015     

Development of the idea of simple colors in the 16th and early 17th centuries

The development of the idea of simple or fundamental colors in Western culture from classical Greece to the early 17th century is shown, with particular emphasis on writers in the 16th and early 17th centuries. Four streams of thought are found: (1) Aristotle's seven colors, congruent with seven tastes and seven tones, thus symptomatic of an underlying general harmony; (2) Four‐basic‐color sequences where colors are emblematic of the four classical elements; (3) Spectral sequences; (4) Three simple chromatic colors between white and black, based on colorant mixture. In the late 16th century seven‐color sequences came to represent categorical sequences, in addition to shorter fundamental color sequences. © 2007 Wiley Periodicals, Inc. Col Res Appl, 32, 92 – 99, 2007     

A novel method for fabric color transfer

Fabric color design is a complex process in textiles and clothing industry. A new method for fabric color selection and transferring is proposed in this study. An automatic way to select the colors from the natural images is developed for fabric color design. Based on these colors, a fabric image is then used for color transferring. The fabric image is processed by a bias field estimation operation, and the membership function of the color deviations of the image has been obtained. According to the selected colors and the color membership function, the fabric image colors can be changed and transferred to a new image that preserves the similar texture appearance but with significantly different color effects. The experimental results confirm the effectiveness of the proposed method. © 2014 Wiley Periodicals, Inc. Col Res Appl, 40, 304–310, 2015     

Suggested optimum primaries and gamut in color imaging

Suggested optimal “primaries” and concomitant optimal gamut for any form of device or product whose output serves as input to the normal human visual system: TV‐like images, or images reflected from illuminated hardcopy. For those devices and products using additive coloration, three spectral primaries 450–530–610 nm, and their associated gamut, are suggested as goals. For those using subtractive coloration, three reflective components, of width perhaps 50–60 nm at half‐height and peaking at the same wavelengths, are suggested. Thus, in either case, the light from each pixel of the generated color image entering the pupil of the normal human observer is composed of a mixture of that observer's prime colors. “Prime colors” are defined as usual as (a) the wavelengths marking the peaks of the three spectral sensitivities of the (trichromatic) normal human visual system, and, thus, (b) those spectral lights to which the normal human visual system responds most strongly per watt of power content input to the pupil. Spectral sensitivities of the normal human visual system are carefully distinguished from those of the CIE Standard Observers. © 2000 John Wiley & Sons, Inc. Col Res Appl, 25, 148–150, 2000