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

Lattice — where it appears

A regular grid of sample points in a space, at which a quantity is computed or measured and between which it is filled in. A press's colours sampled on a lattice of ink coverages, or a profile's table, are exact at the nodes and only as right between them as the filling-in is.

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

A published residual is a mean, and the worst object in the room costs twice it. Three bars for each of the 14 changes of light in the adaptation census, ordered by how uneven the change is across surfaces. The first bar is the published mean residual. The second is the worst single surface in the audit's published test set. The third is the worst surface anywhere in the region that set is drawn from, found by search rather than by reading a maximum off a lattice. The mean-to-worst ratio runs from 1.90 to 4.02 and averages 2.43, so every published adaptation number has a worst case about twice it that no essay had ever quoted. The gap between the second and third bars is the other finding: a maximum over 125 sampled points understates the region's own maximum by up to 34 per cent.

An extremum is still not a sample

Two rounds ago three measurements turned up that took a maximum over a sample of a set and were short by up to a factor of two. The same error was live in a fourth place the whole time, on the set of surfaces every adaptation number is averaged over, and it is short by up to a third.

matching · Gamut Every corner of the press against its own tangent cone, at two samplings of black. For the nine end colours of the margin census, how far each moves per unit of a four-unit margin: as a perfect corner of its own tangent shape would, on the press walked at thirty-three black levels, and on the census's press of nine. At thirty-three every corner sits within seven per cent of its cone; at nine every edge moved a fifth or more further, and the half-black yellow 63 per cent further.

Nine black levels sharpened the press's corners

Three essays measured how far a safety margin pushes the corners of a coated press inward, and found them sharper than anything a smooth solid would have: the solid yellow moving nearly four times the margin, every corner past a cube's. Read by their ink recipes, three of the nine corners are vertices and six are edges, and each has a shape the press model's own derivatives state exactly. Against that shape the edges moved a quarter to two thirds too far. The reason is not the press. It is how the press was built: as three-ink solids at nine levels of black with nothing between them, so that every face black helps to make was scalloped. Walked at thirty-three levels, every corner moves within seven per cent of its own tangent shape, three of the nine are rounder than a cube's corner, and the solid yellow moves 3.2 times the margin, not 3.8.

matching · Gamut

Named alongside it

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

SamplingBoundChromatic adaptationCIEDE2000CIELABConvergenceConvexityExtremumGamutProcess inksReflectanceResidual

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