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

Appearance model — where it appears

A model that predicts what an observer in a stated room would report about a stimulus — its lightness, chroma and hue — rather than which stimuli match. It takes a viewing condition as an argument alongside the stimulus, which is the whole structural difference between it and a colorimetric calculation.

Named by 14 essays across 4 fields — each of them below, with the objects they name alongside it.

How far each unit is from being a rescaling of the one this collection publishes in. One row per unit on the menu. The bar is the root-mean-square scatter about that unit's own best rescaling of ΔE2000, over 374 pairs of surfaces differing by a fraction of a unit to about ten. A bar of zero would mean the unit is ΔE2000 in different money — every printed number would change and no conclusion would. ΔE2000's own row is zero by construction and is the check that the table is computed the right way round. The two units that divide a chroma difference by the chroma it was measured at, ΔE94 at 15 per cent and CAM16-UCS at 24, are closer to it than the three that do not, which run from 28 to 35. The split is by weighting and not by whether the unit is a matching difference or an appearance one.

The weighting is the disagreement

Five colour-difference formulae, three decades and two committees, and the single property that predicts which of them agree is whether a chroma difference gets divided by the chroma it was measured at. It sorts the menu exactly, it cuts across the distinction between a matching difference and an appearance one, and it halves the census's largest sensitivity.

difference · Metric Where on the scale the units disagree. The reference pairs split into bands by how far apart they are in ΔE2000, with each unit's root-mean-square relative departure from the published one plotted per band. Every unit is calibrated once, over the whole sample, so a band is not refitted and the shape is the effect rather than an artefact of fitting. Every one of the five falls: the disagreement is proportionally largest on the pairs that are closest together, which is the opposite of what being fitted to threshold data would suggest. The appearance unit is the extreme case, at 91 per cent on the narrowest band and 17 on the widest, because CAM16-UCS raises its distance to the power 0.63 and a power below one inflates small differences against large ones. In absolute terms every curve here runs the other way — the widest band disagrees by 1.16 to 2.37 ΔE₀₀-equivalent against 0.14 to 0.68 on the narrowest — so which reading is right depends on whether the published quantity is a level or a ratio. This is the mechanism behind the census's own behaviour, where the mildest rows spread furthest across the menu.

The disagreement is at the near end

Every colour-difference formula on the menu was fitted to threshold data, so the expectation is that they agree about pairs an observer can only just tell apart and diverge on large differences. They do the opposite. Proportionally the disagreement is largest at the near end, by a factor of six for the appearance unit, and the cause is an exponent of 0.63.

difference · Metric MacAdam's twenty-five ellipses, measured in each unit. The uniformity instrument used here, applied to units rather than to spaces. The upper bar is anisotropy — the mean over the twenty-five of the largest radius divided by the smallest, where 1 would be a circle. The lower is spread — the largest mean radius divided by the smallest across all twenty-five, which asks whether a step of the same size means the same thing in different parts of the diagram. Reading down the three CIELAB-based formulae in the order they were published, the anisotropy falls 3.42 → 2.89 → 2.74 and the spread rises 3.24 → 3.59 → 4.12: the weighting divides a difference by the chroma it was measured at, which equalises directions at a point and unequalises magnitudes between points. Neither number is scaled, so no calibration is applied here. CAM16-UCS is ahead on both.

A unit rests on a space that was ranked

This collection ranks three colour spaces by how nearly they make MacAdam's ellipses circles, and CIELAB comes last. It then publishes every difference it computes in a formula built on CIELAB. Turning the same instrument on the formulae rather than the spaces shows the repair works — and that it buys roundness by paying in evenness.

matching · Gamut Pairs built to sit exactly on a ΔE2000 tolerance, read in every other unit. Twenty-four pairs of surfaces, each constructed by walking one member along a fixed direction until the difference is exactly 1.0 ΔE2000 under D65. The bar spans what those same pairs read in each unit, after calibration, with the tick at the mean. ΔE2000's own row is a point at 1.0 by construction. Every other unit spreads them: ΔE*uv reads them from 0.69 to 1.75, so a contract written at "one unit" accepts and rejects a different set of deliveries depending on which unit it means. CAM16-UCS rejects all twenty-four: it reads the closest of them at 1.43.

A tolerance is a boundary through pairs

Twenty-four pairs of surfaces built to sit exactly on a ΔE2000 tolerance of one read from 0.69 to 1.93 in the other five units. A contract quoting "one unit" without naming the formula does not become slightly wrong in another; it accepts and rejects a different set of deliveries, and in one case rejects every single one.

applied · Delivery What six of this collection's published numbers do when the unit changes. Six quantities, from six calculations that share nothing: a change of light after an observer has adapted, a camera profile's error, the gap between the two standard observers, a metameric pair under the lamp that breaks it, the same image on two papers, and an observer two seconds into a new room. Each is recomputed under all six units and every unit is calibrated onto ΔE2000's scale first, so the bar is not a change of units in the ordinary sense. The bar is the ratio of the largest reading to the smallest, and it runs from 1.71 to 2.30. Five of the six are printed in ΔE2000 by the essays that report them; the sixth is printed in CAM16-UCS, because the model it comes out of defines that unit.

A model judged in another model's unit

An appearance shift is a change in what an observer would report, not a change in a stimulus, so measuring one with a matching difference means first asking what stimulus a settled observer would need to be shown to give the same report. That step is not bookkeeping — it is the whole distinction the field rests on, and it costs a factor of 1.7 across the menu.

brain · Appearance Every figure a surround dial would apply to, weighed. The eleven generators in the appearance family, by the size of the drawing each emits — which is what a dial multiplies, because every frame carries the figure's whole body. The dashed rules are the thresholds the dial policy here is written in: under 3 KB gets thirteen stops, under 6 gets nine, under 10 gets seven, and above about 12 KB nothing gets a dial at all. The median body here is 2.25 KB and 4 of the eleven are inside the most generous tier, against a policy written when the distribution had a median of 4.0 KB. Two phases deferred a surround dial on the grounds that appearance swatches are not small. The exception is unique-hues at 14.1 KB, which is over the ceiling that says it should have no dial — and it has one, on chroma, declared in the same file as the ceiling.

A dial has a price

Two rounds declined to give the appearance model's surround a continuous control, both times because the frames would be too heavy, and neither time was the weight taken. It is 2.25 kilobytes at the median — the light end of these figures rather than the heavy end — and one figure is already breaking the rule the deferral was made under.

applied · Delivery Two slabs with one reflectance, and two colours through an aperture. Two constructed media whose bulk reflectance agrees at every wavelength to fifteen figures, and whose diffusion lengths differ by a factor of four. The upper curve is that shared reflectance — both slabs lie on it exactly. The two patches on the right are what a 4 millimetre radius returns from each, and they are 6.3 ΔE₀₀ apart. This is a metamerism with no observer in it: the two samples are the same colour to anybody under any light, and the instrument separates them because it is measuring a kernel through a hole rather than measuring a reflectance.

The appearance model has no slot for it

Two slabs with identical reflectance and different kernels come out of CIECAM16 with identical lightness, chroma and hue — to six decimal places, because the model's input is a stimulus and their stimuli are the same. Translucency is a recognised appearance attribute with no correlate in any appearance model, and the reason is structural rather than an oversight.

brain · Appearance What choosing a space to divide the white out in is worth. Three pairs of routes to the same colour, over forty-two surfaces: dividing the white out in tristimulus values, in a published cone space, and in the observer's own cones. The first two agree to 0.59 ΔE₀₀ at the median. Either of them differs from the observer's own cones by more than fifteen. That is why the two exact conditions in this round are exact only in the eye's own coordinates: the identity belongs to the receptors, and every published arithmetic works in a basis somebody else chose.

The appearance model takes XYZ

CIECAM16 predicts how a colour looks, and its input is three tristimulus values computed through a standard observer. Everything this round measures happens before the model is called, so an appearance prediction inherits six observer departures and a choice of cone space before it begins.

brain · Appearance Where a stated appearance has no stimulus under it. The chroma the inverse can still return a light for, at lightness 50, all the way round the hue circle. Below the curve a stated appearance corresponds to a stimulus; above it the formula still returns three numbers and one of them is negative. Over a lattice of 10488 appearances spanning the whole space a specification is written in, 10.8 per cent are of that kind, and only 44 per cent are colours a display could show.

An appearance is not always a stimulus

CIECAM16's inverse is a closed form that returns three numbers for every lightness, chroma and hue it is handed. Whether those three numbers are a light it does not ask, and over a lattice spanning the space a specification is written in, 10.8 per cent of them are not — one tristimulus value negative, or a relative luminance above the white's. Only 43.8 per cent are colours a display could show at all.

brain · Appearance The audit's six departures, read twice. Each departure priced in the matching unit it was published in and in the appearance unit an appearance prediction would be judged by. The model does not scale them by one factor: it amplifies the smallest by 1.58 and the largest by 1.03, so the range between them narrows from 3.34 to 2.17. The mean ranking is unchanged and 14 of the 42 surfaces reorder.

The audit, read as appearances

The previous round priced six observer departures in a matching unit and left them there. Read in the appearance unit an appearance prediction would actually be judged by, they are not the same six numbers scaled by a constant — the model amplifies the smallest by 1.58 and the largest by 1.03, so the range between the largest and smallest term narrows from 3.34 to 2.17. The published ranking survives in the mean and changes on fourteen of the forty-two surfaces it was averaged over.

brain · Appearance What a small neutral deviation costs as the grey darkens, in two lightness scales. The price of a fixed fraction of deviation on a neutral — how much lightness it is worth per unit of luminance — from L 40 down to L 0.25, both axes logarithmic. CIELAB's L is a straight line below L 8 and its price there is exactly flat. The appearance model's J′ has no straight piece: its price keeps rising, by a factor of 5.0 across the same range, as the luminance to the power -0.442 — the derived exponent is -0.441 in an average surround.

The appearance model has no straight piece

CIELAB's lightness is a straight line below L* 8, so a deviation near black has a fixed price and a black has a floor under it. CIECAM16 has no such piece. Its lightness near zero goes as the luminance to a power set by the room, the price of a deviation rises without limit as the black deepens — as Y to the power −0.44 in a lit room and −0.58 in a dark one — and on a projected black a lightness unit in the model allows under half the luminance change a unit of L* allows.

matching · Gamut The same pairs, held at one colour difference, read in a unit that knows the room. 23 pairs of reflectances built to sit at exactly ΔE₀₀ 1.000 under D65, read in CAM16-UCS as the adapting luminance runs from a third of a candela a square metre to ten thousand, in an average surround. ΔE₀₀ has no argument for the room, so in that formula every pair stays at 1.000 all the way across — the flat line. In the model's unit the same pairs rise from a median of 0.76 to 1.30, and they do not rise together: at the bright end they run from 1.11 to 1.65.

A tolerance has no light level

Twenty-three pairs built at exactly one colour difference stay at exactly one in every room, because the formula has no argument for the room. Read in the unit that does have one, the same pairs are 0.72 in a cinema, 1.04 in an office and 1.30 in direct sun — and inside any one room they spread by half again, so no single conversion between the two units exists at all.

difference · Metric How far CIECAM16 moves a monochromatic hue when the light is brightened thirtyfold. A monochromatic stimulus at a relative luminance of 2 and of 60, read through CIECAM16 in one room, and the difference between its two hue angles. The model was never fitted to this effect and has it anyway: the shift is positive at the short end, negative through the greens, positive again in the yellows and reds, and crosses zero at 459, 495, 502, 570 nanometres. The marks are the invariant wavelengths the literature reports — 474, 506, 571.

The model has a hue shift it was never given

A monochromatic light changes hue as it is brightened, except at three wavelengths that do not move — an effect measured since the nineteenth century and not among the things CIECAM16 was fitted to. The model has it anyway: brightening a stimulus thirtyfold moves its hue angle, and the places where the movement crosses zero land at 459, 495, 502 and 570 nanometres against the reported 474, 506 and 571. The sizes are another matter.

brain · Appearance The share of its colour each display hue loses to a quarter of its luminance in white. The twenty-four most saturated colours of an sRGB display, one every fifteen degrees of HSV hue, each scaled to a luminance of 20 and given white of a quarter that luminance: the share of its colourfulness lost, in CIECAM16, CIELAB and Oklab. All three put the fastest loss at an orange and the slowest at a blue. At the orange end they are close — CIECAM16 27 per cent, CIELAB 28 per cent, Oklab 21 per cent — and at the blue end CIECAM16's 1.7 per cent is a quarter of the others'.

White drains the blue last in every model

CIECAM16 says a dab of white costs a deep red wall four times the colour it costs a dark blue one, and the experiment proposed to test it asked whether observers lose colour in that hue order. Held at equal luminance and given equal doses of white, twenty-four display hues are ordered alike by CIECAM16, CIELAB and Oklab — an orange loses fastest and a blue slowest in all three. So the order cannot tell the models apart. What does is how much slower the blue is: CIECAM16 has it losing a sixteenth of what the orange loses, CIELAB and Oklab about a quarter. That ratio is the number an observer study has to measure.

brain · Appearance

Named alongside it

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

CIECAM16Colour differenceChromaSpecificationCalibrationCIEDE2000Colour appearanceViewing conditionSurroundJust-noticeable differenceToleranceAbsolute luminance

All concepts