CIE 1931 color space

Normal human color vision is trichromatic, which is enabled by three classes of cone cells (L, M & S).

These laws laid the theoretical framework necessary for color experiments performed by Hermann von Helmholtz (remembered for popularizing the Trichromatic Theory) and James Clerk Maxwell in the 1850's, and later in the experiments used to develop the CIE 1931 color spaces.

These experiments sought to quantify the typical human chromatic response (color perception) and define it as the standard (colorimetric) observer.

Any spectral distribution can be thought of as a combination of a number of monochromatic sources at varying intensities, so that (by Grassmann's laws) integrating the color matching functions with that spectral distribution will yield the intensities of the three primaries necessary to match it.

While this is physically impossible, it can be approximated (relying on Grassmann's laws) by adding the negative primary to the target field instead of the adjustment field, thereby allowing a match to be made with negative primary brightness.

Likewise, between the green and red primaries, some blue must be added to the target, resulting in negative values of

It can be seen (in the chromaticity diagram to the right) that the deviation of the boundaries of the triangular CIE RGB gamut align well with the spectral locus of the xy chromaticity diagram, except between the blue and green primaries, where rather large amounts of the red primary must be added to the test field, and it is in this band that the red color matching function has the most significant negative values.The CIE RGB color space is one of many RGB color spaces, each distinguished by their particular set of primary colors.

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

The color matching functions and primaries were settled upon by a CIE special commission after considerable deliberation.

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 1:4.5907:0.0601 for source luminance and 72.0962:1.3791:1 for source radiance to reproduce the true color matching functions.

By proposing that the primaries be standardized, the CIE established an international system of objective color notation.

The underlying color matching functions can be thought of as the spectral sensitivity curves of three linear light detectors yielding the CIE tristimulus values X, Y and Z.

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.

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.

The CIE 1931 color space defines the resulting tristimulus values, in which they are denoted by "X", "Y", and "Z".

[11] In XYZ space, all combinations of non-negative coordinates are meaningful, but many, such as the primary locations [1, 0, 0], [0, 1, 0], and [0, 0, 1], correspond to imaginary colors outside the space of possible LMS coordinates; imaginary colors do not correspond to any spectral distribution of wavelengths and therefore have no physical reality.

The unit of the tristimulus values X, Y, and Z is often arbitrarily chosen so that Y = 1 or Y = 100 is the brightest white that a color display supports.

This fact makes XYZ values analogous to, but different from, the LMS cone responses of the human eye.

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.

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.

function be zero above 650 nm means that the line connecting Cg and Cr must be tangent to the gamut in the region of Kr.

The requirement that the equal energy point be defined by x = y = 1/3 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.

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.

Because ymix is unambiguously determined by xmix and vice versa (unless x1 = x2 or y1 = y2), one is enough to compute the mixing ratio.

The tristimulus values for a color with a spectral radiance Le,Ω,λ are given in terms of the standard observer by: where

is the wavelength of the equivalent monochromatic light (measured in nanometers), and customary limits of the integral are

is the wavelength of the equivalent monochromatic light (measured in nanometers), and the standard limits of the integral are

The 1964 Supplementary Standard Observer function is recommended when dealing with more than about a 4° field of view, but some prefer to use it always as "human wide field color discrimination is about 2 to 3 times more accurate than foveal color discrimination".

According to Konica Minolta, the older CIE 1931 CMF exhibits metamerism failure (failure to predict when colors appear the same) for wide color gamut displays containing narrowband emitters like OLED, whereas the 2015 XYZF CMF is not affected.

[30] Older Sony manuals recommend using the Judd-Vos correction by applying an offset to the white point depending on the display technology used.