I.F  Objective representation of colors¶
Given that the perception of colors is eminently subjective, any joint work requires the establishment of an objective reference shared by all (and therefore a certain standardization of techniques, which is not always obvious …).
This work of rationalization was not born with the digital image; since 1913 the International Commission on Illumination (CIE) has worked on the problem.
The modern color spaces ^{1} used in image processing are proposed solutions to this rationalization, standardization of color representation, and are based on the work and early attempts of the CIE.
It is interesting to know that the CIE conducted its work empirically, defining an “average observer” from numerous experiments of color comparison by human observers, in order to characterize the colors and lights as perceived by the average person.
It is in 1931 that the CIE proposed a first representation and rationalization of the colors: the diagram CIE1931, still very used today as an objective reference, in particular to compare the various colorimetric spaces in use.
F.1  Decomposing colors¶
It has been implied so far that a color as we perceive it is physically defined by three independent parameters: its intensity, its dominant wavelength and its Extraction purity.
 Intensity is quite intuitive to understand, and related to what is also called luminosity; it is the number of photons received each second by the cells of the retina.
 Dominant wavelength will primarily influence the hue of the color; it is the most intense monochromatic component in the mixture of all wavelengths forming that particular color.
 Extraction purity represents the proportion between the dominant wavelength and the amount of white that must be added to obtain the color in question. It is close to what is called saturation.
This breakdown is perfectly objective (related to the physical reality of light), it is a good foundation for making an objective representation of colors, which is what the CIE has done since 1931.
F.2  Color diagrams, CIE XYZ of 1931 and CIE xyZ¶
With these three parameters, we can represent the colors in three dimensions.
In order to establish this representation, the CIE chose three theoretical primary colors different from Red, Green and Blue more common, called X, Y and Z, able to include the entirety of the visible colors. This representation is thus the CIE XYZ colorimetric space of 1931, and is still used today as reference to represent and compare all the other colorimetric spaces.
The parameters defining this color space were carefully chosen in order to represent the entirety of the colors perceived by human vision.
Note
The threedimensional representation above is not exact, but does illustrate the general feel of the color space.
For better and easier use and visualization, it is mainly represented in a twodimensional projection, not showing the intensity (brightness) of the color at all.
This projection actually is actually translated to another color space derived from the CIE XYZ where the color is represented on a plane by coordinates named x and y (in lower case) which makes it the CIE xyZ space.
On this diagram, we find the spectrum of visible light, on the upper turn, rounded, going from red to blue.
This outline contains all the possible monochromatic lights, while the inside of the diagram represents the “mixed” colors as we perceive them.
The lower straight line represents the blending of the two extremes of the visible spectrum, which we see as the purple colors, which are not part of the monochromatic lights and close the “color wheel” we know.
This diagram containing all the visible colors is always used as reference in which one can register the other colorimetric spaces, necessarily “smaller” because representing only a subpart of all these colors, as we will see thereafter.
F.3  Other CIE Spaces¶
Since the establishment of these first color spaces and until today, the CIE has continued this work, improving the xyZ space and creating other spaces more specific and for particular uses.
In 1976, two other spaces were published: the CIE L*u*v* (for light) and the CIE L*a*b* (for surface colors, better known as CIE LAB). These two spaces improve and compensate for a “defect” of the xyZ^{2}: the coordinates are no longer linear in order to better match the human vision. Indeed, in the xyZ space, two colors located “at the same distance” can in some areas appear more similar than in other areas. The L*a*b* and L*u*v* correct this “defect” at the price of a greater complexity of calculations.
But it is always the XYZ or xyZ of 1931 which is used as reference to work with and compare all the other colorimetric spaces.
Sources et références
 Color on Wikipedia
 International Commission on Illumination on Wikipedia.
 CIE XYZ on Wikipedia
 L*a*b* CIE on Wikipedia
 L*u*v* CIE on Wikipedia
 Colour representation, Kent State University

The color spaces are the standardized ways of recording and representing the colors (analog as well as digital).
There are for example: sRGB, BT.709, ACES, BT.2020, P3, to name a few from a very large list. ↩ 
L*a*b* and L*u*v* are actually based on another space published in 1976, the CIE U’V’W’ which is linear (and itself based on the CIE UVW of 1960). The chronology of publication of these successive spaces is as follows:
 1931: XYV, and its representation xyZ, linear.
 1960: UVW, and its representation uvW, linear.
 1976 : U’V’W’, linear.
 1976 : L*a*b* and L*u*v*, nonlinear. ↩