Software programmes that support Lab colour also allow colour values such as Lab(0, 100, 100). The example is usually displayed as dark red, but is completely meaningless, because in reality no light in the world can produce these Lab colour values. In other words: a brightness 0 cannot have any a;b values other than 0, or: "at night all cats are grey". In the article it is shown that only about 60% of the usual Lab coordinate space (0..100, -128..127;-128..127) consists of colours, the rest are Lab coordinates without colour correspondence.
It would be important to develop a suitable algorithm for non-colours that corrects incorrect Lab coordinates already during input (= projects them onto the envelope). This would greatly increase the comprehensibility and applicability of the CIELAB model. The task is solvable, because the projection of the non-colour coordinates onto the range of visible colours could be done in a similar way as the gamut mapping of out-of-gamut colours.
Which colours make up the CIELAB shell?
The most intense hues we know are the rainbow colours. These so-called "monochromatic" colours have maximum intensity in one wavelength range. Example: A remission maximum in the interval 570-590nm leads to the CIELAB values (2 degrees D50): Lab 55.91 8.58 96.38. It is the most intense possible for this yellow and this brightness, as there is no spectrum that could produce this colour more intensely at this brightness.
The broader the maximum wavelength range is, the brighter the extremely possible colour is, until white light is produced in maximum intensity for all wavelength ranges.
According to Wilhelm Ostwald, the most possible colour tones are produced by so-called "rectangular spectra": these are spectral distributions in which a more or less broad wavelength range has the maximum intensity and all other wavelength ranges have the intensity 0. Violet is also to be included, which has maximum intensity at the beginning and end of the visible spectrum. Formulated in a calculable way: for rectangular spectra, only minimum (0) or maximum (1) intensity as well as a maximum of 2 jump points (0/1 or 1/0) within the visible wavelength range are the case.
If this rule is applied to the 10-nanometre step size in the range 400-700 nanometres, which is common for colour measuring instruments, 962 rectangular spectra are obtained. These colours form the outer shell of the CIELAB colour space, all other colours lie in the inner area. Lab coordinates that lie outside the body spanned in this way are not colours, but purely theoretical computational variables that have no counterpart in the real world because they cannot be generated with any light spectrum.
(H. Everding CC-BY-SA 4.0)
Software Lab colour input and CIELAB colour space
The usual limits for a and b (-128...127) in software are exceeded in reality in several areas of the rectangular spectra. The outermost conceivable green, for example, has an a-value of -164. It is similar in the yellow range (bmax=146). In other words: not all shades of green and yellow can be reproduced by Lab colour value in software.
More serious is the fact that in Lab-capable software you can work with colour values that lie outside the CIELAB colour space limits. These are even displayed in colour, which is completely nonsensical and confusing. An example: For the coordinates (Lab 0 100 100) software shows a dark red preview. However, common sense alone says that at a brightness of 0, there can be no hue except black: "At night, all cats are grey". This is confirmed by the rectangular spectra: The only colour of brightness 0 is the one where no wavelength range has an intensity, where a=0 and b=0.
So there is a double need for development of Lab colours in software. Above all, an algorithm would be important that, similar to the gamut calculations, returns any colour value to the outer limit of the CIELAB colour space if required, but at least does not display such colour values as a colour.
List of rectangular spectra
The file cielab-boundaries contains the Lab coordinates of the rectangular colours at 10nm measuring interval under the following conditions:
- 2° observer angle, illuminant D50 (common in pre-press)
- 10° observer angle, illuminant D65 (usual for paint colours)
- 2° observer angle, illuminant D65 (sRGB parameters)
You can open the clf files in a text editor, or save them in the Digital colour atlas where the CIELAB colour space is then displayed in 3D in a freely navigable way. There you can also see at a glance that the real colour space is only about 60% of the CIELAB coordinate space.
Author: Holger Everding