|Rolf Kuehni (2010), Scholarpedia, 5(3):9606.
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Color spaces (a colloquial term) are usually three-dimensional geometric constructs in which points representing colors or color stimuli are arranged according to some principle, forming solids.
Colors are, in the normal case, the result of the absorption of light stimuli by the eye’s retina, processing of the resulting electrochemical signals in the eye and the brain, and conversion to conscious experiences. Color stimuli are lights, either directly viewed from the source or reflected from objects in the path of lights (see also Color vision). The process by which we see color is referred to as color perception.
1. Perceptual spaces
Object colorsMost of the colors we experience are connected to materials, so-called object colors. They can be divided into a minor and a major group (Fig. 1).
‘’’Hue’’’: qualitative indicator of the chromatic nature of the color; its range is the hue circle. ‘’’Chroma’ or 'saturation' or 'colorfulness'’’: indicator of the amounts of chromatic perceptual primaries; range: at a given level of lightness, from just beyond the achromatic color to pure chromatic primaries or mixtures of pairs of neighboring primaries. ‘’’Lightness’ or 'value'’’: indicator of the relative amount of perceived whiteness; range: from black to white. All three attributes are continuous in nature. They can serve as dimensions of a three-dimensional geometric ordering system, with members of the attribute hue forming a circle.
The origin of the perceptual characteristics of hues remains a mystery. However, it is well established that there are four fundamental hue percepts: yellow, red, blue, and green, all other existing hues being mixtures of pairs of neighboring fundamentals. This is evident from the fact, already pointed out by Ewald Hering, that color-normal subjects have no problem perceiving, for example, yellowness and redness in orange but they do not perceive orangeness and purpleness in red.
The natural sequence of hues in a circle is implicit in a logically complete series of idealized reflectance functions and the response of the three cone types to light reflected from them. Hues of spectral lights represent only some 75% of the hues of the complete hue circle, the remainder being bluish reds and purples not present in the spectrum but originating from the combination of short- with long-wavelength light. Wavelength is not a convenient scale of hue.
Hues may be quantified either by judgment of the color difference between neighboring samples (Munsell) or by perceptual scaling of the content in “percentage” of chromatic primaries (Hering/NCS). Chromatic primaries have unique hues, defined by the absence of neighboring unique hue percepts: e.g., unique blue is perceived as having neither a reddish nor a greenish cast, and comparably for the other three unique hues. Except under unusual experimental conditions, there are two opponent pairs of unique hues: yellow-blue and red-green; no greenness can be perceived in a red color and vice versa; the same applies to the yellow-blue pair.
In the Munsell system the hue scales are not related to the concept of unique hues and thus its perceptual chromatic diagram does not have fundamentally meaningful Cartesian axes, such as those of Hering’s hue circle, where the axes represent redness-greenness and yellowness-blueness. When the locations of its four unique hues, separated by 90º in its chromatic diagram, are transferred into the perceptual difference diagrams of eight experiments of hue scaling by perceived difference, angular distances between them have been found to range from 63º (yellow – red) to 126º (red – blue), indicating that a perceptual difference-based hue scale and a unique hue increment-based one differ significantly.
Lightness and saturation (chroma) scales
Perceptual lightness scales are gray scales, i.e., scales consisting of grays of various lightness or darkness between white and black, established under a given set of experimental conditions. Estimates of the relationship between perceived lightness of gray and of chromatic samples vary considerably among observers. They also depend significantly on the lightness of the surround, with the perceived difference between two samples experienced as largest if the lightness of the surround color falls between those of the samples (lightness crispening effect). Thus, there is no universally applicable lightness scale.
In the Munsell system perceived lightness, called ‘value’, is the magnitude represented by the third, vertical axis and is taken to apply throughout the complete system. (But perceptual lightness of chromatic colors is not fully expressed by the Munsell Value scale because it does not consider the Helmholtz-Kohlrausch effect, the magnitude of which varies according to hue and chroma.) In the Hering/NCS system lightness only applies to the central vertical gray scale but not to chromatic colors because full colors, located on the same plane in the system, considerably differ in lightness and whiteness/blackness content is related to lightness in a complex way that depends on hue.
In the Hering/NCS system the measure of intensity of chromatic color is an indirect outcome of the scaling of full color, whiteness, and blackness content, not separately assessed as in the Munsell system. In that system chromatic intensity is named ‘chroma’, measured at the different lightness levels by the radial distance from the central lightness axis.
Absolute and relative attribute scales
In the Munsell system all three attributes are expressed in separately absolute terms: the hue scale is a circle encompassing all possible hues; the lightness scale ranges from zero (black) to 10 (white) and is applicable to all samples of the system; the chroma scale is limited by what is known as optimal colors, defined below, differing in maximal value as a function of hue and lightness. The resulting solid has a cylindrical structure of irregular form with samples ordered according to hue (circle), lightness (vertical) and chroma (horizontal)(Fig. 2). Figure 3 shows a constant hue page.
The Hering/NCS solid, on the other hand, is a double cone, formed by arbitrarily placing a full color, black, and white at the corners of an equilateral triangle, thought to contain all colors of the hue of the full color, and arranging all triangles so that their gray scales coincide (Fig. 4). Thus, there is the assumption that all full colors have the same chromatic intensity and this scale is thereby relative. The relationship between its lightness scale and the colors of a constant hue plane (Fig. 5) varies according to hue.
Optimal color stimuli
The form of the geometric solid containing all possible object colors is a function of natural limits on color stimuli, to be discussed in section 2. For reflecting objects the amount of light reflected at each wavelength can vary from 0 (no light reflected) to 1 (all incoming light reflected). Optimal color stimuli are theoretical limiting cases, reflecting zero light at some wavelengths of the spectrum and all light at others. They differ according to hue and level of lightness and, in totality, represent the surface of a solid encompassing all possible object color percepts. The irregular form of the perceptual Munsell color solid, extended by extrapolation to the optimal object color stimulus limit, is shown in Figs. 6 and 7.
Perceptual uniformity: by attribute or isotropic
The internal structure of a constant hue plane in the Hering/NCS system is uniform according to judgments of full color, white, and black content. However, the geometric distances between full colors are largest, while those of veiled (grayish) colors become gradually smaller in a simple geometric fashion that is not the result of perceptual scaling but of the imposition of the geometric model on perceptual results.
In the Munsell system, the unit differences of the three attributes are of arbitrarily different magnitude. In addition, the hue spacing also suffers from the imposition of the Euclidean geometric model.Logically, it would be desirable to develop an isotropic color solid in which color differences from any point in the solid to any other on a sphere around the reference point would be of equal perceived magnitude. In this manner all possible object color percepts would be ordered according to a uniform principle. However, a solid of this kind is impossible because a spatial solid cannot be filled uniformly by spheres without empty spaces between them or overlaps. Geometry teaches that the most complex solid with which a larger space can be filled without gaps is the cubo-octahedron (Fig. 8).
An additional complication is the hue superimportance effect: Analysis of the Munsell system indicated the surprising fact that if the perceptual hue and chroma scales are normalized, to be in geometric agreement the circumference of a hue circle needs to be approximately twice its actual length, implying that the visual system is about twice as sensitive to hue differences as to chroma differences. This is a universal fact for natural viewing conditions of samples, applying to perceptual differences from threshold to large differences and expresses itself by unit difference contours being ellipses in two and ellipsoids in three dimensions of Euclidean space. The major axis of the chromatic ellipses are essentially radially aligned. Thus, it is impossible without complex mathematical methodology (line element integration) to represent even the limited uniformity of the cubo-octahedron in Euclidean geometry. Instead, a Riemannian space (positively curved) is required. The mechanism by which the brain favors the perception of stimulus differences interpreted as hue differences is not known at this time.
2. Color stimulus spaces
In the normal case, colors are the result of interaction of light stimuli with the retinal cells of the eye. Spectral stimuli can be very complex but there are only three kinds of sensors in the eye responsible for color vision. An important result is that many different spectral stimuli, known as metamers, can be the basis of the same perceived color. In addition, as indicated above for the hue superimportance effect, there are a number of neurological processes, presumably developed by evolution, which complicate the relationship between stimulus and percept. It is now abundantly clear that colors are not determined in the retina alone, but there are additional processes in the brain shaping the relationship between stimulus and perceptual experience, the process details and location in the brain often as yet unknown.
On the other hand, color stimuli can be measured with good accuracy in form of radiometric functions of lights or transmittance and reflectance functions of objects. The results can be represented in spaces mathematically generated from the spectral functions alone, or more realistically, in spaces representing the stimuli as absorbed by normalized retinal sensors, the cone functions, functions linearly related to them, such as the International Commission on Illumination (CIE) color matching functions, or other related kinds of functions. Optimal object color stimulus solids can easily be calculated with high accuracy. The structure of the related spaces predicts if two spectral stimuli will match for the standard observer reflected in the sensor functions, but there is nothing that directly predicts attributes of the resulting color experience, perceived distances between two colors, or the shape of the optimal object color solid.
Optimal object color stimulus solid in cone spaceThe axes of the space represent normalized versions of standard sensitivities of the three cone types L, M, and S (standing for long, medium, and short wavelength sensitivity, see article Color Vision for graphical representation of the functions). Figure 9
“Cardinal directions” space (DKL space)Discovery of cells with opponent-color character in the lateral geniculate nuclei (LGN) of rhesus monkeys resulted in the formulation of a neurobiologically based spherical color stimulus solid, with its vertical axis representing luminance as expressed by the sum of the output of L and M cone classes. Its chromatic axes represent constant L+M (R+G) values and constant S (B) values (Fig. 10).
Optimal object color stimulus solid raised over the CIE chromaticity diagram: the Rösch-MacAdam solidA linearly related version of the cone space solid, it is raised over the chromaticity diagram in the CIE x,y,Y space where the lower case letters refer to chromaticity coordinates (relative amounts of tristimulus values X and Y) and Y refers to luminous reflectance (Fig. 11).
Optimal object color stimulus solid in the canonical form of the opponent-color spaceIn its canonical form a space has axes that represent components maximally independent of each other, the axes being orthonormal. The mathematical process to achieve the relevant transformation of cone or color matching functions is ‘singular value decomposition.’ The resulting chromatic functions bear some resemblance to response functions in the LGN, but the third function is much different from the lightness function. Figure 12
All four kinds of stimulus spaces represent the same fundamental data of object color reflectance or transmittance, illuminating light, and standard observer in linearly related form. In each space the shape of the solid differs more or less as a function of the spectral composition of the illuminating light. The relationship between a perceptual solid and any of the stimulus solids is at most of the ordinal kind.
Technically important color stimulus solids are the RGB cube implemented in electronic displays such as color television, computer monitors, and various encoding schemes such as ProPhotoRGB and sRGB, as well as the CMYK (cyan, magenta, yellow, black) solid of the conventional halftone printing process. In the former case the axes represent the three primary light stimuli used in the display units, light bands from the beginning, middle, and end of the spectrum, in the latter case the degree of coverage of white paper with the three primary printing inks. As a result, not all possible stimuli are represented in either of them. In conventional monitors each pixel of the screen can display the lights in relative amounts from 0 to 255 units. Thus, the total possible number of different stimuli is 2563 or approximately 16 million. New monitor types with higher resolution (10 bits) can display even more stimuli. For each display pixel the three separate stimuli are additively mixed in the eye because they cannot be independently detected. Perhaps less than a third of the stimuli are distinguishable. The situation is more complex in case of halftone printing because there is often a substantial overlap of printed dots and the colorants more or less transparent. Here, the number of possible different stimuli is much more limited.
3. Psychophysical models of perceptual solids
The appearance of a colored object (a color chip) can depend strongly on the spectral nature of its reflectance function, on the spectral power distribution of the light in which it is viewed, on the chromatic nature and lightness of the surround, and on the performance of the color vision system of the observer. All but the last can be controlled and objectively specified. To provide a semi-objective basis a number of color space models of various degrees of complexity have been developed.
Line element models
These are mathematical models implementing various ideas about the relationship between increments of color stimuli as absorbed by cones with standard sensitivity and perceived differences. Best known among these are Stiles’s of 1946 and MacAdam’s empirical line element of 1942. However, for various reasons such line elements have not been found to represent perceived differences with good reliability.
Simple Euclidean opponent-color model with signal compression, CIELAB space
The model is based on a simplified lightness scale and an opponent-color model in which compressed normalized CIE tristimulus values are subtracted from each other. The compression power applied to all three scales is cube root. CIE 1976 ‘’L*a*b’’ or CIELAB is the basis of a number of color difference formulas that make it possible to predict average perceived color differences between object color stimuli. In CIELAB space perceptually uniform solids are represented by ellipsoids with the major axis of the chromatic ellipse aligned radially. As a result, several adjustment factors are necessary to correctly represent hue superimportance and a number of other variables. Figure 13 shows a projective view of the optimal object color stimulus solid in CIELAB space.
Appearance model-based Euclidean uniform color solid
In recent years complex mathematical models that predict the appearance of stimuli based on specific conditions of lighting and surround have been developed, among them IPT and CIECAM02, the latter recommended by the CIE. The implicit spaces are Euclidean, with separate multiple variables to account for various perceptual effects. As mentioned, it is possible to mathematically transform the basic space and the variables into Euclidean solids so that some of the appearance effects, such as constancy of hue along a radial line and the hue superimportance effect, are closely represented within the Euclidean model. Figure 14 is a projective view of the optimal object color stimulus solid in the Euclidean space represented by the IPT color appearance model. The difference between this solid and that of the canonical stimulus solid (Fig. 12) and the resemblance between it and the Munsell perceptual solid (Fig. 7) is clearly apparent.
4. Color atlases
Color atlases are collections of color samples that when viewed in the appropriate light by a color-normal individual, are taken to result in specific color experiences. The samples are selected in a manner that represents the concept behind the system and the atlas. Atlases can be based on forms of average perceptual distance, such as the Munsell and NCS systems mentioned earlier, on stimulus increments, such as regular changes in colorant concentrations, on “esthetic increments,” on product marketing concepts, or on other ideas.
There are a number of problems associated with atlases. Their production requires standard colorants and production methods. Both are inherently variable and the actual samples in the atlas or on the screen will differ to a degree from the intended samples. The colorants of atlases will slowly degrade and samples can be stained by use. Atlases can be viewed in different lighting and surrounds affecting the perceived results. Given our inability to objectively describe what we experience when viewing a sample, the degree to which the perceptions of different individuals when viewing a given sample agree or disagree is not known. Color atlases serve important purposes in regard to communication about color, as well as semi-objective description and tolerance setting.
G. Wyszecki and W. S. Stiles, Color Science, 2nd ed. New York: Wiley, 1982, Chapter 6, Uniform color scales.
D. H. Brainard, Color appearance and color difference specification, Chapter 5, in S. K. Shevell (ed.) The science of color, 2nd ed. Amsterdam: Elsevier, 2003.
R. S. Berns, Billmeyer and Saltzman’s Principles of color technology, 3rd ed. New York: Wiley, 2000, Chapter 2, Describing color.
R. G. Kuehni, Color space and its divisions, Hoboken, NJ: Wiley, 2003.
R. G. Kuehni and A. Schwarz, Color ordered, New York: Oxford University Press, 2008.