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 digital image generation; since 1913 the International Commission on Illumination (CIE) has worked on the problem.

The modern color spaces1 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’s 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 an average person.

It’s in 1931 that the CIE proposed a first representation and rationalization of colors: the CIE-1931 diagram, still used a lot today as an objective reference, in particular to compare the various color spaces in use.

Decomposing colors

It’s 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.

This breakdown is perfectly objective (related to the physical reality of light), it’s a good foundation for making an objective representation of colors, which is what the CIE has done since 1931.

Color diagrams, 1931 CIE XYZ and CIE xyZ

With these three parameters, colors can be represented in three dimensions.

In order to establish this representation, the CIE chose three theoretical primary colors different from the more common Red, Green and Blue, called X, Y and Z, able to include the entirety of the visible colors. This representation is the CIE XYZ color space of 1931, and is still used today as reference to represent and compare all the other color 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 three-dimensional representation above is not exact, but does illustrate the general feel of the color space.

For better and easier use and visualization, it’s mainly represented in a two-dimensional projection, not showing the intensity (brightness) of the colors at all.

This projection actually is actually a translation to another color space derived from the CIE XYZ where colors are represented on a plane by coordinates named x and y (in lower case) which makes it the CIE xyZ space.

On this diagram, one can find the spectrum of visible light, on the upper turn, rounded, going from red to blue.

This outline contains all possible monochromatic lights, while the inside of the diagram represents “blended” 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 aren’t part of the monochromatic lights and close the “color wheel” we all know.

This diagram containing all the visible colors is used as reference in which one can register the other color spaces, necessarily “smaller” because representing only a subpart of all these colors, as we will see hereafter.

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 more specific spaces 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 xyZ2: 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 1931 XYZ or xyZ which is used as reference to work with and compare all the other colorimetric spaces.

Sources et références

  1. Color spaces are standardized ways of recording and representing 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. ↩

  2. 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. ↩