Observers for observing conditions
An observing condition (hereafter "condition") is an observer (having a set of sensors) under a light. A source observer, given as cone fundamentals, color-matching functions or other sensor functions (for example an individual's, measured on one of the custom-observer platforms research groups are building), can be converted for any target condition by a MAT: the MAT from the source observer under the target condition's light to the target condition, applied to the source's curves. The converted observer then gives the target condition's responses as the MAT predicts them. An iccMAX profile can be used to carry it in its spectral viewing conditions, which define the profile's connection space (its PCS).
1. The source observer
2. The target condition
CIE 1931 (2°) under D50 is the standard PCS's condition. The profile of section 7 takes the converted observer under the target condition's light as its own PCS, and connects it to the standard PCS by the Wpt MAT from that observer under that light to CIE 1931 (2°) under D50. For the standard condition as the target, that MAT is the identity.
3. The MAT and the converted observer
MAT, source to target condition
Wavelength in nm and the three curves, 380 to 780 nm in steps of 5 nm, at the scale the profile carries them; the file can be pasted back into any lab as your own sensors.
4. How closely the two observers match
Take an object under a light. Its Wpt with the source observer and its Wpt with the target condition's observer, each through that observer's own Wpt normalization, would be the same if a MAT carried one observer onto the other exactly; the WLab difference between them is how far the object moves between the two observers. The mean of that difference over every object and every light is the Observer Matching Equivalency (OME). It is 0 when the two observers agree on every match (the Luther-Ives condition: each observer's curve is a linear mix of the other's), and the larger it is, the more the two disagree about which materials match.
Selecting objects and lights for OME metrics
The objects are the materials the two observers are compared on, and the lights those they are compared under; the more varied their spectra, the more an observer difference shows. They apply to sections 4 to 6 (section 6 sweeps lights of its own).
Objects
A CGATS measurement file (with spectral fields such as SPECTRAL_NM380, as spectrophotometers and chart software write them) 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. A chart you measured yourself can be used this way. The file is read in this page and goes nowhere.
Lights
Light by light
Each row is one light's share of the OME: the WLab differences of the objects under that light. The first row is the target condition's own light, the one the profile is for, whether or not it is among the lights chosen. The last row takes the source observer's responses as if they were the target condition's, with no MAT: for color-matching functions close to the target condition's it is small, for cone fundamentals or other sensors it is large, because their responses are on other axes.
Ways of converting an observer
Section 3 converts the source observer with a Wpt MAT, one way among several. The Wpt MAT predicts material color: it is made so that materials have the same colors with the converted observer as with the target condition's (Wpt based). The other ways match something else: a spectral match, the source's curves regressed onto the target observer's (XYZ based), or a match with the same primaries, the source observer matching the target observer's primaries (primary based). Either can also be white balanced for the target light, each curve rescaled so that the light's white matches; for the primary based way that means matching primaries of the same chromaticities at other intensities, no longer the target observer's own. Unless the two observers meet the Luther-Ives condition, each gives a different converted observer, and how close the curves come is a different question from how close the colors of materials come. The table puts them side by side for the source observer and the target condition above.
Curves: the RMS difference of each converted curve from the target condition's observer's, over 380 to 780 nm as a share of its peak, the three averaged, with the target's curves scaled so that both see the target light with the same second response. Objects: the converted observer's responses read as the target condition's observer's (through that observer's Wpt normalization), against its own, as ΔEWLab, under the target condition's light and averaged over the lights chosen above. The OME cannot tell the methods apart: each converted observer is a linear mix of the source's curves, which leaves every Wpt as it is. The white balances and the Wpt MAT are made for the target condition's light.
5. Which CIE 2006 observer is closest
The OME of one observer against every observer of the CIE 2006 model, for ages 20 to 80 and field sizes 1° to 10°, and against the 10 categorical observers. Each cell is colored by its OME, on the scale under the map, and the ring marks the closest. It places an observer among the standard model's: a measured individual's, a camera's, or a standard observer's (the CIE 1931 observer comes out closest to an older observer with a field of about 4°, the CIE 1964 observer to one of middle age with a field of about 9° to 10°).
Each cell is an OME over the objects and lights of section 4; hover over a cell for its value. The categorical observers are those of Asano and Fairchild, ten groups that together stand for observers at large, each at the field sizes across the bottom.
6. Under which light the source observer comes closest to the target condition
The Observing Conditions Equivalency (OCE) compares two whole conditions, observer and light, over the objects: the mean WLab difference of each object between the two. Here the source observer under each Planckian (blackbody) light from 1750 to 12000 K, and each CIE daylight from 4000 to 14000 K, against the target condition; the target condition's own observer under the same lights shows what the light alone changes. The lowest point of each line is the light under which the observer sees materials most as the target condition does. Where the source observer's lowest point lies away from the target condition's light, a different light makes up for part of the difference between the two observers.
7. Creating a colorimetric encoding profile
An iccMAX (version 5) colorimetric encoding profile, of class spac and subclass pcc,
ready to use (.icc) or as XML for iccDEV's iccFromXml, laid out like the profiles of the ICC's
Colorimetric Encoding conformance package. Its spectral viewing conditions tag holds the converted observer and the
target condition's light, which define the profile's PCS. Its profile connection conditions tags hold the Wpt MAT
from that observer under that light to CIE 1931 (2°) under D50, the standard PCS (custom to standard), and the
inverse of that MAT (standard to custom). The converted observer is a mix of the source observer's curves, so it
matches colors as the source does; the MAT carries its colors to the standard PCS.
Custom PCS to standard PCS
Standard PCS to custom PCS
The .icc is written in this page: the same profile, byte for byte, that iccDEV's
iccFromXml builds from the XML (only the creation date, and the profile ID computed with it, differ
with the moment it is made). The XML is there to read or edit; to build it and check either file with iccDEV's
tools:
The XML
The luminance sets the illuminant's and the surround's XYZ in the spectral viewing conditions (203 cd/m², as in the conformance package's custom-observer profiles); the encoded colors are relative to the light's white either way.