Oklab color space

The Oklab color space is a

Oklab's model is fitted with improved color appearance data: CAM16 data for lightness and chroma, and IPT data for hue. The new fit addresses issues such as unexpected hue and lightness changes in blue colors present in the CIELAB color space, simplifying the creation of color schemes and smoother color gradients.^[1][7][4]

As Ottosson explained,^[1] he chose the name Oklab because the model does an OK (adequate) job and is based on the three color-space coordinates L, a, and b.

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; CSS assigns ±100% to ±0.4 for both^[2]
  • 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; CSS treats +0.4 as 100%^[2]
• 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]

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

1. Applying the linear map:^[b]
   ${\displaystyle {\begin{bmatrix}l\\m\\s\end{bmatrix}}=\mathbf {M} _{1}{\begin{bmatrix}X\\Y\\Z\end{bmatrix}}}$
2. Applying a
   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]

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