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     

Color constancy from invariant wavelength ratios. III: Chromatic adaptation theory,model and tests

A theory of chromatic adaptation is derived from Parts I and II, and presented in terms of relative wavelength, purity, and radiant power, leading directly to a predictive model of corresponding hue, chroma, and lightness. Considering that even simple animals have effective color vision and color constancy, the aim was to develop a simple model of complete adaptation. The model is tested against well‐known data sets for corresponding colors in illuminants D65, D50, and A, and for small and large visual fields, and performs comparably to CIECAM02. Constant hue is predicted from Part I's mechanism of color constancy from invariant wavelength ratios, where constant hues shift wavelength linearly with reciprocal illuminant color temperature. Constant chroma is predicted from constant colorimetric purity. Constant lightness is predicted from chromatic adaptation of spectral sensitivity represented by power ratios of complementary colors (rather than cone responses which lack spectral sharpening). This model is the first of its type and is not formatted for ease of computation. © 2010 Wiley Periodicals, Inc. Col Res Appl, 2010     

Color constancy from invariant wavelength ratios. II. The nonspectral and global mechanisms

Given the spectral mechanism of color constancy (Part I of this series), the remaining nonspectral mechanism is formulated here in Part II by the constraint of correlation with known spectral illuminant–invariant functions, i.e., invariant wavelength ratios between constant hues, which plot straight parallel lines in the plane of wavelength and reciprocal illuminant color temperature (MK^?1). The same is assumed to apply to nonspectral constant hues in the same plane and dominant wavelength scale extended to cover the nonspectrals (see accompanying article “Relative wavelength metric for the complete hue cycle …”). To simplify analysis, stimuli are optimal aperture colors; their monochromatic stimuli lie between 442 and 613 nm, common boundaries with optimal compound stimuli (nonspectrals). It is shown that the wavelengths and invariant ratios of spectral constant hues can be formulated exactly (±0.5%) from the ratios of an harmonic period, which shifts wavelength with MK^?1. The formula implies this color‐constant hue cycle is isomorphic across illuminants and allows prediction of nonspectral constant hues. To identify these colorimetrically, their spectral complementary wavelengths are specified for various illuminants. This completes theglobal color constancy mechanism for the illuminant color temperature range 2800 to 25,000 K. © 2010 Wiley Periodicals, Inc. Col Res Appl, 2010     

Helical structure of complementary colors' relative spectral distribution function

I report a curious double helix in psychophysical data. As recently reported, color complementarism structures at least 40 functional roles in vision including all Red‐, Green‐, Blue‐peaked functions (e.g., color matching functions, Helmholtz–Kohlrausch effect, saturation discrimination, lightness discrimination, and wavelength discrimination). These can be modeled from the relative spectral power distribution (SPD) function of complementary colors (at requisite power ratios to neutralize complements). So, the SPDs three‐dimensional (3D) structure is of interest. Extended to the hue cycle, the SPD is plotted in a rectilinear graph of wavelength versus wavelength with radiance vertical to the plane. In this rectilinear color mixture space, the white locus representing the illuminant chromaticity is not a single point (representing the junction of complementary pairs of wavelengths) but a sinusoidal curve whose 3D structure is a double helix, representing an SPD and its complementary SPD. The structure's purpose is possibly to store and access global complementary colors data across illuminants. © 2012 Wiley Periodicals, Inc. Col Res Appl, 38, 292–296, 2013     

Chromatic adaptation to illumination investigated with adapting and adapted color

The state of chromatic adaptation was investigated by using the two‐room technique. This technique involves a subject in a room who looks a white board in a separate test room through a window and judges the color of the window using the elementary color naming method. When the subject room is illuminated with a colored light and the test room with a white light, the window appears to be a very vivid color, for which the apparent hue depends on the color of the subject room. The color is referred to as the adapted color. The subject also evaluated the appearance of the illumination color of the subject room, which is called the adapting color. Two types of illuminating light in the subject room, fluorescent lamps with 7 colors and LED lamps with 19 colors, were employed. The adapting and the adapted colors were plotted on a polar diagram that was used in the opponent color theory, from which the hue angles were obtained. The hue angle difference between the two colors did not appear to be 180° except for one pair of adapting and the adapted colors, which implies that chromatic adaptation does not follow the opponent color concept. An improvement was achieved to explain the results by introducing complementary colors relation between the adapting and adapted color.     

Categorical color constancy under RGB‐LED light sources

The light‐emitting diode (LED)‐based light sources have been widely applied across numerous industries and in everyday practical uses. Recently, the LED‐based light source consisting of red, green and blue LEDs with narrow spectral bands (RGB‐LED) has been a more preferred illumination source than the common white phosphor LED and other traditional broadband light sources because the RGB‐LED can create many types of illumination color. The color rendering index of the RGB‐LED, however, is considerably lower compared to the traditional broadband light sources and the multi‐band LED light source (MB‐LED), which is composed of several LEDs and can accurately simulate daylight illuminants. Considering 3 relatively narrow spectral bands of the RGB‐LED light source, the color constancy, which is referred to as the ability of the human visual system to attenuate influences of illumination color change and hold the perception of a surface color constant, may be worse under the RGB‐LED light source than under the traditional broadband light sources or under the MB‐LED. In this study, we investigated categorical color constancy using a color naming method with real Munsell color chips under illumination changes from neutral to red, green, blue, and yellow illuminations. The neutral and 4 chromatic illuminants were produced by the RGB‐LED light source. A modified use of the color constancy index, which describes a centroid shift of each color category, was introduced to evaluate the color constancy performance. The results revealed that categorical color constancy under the 4 chromatic illuminants held relatively well, except for the red, brown, orange, and yellow color categories under the blue illumination and the orange color category under the yellow illumination. Furthermore, the categorical color constancy under red and green illuminations was better than the categorical color constancy under blue and yellow illuminations. The results indicate that a color constancy mechanism in the visual system functions in color categories when the illuminant emits an insufficient spectrum to render the colors of reflecting surfaces accurately. However, it is not recommended to use the RGB‐LED light source to produce blue and yellow illuminations because of the poor color constancy.     

Color constancy from invariant wavelength ratios: I. The empirical spectral mechanism

The wavelengths of several constant hues over four illuminants (D95, D65, D50, A) are derived from several sets of published data. In the plane of wavelength and reciprocal illuminant color temperature (MK^?1), the wavelengths of constant hues plot straight approximately parallel lines whose mean slope is about 87°. Parallel lines give invariant wavelength ratios, hence constant hues in this plane are near‐invariant wavelength ratios across illuminants. As recently demonstrated, the complementary wavelengths to a constant hue (across illuminants) represent the complementary constant hue; these complementary wavelengths also plot a near‐parallel line to the first constant hue. To confirm and further define the constant slope of these lines, it is shown that complementary wavelength pairs, per CIE data, can only plot parallel straight lines at the angle of 87° ± 1. In summary, near‐parallel sloping lines represent constant hues at near‐invariant wavelength ratios. This mechanism of color constancy is shown to relate to the well‐known theory of relational color constancy from invariant cone‐excitation ratios. In the visual process, the latter ratios are presumably the source of the former (invariant wavelength ratios). © 2008 Wiley Periodicals, Inc. Col Res Appl, 33, 238–249, 2008     

A hue rectangle and its color metrics in a modified opponent‐colors system

In the proposed modified opponent‐colors system, the hue regular rectangles show the chromatic coordinates of any chromatic colors better than hue circles. In the hue rectangles equihue and equichroma loci are shown together with equigrayness loci. In the color perception space of the modified opponent‐colors system, a city‐block metric must be used instead of a Euclidean one for distance. The reason for this is described in detail. The proposed color perception space constitutes a regular octahedron. © 2002 Wiley Periodicals, Inc. Col Res Appl, 27, 171–179, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.10046     

Differences in attributes between color difference and color appearance (chroma and hue) for near‐neutral colors

Chroma‐step perception and its corresponding color difference in the same hue direction are the different attributes on color perception. The differences between them are different for different hues. Hue‐appearance step and its corresponding color difference along the same hue circle also have completely different concepts. The causes of the above two facts are clarified. The information based on various experiments and theoretical considerations are given for supporting the facts. In addition, it is clarified that the relationship on color‐appearance step and color difference has completely different characteristics between the quantitative (chroma) and the qualitative (hue) attributes of object colors. The importance of chromatic strength (CS) on hue is clarified in each of the three color attributes hue, value, and chroma. © 2004 Wiley Periodicals, Inc. Col Res Appl, 30, 42–52, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.20073     

What color do you feel? Color choices are driven by mood

Popular opinion holds that color has specific affective meaning. Brighter, more chromatic, and warm colors were conceptually linked to positive stimuli and darker, less chromatic, and cool colors to negative stimuli. Whether such systematic color associations exist with actually mood felt remains to be tested. We experimentally induced four moods—joy, relaxation, fear, and sadness—in a between‐subject design (N = 96). Subsequently, we asked participants to select a color, from an unrestricted sample, best representing their current mood. Color choices differed between moods on hue, lightness, and chroma. Yellow hues were systematically associated with joy while yellow‐green hues with relaxation. Lighter colors were matched to joy and relaxation (positive moods) than fear and sadness (negative moods). Most chromatic colors were matched to joy, then relaxation, fear, and sadness. We conclude that color choices represent felt mood to some extent, after accounting for a relatively low specificity for color‐mood associations.     

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     

Chromatic induction: Opponent color or complementary color process?

In present convention, chromatic induction (simultaneous and successive contrast) is usually held to be an opponent color process. Fifty years ago, it was an accepted complementary color process. The latter was never disputed yet apparently overlooked, and is here shown to be the more accurate account by inspecting afterimages and published data on simultaneous and successive hue induction. © 2007 Wiley Periodicals, Inc. Col Res Appl, 33, 77–81, 2008     

Color names,stimulus color,and their subjective links

The aim of the research reported by this study was on the one hand to identify what colors were associated with particular words in relation to a specific language (Italian), by portraying them in color stimuli on the screen of a monitor; and on the other hand to verify whether some words of that language denoted colors that were either particularly well defined or confused with others. In an experiment using special software, the subjects were asked to produce colors directly, instead of choosing among a number of colors presented on the screen. The results showed that (i) it is possible to identify the color‐stimuli to which the terms of a language refer; that (ii) the “best” colors Giallo (Yellow), Rosso (Red), Blu (Blue), and Verde (Green) which the subjects were requested to produce were very similar to the corresponding unique hues; that (iii) among the mixed hues there were perceptually intermediate colors, that is, ones exactly midway between two consecutive unique colors: Arancione (Orange) and Viola (bluish Purple); that (iv) Turquoise and Lime were clearly positioned in the mental space of color of the participants; and that (v) for Italian speakers some hues coincide: Azzurro (Azure) and Celeste (Cerulean); Arancione (Orange), RossoGiallo (RedYellow) and Carota (Carrot); Lime and GialloVerde (YellowGreen), so that their color terms can be considered synonyms. Our most interesting finding, however, is that for Italian speakers these four mixed colors with their specific names (Lime, Turchese (Turquoise), Viola (bluish Purple) and Arancione (Orange) fall perceptually in the middle of each of the four quadrants formed in the hue circle by the four unique hues. The resulting circle is therefore characterized by eight colors of which four are unique and four are intermediate mixed. It would be advisable to repeat the study cross‐culturally to test for possible similarities and differences in color meanings with speakers of different languages. © 2016 Wiley Periodicals, Inc. Col Res Appl, 42, 89–101, 2017     

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     

Experimental determination of laws of color harmony. Part 3: Harmony content of different hue pairs

At the Budapest University of Technology and Economics in 1956, we decided to start large‐scale experiments on color harmony. The experiments and the processing of the experimental data were completed in 2006. The experiments described in this article were based on a long established experience that harmony content of different hue pairs greatly differ from each other. The vast majority of former research activities on the subject of color harmony narrowed down mostly to investigations of saturated color pairs. Color samples of our experiments have been defined within the color space of the Coloroid color system, built on harmony thresholds. The compositions, prepared for the experiments, always consisted of two saturated hues and three low saturation colors of each hue at varying brightness, making it a total of eight colors. Within the framework of the experiments, 48 hues were used. Out of these, each of the 24 was formed into composition pairs with the remaining 48 hues, forming a total of 852 compositions. The paired‐comparison experiments were conducted with the use of the compositions prepared by collage technique. Color samples made of painted paper, between 1980 and 1985, have been repeated between 2002 and 2006 with the same color selection but with computer‐generated pseudorandom patch system compositions. It has been established that harmony content of hue pairs can be expressed by the relative angle of their hue planes in the Coloroid color space. The harmony content of hue pairs exceeds that of other pairs, when this angle is below 10°, between 30° and 40°, between 130° and 140° or near to 180°. Those color pairs of which hue planes are between 60° and 90° to each other in Coloroid color space, exhibit the least harmony content. © 2008 Wiley Periodicals, Inc. Col Res Appl, 34, 33–44, 2009.     

Experimental determination of laws of color harmony. Part 5: The harmony content of the various hue triads

We, in 1956 the Department of Architecture at the Budapest University of Technology and Economics, decided to start an extensive color harmony experiment. The experimental work, the collation, and processing of the collected data, lasting 50 years, was completed in 2006. The experiments described in this article are based on earlier experimental results obtained from investigation into the harmony content of hue pairs. We then decided to search for a third hue, which in association with an existing pair, with high‐color harmony, forms a hue triad with high‐harmony content too. The compositions prepared for the experiment were composed in each case of three hues of four identical saturation but different brightness, forming a group of 12 colors. The color content of the compositions covered the color space uniformly. That was the first stage in the experiment, carried out with 60 compositions. In the second stage, we investigated the effect of the saturation content of the colors used in the composition, on the harmony content of the hue triads. For this experiment, we prepared 48 compositions. In these experiments, we applied the method of grading. We concluded that the level of the harmony content of the hue triads depends on the inclination between the hue planes in the Coloroid color space. We also concluded that to every hue, selected for starting point, six well‐definable groups of hues can be ordered from the Coloroid color space, from which color triads with high harmony content, can be selected. It showed conclusively that the saturation level of the individual members of the triads has a significant influence on their harmony content. © 2010 Wiley Periodicals, Inc. Col Res Appl, 2011     

Chromatic luminance,colorimetric purity,and optimal aperture‐color stimuli

Chromatic luminance (i.e., luminance of a monochromatic color) is the source of all luminance, since achromatic luminance arises only from mixing colors and their chromatic luminances. The ratio of chromatic luminance to total luminance (i.e., chromatic plus achromatic luminance) is known as colorimetric purity, and its measurement has long been problematic for nonspectral hues. Colorimetric purity (p_c) is a luminance metric in contrast to excitation purity, which is a chromaticity‐diagram metric approximating saturation. The CIE definition of p_c contains a fallacy. CIE defines maximum (1.0) p_c for spectral stimuli as monochromatic (i.e., optimal) stimuli, and as the line between spectrum ends for nonspectrals. However, this line has <0.003 lm/W according to CIE colorimetric data and is therefore effectively invisible. It only represents the limit of theoretically attainable colors, and is of no practical use in color reproduction or color appearance. Required is a locus giving optimal rather than invisible nonspectral stimuli. The problem is partly semantic. CIE wisely adopted the term colorimetric purity, rather than the original spectral luminance purity, to permit an equivalent metric for spectrals and nonspectrals, but the parameter of equivalence was never clear. Since 1 p_c denotes optimal aperture‐color stimuli for spectrals, arguably 1 p_c should denote optimal stimuli consistently for all stimuli. The problem reduces to calculating optimal aperture‐color stimuli (“optimal” in energy efficiency in color‐matching) for nonspectrals, shown to comprise 442 + 613 nm in all CIE illuminants. This remedy merely requires redefinition of 1 p_c for nonspectrals as the line 442–613 nm, and gives meaningful p_c values over the hue cycle allowing new research of chromatic luminance relations with color appearance. © 2007 Wiley Periodicals, Inc. Col Res Appl, 32, 469–476, 2007     

Proposal of an opponent‐colors system based on color‐appearance and color‐vision studies

A new theoretical color order system is proposed on the basis of various studies on color appearance and color vision. It has three orthogonal opponent‐colors axes and an improved chromatic strength of each hue. The system has color attributes whiteness w, blackness bk, grayness gr, chroma C, and hue H. A method is given for determining Munsell notations of any colors on any equi‐hue planes in the system. A method is also given for determining grayness regions and grayness values on hue‐chroma planes in the system. It is concluded that colors with the same color attributes [w, gr, bk, C] but with different hues in the theoretical space have approximately the same perceived lightness, the same degree of vividness (“azayakasa” in Japanese), and also the same color tone. The tone concept, for example used in the Practical Color Coordinate System (PCCS), is clarified perceptually. The proposed system is a basic and latent color‐order system to PCCS. In addition, the concept of veiling grayness by a pure color with any hue is introduced. Further, relationships are clarified between generalized chroma c(gen) and grayness. © 2004 Wiley Periodicals, Inc. Col Res Appl, 29, 135–150, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.10234     

Color appearance of afterimages compared to the chromatic adaptation to illumination

The color appearance of negative afterimages was measured by the elementary color naming method, and the results were compared with those obtained by the two‐room technique. Twenty adapting stimuli were presented on a display sequentially. Subjects first assessed the color appearance of the stimuli. After looking at the adapting stimulus for 10 seconds, the subjects assessed color of the afterimage. Apparent hue of the afterimage was in general not opponent color to the adapting color. The relation between the adapting stimuli and the afterimages was analyzed by the angle difference Δθ, when apparent hues are expressed by the angles of the points on the polar diagram of the opponent color theory. The relation relationship of Δθ to the angle of the adapting color θ_ing was quite similar to the results obtained by the two‐room technique, implying that the chromatic adaptation shown by the afterimage also occurs in the brain rather than in the retina.     

Hue cycle described by graphs and color names

The color appearance of the hue cycle in equal radiance is described in hue, saturation, and brightness/lightness. The latter does not resemble CIE luminance Y (peaking at 555 nm green), but peaks near 570 nm yellow with minor peaks near 490 nm cyan and 530 c magenta. Saturation per watt peaks near 450, 530, 610 nm (blue, green, red). Newton's choice of seven spectrum colors, and particularly his two bluish colors, is explained as major colors rather than merely different hues.