CIELAB Boundaries

CIELAB boundaries – the borders of the CIELAB color space

Software programs that support Lab colours permit values like e.g. Lab (0, 100, 100). The example is usually displayed as a dark red, but it is completely meaningless, because in reality, no light in the world can produce such Lab values. In other words, a brightness 0 can have no other a;b values ​​than 0. “All cats are gray at night”. In the article, it is shown that only about 60% of the usual Lab coordinate space (0..100, -128..127; -128..127) consists of colors, the rest are Lab coordinates without meaning as colour.

It would be important to develop a suitable algorithm that corrects non-colour Lab coordinates when entered (= projected onto the body surface). This would increase the intelligibility and applicability of the CIELAB model. The task is solvable because the projection of the non-colour coordinates to the range of visible colors is similar to the gamut mapping of out-of-gamut colors.

Which are the borders of CIELAB?

The most intense shades we know are the rainbow colors. These so-called “monochromatic” colors exhibit maximum intensity at a single wavelength interval. Example: a remission maximum in the interval 570-590nm leads to the CIELAB values (2 degrees D50)  Lab 55,91 8,58  96,38. This rainbow yellow is the most intense one, no yellow of this lightness can be more intense as there is no spectrum that can generate more intense values. The wider the maximum wavelength range is, the brighter is the most extreme possible color, until white light is generated by all wavelength ranges of maximum intensity.

According to Wilhelm Ostwald, the most extreme color shades possible are generated by so-called “rectangular spectra”: spectral distributions in which a more or less broad wavelength range has the maximum intensity and all other wavelength ranges have no intensity. Violet spectra are also included (beginning and end of the spectrum). In other words, only minimal (0) or maximum (1) intensity as well as a maximum of two jump points (0/1 or 1/0) within the visible wavelength range are permitted for rectangular spectra.

If this rule is applied to the conventional 10 nanometer stepwidth in the range 400-700 nanometer, 962 different rectangular spectra are obtained. Their Lab color values ​​form the outer shape of the CIELAB color space. All colors are inside this body. Lab coordinates lying outside are not colors, but purely theoretical computation variables that are not existing in the real world, because no spectrum can generate these colors.


CIELAB color space from above.


CIELAB colour space front view


Software Lab values and CIELAB color space

In reality, the usual limits for a and b (-128 … 127) are exceeded in several areas. The outermost conceivable green has, for example, a b-value of -164. Similarly, it is in the yellow range (b = 146). In other words, not all greens and yellows can be described by Lab in software.

The fact that Lab-enabled software can work with values ​​outside the CIELAB color space limits is far more serious. These are even displayed in color, which is completely nonsensical and confusing. For example, the coordinates (Lab 0 100 100) can be entered in Photoshop and the program displays a dark red preview. Even the healthy understanding of the human being states that at a brightness 0 no color of any intensity can be present: “At night all cats are grey”. This is confirmed by the rectangular colors: the only color of the brightness 0 is that in which no wavelength range has an intensity (a = 0 and b = 0).

Photoshop shows non-colors in color.

There is, therefore, a double need for improvement. An algorithm which, similar to the gamut calculations, would return an arbitrary color value as required to the outer limit of the CIELAB color space, but at least not display such color values ​​as a color.

List of boundary color values

The cielab-boundaries file contains a complete list of rectangle spectra at 10nm measurement interval under the following conditions:

  • 2 ° observer angle, light D50 (usual in prepress)
  • 10 ° observer angle, light D65 (customary for lacquer paints)
  • 2 ° observer angle, light D65 (usual sRGB parameter)

. The list can be included in the Digital Color Atlas where you see the CIELAB space navigable and zoomable in 3D. Here, at a glance is visible that the real color space is only about 60% of the CIELAB coordinate space.

Author: Holger Everding