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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 LMSEdit

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

### CMCCAT97Edit

The CMCCAT97 color appearance model uses the Bradford transformation matrix (MB):[2]

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

### RLABEdit

The RLAB color appearance model uses the Hunt-Pointer-Estevez (HPE) transformation matrix (MH) for conversion from CIE XYZ to LMS:[1][3]

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

### CAT97sEdit

CIECAM97s uses a spectrally-sharpened Bradford chromatic adaptation matrix:[1]

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

### CAT02Edit

The chromatic adaptation matrix (MCAT02) from the CIECAM02 model is:[1]

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

## ReferencesEdit

1. 1.0 1.1 1.2 1.3 1.4 Fairchild, Mark D. (2005). Color Appearance Models, 2E, Wiley Interscience.
2. Westland, Stephen; Ripamonti, Caterina (2004). "6.2.2 CMCCAT97" Computational Colour Science Using MATLAB, Wiley Interscience.
3. Moroney, Nathan; Fairchild, Mark D.; Hunt, Robert W.G.; Li, Changjun; Luo, M. Ronnier; Newman, Todd (November 12 2002). "The CIECAM02 Color Appearance Model". IS&T/SID Tenth Color Imaging Conference, Scottsdale, Arizona: The Society for Imaging Science and Technology. ISBN 0-89208-241-0.

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