Colour Science & Perception
what the eye settles, and what it cannot
Concept

Model selection — where it appears

Choosing how many parameters a description should carry, which is a trade between following the data and following the noise. On a fitted colour model the honest criterion is rarely the residual, because a residual falls monotonically as parameters are added.

Named by 4 essays across 3 fields — each of them below, with the objects they name alongside it.

What each fitted thing in these essays carries, what its data fix, and what is left. Three columns per row: how many numbers the model has, how many the stated data determine, and the difference — the dimension of the family that fits equally well. The third column is the one nobody publishes. A zero there does not mean the model is right; it means it is determined, which is a much weaker property and is compatible with being determined badly, as the camera row is.

A fit can be exact and empty

Every fitted object here reports one number, the residual on the data it was fitted to, and every one of them has two more that nobody publishes — how many of its parameters the data actually determine, and how large the family of equally good answers is. The third column is where the failures live.

limits · Limits What the next thousand patches buy a printer profile. A profile is a table, exact at its nodes and interpolated everywhere else. Each mark is a grid: the horizontal axis is how many patches somebody had to print and measure, the vertical is the worst error found between the nodes. Going from 135 patches to 3645 — 27.0× the work — buys 8.4× the accuracy. The error falls with the square of the spacing and the count rises with its cube.

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.

applied · Delivery Only a curve per temperature brings the bin back. The camera's colour error under eighty-nine white LEDs — thirty on the Planckian locus, fifty-nine at a Duv of ±0.003 — read through the red phosphor estimated from the 600 nm line and an error line within each pump, each LED left out, as the Duv enters the lines in turn: not at all, as one term, as a slope in mireds, as a slope for each temperature, and as a slope and a curve for each. Beside them the line learned on the locus alone. With a slope and curve per temperature: ±0.073 on the locus, ±0.056 below, ±0.048 above.

Across a bin, the camera's error bends with the temperature

White LEDs a Duv of 0.003 off the Planckian locus have their red phosphor read by an ambient sensor as well as LEDs on it, and their camera colour error read a third to a half worse, because the error itself moves with the Duv. The prediction was that one Duv term in the error's line, learned over all eighty-nine LEDs, brings those beside the locus back to the locus's ±0.074 ΔE₀₀ and costs the locus LEDs nothing. One term buys little: ±0.109 below the locus and ±0.085 above. The error turns across the locus one way at 2,700 K and the other at 4,000 and 6,500 K, and bends most where it is warmest, so the Duv has to enter as a slope and a curve for each temperature — ten numbers a pump, not five — before both sides come back, to ±0.056 and ±0.048. That line then reads the locus LEDs at ±0.073, worse than the ±0.062 a line with no Duv in it manages once it is learned across the bin.

imaging · Capture The curve holds inside the bin and fails outside it. Four error lines learned on eighty-nine white LEDs at a Duv of nought and ±0.003, each read at those three values with every LED left out and at ±0.0015 and ±0.006 on 119 LEDs none of them was fitted on. The slope and curve per temperature reads ±0.045 and ±0.043 inside the bin and ±0.153 and ±0.161 at twice its edge, where a slope per temperature alone reads ±0.093 and ±0.110.

The bin's curve holds between its points and breaks beyond them

A camera's colour error under a white LED was read from an ambient sensor across a manufacturing bin by a line with a slope and a curve in Duv for each colour temperature, fitted at three Duv values — on the locus and 0.003 either side — and reading the LEDs beside the locus within ±0.056 and ±0.048 ΔE₀₀. A curve through three points passes through them whatever happens between them. The prediction was that 119 new LEDs built at ±0.0015 are read within ±0.06, and those at ±0.006 worse than ±0.10. Both halves hold: ±0.045 and ±0.043 inside, ±0.153 and ±0.161 outside. But the error's own mean course stays on its parabola within 0.02 out to ±0.006. The line's bend is not the error's: it is the gap the line leaves between the locus LEDs and the bin's edges, and a gap spent as a curvature quadruples at twice the distance.

imaging · Capture

Named alongside it

The objects these essays reach for when they reach for this one.

Held-out validationIdentifiabilityCalibrationCamera rawOverfittingWhite LEDArea coverageCorrelated colour temperatureDegrees of freedomThe ICC profileInterpolationLeast-squares

All concepts