LMS color space

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). It's also useful in the study of color blindness, when one or more cone types are defective.

XYZ to LMS

Typically, colors to be adapted chromatically will be specified in a color space other than LMS. The chromatic adaptation matrix in the von Kries transform method, however, expects the LMS color space. Since colors in any color space can, by definition, be transformed to the XYZ color space, only one additional transformation matrix is required to transform colors from the XYZ color space to the LMS color space.

Since the LMS color space is supposed to model the complex human color perception, no single, “objective” transformation matrix between XYZ and LMS exists. Instead, various Color Appearance Models (CAMs) offer various Chromatic Adaptation Transform (CAT) matrices M as part of their modeling of human color perception.

The CAT matrices for some CAMs in terms of CIEXYZ coordinates are presented here.

Notes 

• All tristimulus values are normally calculated using the CIE 1931 2° standard colorimetric observer.^[1]
• Unless specified otherwise, the CAT matrices are 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.^[1]

Hunt, RLAB

The Hunt and RLAB color appearance models use the Hunt-Pointer-Estevez transformation matrix (M_HPE) for conversion from CIE XYZ to LMS.^[1][2] This is the transformation matrix which was originally used in conjunction with the von Kries transform method, and is therefore also called von Kries transformation matrix (M_vonKries).

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:	$\begin{bmatrix} L\\M\\S \end{bmatrix} = \begin{bmatrix} 0.4002 & 0.7076 & -0.0808 \\ -0.2263 & 1.1653 & 0.0457 \\ 0 & 0 & 0.9182 \end{bmatrix} \begin{bmatrix} X\\Y\\Z \end{bmatrix}$

CIECAM97s, LLAB

The original CIECAM97s color appearance model uses the Bradford transformation matrix (M_BFD) (as does the LLAB color appearance model).^[1] This is a “spectrally sharpened” transformation matrix (i.e. the L and M cone response curves are narrower and more distinct from each other). The Bradford transformation matrix was supposed to work in conjunction with a modified von Kries transform method which introduced a small non-linearity in the S (blue) channel. However, outside of CIECAM97s and LLAB this is often neglected and the Bradford transformation matrix is used in conjunction with the linear von Kries transform method, explicitly so in ICC profiles.^[3]

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

A revised version of CIECAM97s switches back to a linear transform method and introduces a corresponding transformation matrix (M_CAT97s):^[4]

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

CIECAM02

CIECAM02 is the successor to CIECAM97s; its transformation matrix (M_CAT02) is:^[1]

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

See also

• Color balance
• Color vision
• Luminosity function
• Trichromacy

References

1. Fairchild, Mark D. (2005). Color Appearance Models (2E ed.). Wiley Interscience. ISBN 978-0-470-01216-1.
2. Moroney, Nathan; Fairchild, Mark D.; Hunt, Robert W.G.; Li, Changjun; Luo, M. Ronnier; Newman, Todd (November 12, 2002). "The CIECAM02 Color Appearance Model" (PDF). IS&T/SID Tenth Color Imaging Conference. Scottsdale, Arizona: The Society for Imaging Science and Technology. ISBN 0-89208-241-0.
3. Specification ICC.1:2010 (Profile version 4.3.0.0). Image technology colour management — Architecture, profile format, and data structure, Annex E.3, pp. 102.
4. Fairchild, Mark D. (2001). "A Revision of CIECAM97s for Practical Applications" (PDF). Color Research & Applications. Wiley Interscience. 26: 13.