CIE 1931 color space
In 1931, the International Commission on Illumination published the CIE 1931 color spaces which define the relationship between the visible spectrum and human color vision. The CIE color spaces are mathematical models that comprise a "standard observer", which is a static idealization of the color vision of a normal human. A useful application of the CIEXYZ colorspace is that a mixture of two colors in some proportion lies on the straight line between those two colors. One disadvantage is that it is not perceptually uniform. This disadvantage is remedied in subsequent color models such as CIELUV and CIELAB, but these and modern color models still use the CIE 1931 color spaces as a foundation.
The CIE developed and maintains many of the standards in use today relating to colorimetry. The CIE color spaces were created using data from a series of experiments, where human test subjects adjusted red, green, and blue primary colors to find a visual match to a second, pure color. The original experiments were conducted in the mid-1920s by William David Wright using ten observers and John Guild using seven observers. The experimental results were combined, creating the CIE RGB color space. The CIE XYZ color space was derived from CIE RGB in an effort to simplify the math.
These color spaces are fundamental tools for measuring color for industry, including inks, dyes, and paints, illumination, color imaging, etc. The CIE color spaces contributed to the development of color television, the creation of instruments for maintaining consistent color in manufacturing processes, and other methods of color management.
Background
Color vision
Normal human color vision is trichromatic, which is enabled by three classes of cone cells. Each cone class contains a slightly different photopsin with a different spectral sensitivity. The spectral sensitivities are summarized by their peak wavelengths, which are at long, medium, and short wavelengths, sometimes shorthanded inexactly as red, green and blue cones, respectively. The differential excitation levels of these three cones comprise the tristimulus values, denoted "L", "M", and "S", and are the parameters that define the 3-dimensional "LMS color space", which is one of many color spaces devised to quantify human color vision. In principle, any human color sensation can be described by a set of tristimulus values. A continuous spectral power distribution of light is converted to the discrete tristimulus values by integrating over a spectral sensitivity of one of the cone classes :These are all inner products and can be thought of as a projection of an infinite-dimensional spectrum to a three-dimensional color. This LMS color model is refined to the LMS color space when the spectral sensitivity "primaries" are defined according to the standard observer. The LMS color space can be further transformed into similar three-dimensional color spaces, such as RGB, XYZ, HSV or cognates thereof. The tristimulus values associated with a color space can be conceptualized as amounts of three primary colors in a trichromatic, 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 spectral power distribution of light.
Metamerism and Grassmann's laws
Since a lot of information is lost during the conversion of a continuous light spectrum to tristimulus values, it follows that there are disparate spectra that can stimulate the same tristimulus values. These disparate spectra are known as metamers. For example, a monochromatic light is metameric with a dichromatic light spectrum comprising 2 parts monochromatic light and 1 part monochromatic light. In 1853, Hermann Grassmann developed Grassmann's laws, which aimed to describe color mixing algebraically. These laws laid the theoretical framework necessary for color experiments performed by Hermann von Helmholtz and James Clerk Maxwell in the 1850's, and later in the experiments used to develop the CIE 1931 color spaces. The laws can be summarized in three principles:- Additivity: if a third light is added equally to two metamers, the results are metamers.
- Proportionality: if the luminances of two metamers are equally increased or reduced by some constant, the results are metamers.
- Transitivity: If one of two metamers is metameric with a third color, then all colors are metameric
Origin
The CIE 1931 color spaces are 4 interrelated color spaces with the same origin. 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. How their results laid the foundation of the CIE 1931 color spaces is described in this section.CIE standard observer
These experiments sought to quantify the typical human chromatic response and define it as the standard observer. The standard observer is defined by the 3 color matching functions in one of the CIE 1931 color spaces. Due to the design of the experiments, the standard observer has the following constraints:- Due to the distribution of cones in the eye, the tristimulus values depend on the observer's field of view. The standard observer was limited to stimuli subtending the 2° arc inside the fovea of the retina. This angle was chosen owing to the belief that the color-sensitive cones resided within a 2° arc of the fovea. This original observer is often referred to as the 2° Standard Observer, in contrast to a later alternative using 10° stimuli and referred to as the 10° standard observer, which is discussed later.
- It is applicable for brightnesses that range from mid-mesopic to photopic light.
- It is applicable only to additive color mixing, not subtractive color mixing.
Color matching
If the test color were simply a monochromatic color at wavelength λ, and if it could be matched by a combination of the three primaries at relative intensities,, and respectively, then a tabulation of these values at various λ will estimate three functions of wavelength. These are the RGB color-matching functions. Any spectral distribution can be thought of as a combination of a number of monochromatic sources at varying intensities, so that integrating the color-matching functions with that spectral distribution will yield the intensities of the three primaries necessary to match it. The problem is that the three primaries can only produce colors which lie within their gamut the triangle in color space formed by the primaries, which never touches the monochromatic locus nor the purple line except at the three primaries. In other words, there is no monochromatic target that can be matched by a combination of the three primaries, except at the wavelengths of the three primaries themselves. Matching a monochromatic target would require one of the primaries to have a negative brightness. While this is physically impossible, it can be approximated by adding the negative primary to the target field instead of subtracting it from the adjustment field, thereby allowing a match to be made with negative primary brightness.
For wavelengths between the blue and green primaries, some red primary must be added to the target, resulting in negative values of. Likewise, between the green and red primaries, some blue must be added to the target, resulting in negative values of. For wavelengths below the wavelength of the blue primary, or above the wavelength of the red primary, some green must be added and will be negative. For every spectral color, except those defined by the primary colors, there will always be two positive color-matching functions and one negative. It can be seen 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.
CIE RGB color space
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,, and, obtained using three monochromatic primaries at standardized wavelengths of , and . 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 are the amounts of primaries needed to match the monochromatic target color. These functions are shown in the plot on the right. Note how and are zero at, and are zero at and and are zero at, since in these cases the test color is exactly equal to the non-zero primary.The color matching functions and primaries were settled upon by a CIE special commission after considerable deliberation. 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". 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 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.
Given these scaled color matching functions, the RGB tristimulus values for
a color with a spectral power distribution would then be given by:
These are all inner products and can be thought of as a projection of an infinite-dimensional spectrum to a three-dimensional color.