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 2 essays across 2 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

Named alongside it

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

CalibrationHeld-out validationIdentifiabilityArea coverageDegrees of freedomThe ICC profileInterpolationLeast-squaresLinear modelMeasurement errorMeasurement uncertaintyNull space

All concepts