Oklab color space

Oklab uses the same spatial structure as CIELAB, representing color using three components:

• L for perceptual lightness, ranging from 0 (pure black) to 1 (reference white, if achromatic), often denoted as a percentage
• a and b for opponent channels of the four unique hues, unbounded but in practice ranging from −0.5 to +0.5
  • a for green (negative) to red (positive)
  • b for blue (negative) to yellow (positive)

Like CIELCh, Oklch represents colors using:

• L for perceptual lightness
• C for chroma representing chromatic intensity, with values from 0 (achromatic) with no upper limit, but in practice not exceeding +0.5
• h for hue angle in a color wheel, typically denoted in decimal degrees

Neutral greys, pure black and the reference white are achromatic, that is, ${\displaystyle C=0}$ , ${\displaystyle a=0}$ , ${\displaystyle b=0}$ , and h is undefined. Assigning any real value to their hue component has no effect on conversions between color spaces.^[2]

While pure black is a coordinate singularity in Oklab and Oklch spaces, high-dynamic-range displays can display many chromatic colors (${\displaystyle C>0}$ ) at ${\displaystyle L=1}$  (the lightness of the reference white) due to the extended gamut.

The perceptual color difference in Oklab is calculated as the Euclidean distance between the (L, a, b) coordinates.^[8][2]

Like CIELCh, the Cartesian coordinates a and b are converted to the polar coordinates C and h as follows:

${\displaystyle {\begin{aligned}C&={\sqrt {a^{2}+b^{2}}}\\h&=\operatorname {atan2} (b,a)\end{aligned}}}$ 

And the polar coordinates are converted to the Cartesian coordinates as follows:

${\displaystyle {\begin{aligned}a&=C\cos(h)\\b&=C\sin(h)\end{aligned}}}$ 

Converting from CIE XYZ with a Standard Illuminant D65 involves:^[1]

1. Converting to an LMS color space with a linear map:
   ${\displaystyle {\begin{bmatrix}l\\m\\s\end{bmatrix}}=\mathbf {M} _{1}{\begin{bmatrix}X\\Y\\Z\end{bmatrix}}}$ 
2. Applying a cube root non-linearity:
   ${\displaystyle {\begin{bmatrix}l'\\m'\\s'\end{bmatrix}}={\begin{bmatrix}l^{1/3}\\m^{1/3}\\s^{1/3}\end{bmatrix}}}$ 
3. Converting to Oklab with another linear map:
   ${\displaystyle {\begin{bmatrix}L\\a\\b\end{bmatrix}}=\mathbf {M} _{2}{\begin{bmatrix}l'\\m'\\s'\end{bmatrix}}}$ 

Given:

${\displaystyle {\begin{aligned}\mathbf {M} _{1}&={\begin{bmatrix}0.8189330101&{\phantom {-}}0.3618667424&-0.1288597137\\0.0329845436&{\phantom {-}}0.9293118715&{\phantom {-}}0.0361456387\\0.0482003018&{\phantom {-}}0.2643662691&{\phantom {-}}0.6338517070\end{bmatrix}}\\\mathbf {M} _{2}&={\begin{bmatrix}0.2104542553&{\phantom {-}}0.7936177850&-0.0040720468\\1.9779984951&-2.4285922050&{\phantom {-}}0.4505937099\\0.0259040371&{\phantom {-}}0.7827717662&-0.8086757660\end{bmatrix}}\end{aligned}}}$ 

Converting from sRGB requires first converting from sRGB to CIE XYZ with a Standard Illuminant D65. As the last step of this conversion is a linear map from linear RGB to CIE XYZ, the reference implementation directly employs the multiplied matrix representing the composition of the two linear maps:^[1]

${\displaystyle {\begin{bmatrix}l\\m\\s\end{bmatrix}}={\begin{bmatrix}0.4122214708&0.5363325363&0.0514459929\\0.2119034982&0.6806995451&0.1073969566\\0.0883024619&0.2817188376&0.6299787005\end{bmatrix}}{\begin{bmatrix}R_{\text{linear}}\\G_{\text{linear}}\\B_{\text{linear}}\end{bmatrix}}}$ 

Converting to CIE XYZ and sRGB simply involves applying the respective inverse functions in reverse order:^[1]

${\displaystyle {\begin{aligned}{\begin{bmatrix}l'\\m'\\s'\end{bmatrix}}&=\mathbf {M} _{2}^{-1}{\begin{bmatrix}L\\a\\b\end{bmatrix}}\\{\begin{bmatrix}l\\m\\s\end{bmatrix}}&={\begin{bmatrix}\left(l'\right)^{3}\\\left(m'\right)^{3}\\\left(s'\right)^{3}\end{bmatrix}}\\{\begin{bmatrix}X\\Y\\Z\end{bmatrix}}&=\mathbf {M} _{1}^{-1}{\begin{bmatrix}l'\\m'\\s'\end{bmatrix}}\end{aligned}}}$