# Valid Colors in the CIE 1976 Lab Color Space

August 23, 2011

I was curious about which values are valid in the CIELAB color space. The lightness coordinate, L, is defined to range from 0 to 100, but the chromaticity coordinates, a and b, have no defined bounds. So I wrote a program to find which CIELAB coordinates can be created physically.

Each wavelength of light produces a well defined color that be found in a table. But as most colors are a combination of different wavelengths, you need to solve a number of equations to find which wavelengths that are needed to create that color. This can be modeled as a Linear Programming Problem. A color is physically possible if the Linear Programming Problem has at least one solution.

I ran the program to create images of the a and b plane for a given L-value. The Physically reproducible colors are drawn in a light gray color, and if the color is whithin the sRGB gamut, it is drawn as is. L* = 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 , a* ∈ [-128, 128], b* ∈ [-128, 128]

## References

1. A Standard Default Color Space for the Internet - sRGB, M. Stokes, M. Anderson, S. Chandrasekar, R. Motta 1996. http://www.color.org/sRGB.xalter
2. CIE 1931 color space, Wikipedia. http://en.wikipedia.org/wiki/CIE_1931_color_space
3. Lab color space, Wikipedia. http://en.wikipedia.org/wiki/Lab_color_space
4. Color Science, 2nd Edition, G. Wyszecki, W.S. Stiles 2000. ISBN 978-0-471-39918-6.
5. Linear Programming, Wikipedia. http://en.wikipedia.org/wiki/Linear_programming