Apéry's constant

Normalized responsivity spectra of human cone cells, S, M, and L types

LMS is a color space represented by the response of the three types of cones of the human eye, named after their responsivity (sensitivity) at long, medium and short wavelengths.

It is common to use the LMS color space when performing chromatic adaptation (estimating the appearance of a sample under a different illuminant).

XYZ to LMS

Typically, the color to be adapted will be specified in a color space other than LMS, but easily convertible to XYZ. The chromatic adaptation matrix in the von Kries transform method, however, is diagonal in LMS space, thus the usefulness of a transformation matrix M between spaces. The transformation matrices for some chromatic adaptation models in terms of CIEXYZ coordinates are presented here.

Notes

• All tristimulus values are normally calculated using the CIE 1931 2° standard colorimetric observer.
• Unless specified otherwise, M is normalized (the elements in a row add up to unity) so the tristimulus values for an equal-energy illuminant (X=Y=Z), like CIE Illuminant E, produce equal LMS values.

CMCCAT97

The CMCCAT97 color appearance model uses the Bradford transformation matrix (M_B):

${\begin{bmatrix}L\\M\\S\end{bmatrix}}={\begin{bmatrix}0.8951&0.2664&-0.1614\\-0.7502&1.7135&0.0367\\0.0389&-0.0685&1.0296\end{bmatrix}}{\begin{bmatrix}X\\Y\\Z\end{bmatrix}}$

RLAB

The RLAB color appearance model uses the Hunt-Pointer-Estevez (HPE) transformation matrix (M_H) for conversion from CIE XYZ to LMS:

Equal-energy illuminants:	${\begin{bmatrix}L\\M\\S\end{bmatrix}}={\begin{bmatrix}0.38971&0.68898&-0.07868\\-0.22981&1.18340&0.04641\\0.00000&0.00000&1.00000\end{bmatrix}}{\begin{bmatrix}X\\Y\\Z\end{bmatrix}}$
Normalized to D65:	${\begin{bmatrix}L\\M\\S\end{bmatrix}}={\begin{bmatrix}0.4002&0.7076&-0.0808\\-0.2263&1.1653&0.0457\\0&0&0.9182\end{bmatrix}}{\begin{bmatrix}X\\Y\\Z\end{bmatrix}}$

CAT97s

CIECAM97s uses a spectrally-sharpened Bradford chromatic adaptation matrix:

${\begin{bmatrix}L\\M\\S\end{bmatrix}}={\begin{bmatrix}0.8562&0.3372&-0.1934\\-0.8360&1.8327&0.0033\\0.0357&-0.0469&1.0112\end{bmatrix}}{\begin{bmatrix}X\\Y\\Z\end{bmatrix}}$

CAT02

The chromatic adaptation matrix (M_CAT02) from the CIECAM02 model is:

${\begin{bmatrix}L\\M\\S\end{bmatrix}}={\begin{bmatrix}0.7328&0.4296&-0.1624\\-0.7036&1.6975&0.0061\\0.0030&0.0136&0.9834\end{bmatrix}}{\begin{bmatrix}X\\Y\\Z\end{bmatrix}}$

See also

• Color balance
• Color vision
• Luminosity function
• Trichromacy