From the onramp to using material color in practice

The guide gave three things. Materials that look alike in one place can be told apart from materials that stay alike everywhere. Every material has a place, Wpt, that stays nearly the same whatever the light and whoever is looking, and WLab reshapes that place so that distances read like familiar ΔE values. And a material adjustment transform (MAT) carries measurements from one light or viewer to another by way of the material.

The labs add the rest of the road: the same ideas tried on your own spectra, sensors and lights, over many lights, observers and objects at once. Everything runs in your browser, and nothing you enter or load is sent anywhere.

Each lab takes up one question. The line under it says how the lab answers.

• How do I give my sensors (an observer's, a camera's) a Wpt, and carry colors from one condition to another? Wpt normalization and MATs Builds the normalization of any sensors under any light, shows its four steps, and tests the MAT between two conditions.
• How far apart are two colors measured under one light? WLab and color differences ΔE_WLab for pairs measured in any condition, beside ΔE₀₀ for the CIE observers, with plots of where the colors sit.
• Does WLab hold hue constant as colors get lighter and grayer? Uniformity and hue Lines of constant hue and the Munsell loci in WLab beside CIELAB and CAM16-UCS, and the object-color solid of two conditions.
• Does a material keep its color across lights and observers, and do two that match here match everywhere? Objects Each material's shift manifold over the conditions you choose, and pairs compared condition by condition.
• How different is an observer (a person's own, or a camera's) from the standard ones, and how is it carried in an iccMAX profile? Observers The OME and OCE against the CIE observers, the closest CIE 2006 observer, and a profile that carries the observer.
• How alike do two lights render materials, and how does that sit beside the color rendering index and TM-30? Lighting The IRE over libraries of objects and observers, the lights that come closest, and the CCT and color rendering indices beside it.
• How closely does a MAT predict what a material will measure under another light, beside a chromatic adaptation transform? Comparing MATs and CATs For one material, a library of objects and many lights, with each transform's steps animated.

Planned: metamers and material color equivalency classes (the reflectances that share a Wpt), and profiles run through iccDEV's own tools in the page.

Observing condition

An observer under a light, shortened to "condition". The observer is any set of sensors: a standard observer's color-matching functions, cone fundamentals (the CIE 2006 model for any age and field size, or curves measured for one person), the categorical observers, or a camera's sensors. A material enters only through its spectral reflectance, so one material can be measured in any number of conditions.

Wpt normalization and its four steps

One 3 × 3 matrix per condition that turns the condition's responses into Wpt, the common representation of materials. It is built in four steps: white is turned onto the first axis, scaled to W = 100, the base colors (40 Munsell colors of Value 5 and Chroma 6, one per hue) are leveled to one W, and their p and t are fitted to the reference's. Wpt has three coordinates: W, for how much light the material reflects (white is 100), and p and t across it (0 for white and every gray).

WLab and ΔE_WLab

WLab reshapes Wpt so that a distance in it, ΔE_WLab, predicts the color difference the reference observer (CIE 1931 under illuminant C) would see between two materials, whatever condition they were measured in. WLab is not a color appearance model; it is a material color equivalency model: two materials with the same WLab are equivalent as materials.

MAT, and how it differs from a CAT

A material adjustment transform (MAT) is the normalization of one condition followed by the inverse of another's: it predicts what a material measured in the first will measure in the second (material color). A chromatic adaptation transform (CAT: von Kries, Bradford, CAT02) has the same shape but is built from the two lights' white points alone, and it predicts what will look the same to a viewer who has adapted to each light (corresponding color). Both carry white exactly; they differ in what they do to every other color.

Shift and shift manifold

A material's shift is how far and which way its Wpt (or WLab) moves between two conditions. Measured in many conditions, one material makes a small cloud of points, its Wpt shift manifold. How large the cloud is, and its shape, are the material's own behavior.

The equivalency metrics, one family

Each is a mean ΔE_WLab over materials, with one thing varied and the rest held, and each is 0 when the thing varied makes no difference to any material.

Metric	Varies	Averaged over	In
Observer Matching Equivalency (OME)	the observer	objects and lights	Observers
Observing Conditions Equivalency (OCE)	the whole condition, observer and light	objects	Observers
Illuminant Rendering Equivalency (IRE)	the light	objects and observers	Lighting

The libraries, and your own data

Every lab draws on the same libraries: objects (the corrected Munsell colors, the CIE's color evaluation samples, natural objects, skin, soils and others, each with its source and terms), lights (the CIE illuminants, fluorescent and LED lights, Planckian and daylight series) and observers (CIE, CIE 2006, categorical, cameras). Your own spectra, sensors and lights can be pasted or loaded beside them.

Each familiar term answers a question for one condition, or for one change of it. Its counterpart answers it for the material, across conditions.

Familiar	Material color counterpart	In
CIELAB and ΔE00, under one light for one observer	Wpt, WLab and ΔEWLab, for measurements from any condition	WLab and color differences
A CAT: what looks the same to an adapted viewer	A MAT: what the material will measure	Comparing MATs and CATs
A camera's matrix to XYZ	A MAT from the camera's condition to a CIE observer's	Wpt normalization and MATs
An index of metamerism: how far a matching pair parts under one change of light or observer	The pair's WLab difference in every condition, and each material's shift manifold	Objects
Observer metamerism: two viewers disagree about a match	The OME between the two observers	Observers
The color rendering index (CIE 13.3), CIE 224 Rf, TM-30 Rf and Rg	The IRE against a reference light	Lighting
The correlated color temperature: the Planckian light nearest in chromaticity	The Planckian or daylight reference with the lowest IRE: the one nearest in how it renders materials	Lighting
Hue angle in CIELAB or CAM16-UCS	Hue in WLab	Uniformity and hue

Every lab can be opened first. Where one leans on another, it is this:

Lab	Leans on
Wpt normalization and MATs	The guide alone. The others build on its normalization and MAT.
WLab and color differences	The normalization; ΔEWLab, defined here, is the measure the later labs report.
Uniformity and hue	WLab.
Objects	WLab; it introduces shifts and shift manifolds.
Observers	The MAT and shifts, between observers; its OME and OCE are means of shifts.
Lighting	Shifts between lights; the IRE is their mean.
Comparing MATs and CATs	The MAT, and the CATs it is set beside.

The equations are in the guide's Technical annex, which maps each one to the function in wlab that computes it. Math pages, one topic per page and each linked to the lab that computes it, are planned. Each lab names the standards and data it rests on in its own footer.

• Wpt, WLab and the MAT: the guide, and the Wpt and WLab papers (Derhak and Berns, Color Research & Application 40(6), 2015).
• Shift manifolds and the OME, OCE and IRE: M. W. Derhak, Spectrally Based Material Color Equivalency: Modeling and Manipulation, PhD dissertation, Rochester Institute of Technology, 2015.
• Colorimetry, the CIE observers and illuminants: CIE 15:2018; the CIE 2006 model: CIE 170-1:2006.
• Color rendering: CIE 13.3-1995, CIE 224:2017 and ANSI/IES TM-30; CAM16-UCS: CIE 248:2022.
• Profiles: ICC.2 (iccMAX), built and checked with iccDEV.