Comparing MATs and CATs
A measurement made in one observing condition (hereafter "condition": an observer under a light) often has to be carried to another. There are two different things to predict there, and two kinds of transform made for them.
- Corresponding color: the color that looks the same, in the new condition, as the original did in its own, to a viewer adapted to each. It is about appearance, and is measured by asking observers. A chromatic adaptation transform (CAT) is made to predict it.
- Material color: the color the same material will measure in the new condition. It is about the material, and is measured with an instrument. A material adjustment transform (MAT) is made to predict it.
The two are not the same: a material whose color changes with the light does not look the same to an adapted viewer under both, and its corresponding color is not what it measures. This page tests material color: it takes objects whose spectra are known, so that their colors under every light can be computed, and asks how close each transform comes to them. That is the MAT's job; for the CATs, it is a job they were not made for. How well they predict corresponding colors, their own job, needs data from observers and is not tested here (on such data, the Wpt paper found CAT02 ahead of the MAT). Here the observer stays the same and the light changes, as a CAT assumes; for a change of observer, where no CAT applies, the observer lab compares the MAT with other ways of converting an observer (Observers, section 4).
1. One shape for every transform
Every transform here works the same way. It takes a color measured under the first light, cmeasured, into a common representation, one meant to hold whatever the light, and brings it back out as the color it predicts under the second light, cpredicted:
cpredicted = Tdest−1 Tsrc cmeasured
Tsrc, for the first light (the source), takes the color into the common representation, and Tdest−1, for the second light (the destination), brings it out under that light. The transforms differ only in T, the matrix that takes a condition's colors into the common representation, and so in what the common representation holds:
| Transform | What its T does | Built from |
|---|---|---|
| von Kries scaling | scales each channel of XYZ so that the light's white becomes 1 | the light's white point |
| Bradford, CAT02 | first turns XYZ into cone-like channels (each its own matrix), then scales them so that white becomes 1: a model of how the eye adapts to a light's white | the light's white point |
| Wpt MAT | the condition's Wpt normalization: it puts white at W = 100, then places a set of base materials (40 Munsell colors) where they belong in the reference's material coordinates, so that materials, not only white, land together | the light's spectrum, as the observer's sensors see it through those materials |
That makes two families. White point based transforms (von Kries, Bradford, CAT02) are built from the two lights' white points alone: the color a perfect white measures under each. Spectrally based transforms (the Wpt MAT) are built from the two lights' whole spectra, through the colors materials measure under each. The difference shows most plainly with two lights of the same white point but different spectra, such as daylight and an LED made to match its white. To every white point based transform they are the same light: it predicts no change at all, for any material. Materials do change between such lights, by how far depends on their spectra, and a spectrally based transform sees that.
Every one of them carries white exactly: a perfect white under the first light comes out as a perfect white under the second. They differ in what they do to everything else. A CAT moves every color by the same rule that moves white, as an eye adapting to the new light would; that is what corresponding color asks for. A MAT moves each color as materials of that color move between the two lights; that is what material color asks for. A CAT keeps one observer and changes the light; the MAT can change the light, the observer or both, because its T is built for each condition from its own sensors. The sections below put the transforms to the test of material color: first for one material, then for many, then for many lights.
2. One material, one change of light
A material is measured under one light. What will it measure under another? Each transform takes the first measurement and predicts the second; here are its predictions beside the color the material actually measures there. The chips show each color as its numbers would look on a screen (so the measurement under the first light keeps that light's color cast).
The material opens on the one, among the objects of section 3, whose CAT02 prediction is furthest from its MAT prediction under these lights; any other can be chosen. ΔE00 is in the CIELAB of the second light (its white as the white), as the guide and the Wpt paper report it; ΔEWLab beside it.
A challenge
Find two lights in the menus above whose white points nearly match but whose spectra differ. To every white point based transform they are nearly the same light, so its prediction hardly differs from the measurement it started from; but the material's measurement still moves between them. The line under the plots says how far apart the two white points are (Δu′v′, the distance in the CIE 1976 u′, v′ diagram) and how much the measurement moves and CAT02 changes it. Watch the swatches: the CATs' predictions stay with the first measurement, the MAT's goes with the second.
Some answers
A and LED-BH1, both near 2850 K (white points 0.0004 apart); LED-B1 and LED-V1, near 2730 K; D65 and LED-B5, daylight and a blue-pumped LED of about the same white; F2 and LED-V2, a fluorescent and a violet-pumped LED. Over the Munsell colors, from F2 to LED-V2 the measurements move by a mean ΔE00 of 4.3, CAT02's predictions are 3.9 from where they land and the MAT's 0.7.
The limit of the challenge is the last light in the menus, the RGB LED (D65's white): three LED peaks (blue at 455 nm, green at 530 nm and red at 630 nm, 20, 35 and 18 nm wide at half their height), mixed so that the chosen observer's white under it is exactly D65's. Between D65 and the RGB LED every white point based transform changes nothing, so von Kries, Bradford and CAT02 give one prediction: the measurement itself. Over the Munsell colors, for CIE 1931, the measurements move by a mean ΔE00 of 4.07 between the two lights, and that is how far the CATs' predictions are from where they land; the MAT's are 1.23 from them (D65 to the RGB LED) and 1.19 (back). For CIE 1964: 3.41 for the CATs, 1.44 and 1.34 for the MAT.
3. Many materials, the same change of light
The same prediction for every object of a library: how far each transform's predictions are from the colors the objects actually measure under the second light, for the observer and lights of section 2.
By default 759 objects: 271 of the corrected Munsell colors (ten hues at every Value and at Chroma 4 to 16, and the neutrals), the CIE's 99 color evaluation samples, the 30 patches of the PMCC and 359 natural objects measured in Japan.
A CGATS measurement file (with spectral fields such as SPECTRAL_NM380) or a table: wavelength in the first column and one object per column, or one object per row with the wavelengths across the header row; values from 0 to 1 or in percent, covering at least 420 to 680 nm. Read in this page; it goes nowhere.
The materials hardest to predict
The eight objects whose MAT prediction is furthest from what they measure, with every transform's ΔE00. Choose one in section 2 to see its colors.
The guide's numbers, checked
The guide to Wpt and WLab, WLab and Wpt:
Color Without the Fine Print, quotes a result of the Wpt paper: over 5,162 measured reflectances, the Wpt
MAT predicted D65 colorimetry (material color) from illuminant A more closely than CAT02 (mean ΔE00 1.24
against 2.35, CIE 1964 observer). Not all of the 5,162 are open data, so that test is not rerun here. The code that
goes with the guide (wpt-onramp, its example
ex05) reruns a smaller version on the 1,600 corrected Munsell colors (1.09 against 2.26, CIE 1931);
this page gives the same, below, with the Munsell colors in place of this section's objects and illuminant A to
D65. The Munsell colors include the 40 the Wpt normalization is built from.
4. Many lights
The same, for every light of a set: each light's objects predicted for the second light of section 2 (D65 by default), one row per light. Each number is the mean ΔE00 over the objects of section 3; the smallest of each row is in italics.
Lights to pair reference with
More choices
Hover over a dot for its light and value.
5. Watching the transforms work
The formula of section 1, played out. A set of Munsell colors is measured in three conditions at once, each condition's points in its own color: the 40 base colors of the Wpt normalization, a hue circle at Value 5, and ten hue spokes, from gray outward, in three planes, at Values 2, 5 and 8. Press play: each condition's T takes its measurements, step by step, into the common representation, and then they come back out again. In the common representation, colors that are the same material should land together. With a white point based transform only white and the grays do; the other colors keep the spread their conditions gave them. With the Wpt MAT the materials land together, white and color alike, as far as the conditions allow.
Drag the view to turn it; the slider moves through the steps by hand. The scale follows the points, so they fill the view at every step (the extent of each axis is under the view). The view's vertical axis is the first channel of each step (W in Wpt), the other two across. Each condition's measurements are its sensor excitations, scaled so that white's second one is 100; a CAT's common representation is shown with white at 100, 100, 100.