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The CIE 1931 color spaces are the first defined quantitative links between distributions of wavelengths in the electromagnetic
visible spectrum The visible spectrum is the portion of the electromagnetic spectrum that is visual perception, visible to the human eye. Electromagnetic radiation in this range of wavelengths is called ''visible light'' or simply light. A typical human eye wil ...
, and physiologically perceived colors in human
color vision Color vision, a feature of visual perception, is an ability to perceive differences between light composed of different wavelengths (i.e., different spectral power distributions) independently of light intensity. Color perception is a part of ...
. The mathematical relationships that define these
color space A color space is a specific organization of colors. In combination with color profiling supported by various physical devices, it supports reproducible representations of colorwhether such representation entails an analog or a digital represent ...
s are essential tools for
color management In digital imaging systems, color management (or colour management) is the controlled conversion between the color representations of various devices, such as image scanners, digital cameras, monitors, TV screens, film printers, computer printer ...
, important when dealing with color inks, illuminated displays, and recording devices such as digital cameras. The system was designed in 1931 by the ''"Commission Internationale de l'éclairage"'', known in English as the
International Commission on Illumination The International Commission on Illumination (usually abbreviated CIE for its French name, Commission internationale de l'éclairage) is the international authority on light, illumination, colour, and colour spaces. It was established in 1913 a ...
. The CIE 1931 RGB color space and CIE 1931 XYZ color space were created by the
International Commission on Illumination The International Commission on Illumination (usually abbreviated CIE for its French name, Commission internationale de l'éclairage) is the international authority on light, illumination, colour, and colour spaces. It was established in 1913 a ...
(CIE) in 1931. They resulted from a series of experiments done in the late 1920s by William David Wright using ten observers and John Guild using seven observers. The experimental results were combined into the specification of the CIE RGB color space, from which the CIE XYZ color space was derived. The CIE 1931 color spaces are still widely used, as is the 1976
CIELUV In colorimetry, the CIE 1976 ''L''*, ''u''*, ''v''* color space, commonly known by its abbreviation CIELUV, is a color space adopted by the International Commission on Illumination (CIE) in 1976, as a simple-to-compute transformation of the 1931 CI ...
color space.


Tristimulus values

The
human eye The human eye is a sensory organ, part of the sensory nervous system, that reacts to visible light and allows humans to use visual information for various purposes including seeing things, keeping balance, and maintaining circadian rhythm. ...
with normal vision has three kinds of
cone cells Cone cells, or cones, are photoreceptor cells in the retinas of vertebrate eyes including the human eye. They respond differently to light of different wavelengths, and the combination of their responses is responsible for color vision. Cones ...
that sense light, having peaks of
spectral sensitivity Spectral sensitivity is the relative efficiency of detection, of light or other signal, as a function of the frequency or wavelength of the signal. In visual neuroscience, spectral sensitivity is used to describe the different characteristics o ...
in short ("S", – ), middle ("M", – ), and long ("L", – ) wavelengths. These cone cells underlie human color perception in conditions of medium and high brightness; in very dim light
color vision Color vision, a feature of visual perception, is an ability to perceive differences between light composed of different wavelengths (i.e., different spectral power distributions) independently of light intensity. Color perception is a part of ...
diminishes, and the low-brightness, monochromatic "night vision" receptors, denominated "
rod cells Rod cells are photoreceptor cells in the retina of the eye that can function in lower light better than the other type of visual photoreceptor, cone cells. Rods are usually found concentrated at the outer edges of the retina and are used in per ...
", become effective. Thus, three parameters corresponding to levels of stimulus of the three kinds of cone cells, in principle describe any human color sensation. Weighting a total light power spectrum by the individual spectral sensitivities of the three kinds of cone cells renders three effective values of
stimulus A stimulus is something that causes a physiological response. It may refer to: *Stimulation **Stimulus (physiology), something external that influences an activity **Stimulus (psychology), a concept in behaviorism and perception *Stimulus (economi ...
; these three values compose a tristimulus specification of the objective color of the light spectrum. The three parameters, denoted "S", "M", and "L", are indicated using a
3-dimensional Three-dimensional space (also: 3D space, 3-space or, rarely, tri-dimensional space) is a geometric setting in which three values (called ''parameters'') are required to determine the position of an element (i.e., point). This is the informal ...
space denominated the "
LMS color space LMS (long, medium, short), is a color space which represents the response of the three types of cones of the human eye, named for their responsivity (sensitivity) peaks at long, medium, and short wavelengths. The numerical range is generally n ...
", which is one of many color spaces devised to quantify human
color vision Color vision, a feature of visual perception, is an ability to perceive differences between light composed of different wavelengths (i.e., different spectral power distributions) independently of light intensity. Color perception is a part of ...
. A color space maps a range of physically produced colors from mixed light,
pigment A pigment is a colored material that is completely or nearly insoluble in water. In contrast, dyes are typically soluble, at least at some stage in their use. Generally dyes are often organic compounds whereas pigments are often inorganic compo ...
s, etc. to an objective description of color sensations registered in the human eye, typically in terms of tristimulus values, but not usually in the
LMS color space LMS (long, medium, short), is a color space which represents the response of the three types of cones of the human eye, named for their responsivity (sensitivity) peaks at long, medium, and short wavelengths. The numerical range is generally n ...
defined by the spectral sensitivities of the
cone cells Cone cells, or cones, are photoreceptor cells in the retinas of vertebrate eyes including the human eye. They respond differently to light of different wavelengths, and the combination of their responses is responsible for color vision. Cones ...
. The tristimulus values associated with a color space can be conceptualized as amounts of three
primary color A set (mathematics), set of primary colors or primary colours (see American and British English spelling differences#-our, -or, spelling differences) consists of colorants or colored lights that can be mixed in varying amounts to produce a gamu ...
s in a tri-chromatic,
additive Additive may refer to: Mathematics * Additive function, a function in number theory * Additive map, a function that preserves the addition operation * Additive set-functionn see Sigma additivity * Additive category, a preadditive category with f ...
color model A color model is an abstract mathematical model describing the way colors can be represented as tuples of numbers, typically as three or four values or color components. When this model is associated with a precise description of how the compon ...
. In some color spaces, including the LMS and XYZ spaces, the primary colors used are not real colors in the sense that they cannot be generated in any light spectrum. The CIE XYZ color space encompasses all color sensations that are visible to a person with average eyesight. That is why CIE XYZ (Tristimulus values) is a device-invariant representation of color. It serves as a standard reference against which many other color spaces are defined. A set of color-matching functions, like the spectral sensitivity curves of the
LMS color space LMS (long, medium, short), is a color space which represents the response of the three types of cones of the human eye, named for their responsivity (sensitivity) peaks at long, medium, and short wavelengths. The numerical range is generally n ...
, but not restricted to non-negative sensitivities, associates physically produced light spectra with specific tristimulus values. Consider two light sources composed of different mixtures of various wavelengths. Such light sources may appear to be the same color; this effect is called " metamerism." Such light sources have the same apparent color to an observer when they produce the same tristimulus values, regardless of the
spectral power distribution In radiometry, photometry, and color science, a spectral power distribution (SPD) measurement describes the power per unit area per unit wavelength of an illumination (radiant exitance). More generally, the term ''spectral power distribution'' ...
s of the sources. Most wavelengths stimulate two or all three kinds of
cone cell Cone cells, or cones, are photoreceptor cells in the retinas of vertebrate eyes including the human eye. They respond differently to light of different wavelengths, and the combination of their responses is responsible for color vision. Cone ...
because the spectral sensitivity curves of the three kinds overlap. Certain tristimulus values are thus physically impossible: e.g. LMS tristimulus values that are non-zero for the M component and zero for both the L and S components. Furthermore pure spectral colors would, in any normal trichromatic additive color space, e.g., the
RGB color space An RGB color space is any additive color space based on the RGB color model. An RGB color space is defined by chromaticity coordinates of the red, green, and blue additive primaries, the white point which is usually a standard illuminant, and t ...
s, imply negative values for at least one of the three
primaries Primary elections, or direct primary are a voting process by which voters can indicate their preference for their party's candidate, or a candidate in general, in an upcoming general election, local election, or by-election. Depending on the c ...
because the
chromaticity Chromaticity is an objective specification of the quality of a color regardless of its luminance. Chromaticity consists of two independent parameters, often specified as hue (h) and colorfulness (s), where the latter is alternatively called ...
would be outside the
color triangle A color triangle is an arrangement of colors within a triangle, based on the additive combination of three primary colors at its corners. An additive color space defined by three primary colors has a chromaticity gamut that is a color trian ...
defined by the primary colors. To avoid these negative RGB values, and to have one component that describes the perceived
brightness Brightness is an attribute of visual perception in which a source appears to be radiating or reflecting light. In other words, brightness is the perception elicited by the luminance of a visual target. The perception is not linear to luminance, ...
, "imaginary" primary colors and corresponding color-matching functions were formulated. The CIE 1931 color space defines the resulting tristimulus values, in which they are denoted by "X", "Y", and "Z". In XYZ space, all combinations of non-negative coordinates are meaningful, but many, such as the primary locations , 0, 0 , 1, 0 and , 0, 1 correspond to
imaginary color Impossible colors are colors that do not appear in ordinary visual functioning. Different color theories suggest different hypothetical colors that humans are incapable of perceiving for one reason or another, and fictional colors are rou ...
s outside the space of possible LMS coordinates; imaginary colors do not correspond to any spectral distribution of wavelengths and therefore have no physical reality.


Meaning of ''X'', ''Y'' and ''Z''

In the CIE 1931 model, ''Y'' is the
luminance Luminance is a photometric measure of the luminous intensity per unit area of light travelling in a given direction. It describes the amount of light that passes through, is emitted from, or is reflected from a particular area, and falls withi ...
, ''Z'' is quasi-equal to blue (of CIE RGB), and ''X'' is a mix of the three CIE RGB curves chosen to be nonnegative (see ). Setting ''Y'' as luminance has the useful result that for any given ''Y'' value, the XZ plane will contain all possible chromaticities at that luminance. The unit of the tristimulus values , , and is often arbitrarily chosen so that or is the brightest white that a color display supports. In this case, the Y value is known as the
relative luminance Relative luminance Y follows the photometric definition of luminance L including spectral weighting for human vision, but while luminance L is a measure of light in units such as cd/m^2, Relative luminance Y values are normalized as 0.0 to 1.0 ...
. The corresponding whitepoint values for and can then be inferred using the
standard illuminant A standard illuminant is a theoretical source of visible light with a spectral power distribution that is published. Standard illuminants provide a basis for comparing images or colors recorded under different lighting. CIE illuminants The Inter ...
s. Since the XYZ values are defined much earlier than the characterization of cone cells in the 1950s (by
Ragnar Granit Ragnar Arthur Granit (30 October 1900 – 12 March 1991) was a Finnish-Swedish scientist who was awarded the Nobel Prize in Physiology or Medicine in 1967 along with Haldan Keffer Hartline and George Wald "for their discoveries concerning the ...
), the physiological meaning of these values are known only much later. The Hunt-Pointer-Estevez matrix from the 1980s relates XYZ with LMS. When inverted, it shows how the three cone responses add up to XYZ functions: : \begin X\\Y\\Z \end = \left begin 1&.910\,20 \!\!\!&\!\! -1&.112\,12 \!\!\!&\!\! 0&.201\,91 \\ 0&.370\,95 \!\!\!&\!\! 0&.629\,05 \!\!\!&\!\! 0& \\ 0& \!\!\!&\!\! 0& \!\!\!&\!\! 1&.000\,00 \end\right\begin L\\M\\S \end_ In other words, the Z value is solely made up of the S cone response, the Y value a mix of L and M responses, and X value a mix of all three. This fact makes XYZ values analogous to, but different from, the LMS cone responses of the human eye.


CIE standard observer

Due to the distribution of cones in the eye, the tristimulus values depend on the observer's
field of view The field of view (FoV) is the extent of the observable world that is seen at any given moment. In the case of optical instruments or sensors it is a solid angle through which a detector is sensitive to electromagnetic radiation. Humans a ...
. To eliminate this variable, the CIE defined a color-mapping function called the standard (colorimetric) observer, to represent an average human's chromatic response within a 2° arc inside the
fovea Fovea () (Latin for "pit"; plural foveae ) is a term in anatomy. It refers to a pit or depression in a structure. Human anatomy *Fovea centralis of the retina * Fovea buccalis or Dimple * Fovea of the femoral head * Trochlear fovea of the fr ...
. This angle was chosen owing to the belief that the color-sensitive cones resided within a 2° arc of the fovea. Thus the ''CIE 1931 Standard Observer'' function is also known as the ''CIE 1931 2° Standard Observer''. A more modern but less-used alternative is the ''CIE 1964 10° Standard Observer'', which is derived from the work of Stiles and Burch, and Speranskaya. For the 10° experiments, the observers were instructed to ignore the central 2° spot. The 1964 Supplementary Standard Observer function is recommended when dealing with more than about a 4° field of view. Both standard observer functions are discretized at wavelength intervals from to and distributed by the CIE. All corresponding values have been calculated from experimentally obtained data using
interpolation In the mathematical field of numerical analysis, interpolation is a type of estimation, a method of constructing (finding) new data points based on the range of a discrete set of known data points. In engineering and science, one often has a n ...
. The standard observer is characterized by three ''color matching functions''. There is also a -interval dataset of CIE 1931 and CIE 1964 provided by Wyszecki 1982. A CIE publication in 1986 appears also to have a 1 nm dataset, probably using the same data. Like the regular dataset, this dataset is also derived from interpolation. The derivation of the CIE standard observer from color matching experiments is given
below Below may refer to: *Earth *Ground (disambiguation) *Soil *Floor *Bottom (disambiguation) Bottom may refer to: Anatomy and sex * Bottom (BDSM), the partner in a BDSM who takes the passive, receiving, or obedient role, to that of the top or ...
, after the description of the CIE RGB space.


Color matching functions

The CIE's color matching functions \overline(\lambda), \overline(\lambda) and \overline(\lambda) are the numerical description of the chromatic response of the ''observer'' (described above). They can be thought of as the spectral sensitivity curves of three linear light detectors yielding the CIE tristimulus values ''X'', ''Y'' and ''Z''. Collectively, these three functions describe the CIE standard observer.


Analytical approximation

Table lookup can become impractical for some computational tasks. Instead of referring to the published table, the CIE XYZ color matching functions can be approximated by a sum of
Gaussian function In mathematics, a Gaussian function, often simply referred to as a Gaussian, is a function of the base form f(x) = \exp (-x^2) and with parametric extension f(x) = a \exp\left( -\frac \right) for arbitrary real constants , and non-zero . It is n ...
s, as follows: Let ''g''(''x'') denote a piecewise-Gaussian function, defined by : g(x; \mu, \sigma_1, \sigma_2) = \begin \exp \bigl(\bigr), &x < \mu, \\ mu\exp \bigl(\bigr), &x \geq \mu. \end That is, ''g''(''x'') resembles a bell curve with its peak at , a spread/standard deviation of ''σ'' to the left of the mean, and spread of ''σ'' to the right of the mean. With the wavelength ''λ'' measured in
nanometer 330px, Different lengths as in respect to the molecular scale. The nanometre (international spelling as used by the International Bureau of Weights and Measures; SI symbol: nm) or nanometer (American and British English spelling differences#-re ...
s, we then approximate the 1931 color matching functions:
List of colors These are the lists of colors; * List of colors: A–F * List of colors: G–M * List of colors: N–Z * List of colors (compact) * List of colors by shade * List of color palettes * List of Crayola crayon colors * List of RAL colors * List ...
: \begin \overline(\lambda) &= 1.056 g(\lambda; 599.8, 37.9, 31.0) + 0.362 g(\lambda; 442.0, 16.0, 26.7) \\ mu&\quad - 0.065 g(\lambda; 501.1, 20.4, 26.2), \\ mu\overline(\lambda) &= 0.821 g(\lambda; 568.8, 46.9, 40.5) + 0.286 g(\lambda; 530.9, 16.3, 31.1), \\ mu\overline(\lambda) &= 1.217 g(\lambda; 437.0, 11.8, 36.0) + 0.681 g(\lambda; 459.0, 26.0, 13.8). \end It is also possible to use fewer gaussian functions, with one gaussian for each "lobe". CIE 1964 fits well with a one-lobe function. The CIE XYZ color matching functions are nonnegative, and lead to nonnegative XYZ coordinates for all real colors (that is, for nonnegative light spectra). Other observers, such as for the CIE RGB space or other
RGB color space An RGB color space is any additive color space based on the RGB color model. An RGB color space is defined by chromaticity coordinates of the red, green, and blue additive primaries, the white point which is usually a standard illuminant, and t ...
s, are defined by other sets of three color-matching functions, not generally nonnegative, and lead to tristimulus values in those other spaces, which may include negative coordinates for some real colors.


Computing XYZ from spectral data


Emissive case

The tristimulus values for a color with a
spectral radiance In radiometry, spectral radiance or specific intensity is the radiance of a surface per unit frequency or wavelength, depending on whether the Spectral radiometric quantity, spectrum is taken as a function of frequency or of wavelength. The Internat ...
''L''e,Ω,λ are given in terms of the standard observer by: :\begin X &= \int_\lambda L_(\lambda)\,\overline(\lambda)\,d\lambda, \\ muY &= \int_\lambda L_(\lambda)\,\overline(\lambda)\,d\lambda, \\ muZ &= \int_\lambda L_(\lambda)\,\overline(\lambda)\,d\lambda. \end where \lambda is the wavelength of the equivalent
monochromatic A monochrome or monochromatic image, object or color scheme, palette is composed of one color (or lightness, values of one color). Images using only Tint, shade and tone, shades of grey are called grayscale (typically digital) or Black and wh ...
light (measured in
nanometers 330px, Different lengths as in respect to the molecular scale. The nanometre (international spelling as used by the International Bureau of Weights and Measures; SI symbol: nm) or nanometer (American and British English spelling differences#-re ...
), and customary limits of the integral are \lambda\in
80, 780 8 (eight) is the natural number following 7 and preceding 9. In mathematics 8 is: * a composite number, its proper divisors being , , and . It is twice 4 or four times 2. * a power of two, being 2 (two cubed), and is the first number of t ...
/math>. The values of ''X'', ''Y'', and ''Z'' are bounded if the radiance spectrum ''L''e,Ω,λ is bounded.


Reflective and transmissive cases

The reflective and transmissive cases are very similar to the emissive case, with a few differences. The spectral radiance ''L''e,Ω,λ is replaced by the spectral
reflectance The reflectance of the surface of a material is its effectiveness in reflecting radiant energy. It is the fraction of incident electromagnetic power that is reflected at the boundary. Reflectance is a component of the response of the electronic ...
(or
transmittance Transmittance of the surface of a material is its effectiveness in transmitting radiant energy. It is the fraction of incident electromagnetic power that is transmitted through a sample, in contrast to the transmission coefficient, which is th ...
) ''S(λ)'' of the object being measured, multiplied by the spectral power distribution of the illuminant ''I(λ)''. :\begin X &= \frac\int_\lambda S(\lambda)\,I(\lambda)\,\overline(\lambda)\,d\lambda, \\ muY &= \frac\int_\lambda S(\lambda)\,I(\lambda)\,\overline(\lambda)\,d\lambda, \\ muZ &= \frac\int_\lambda S(\lambda)\,I(\lambda)\,\overline(\lambda)\,d\lambda, \end where :N = \int_\lambda I(\lambda)\,\overline(\lambda)\,d\lambda, ''K'' is a scaling factor (usually 1 or 100), and \lambda is the wavelength of the equivalent
monochromatic A monochrome or monochromatic image, object or color scheme, palette is composed of one color (or lightness, values of one color). Images using only Tint, shade and tone, shades of grey are called grayscale (typically digital) or Black and wh ...
light (measured in
nanometers 330px, Different lengths as in respect to the molecular scale. The nanometre (international spelling as used by the International Bureau of Weights and Measures; SI symbol: nm) or nanometer (American and British English spelling differences#-re ...
), and the standard limits of the integral are \lambda\in
80, 780 8 (eight) is the natural number following 7 and preceding 9. In mathematics 8 is: * a composite number, its proper divisors being , , and . It is twice 4 or four times 2. * a power of two, being 2 (two cubed), and is the first number of t ...
/math>.


CIE xy chromaticity diagram and the CIE xyY color space

Since the
human eye The human eye is a sensory organ, part of the sensory nervous system, that reacts to visible light and allows humans to use visual information for various purposes including seeing things, keeping balance, and maintaining circadian rhythm. ...
has three types of color sensors that respond to different ranges of
wavelength In physics, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats. It is the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, tro ...
s, a full plot of all visible colors is a three-dimensional figure. However, the concept of color can be divided into two parts: brightness and
chromaticity Chromaticity is an objective specification of the quality of a color regardless of its luminance. Chromaticity consists of two independent parameters, often specified as hue (h) and colorfulness (s), where the latter is alternatively called ...
. For example, the color white is a bright color, while the color grey is considered to be a less bright version of that same white. In other words, the chromaticity of white and grey are the same while their brightness differs. The CIE XYZ color space was deliberately designed so that the ''Y'' parameter is also a measure of the
luminance Luminance is a photometric measure of the luminous intensity per unit area of light travelling in a given direction. It describes the amount of light that passes through, is emitted from, or is reflected from a particular area, and falls withi ...
of a color. The chromaticity is then specified by the two derived parameters ''x'' and ''y'', two of the three normalized values being functions of all three tristimulus values ''X'', ''Y'', and ''Z'': :\begin x &= \frac \\ muy &= \frac \\ muz &= \frac = 1 - x - y \end The derived color space specified by ''x'', ''y'', and ''Y'' is known as the CIE xyY color space and is widely used to specify colors in practice. The ''X'' and ''Z'' tristimulus values can be calculated back from the chromaticity values ''x'' and ''y'' and the ''Y'' tristimulus value: :\begin X &= \fracx, \\ muZ &= \frac(1 - x - y). \end The figure on the right shows the related chromaticity diagram. The outer curved boundary is the ''spectral locus'', with wavelengths shown in nanometers. Note that the chromaticity diagram is a tool to specify how the human eye will experience light with a given spectrum. It cannot specify colors of objects (or printing inks), since the chromaticity observed while looking at an object depends on the light source as well. Mathematically the colors of the chromaticity diagram occupy a region of the
real projective plane In mathematics, the real projective plane is an example of a compact non-orientable two-dimensional manifold; in other words, a one-sided surface. It cannot be embedded in standard three-dimensional space without intersecting itself. It has bas ...
. The chromaticity diagram illustrates a number of interesting properties of the CIE XYZ color space: * The diagram represents all of the chromaticities visible to the average person. These are shown in color and this region is called the
gamut In color reproduction, including computer graphics and photography, the gamut, or color gamut , is a certain ''complete subset'' of colors. The most common usage refers to the subset of colors which can be accurately represented in a given circ ...
of human vision. The gamut of all visible chromaticities on the CIE plot is the tongue-shaped or horseshoe-shaped figure shown in color. The curved edge of the gamut is called the ''spectral locus'' and corresponds to monochromatic light (each point representing a pure hue of a single wavelength), with wavelengths listed in nanometers. The straight edge on the lower part of the gamut is called the
line of purples In color theory, the line of purples or purple boundary is the locus on the edge of the chromaticity diagram formed between extreme spectral red and violet. Except for these endpoints of the line, colors on the line are non-spectral (no monochr ...
. These colors, although they are on the border of the gamut, have no counterpart in monochromatic light. Less saturated colors appear in the interior of the figure with white at the center. * It is seen that all visible chromaticities correspond to non-negative values of ''x'', ''y'', and ''z'' (and therefore to non-negative values of ''X'', ''Y'', and ''Z''). * If one chooses any two points of color on the chromaticity diagram, then all the colors that lie in a straight line between the two points can be formed by mixing these two colors. It follows that the gamut of colors must be
convex Convex or convexity may refer to: Science and technology * Convex lens, in optics Mathematics * Convex set, containing the whole line segment that joins points ** Convex polygon, a polygon which encloses a convex set of points ** Convex polytope ...
in shape. All colors that can be formed by mixing three sources are found inside the triangle formed by the source points on the chromaticity diagram (and so on for multiple sources). * An equal mixture of two equally bright colors will not generally lie on the midpoint of that
line segment In geometry, a line segment is a part of a straight line that is bounded by two distinct end points, and contains every point on the line that is between its endpoints. The length of a line segment is given by the Euclidean distance between ...
. In more general terms, a distance on the CIE xy chromaticity diagram does not correspond to the degree of difference between two colors. In the early 1940s,
David MacAdam David Lewis MacAdam (July 1, 1910 – March 9, 1998) was an American physicist and color scientist who made important contributions to color science and technology in the fields of colorimetry, color discrimination, color photography and televisi ...
studied the nature of visual sensitivity to
color difference In color science, color difference or color distance is the separation between two colors. This metric allows quantified examination of a notion that formerly could only be described with adjectives. Quantification of these properties is of great ...
s, and summarized his results in the concept of a
MacAdam ellipse In the study of color vision, a MacAdam ellipse is a region on a chromaticity diagram which contains all colors which are indistinguishable, to the average human eye, from the color at the center of the ellipse. The contour of the ellipse therefore ...
. Based on the work of MacAdam, the CIE 1960, CIE 1964, and CIE 1976 color spaces were developed, with the goal of achieving perceptual uniformity (have an equal distance in the color space correspond to equal differences in color). Although they were a distinct improvement over the CIE 1931 system, they were not completely free of distortion. * It can be seen that, given three real sources, these sources cannot cover the gamut of human vision. Geometrically stated, there are no three points within the gamut that form a triangle that includes the entire gamut; or more simply, the gamut of human vision is not a triangle. * Light with a flat power spectrum in terms of wavelength (equal power in every interval) corresponds to the point .


Mixing colors specified with the CIE xy chromaticity diagram

When two or more colors are additively mixed, the x and y chromaticity coordinates of the resulting color (xmix,ymix) may be calculated from the chromaticities of the mixture components (x1,y1; x2,y2; …; xn,yn) and their corresponding luminances (L1, L2, …, Ln) with the following formulas: : x_ = \frac \quad,\quad y_ = \frac These formulas can be derived from the previously presented definitions of x and y chromaticity coordinates by taking advantage of the fact that the tristimulus values X, Y, and Z of the individual mixture components are directly additive. In place of the luminance values (L1, L2, etc.) one can alternatively use any other photometric quantity that is directly proportional to the tristimulus value Y (naturally meaning that Y itself can also be used as well). As already mentioned, when two colors are mixed, the resulting color xmix, ymix will lie on the straight line segment that connects these colors on the CIE xy chromaticity diagram. To calculate the mixing ratio of the component colors x1,y1 and x2,y2 that results in a certain xmix,ymix on this line segment, one can use the formula : \frac = \frac = \frac where L1 is the luminance of color x1,y1 and L2 the luminance of color x2,y2. Note that because ymix is unambiguously determined by xmix and vice versa, knowing just one or the other of them is enough for calculating the mixing ratio. Also note that, in accordance with the remarks concerning the formulas for xmix and ymix, the mixing ratio L1/L2 may well be expressed in terms of other photometric quantities than luminance.


Definition of the CIE XYZ color space


CIE RGB color space

The CIE RGB color space is one of many
RGB color spaces An RGB color space is any additive color space based on the RGB color model. An RGB color space is defined by chromaticity coordinates of the red, green, and blue additive primaries, the white point which is usually a standard illuminant, and t ...
, distinguished by a particular set of monochromatic (single-wavelength)
primary color A set (mathematics), set of primary colors or primary colours (see American and British English spelling differences#-our, -or, spelling differences) consists of colorants or colored lights that can be mixed in varying amounts to produce a gamu ...
s. In the 1920s, two independent experiments on human color perception were conducted by W. David Wright with ten observers, and John Guild with seven observers. Their results laid the foundation for the trichromatic CIE XYZ color space specification. The experiments were conducted by using a circular split screen (a bipartite field) 2 degrees in diameter, which is the angular size of the human
fovea Fovea () (Latin for "pit"; plural foveae ) is a term in anatomy. It refers to a pit or depression in a structure. Human anatomy *Fovea centralis of the retina * Fovea buccalis or Dimple * Fovea of the femoral head * Trochlear fovea of the fr ...
. On one side a ''test'' color was projected while on the other an observer-adjustable color was projected. The adjustable color was a mixture of three ''primary'' colors, each with fixed
chromaticity Chromaticity is an objective specification of the quality of a color regardless of its luminance. Chromaticity consists of two independent parameters, often specified as hue (h) and colorfulness (s), where the latter is alternatively called ...
, but with adjustable
brightness Brightness is an attribute of visual perception in which a source appears to be radiating or reflecting light. In other words, brightness is the perception elicited by the luminance of a visual target. The perception is not linear to luminance, ...
. The observer would alter the brightness of each of the three primary beams until a match to the test color was observed. Because the RGB-gamut does not cover the whole color spectrum, not all test colors could be matched using this technique. When this was the case, a variable amount of one of the primaries could be added to the test color, and a match with the remaining two primaries was carried out with the variable color spot. For these cases, the amount of the primary added to the test color was considered to be a negative value. In this way, the entire range of human color perception could be covered. When the test colors were monochromatic, a plot could be made of the amount of each primary used as a function of the wavelength of the test color. These three functions are called the ''color matching functions'' for that particular experiment. Although Wright and Guild's experiments were carried out using various primaries at various intensities, and although they used a number of different observers, all of their results were summarized by the standardized CIE RGB color matching functions \overline(\lambda), \overline(\lambda), and \overline(\lambda), obtained using three monochromatic primaries at standardized wavelengths of (red), (green) and (blue). The color matching functions are the amounts of primaries needed to match the monochromatic test primary. These functions are shown in the plot on the right (CIE 1931). Note that \overline(\lambda) and \overline(\lambda) are zero at , \overline(\lambda) and \overline(\lambda) are zero at and \overline(\lambda) and \overline(\lambda) are zero at , since in these cases the test color is one of the primaries. The primaries with wavelengths and were chosen because they are easily reproducible monochromatic lines of a mercury vapor discharge. The wavelength, which in 1931 was difficult to reproduce as a monochromatic beam, was chosen because the eye's perception of color is rather unchanging at this wavelength, and therefore small errors in wavelength of this primary would have little effect on the results. The color matching functions and primaries were settled upon by a CIE special commission after considerable deliberation. and The cut-offs at the short- and long-wavelength side of the diagram are chosen somewhat arbitrarily; the human eye can actually see light with wavelengths up to about , but with a sensitivity that is many thousand times lower than for green light. These color matching functions define what is known as the "1931 CIE standard observer". Note that rather than specify the brightness of each primary, the curves are normalized to have constant area beneath them. This area is fixed to a particular value by specifying that : \int_0^\infty \overline(\lambda)\,d\lambda = \int_0^\infty \overline(\lambda)\,d\lambda = \int_0^\infty \overline(\lambda)\,d\lambda. The resulting normalized color matching functions are then scaled in the r:g:b ratio of 1:4.5907:0.0601 for source
luminance Luminance is a photometric measure of the luminous intensity per unit area of light travelling in a given direction. It describes the amount of light that passes through, is emitted from, or is reflected from a particular area, and falls withi ...
and 72.0962:1.3791:1 for source
radiance In radiometry, radiance is the radiant flux emitted, reflected, transmitted or received by a given surface, per unit solid angle per unit projected area. Radiance is used to characterize diffuse emission and reflection of electromagnetic radiatio ...
to reproduce the true color matching functions. By proposing that the primaries be standardized, the CIE established an international system of objective color notation. Given these scaled color matching functions, the RGB
tristimulus The CIE 1931 color spaces are the first defined quantitative links between distributions of wavelengths in the electromagnetic visible spectrum, and physiologically perceived colors in human color vision. The mathematical relationships that defi ...
values for a color with a
spectral power distribution In radiometry, photometry, and color science, a spectral power distribution (SPD) measurement describes the power per unit area per unit wavelength of an illumination (radiant exitance). More generally, the term ''spectral power distribution'' ...
S(\lambda) would then be given by: :\begin R &= \int_0^\infty S(\lambda)\,\overline(\lambda)\,d\lambda, \\ muG &= \int_0^\infty S(\lambda)\,\overline(\lambda)\,d\lambda, \\ muB &= \int_0^\infty S(\lambda)\,\overline(\lambda)\,d\lambda. \end These are all
inner products In mathematics, an inner product space (or, rarely, a Hausdorff pre-Hilbert space) is a real vector space or a complex vector space with an operation called an inner product. The inner product of two vectors in the space is a scalar, often d ...
and can be thought of as a projection of an infinite-dimensional spectrum to a three-dimensional color.


Grassmann's laws

One might ask: "Why is it possible that Wright and Guild's results can be summarized using different primaries and different intensities from those actually used?" One might also ask: "What about the case when the test colors being matched are not monochromatic?" The answer to both of these questions lies in the (near) linearity of human color perception. This linearity is expressed in Grassmann's laws of color. The CIE RGB space can be used to define chromaticity in the usual way: The chromaticity coordinates are ''r'', ''g'' and ''b'' where: :\begin r &= \frac, \\ mug &= \frac, \\ mub &= \frac. \end


Construction of the CIE XYZ color space from the Wright–Guild data

Having developed an RGB model of human vision using the CIE RGB matching functions, the members of the special commission wished to develop another color space that would relate to the CIE RGB color space. It was assumed that Grassmann's law held, and the new space would be related to the CIE RGB space by a linear transformation. The new space would be defined in terms of three new color matching functions \overline(\lambda), \overline(\lambda), and \overline(\lambda) as described above. The new color space would be chosen to have the following desirable properties: # The new color matching functions were to be everywhere greater than or equal to zero. In 1931, computations were done by hand or slide rule, and the specification of positive values was a useful computational simplification. # The \overline(\lambda) color matching function would be exactly equal to the photopic luminous efficiency function ''V''(''λ'') for the "CIE standard photopic observer". The luminance function describes the variation of perceived brightness with wavelength. The fact that the luminance function could be constructed by a linear combination of the RGB color matching functions was not guaranteed by any means but might be expected to be nearly true due to the near-linear nature of human sight. Again, the main reason for this requirement was computational simplification. # For the constant energy
white point A white point (often referred to as reference white or target white in technical documents) is a set of tristimulus values or chromaticity coordinates that serve to define the color "white" in image capture, encoding, or reproduction. Depending on ...
, it was required that . # By virtue of the definition of
chromaticity Chromaticity is an objective specification of the quality of a color regardless of its luminance. Chromaticity consists of two independent parameters, often specified as hue (h) and colorfulness (s), where the latter is alternatively called ...
and the requirement of positive values of ''x'' and ''y'', it can be seen that the gamut of all colors will lie inside the triangle , 0 , 0
, 1 The comma is a punctuation mark that appears in several variants in different languages. It has the same shape as an apostrophe or single closing quotation mark () in many typefaces, but it differs from them in being placed on the baseline (t ...
It was required that the gamut fill this space practically completely. # It was found that the \overline(\lambda) color matching function could be set to zero above while remaining within the bounds of experimental error. For computational simplicity, it was specified that this would be so. In geometrical terms, choosing the new color space amounts to choosing a new triangle in ''rg'' chromaticity space. In the figure above-right, the ''rg'' chromaticity coordinates are shown on the two axes in black, along with the gamut of the 1931 standard observer. Shown in red are the CIE ''xy'' chromaticity axes which were determined by the above requirements. The requirement that the XYZ coordinates be non-negative means that the triangle formed by Cr, Cg, Cb must encompass the entire gamut of the standard observer. The line connecting Cr and Cb is fixed by the requirement that the \overline(\lambda) function be equal to the luminance function. This line is the line of zero luminance, and is called the alychne. The requirement that the \overline(\lambda) function be zero above means that the line connecting Cg and Cr must be tangent to the gamut in the region of Kr. This defines the location of point Cr. The requirement that the equal energy point be defined by puts a restriction on the line joining Cb and Cg, and finally, the requirement that the gamut fill the space puts a second restriction on this line to be very close to the gamut in the green region, which specifies the location of Cg and Cb. The above described transformation is a linear transformation from the CIE RGB space to XYZ space. The standardized transformation settled upon by the CIE special commission was as follows: The numbers in the conversion matrix below are exact, with the number of digits specified in CIE standards. :\begin \begin X \\ Y \\ Z \end &= \begin b_ & b_ & b_ \\ b_ & b_ & b_ \\ b_ & b_ & b_ \end \begin R \\ G \\ B \end \\ 0mu&= \begin 0.490\,00 & 0.310\,00 & 0.200\,00 \\ 0.176\,97 & 0.812\,40 & 0.010\,63 \\ 0.000\,00 & 0.010\,00 & 0.990\,00 \end \begin R \\ G \\ B \end \end The above matrix is balanced for the equi-energy stimulus: it has coordinates (1,1,1) in both RGB and XYZ coordinates. While the above matrix is exactly specified in standards, the inverse is left unspecified so that it can be approximated to machine precision to reduce round-trip rounding errors. Its values can be computed precisely using rational numbers: : \begin R \\ G \\ B \end = \frac \begin 8041697 & -3049000 & -1591847 \\ -1752003 & 4851000 & 301853 \\ 17697 & -49000 & 3432153 \end \begin X \\ Y \\ Z \end Which has these approximate values: : \begin R \\ G \\ B \end \approx \begin 2.364\,61385 & -0.896\,54057 & -0.468\,07328 \\ -0.515\,16621 & 1.426\,4081 & 0.088\,7581 \\ 0.005\,2037 & -0.014\,40816 & 1.009\,20446 \end \begin X \\ Y \\ Z \end The integrals of the XYZ color matching functions must all be equal by requirement 3 above, and this is set by the integral of the photopic luminous efficiency function by requirement 2 above. The tabulated sensitivity curves have a certain amount of arbitrariness in them. The shapes of the individual ''X'', ''Y'' and ''Z'' sensitivity curves can be measured with a reasonable accuracy. However, the overall luminosity curve (which in fact is a weighted sum of these three curves) is subjective, since it involves asking a test person whether two light sources have the same brightness, even if they are in completely different colors. Along the same lines, the relative magnitudes of the ''X'', ''Y'', and ''Z'' curves are arbitrary. Furthermore, one could define a valid color space with an ''X'' sensitivity curve that has twice the amplitude. This new color space would have a different shape. The sensitivity curves in the CIE 1931 and 1964 XYZ color spaces are scaled to have equal areas under the curves.


Similar color spaces

A few other XYZ-style color-matching functions have been available. These functions imply their own XYZ-like and xyY-like color spaces. ; Judd and Vos corrections for the 2° CMF : The CIE 1931 CMF is known to underestimate the contribution of the shorter blue wavelengths. The Judd (1951) and its following Vos (1978) corrections sought to correct for the issue without deviating from the original methology. ; CIE 1964 X10Y10Z10 : X10Y10Z10 (also written XYZ10 and analogously for the following) is the XYZ-style color space defined using the CIE 1964 10° observer CMFs. ; CIE 170-2 XFYFZF : XFYFZF is the XYZ-style color space defined using the Stockman & Sharpe (2000) physiological 2° observer, which is in turn a linear combination of the group's LMS fundamentals. The CMF data, along with the physiological 10° dataset, is available from the Colour & Vision Research laboratory of
University College London , mottoeng = Let all come who by merit deserve the most reward , established = , type = Public research university , endowment = £143 million (2020) , budget = ...
down to 0.1 nm resolution. ; CIE 170-2 XF,10YF,10ZF,10 : This space is based on the Stockman & Sharpe (2000) physiological 10° observer. According to
Konica Minolta is a Japanese multinational technology company headquartered in Marunouchi, Chiyoda, Tokyo, with offices in 49 countries worldwide. The company manufactures business and industrial imaging products, including copiers, laser printers, multi-fu ...
, the older CIE 1931 CMF exhibits metamerism failure (failure to predict when colors appear the same) for
wide color gamut In color reproduction, including computer graphics and photography, the gamut, or color gamut , is a certain ''complete subset'' of colors. The most common usage refers to the subset of colors which can be accurately represented in a given cir ...
displays containing narrowband emitters like
OLED An organic light-emitting diode (OLED or organic LED), also known as organic electroluminescent (organic EL) diode, is a light-emitting diode (LED) in which the emissive electroluminescent layer is a film of organic compound that emits light i ...
, whereas the 2015 XYZF CMF is not affected. Older
Sony , commonly stylized as SONY, is a Japanese multinational conglomerate corporation headquartered in Minato, Tokyo, Japan. As a major technology company, it operates as one of the world's largest manufacturers of consumer and professional ...
manuals recommend using the Judd-Vos correction by applying an offset to the
white point A white point (often referred to as reference white or target white in technical documents) is a set of tristimulus values or chromaticity coordinates that serve to define the color "white" in image capture, encoding, or reproduction. Depending on ...
depending on the display technology used.


See also

*
Trichromacy Trichromacy or trichromatism is the possessing of three independent channels for conveying color information, derived from the three different types of cone cells in the eye. Organisms with trichromacy are called trichromats. The normal expla ...
*
Impossible color Impossible colors are colors that do not appear in ordinary visual functioning. Different color theories suggest different hypothetical colors that humans are incapable of perceiving for one reason or another, and fictional colors are rou ...
*
CIELAB color space The CIELAB color space, also referred to as ''L*a*b*'' , is a color space defined by the International Commission on Illumination (abbreviated CIE) in 1976. (Referring to CIELAB as "Lab" without asterisks should be avoided to prevent confusion ...
*
Standard illuminant A standard illuminant is a theoretical source of visible light with a spectral power distribution that is published. Standard illuminants provide a basis for comparing images or colors recorded under different lighting. CIE illuminants The Inter ...
, the definition of white point used by CIE and commonly shown in color space diagrams as E, D50 or D65


References


Further reading

* * * (originally published by the
Society of Dyers and Colourists The Society of Dyers and Colourists (SDC) is an international professional society, with headquarters in Bradford, West Yorkshire, UK, specializing in colour in all its manifestations. Founded in 1884, it was granted a Royal Charter of Incorporation ...
, Bradford, 1981.)


External links


Introduction to Colour Science
William Andrew Steer.

an
Delphi source

CIE Color Space
Gernot Hoffmann

Andrew Stockman and Lindsay T. Sharpe.
Calculation from the original experimental data of the CIE 1931 RGB standard observer spectral chromaticity co-ordinates and color matching functions

Colorimetric data useful for calculation
in various file formats

MATLAB toolbox for color science computation and accurate color reproduction (by Jesus Malo and Maria Jose Luque, Universitat de Valencia). It includes CIE standard tristimulus colorimetry and transformations to a number of non-linear color appearance models (CIE Lab, CIE CAM, etc.).

Konica Minolta Sensing
CIE 1931 and LED Binning Explained
Edaphic Scientific Knowledge Base (Dead link)
Measuring color in a world of light
Admesy, advanced measurement systems (404 error, dead link) {{DEFAULTSORT:Cie 1931 Color Space Color space 1931 introductions Articles with example C code