LMS color space
LMS (long, medium, short), is a color space which represents the response of the three types of cones of the human eye, named for their responsivity (sensitivity) peaks 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).
are defined as: The cone response functions are normalized to have their maxima equal to unity.
The chromatic adaptation matrix in the diagonal von Kries transform method, however, operates on tristimulus values in the LMS color space.
[3] In addition, many color adaption methods, or color appearance models (CAMs), run a von Kries-style diagonal matrix transform in a slightly modified, LMS-like, space instead.
[3] The chromatic adaptation transform (CAT) matrices for some CAMs in terms of CIEXYZ coordinates are presented here.
Notes: The Hunt and RLAB color appearance models use the Hunt–Pointer–Estevez transformation matrix (MHPE) for conversion from CIE XYZ to LMS.
[3] 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.
A "spectrally sharpened" matrix is believed to improve chromatic adaptation especially for blue colors, but does not work as a real cone-describing LMS space for later human vision processing.
Although the outputs are called "LMS" in the original LLAB incarnation, CIECAM97s uses a different "RGB" name to highlight that this space does not really reflect cone cells; hence the different names here.
LLAB proceeds by taking the post-adaptation XYZ values and performing a CIELAB-like treatment to get the visual correlates.
On the other hand, CIECAM97s takes the post-adaptation XYZ value back into the Hunt LMS space, and works from there to model the vision system's calculation of color properties.
As in CIECAM97s, after adaptation, the colors are converted to the traditional Hunt–Pointer–Estévez LMS for final prediction of visual results.
From a physiological point of view, the LMS color space describes a more fundamental level of human visual response, so it makes more sense to define the physiopsychological XYZ by LMS, rather than the other way around.
A set of physiologically-based LMS functions were proposed by Stockman & Sharpe in 2000.
Then, by definition, the new XYZ color matching functions are: where the transformation matrix
The inverse matrix is shown here for comparison with the ones for traditional XYZ:
In addition, it offers a one-to-one relationship between the LMS chromaticity coordinates and the new XFYFZF chromaticity coordinates, which was not the case for the CIE 1931 color matching functions.
The transformation for a particular color between LMS and the CIE 1931 XYZ space is not unique.
Any such transformation will be an approximation at best, generally requiring certain assumptions about the spectral distributions producing the color.
For example, if the spectral distributions are constrained to be the result of mixing three monochromatic sources, (as was done in the measurement of the CIE 1931 and the Stiles and Burch[1] color matching functions), then there will be a one-to-one relationship between the LMS and CIE 1931 XYZ coordinates of a particular color.
As of Nov 28, 2023, CIE 170-2 CMFs are proposals that have yet to be ratified by the full TC 1-36 committee or by the CIE. For theoretical purposes, it is often convenient to characterize radiation in terms of photons rather than energy.
The energy E of a photon is given by the Planck relation where E is the energy per photon, h is the Planck constant, c is the speed of light, ν is the frequency of the radiation and λ is the wavelength.
Using the above equation for the energy tristimulus values CEi For the LMS color space,
An early emulation of dichromats were produced by Brettel et al. 1997 and was rated favorably by actual patients.
[21] JPEG XL uses an XYB color space derived from LMS.
This can be interpreted as a hybrid color theory where L and M are opponents but S is handled in a trichromatic way, justified by the lower spatial density of S cones.
In practical terms, this allows for using less data for storing blue signals without losing much perceived quality.
[22] The colorspace originates from Guetzli's butteraugli metric,[23] and was passed down to JPEG XL via Google's Pik project.
