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 visible to the human eye. Electromagnetic radiation in this range of wavelengths is called ''visible light'' or simply light. A typical human eye will respond to wa ...
, and physiologically perceived colors in human
color vision. 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 represen ...
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 color space.
Tristimulus values
![Cones SMJ2 E](https://upload.wikimedia.org/wikipedia/commons/1/1e/Cones_SMJ2_E.svg)
The
human eye with normal vision has three kinds of
cone cells 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 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 p ...
", 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.
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 compou ...
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. The tristimulus values associated with a color space can be conceptualized as amounts of three
primary color
A set of primary colors or primary colours (see spelling differences) consists of colorants or colored lights that can be mixed in varying amounts to produce a gamut of colors. This is the essential method used to create the perception of a ...
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 distributions of the sources.
Most wavelengths stimulate two or all three kinds of
cone cell 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, an ...
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
A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices ''A'', ''B'', and ''C'' is denoted \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 luminan ...
, "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
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 o ...
, 1, 0
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 o ...
and
, 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 o ...
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''
![Comparison between CIE luminosity function and M cone response](https://upload.wikimedia.org/wikipedia/commons/6/65/Comparison_between_CIE_luminosity_function_and_M_cone_response.svg)
In the CIE 1931 model, ''Y'' is the
luminance, ''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:
:
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.
Human ...
. 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. 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, after the description of the CIE RGB space.
Color matching functions
![CIE1931 RGBCMF](https://upload.wikimedia.org/wikipedia/commons/3/36/CIE1931_RGBCMF.png)
The CIE's color matching functions
,
and
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 ...
s, as follows:
Let ''g''(''x'') denote a piecewise-Gaussian function, defined by
:
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
nanometers, 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 of X ...
:
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, an ...
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 spectrum is taken as a function of frequency or of wavelength. The SI unit of spectral radiance in frequen ...
''L''e,Ω,λ are given in terms of the standard observer by:
:
where is the wavelength of the equivalent monochromatic 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