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

Fitting — where it appears

Choosing a model's free numbers so that it reproduces a set of observations as closely as some objective asks. The reported residual is a statement about the observations used, so a fit can be excellent and still be reproducing targets that were themselves wrong.

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

A camera matrix refitted to minimise each unit, rather than solved in XYZ. Every camera profile here, and as far as can be told every camera profile anybody ships, is a linear least-squares solve in XYZ. That is an objective and it is on nobody's menu: it weights a difference by how large the tristimulus values are. Each row here refits the same 3×3 by direct search to minimise one of the six units instead. The upper bar is how much better the fit gets in that unit; the lower is how far the matrix itself moves, as a relative Frobenius norm. Both matter and they do not agree: CAM16-UCS moves the matrix least, at 0.34 per cent, for the largest improvement of the six, while ΔE*94 moves it 6.8 times as far for less. A score that changes is a report changing; a matrix that changes is the camera rendering different pixels.

The objective nobody chose

Every camera profile here, and as far as can be told everywhere, is a linear least-squares solve in tristimulus space. That is an objective and it is on nobody's menu — it weights an error by how bright the patch is. Refitting the same matrix to minimise a real colour-difference formula improves the fit in all six, and moves the matrix, which means different pixels rather than a different report.

imaging · Capture The collection's adaptation census, with its surfaces departed. Each row is one of the fourteen changes of light in this site's adaptation census, and the bar is what a von Kries gain leaves behind. The open marks are the published numbers; the filled ones are the same computation with every one of the hundred and twenty-five test surfaces replaced by what an instrument with an aperture, or a room with a direction in it, actually reports. Nothing moves by more than 9 per cent. A departure that does not depend on the light is very largely absorbed by the observer's own gain, because it changes the reflectance and the gain is applied afterwards. The fourth departure is not on this chart and cannot be: a fluorescent sample has a different curve under every light, so there is no set of reflectances to hand the census at all.

The chart was measured, not photographed

A camera profile is fitted so that the camera's response maps onto the chart's tristimulus values, and those values came out of a spectrophotometer. So the profile's target carries the instrument's departures and the camera does not — a mildly translucent chart read through a four-millimetre aperture supplies targets 2.55 ΔE₀₀ from the truth, which is twice the profile's own fitting error.

imaging · Capture

Named alongside it

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

CalibrationCamera profileLeast-squaresApertureColour differenceInverse problemLuther conditionMarginalisationMeasurement errorObjectiveOptimisationSpecular

All concepts