It defines a color space in terms of three components:. The RGB color model is an additive one. In other words, R ed, G reen and B lue values known as the three primary colors are combined to reproduce other colors. It is a nonlinear transformation of the RGB color space.

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The CIE 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 define these color spaces are essential tools for color management , important when dealing with color inks, illuminated displays, and recording devices such as digital cameras. The human eye with normal vision has three kinds of cone cells that sense light, having peaks of spectral sensitivity in short "S", nm — nm , middle "M", nm — nm , and long "L", nm — nm 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 ", 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 ; 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 space denominated the " LMS color space ", 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, pigments , etc. The tristimulus values associated with a color space can be conceptualized as amounts of three primary colors in a tri-chromatic, additive color model.

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. A set of color-matching functions, like the spectral sensitivity curves of the LMS color space , 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 denominated " 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, for example LMS tristimulus values that are non-zero for the M component and zero for both the L and S components. Furthermore, LMS tristimulus values for pure spectral colors would, in any normal trichromatic additive color space, e.

To avoid these negative RGB values, and to have one component that describes the perceived brightness , "imaginary" primary colors and corresponding color-matching functions were formulated. When judging the relative luminance brightness of different colors in well-lit situations, humans tend to perceive light within the green parts of the spectrum as brighter than red or blue light of equal power.

The luminosity function that describes the perceived brightnesses of different wavelengths is thus roughly analogous to the spectral sensitivity of M cones. The CIE model capitalizes on this fact by setting Y as luminance. Z is quasi-equal to blue, or the S cone response, and X is a mix of response curves chosen to be nonnegative. 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.

In this case, the Y value is known as the relative luminance. The corresponding whitepoint values for X and Z can then be inferred using the standard illuminants. Due to the distribution of cones in the eye, the tristimulus values depend on the observer's field of view. Both standard observer functions are discretized at 5 nm wavelength intervals from nm to nm and distributed by the CIE.

The standard observer is characterized by three color matching functions. 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 are known as the CIE standard observer. This approximation can be easily employed in a programming language in a functional style. For example, here is a Haskell implementation:.

Here is a semi-functional style implementation in C :. Other observers, such as for the CIE RGB space or other RGB color spaces , 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.

The reflective and transmissive cases are very similar to the emissive case, with a few differences. Since the human eye has three types of color sensors that respond to different ranges of wavelengths , 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. 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 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 : [12]. 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: [13].

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. When two or more colors are additively mixed, the x and y chromaticity coordinates of the resulting color x mix ,y mix may be calculated from the chromaticities of the mixture components x 1 ,y 1 ; x 2 ,y 2 ; …; x n ,y n and their corresponding luminances L 1 , L 2 , …, L n with the following formulas: [14].

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 L 1 , L 2 , etc. As already mentioned, when two colors are mixed, the resulting color x mix ,y mix 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 x 1 ,y 1 and x 2 ,y 2 that results in a certain x mix ,y mix on this line segment, one can use the formula. Note that because y mix is unambiguously determined by x mix and vice versa, knowing just one or the other of them is enough for calculating the mixing ratio. In the s, two independent experiments on human color perception were conducted by W. David Wright [3] with ten observers, and John Guild [4] with seven observers.

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.

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 , but with adjustable brightness. The observer would alter the brightness of each of the three primary beams until a match to the test color was observed.

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. 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 The primaries with wavelengths The nm wavelength, which in 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. These color matching functions define what is known as the " 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. The resulting normalized color matching functions are then scaled in the r:g:b ratio of By proposing that the primaries be standardized, the CIE established an international system of objective color notation. These are all inner products and can be thought of as a projection of an infinite-dimensional spectrum to a three-dimensional color. 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?

This linearity is expressed in Grassmann's law. The new color space would be chosen to have the following desirable properties:. 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 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 C r , C g , C b must encompass the entire gamut of the standard observer.

This line is the line of zero luminance, and is called the alychne. This defines the location of point C r. 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.

While the above matrix is exactly specified in standards, going the other direction uses an inverse matrix that is not exactly specified, but is approximately:. 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. From Wikipedia, the free encyclopedia. Color space defined by the CIE in This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources.

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## CIELAB color space

CIELAB was designed so that the same amount of numerical change in these values corresponds to roughly the same amount of visually perceived change. With respect to a given white point , the CIELAB model is device-independent—it defines colors independently of how they are created or displayed. Because three parameters are measured, the space itself is a three-dimensional real number space, which allows for infinitely many possible colors. The CIELAB color space was derived from the prior "master" CIE XYZ color space , which predicts which spectral power distributions will be perceived as the same color see metamerism , but is not particularly perceptually uniform. Often, in practice, the white point is assumed to follow a standard and is not explicitly stated e. It aspires to perceptual uniformity, and its L component closely matches human perception of lightness, although it does not take the Helmholtz—Kohlrausch effect into account. Thus, it can be used to make accurate color balance corrections by modifying output curves in the a and b components, or to adjust the lightness contrast using the L component.

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## CIE 1931 color space

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