Colour Space Encoding

Colour information in the various colour spaces can be encoded in different ways. This encoding on the one hand refers to the specific colour space used, and on the other hand the encoding into a numerical value. There are enough pages dealing with various colour spaces already. This little HOWTO tries to enlighten on how often the numbers are encoded

Positive-Only Colour Spaces

Colour spaces with positive values only (e. g. RGB, XYZ, CMY(K)) are fairly simple. Their origin is at a zero vector (0.0, 0.0, 0.0), and their maximum at the ones vector (1.0, 1.0, 1.0) in floating point notation. For a notation with 8 or 16 bit (unsigned) integers they are just scaled by the maximum per channel encoding value (255 or 65535) and rounded by some means to the full integers. Although, strictly speaking some colour spaces like XYZ can contain negative coordinate values. Although, these are usually then not encodable by the commonly used systems.

CIE LAB

For CIE LAB the issue is not quite as simple. Many ways of encoding are used. Some are exposing the positive and negative values through signed 8/16 bit integers, others project them all into the positive integer space, and they are also then often using different origin offsets. And then there is also the ICC V4 16 bit, ICC 8 bit standard. Below summarised into a simple formula is the way LCMS handles the conversion for their 8 and 16 bit unsigned integer colour space encoding.

Conversion floating point Lab encoding ...

• ... to 8 bit integer encoding:

 L' = 2.54 * L
 a' = a + 127
 b' = b + 127

• ... to 16 bit integer encoding:

 L' = 650.26 * L
 a' = 255.02 * a + 32640
 b' = 255.02 * b + 32640