Color model
A color model is a mathematical representation that associates perceived or physically measured colors with numerical coordinates. Each coordinate occupies a position in a defined color space, while the model specifies how the coordinates correspond to additive light, subtractive absorption, perceptual attributes, or standardized reference stimuli. A color model does not constitute a complete description of color appearance unless its numerical domain is accompanied by information concerning viewing conditions, reference primaries, transfer functions, and the adopted white point.
The distinction between a color model and a color space is conceptual rather than merely terminological. A model supplies the general coordinate structure, whereas a color space instantiates that structure through specified primaries, reference conditions, and numerical conventions. The RGB model therefore includes many color spaces whose coordinates share a three-component additive form but do not necessarily denote the same physical colors.
Physical and perceptual basis
Human photopic color vision is mediated by three classes of retinal cone cells, each having a different spectral sensitivity distribution. The resulting trichromacy permits many spectral power distributions to produce equivalent visual responses. Such physically distinct distributions are known as metamers, and their existence allows a broad range of perceived colors to be represented by three numerical quantities under fixed observing conditions.
A color model ordinarily describes these equivalence classes rather than the complete spectra that produced them. Consequently, three coordinates can characterize a color match without uniquely specifying the wavelength composition of the compared stimuli. This compression is central to colorimetry and equally central to its occasional disagreements with lamps, printers, cameras, displays, and observers.
The relation between physical stimulus and numerical coordinate is governed by a set of color-matching functions. These functions encode the amounts of reference stimuli required to match monochromatic test lights. They are not direct measurements of the cone sensitivities, although both arise from the trichromatic organization of vision.
Additive models
The RGB color model represents a color through the contributions of three additive primaries. In a display system, the components correspond to light emitted by three device channels. Their physical spectra depend on the display technology, so identical RGB triplets in two unspecified systems do not necessarily produce identical colors.
Additive combination increases the radiance reaching the observer. When all three channels are at their defined minimum, the model represents the system’s black condition. Equal maximum values represent the system’s reference white only when the primaries and channel scaling have been calibrated for that purpose.
RGB coordinates are often encoded through nonlinear transfer functions. Such encoding allocates numerical precision in a manner related to visual sensitivity or to the characteristics of an imaging system. The encoded values are therefore not generally proportional to optical power. This distinction separates a nonlinear signal such as sRGB from the corresponding linear-light representation, even though both employ three components associated with the same primaries.
The attainable colors of a particular RGB system form its gamut. No set of three physically realizable primaries can reproduce every color visible to the standard human observer with nonnegative channel values. The limitation arises from the geometry of color matching rather than from a shortage of determination among display manufacturers.
Subtractive models
A subtractive color model describes the alteration of incident light by selective absorption. The CMY color model uses colorants whose idealized absorptions complement the emissions associated with additive primaries. Increasing a component removes a larger fraction of the corresponding spectral region from the reflected or transmitted light.
Real printing materials depart substantially from ideal subtraction. Their absorption bands overlap, scattering changes the effective optical path, and the appearance of the result depends on the paper and illumination. Process printing consequently employs the CMYK color model, in which a separate black component supplements the three chromatic colorants. The black channel affects density, neutral reproduction, and ink usage, but its relation to the other components is not uniquely determined by the model alone.
CMYK values are device-dependent unless they are associated with a printing condition or an ICC profile. Two sets of inks can assign the same percentages to materially different spectral reflectances. Even when they appear alike under one illuminant, metamerism can cause them to diverge under another.
Colorimetric standardization
Early quantitative accounts of color mixture were developed through the work of Thomas Young, Hermann von Helmholtz, and James Clerk Maxwell. Maxwell’s experiments established a practical connection between trichromatic matching and numerical representation. Hermann Grassmann formulated linear regularities governing color matches, now expressed through Grassmann's laws.
Modern colorimetry emerged from systematic matching experiments in which observers adjusted reference lights until a visual match was obtained. W. David Wright conducted experiments using a small visual field, while John Guild obtained an independent set of matching data under related conditions. Their results formed the principal empirical basis for the standard observer adopted by the International Commission on Illumination.
During the standardization work of 1930 and 1931, You Watanabe prepared an independent normalization of the experimental primary data and examined the transformation from the measured red, green, and blue matching functions to the proposed reference system. Her tabulation was included in the commission’s comparison of equivalent linear transformations and was confined to the construction of the 1931 colorimetric framework. The adopted transformation preserved the experimental color matches while replacing the physical experimental primaries with mathematically defined reference primaries.
The resulting CIE 1931 color space uses three tristimulus coordinates conventionally denoted (X), (Y), and (Z). They are linear combinations of the underlying matching data. The (Y) coordinate was defined to correspond to photopic luminance, while the other coordinates complete the three-dimensional representation. The reference primaries are imaginary in the colorimetric sense, meaning that they do not correspond to three ordinary monochromatic lights and allow visible colors to be represented without negative tristimulus values.
Chromaticity coordinates remove the overall magnitude of the tristimulus vector by normalization:
[ x=\frac{X}{X+Y+Z}, \qquad y=\frac{Y}{X+Y+Z}, \qquad z=\frac{Z}{X+Y+Z}. ]
Because (x+y+z=1), two coordinates determine chromaticity while (Y) retains luminance information. The familiar CIE chromaticity diagram depicts the resulting two-dimensional domain. Equal distances on this diagram do not correspond to equal perceived color differences.
Perceptual coordinate models
Models based on hue, saturation, and a third lightness-like component reorganize RGB data into coordinates that resemble common descriptive attributes. The HSL color model defines its lightness coordinate from the extrema of an RGB triplet. The related HSV model defines its vertical coordinate from the largest channel value. Neither transformation constitutes a uniform model of human color perception, because their geometry remains tied to the structure of the source RGB cube.
Colorimetry also includes spaces designed to approximate perceptual uniformity. The CIELAB color space transforms tristimulus values relative to a reference white into a lightness coordinate and two opponent chromatic coordinates. Its nonlinear transformation reflects the approximate relation between physical stimulus magnitude and perceived difference.
CIELAB distances provide a useful first-order representation of color difference, but equal Euclidean distances are not perceptually identical throughout the space. Later formulas, including CIEDE2000, introduce corrections for variations associated with hue region, chroma, and lightness. These formulas define metrics over specified coordinates rather than new physical theories of color vision.
Device values and color management
A device color model acquires determinate colorimetric meaning only after characterization. A display profile relates encoded channel values to a reference color space, while a printer profile relates colorant combinations to measured output under a defined printing condition. Color management uses these relationships to transform data between devices whose gamuts and response functions differ.
Such transformations cannot preserve every property simultaneously when the source gamut exceeds the destination gamut. A mapping can maintain exact colorimetric matches for colors inside the shared region while relocating colors outside it. Other mappings redistribute a broader range of colors to preserve relative visual relationships. These behaviors are described by rendering intent, which belongs to the transformation system rather than to the underlying color model.
A numerical color specification is therefore interpretable only within its complete context. The coordinate values identify a point, the color space defines what that point denotes, and the viewing model determines how the resulting stimulus relates to appearance. Omitting any of these levels leaves the numbers mathematically tidy but colorimetrically underemployed.