Wpt normalization and MATs
An observing condition (hereafter "condition") is an observer (having a set of sensors: a standard observer's, cone fundamentals, a camera's) under a light. Its Wpt normalization is one 3 × 3 matrix that turns the condition's responses into Wpt, the common representation of materials. Two normalizations give a material adjustment transform (MAT) between their conditions. The sensors can be your own: custom cone fundamentals or color-matching functions measured for an individual can be pasted in as they are.
1. The observing condition
2. The normalization
Responses to Wpt
Wpt to responses
3. The MAT to another condition
A MAT is not possible with more than three sensors: the normalization goes one way, from the sensors' responses to Wpt, with no way back to the responses of another condition.
A MAT carries responses from the condition above (the source) to this one (the destination) by way of the material: M = Adestination−1 Asource.
MAT, source to destination
Reverse MAT, destination to source
The reverse MAT is the inverse of the MAT, M−1 = Asource−1 Adestination: it carries the destination's responses back to the source.
How well does it predict?
For each material, the destination responses predicted from the source responses are compared with the true ones, in ΔEWLab; the MAT is compared with the chromatic adaptation transforms (CATs) that apply.
Reflectances from 0 to 1, or percent; names optional; any wavelength grid covering at least 420 to 680 nm.
Where the MAT does worst
The two directions differ for the CATs, each measured in the WLab of the condition it predicts. For the MAT they are the same: the MAT's prediction of a material in one condition is its Wpt in the other, so its error is the WLab difference between the material's Wpt in the two conditions, its shift between them, which reads the same both ways.
A CAT adapts colors from the source white to the destination white within one observer. Bradford and CAT02 are defined on CIE XYZ, so they are shown only for the CIE color-matching functions; for cone fundamentals and other sensors the CAT is von Kries scaling in the sensors' own space. When the two conditions have different observers, no CAT applies: only the MAT carries colors across. The 1,600 Munsell colors (UEF measurements, corrected by Derhak and Berns, 2012) include the 40 base colors, left out here unless chosen.
4. Evaluating the Wpt normalization
The normalization of the condition in section 1 is built from its responses to a perfect white and to 40 Munsell colors of equal lightness (Value 5, Chroma 6), one per 2.5 hue steps: the base set. Here are its four steps; the Technical annex of the guide, section A.3, gives the equations.