Profile inversion — where it appears
Named by 6 essays across one field — each of them below, with the objects they name alongside it.
A profile is a table
An ICC profile does not contain a model of the device it describes. It contains a lattice of patches that were printed and measured, and everything between them is interpolation — which is exactly zero at every patch, so a profile checked against its own target reports perfection for ever.
A profile is a fit between its nodes
A printer profile is a table, exact at every patch that was printed and interpolated everywhere else — and everywhere else is where every job lives. Going from a hundred and thirty-five patches to three and a half thousand is twenty-seven times the work for eight times the accuracy, and the exponents say that is as good as it gets.
A strategy keeps the refit only where black prints
Refitting an inverse table's nodes against their own error halves it, and in a four-ink table the refit has to leave the separation strategy's choice of black alone. Held to the strategy, it keeps the whole of its gain wherever the strategy prints black and almost none of it where the strategy does not — and the share it keeps equals the share of the grey ramp printed with black, to within three hundredths. The start of black generation, predicted to be where the refit would fail, is where the table needs it least.
A little black ends the cast
A four-ink inverse table errs by a warm cast along the grey axis wherever the separation strategy prints only three inks, and almost only in lightness wherever it prints black. Real strategies start black gently, and the gentle start was expected to keep the cast until black carried much of the grey. It does not. The cast falls to a tenth of its three-ink size once black supplies a tenth to a sixth of the grey's darkening, at every toe from nothing to thirty units wide — because inside the toe the table's chord runs along the trade of black against the other three inks, which errs in lightness. What the toe does cost is the segment where black begins, which goes from the table's best to its worst.
The cast returns where black is steep
Below a black-generation toe a four-ink table's grey picks up a small cast again, up to a third of the three-ink cast at the widest toe, and the explanation offered was the jump in black's curvature where the toe ends. It is not. A toe whose curvature is nothing at its end returns exactly the same cast, segment for segment, and a kink put into straight black casts in its own segment once in twelve tries. What the returned cast follows is how steep black has to be once the toe is done — how far the chromatic inks climbed while black was held back, and how fast they then have to come down.
An ink limit takes the shadows' cast away
A cap on total ink forces black up and the chromatic inks down where it is reached, which is the descent that brought a small cast back below a black-generation toe, and the prediction was that a cap would bring one back too. Measured against what the same strategy prints with no cap, it does the opposite. Below where it binds the cap decides the separation outright — nine strategies print one table there — and in 32 of 33 cases its shadows cast less than the strategy's own would have.
Named alongside it
The objects these essays reach for when they reach for this one.
InterpolationSeparationThe ICC profileProcess inksChromaGrey component replacementInverse modelLightnessLeast-squaresQuality controlArea coverageCalibration