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

Metric — where it appears

A rule that assigns a length to every small step in a colour space, given as a quadratic form that varies from place to place. A colour-difference formula is one: it prices a step, and the distance between two distant colours is then whatever the cheapest path between them costs, not the straight line's price.

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

Three numbers for one set of ellipses, and which of them is which. Two curves and a horizontal line, against the size the ellipses are drawn at. The line is the analytic axis ratio — the ratio of the singular values of the map's own derivative, which is what "does this space make discrimination contours circles" means. The upper curve is a very finely sampled ring, which sits 0.6 per cent above the line at full size and converges onto it as the ellipse shrinks, because the gap between them is the second-order distortion of the map across a real ellipse rather than an error. The lower curve is the forty-eight-point sample used for this until now: it does not converge onto anything, because its error is set by the sample and not by the size.

Three numbers for one ellipse

How far a colour space is from making a discrimination contour circular has three different answers — what a coarse sample of the boundary reports, what a converged sample of a contour of stated size reports, and what the map's own derivative says. They differ by up to a factor of two, they mean different things, and only one of them is what the question is asking.

difference · Metric The straight line between two colours, and the formula's own shortest path. Five gradients seen from above, in the a and b plane of CIELAB: the straight line between the two colours in grey, and the shortest path under ΔE₀₀'s own local metric in colour. The lightness coordinate bows too and is not drawn. red to green saves 3.6 per cent and leaves the straight line by 13; blue to yellow saves 7.5 per cent and leaves the straight line by 21; cyan to magenta saves 3.9 per cent and leaves the straight line by 10; black to white saves 0.0 per cent and leaves the straight line by 0; red to blue saves 0.3 per cent and leaves the straight line by 4 CIELAB units at the widest. Black to white is the flat case: its shortest path is the straight one.

The straight line is not the shortest gradient

A colour difference formula says what a small step costs at every colour, and that is enough to ask which path between two colours is shortest. It is not the straight line: between red and green the shortest path bows thirteen CIELAB units away, saves four per cent — and stays inside sRGB on every step where the straight line leaves it. The formula's own answer for the two endpoints, meanwhile, is neither length.

matching · Gamut

Named alongside it

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

AnisotropyCIELABCIEDE2000Colour differenceConvergenceGamutGradientInterpolationJacobianJust-noticeable differenceMacAdam's ellipsesPerceptual uniformity

All concepts