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

Projection — where it appears

Discarding a dimension by mapping onto a lower-dimensional space, which is what a chromaticity diagram does to luminance. What the projection removes is not recoverable from the picture, so areas on such a diagram mean much less than they appear to.

Named by 5 essays across 2 fields — each of them below, with the objects they name alongside it.

A spectrum, weighted three ways, and the three numbers left over. The illuminant D65 above; below, the same spectrum multiplied by each matching function. The area under each product is one coordinate of XYZ. Everything else about the spectrum — its shape, its structure, all its remaining degrees of freedom — is discarded here.

Three numbers

A spectrum has as many degrees of freedom as anyone cares to give it. The eye reports three. Everything colour science can do, and every way it fails, follows from that one collapse.

eye · Cones A camera's spectral sensitivities, after the infrared-cut filter. Silicon quantum efficiency times the colour-filter dye times the infrared-cut filter, per channel, on a grid running to 1100 nm rather than to 780. With the filter removed, 68 per cent of the area under the three curves lies beyond the visible band, and all three curves are the same curve out there.

A camera is a fourth observer

The 1931 functions, the 1964 functions and a person's own cones are three sets of three curves that collapse a spectrum onto three numbers. A camera is a fourth, built from silicon and dye rather than from pigment and neural wiring, and it agrees with none of them.

imaging · Capture A silicon sensor's best possible impersonation of the standard observer. The 1931 matching functions in outline, and the closest linear combination of the sensor's three sensitivities laid over them; underneath, what is left over at each wavelength. The residual is 31.7 per cent of the matching functions' own magnitude, worst at 440 nm. Colour reproduction is exact if and only if this is zero.

Luther said when it would work

There is an exact condition under which a fixed three-by-three matrix converts camera raw to XYZ correctly for every spectrum in existence. It was stated in 1927, it is a theorem rather than a guideline, and no camera ever built satisfies it.

imaging · Capture Two reflectances the camera records as identical. Constructed by projecting onto the null space of the sensor's own sensitivities, so the two raw triples agree to 0.0000 per cent. To the eye they are ΔE00 15.33 apart, which the swatches show.

The camera has its own metamers

Two surfaces a camera records as identical can be plainly different to a person, and two a person cannot tell apart can be recorded as different. Both pairs are constructed rather than found, from one projection, used for both.

imaging · Capture The arguments a standard observer does not have. Seven choices inside a set of colour-matching functions, each with the shape it takes and what it is worth in ΔE₀₀ on a red pigment under a 6500 K radiator. Six are measurements: a field size, an age, a macular density, a cone optical density, three peak wavelengths and a rod contribution. The seventh is not — a change of basis is a change of curves and not a change of observer, and its entry is exactly zero because the space an experiment measures is what an observer is. Printing that zero beside the others is the clearest statement of what the other six are measurements of.

Three curves for one space

Rotate a set of colour-matching functions by an arbitrary invertible matrix, undo the rotation at the end, and the computed colour is identical to eight parts in a thousand million million. An observer is a three-dimensional subspace, not a set of curves, and the literature keeps reopening a question that is a theorem.

eye · Cones

Named alongside it

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

Standard observerNull spaceCamera rawCone fundamentalsMetamerismSpectral sensitivityColour-matching functionsLuther conditionMetameric blackTrichromacyXYZAssertion

All concepts