oklab2rgb: Perceptual Color Space to RGB Conversion

Mathematical Foundation of Perceptual Color Transformation

OKLab represents a perceptually uniform color space where equal distances correspond to equal perceived color differences. The conversion to RGB involves two matrix transformations with intermediate cubic root processing.

The mathematical operation follows this sequence: $\text{LMS} = M_A \cdot \text{OKLab}$ $\text{RGB} = M_B \cdot (\text{LMS}^3)$

Where $M_A$ and $M_B$ are transformation matrices calibrated for human visual perception, and the cubic operation reverses the cube root applied during RGB to OKLab conversion.

Transformation Properties

The function implements a two-stage linear-nonlinear-linear pipeline. Matrix $M_A$ transforms OKLab coordinates to LMS (Long, Medium, Short wavelength) response space, representing cone cell responses. The cubic operation reconstructs linear light values from perceptual coordinates. Matrix $M_B$ converts LMS to linear RGB values.

Key mathematical properties:

• Bijective mapping: Every valid OKLab coordinate maps to exactly one RGB value
• Perceptual linearity: Equal distances in OKLab correspond to equal perceived color differences
• Gamut preservation: The transformation maintains valid RGB ranges for displayable colors

ライブエディター

const fragment = () => {
      const oklabColor = vec3(0.7, uv.x.sub(0.5), uv.y.sub(0.5))
      const rgbColor = oklab2rgb(oklabColor)
      return vec4(rgbColor, 1)
}

ライブエディター

const fragment = () => {
      const originalRgb = vec3(uv.x, 0.3, uv.y)
      const oklab = rgb2oklab(originalRgb)
      const recovered = oklab2rgb(oklab)
      return vec4(recovered, 1)
}