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

Overfitting — where it appears

A model following the particular data it was fitted to more closely than it follows anything else, so that its reported residual is optimistic. It is diagnosed by evaluating on data the fit never saw, and it is a different failure from a badly conditioned design.

Named by 2 essays across 2 fields — each of them below, with the objects they name alongside it.

What a camera matrix reports on its own chart, and what it delivers off it. The same camera fitted on charts of increasing chromatic range. The left bar of each pair is the mean error on the chart the matrix was fitted to, which is the number a profile comes with; the right bar is the error on a saturated set it never saw. At the thinnest chart the fit reports 0.19 ΔE00 and delivers 1.65, a factor of 8.6. The gap closes as the chart widens, and it closes because the chart improves rather than because the camera does.

The chart decides the profile

A camera's colour matrix is nine numbers fitted to a set of patches somebody chose, and the number that comes with it is the error on those patches. On a chart with no chromatic range that number is 0.19 ΔE00 and the matrix delivers 1.65 — and a second matrix, indistinguishable on the chart, delivers 2.03.

imaging · Capture 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

Named alongside it

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

CalibrationDegrees of freedomHeld-out validationIdentifiabilityLeast-squaresRankCamera rawColour matrixLinear modelLuther conditionMeasurement uncertaintyModel selection

All concepts