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

Banding — where it appears

The visible steps a quantised gradient leaves, whose visibility is set by the local contrast of each step rather than by the bit depth. Adding noise before quantising makes the error larger and the artefact smaller, which is the trade a dither is.

Named by 4 essays across 2 fields — each of them below, with the objects they name alongside it.

A chromatic line screen at 10.0 cycles per degree. The upper strip is the pattern as delivered and the lower one is the same pattern after each opponent channel has been low-passed at its own cutoff. Against a flat field of the same mean, the delivered pattern differs by up to ΔE00 14.22 and the filtered one by 7.77 — a ratio of 1.8. Every number quoted elsewhere for a difference of this kind is the first one.

A difference has no size

A colour difference formula answers a question about two large patches seen side by side. Applied to a pattern, it reports fourteen units where the eye is left with less than one — and the ratio depends on nothing but how finely the difference is spread.

difference · Metric A 8-bit ramp from 0.0008 to 0.006 of white, 12° wide. The top strip is the ramp as delivered: 16 distinct levels, each a step of one code value. Below it is the quantisation error as a Weber contrast against the local luminance, filtered by the luminance sensitivity function. The largest response is 8.51 per cent contrast against a threshold of 0.3, which is 28.4 times over — and it occurs at 0.09 per cent of white, at the dark end, because a code step is a Weber contrast and the same step is a larger fraction of less light.

Banding is not a bit depth

Eight bits bands at thirty times threshold in the shadows and at under three at mid grey, on the same ramp with the same encoding. What decides is where in the tone scale the gradient sits, how sharp each step's edge is, and how far away the reader is — and a bit count contains none of the three.

limits · Limits What a dither mask is worth, read as components, in two dimensions. Five luminance ramps, each quantised to 8 bits with and without a high-passed mask of the same power. The bars are the most visible single sinusoidal component of the error, as a multiple of the contrast that component needs to be seen: above the line at one it is visible. The mask lowers it by 20–22×, on every ramp — which the one-dimensional model on this site says it does not, and that disagreement is the finding.

Every threshold was measured with a grating

An earlier essay here claimed that the model cannot explain why dither works, and named two missing pieces. One of them was real and worth thirteen times the guess; the other was not needed. The piece nobody named was the detector — and reading the same model two ways changes the answer by a factor of fifty.

limits · Limits Every filtered claim in these essays, read at a point and read as components. Each row is a comparison one of the essays makes. The bar is the ratio between the two readings — how many times larger the component answer is than the point answer, or the reverse — on a logarithmic scale. 5 of 7 disagree by more than half again, and 4 disagree about the direction of the effect rather than merely its size. The three marked as noisy are the ones with a noise field on one side of the comparison, and they are the three largest.

The list nobody made

The last phase found that reading a filtered signal at a point asks a question its thresholds were never fitted to, made it a standing rule, and admitted that nobody had gone back through the site to see which claims it touched. Here is the list. Every claim with noise on one side of it moves — and so do two that have no noise in them at all, which the rule said would not.

limits · Limits

Named alongside it

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

Contrast sensitivityDitherSpatial frequencyQuantisationSamplingThresholdHalftoneImage differenceScreen angleTransfer functionViewing distanceAssertion

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