CIELABCIEXYZ

CIELABCIEXYZ is a term used to describe the essential relationship between the CIELAB perceptual color space and the CIEXYZ linear tristimulus space. It is not a standalone, separate color space, but a label for the standard transformations that convert between L*, a*, b* values and X, Y, Z tristimulus values. These conversions are central to color management because CIELAB aims to be perceptually uniform, while CIEXYZ provides a device-independent reference tied to a defined white point.

Background and concept

CIELAB was defined by the CIE to approximate uniform color differences and to provide a device-independent description of color. CIEXYZ is a linear, physical color space based on human vision under a specified standard observer and reference white. The Lab↔XYZ transformations underpin many color workflows, including ICC profiles, color matching, and color difference calculations (ΔE*ab).

Forward and inverse transformations

From Lab to XYZ: given L*, a*, b*, and a reference white (Xn, Yn, Zn), compute fy = (L* + 16) / 116, fx = fy + a*/500, fz = fy - b*/200. Then X = Xn·f^(-1)(fx), Y = Yn·f^(-1)(fy), Z = Zn·f^(-1)(fz). The function f(t) is f(t) = t^(1/3) if t > (6/29), and f(t) = (t / (3(6/29)^2)) + 4/29 otherwise; its inverse f^(-1)(u) uses u^3 when u > 6/29, and 3(6/29)^2(u - 4/29) otherwise.

From XYZ to Lab: L* = 116·f(Y/Yn) − 16, a* = 500·[f(X/Xn) − f(Y/Yn)], b* = 200·[f(Y/Yn) − f(Z/Zn)], using the same f(t) function.

Applications and limitations

CIELABCIEXYZ transformations are foundational in color management, enabling device-independent color specification, color matching, and perceptual color difference assessments. The results depend on the chosen reference white (commonly D65 for viewing conditions or D50 for print), and perceptual uniformity has limits across all colors.

See also

CIELAB, CIEXYZ, color management, ICC profiles, ΔE.