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

Chroma — where it appears

How far a colour lies from the neutral of the same lightness, which is a distance in a stated space rather than a property of the light. Colourfulness is its absolute counterpart and rises with the light level; chroma is referred to the white in the field and does not.

Named by 42 essays across 8 fields — each of them below, with the objects they name alongside it.

A grey edge, reconstructed from a Bayer row, arrives coloured. Above: an achromatic step through 24 sensor sites, with green sampled on the even ones and red on the odd. Interpolating each channel separately reconstructs them from data taken on either side of the edge, so their ratio moves. Below: the resulting chroma, peaking at 144 per cent of the local mean, and 112 per cent once colour differences are interpolated instead.

A grey edge arrives coloured

A sensor site measures one channel and the other two are interpolated from neighbours that sat somewhere else. Across a black-and-white step that reconstruction gives an achromatic scene a chroma of 144 per cent of its own local mean, and nothing in the scene or the sensor was coloured.

imaging · Capture A gradient of one hue, mapped into a press's gamut 2 ways. Chroma asked for along the bottom, chroma delivered up the side, for a ramp at lightness 55 and hue angle 25°. A colorimetric intent follows the diagonal until the press runs out and is flat afterwards — the flat part is a gradient arriving as a single colour. The perceptual intent is under the diagonal from the start, which is the price of never going flat.

No mapping preserves everything

More than half the sRGB solid is outside a press's gamut, so something has to be done with it, and there are two things that can be done. One leaves every reproducible colour exactly where it was and delivers a gradient as a flat area. The other keeps the gradient and moves every colour that needed no help by about three.

applied · Delivery Contrast sensitivity, three channels, normalised to each channel's peak. Spatial frequency in cycles per degree against relative sensitivity. The luminance channel runs to 50 cycles per degree, red–green to 12 and blue–yellow to 8, each by the same criterion of 5 per cent of that channel's own peak. Only the luminance channel dips at low frequency; the two chromatic ones are low-pass, so a chromatic edge of any size at all is seen at its full contrast.

How fine a colour edge can be

The eye resolves a lightness pattern to about fifty cycles per degree and a red–green one to twelve. Every colour difference here is quoted as though a patch had no size, and the same difference is plainly visible at one scale and gone at another.

eye · Cones One pair of colours, blended in four spaces. Every row starts and ends at the same two colours and visits different ones in between. The chroma of the middle falls furthest in linear light, by 83 units below the straight line between the endpoints' chromas — the grey dead zone that every blue-to-yellow gradient has and that no endpoint mentions. Any colour a route visits that this display cannot show is hatched rather than clipped.

A gradient is a path

Two colours fix the ends of a blend and nothing else. The middle is decided by the space the interpolation happens in, and four spaces in daily use put the halfway point of one ordinary gradient as much as thirty-seven units of colour difference apart.

matching · Gamut A colour-order system's chips, sorted by what they would be called. A regular lattice in lightness, chroma and hue — the idealisation of a swatch book, and regular by construction because a person has to be able to find a page. Named, it comes apart: 1320 chips inside the gamut divide into 198 for grey and 66 for blue. And 22 per cent of one-step moves in the lattice change the name, so a page of a swatch book is not a page of a vocabulary.

A catalogue is not a vocabulary

A colour order system is a regular lattice, because a person has to be able to find a page. Sorted by what its chips would be called, that lattice comes apart into piles differing by a factor of three — and a fifth of all one-step moves in it change the name.

matching · Gamut The three constants a specification does not quote. ΔE2000 is defined with three parametric factors in it — kL, kC and kH — which the CIE leaves to the industry using the formula rather than fixing. Graphic arts uses ones throughout; the textile standard weighs lightness at half, which is kL = 2. Applied to 4000 pairs at a tolerance of 1, the two settings accept 46 and 75 per cent, and 29 per cent of pairs change verdict — a larger disagreement than any between the formulae themselves. The reference conditions the ones assume are diffuse illumination at 1000 lux, a mid-grey surround, samples abutting, subtending over four degrees, differing by under five units, with no visible texture.

Three constants nobody quotes

CIEDE2000 is defined with three parametric factors in it, the CIE leaves them to the industry using the formula, and the two settings in ordinary use differ by a factor of two in one of them. Twenty-nine per cent of acceptance decisions change between the two — a larger disagreement than any between the formulae themselves.

difference · Metric The hue circle cut into names, at L 60 and C 40. Left, the arcs each name claims, drawn at the colour of their midpoints; right, the same arcs measured in ΔE00 by integrating the difference along the ring rather than in degrees. The widest is 5.3 times the narrowest in degrees and 4.5 times in colour difference, so the metric accounts for 15 per cent of the inequality and no more. Only the eight chromatic terms compete on this ring: at this chroma the achromatic three would otherwise take the region where no basic English term sits, which is a defect of the model and is named in the essay.

There is no word for that colour

The naming model built this phase gives a saturated cyan the name green, calls part of a chromatic ring grey, and puts one of the eleven focal colours outside what a display can show. Each failure is a measurement rather than a disclaimer, and together they say what a vocabulary is that eleven points and a distance are not.

limits · Limits How blue the sheet reads, and how much of that is the room. Chroma in an appearance model, with the observer adapted to the light the sheet is under. The three markers on each row are an average, a dim and a dark surround; the open marker at the left is the same sheet with the ultraviolet removed. Every stock is close to neutral without the excitation and carries real chroma with it, at a hue of about 295 degrees — blue-violet — so the colour is the fluorescence and not the substrate. And it falls by nearly half between a bright room and a dark one, which makes how blue a sheet looks a property of where it is being looked at.

A brighter white still looks white

Colorimetry says a brightened sheet is nine units of b* from neutral, which sounds like a visible blue. An appearance model with the observer adapted to the room says it carries eleven units of chroma at a hue of 295 degrees — genuinely blue-violet — and that the number falls by nearly half between a bright room and a dark one. What it cannot say is why anybody calls the result white.

brain · Appearance How far each census row moves when the test set's own description does. A grid of bars, one row per change of light in the census and one bar in each row per number that describes the region the test surfaces are drawn from: how saturated they are, how bright, and how far the two modulations may go together. A bar's length is the elasticity — the proportional change in the published residual for a proportional change in that number. Saturation runs from 0.49 to 0.91 and brightness averages 0.104, so a test set's chroma range is nearly everything and its lightness range is nearly nothing. For scale, the largest elasticity found anywhere among this collection's five declared population widths is about a half — and those at least have declared ranges, while these three numbers have never been quoted with one.

Saturation is nearly everything

The set of test surfaces has three numbers describing it, and only one of them matters. How saturated the surfaces are carries an elasticity of about 0.7 on every result computed over them; how bright they are carries 0.10. A test chart's chroma range decides its answer and its lightness range does not.

difference · Metric How far each census row moves when the test set's own description does. A grid of bars, one row per change of light in the census and one bar in each row per number that describes the region the test surfaces are drawn from: how saturated they are, how bright, and how far the two modulations may go together. A bar's length is the elasticity — the proportional change in the published residual for a proportional change in that number. Saturation runs from 0.49 to 0.91 and brightness averages 0.104, so a test set's chroma range is nearly everything and its lightness range is nearly nothing. For scale, the largest elasticity found anywhere among this collection's five declared population widths is about a half — and those at least have declared ranges, while these three numbers have never been quoted with one.

A chart decides what a camera scores

A camera profile's reported error changes by a factor of five when the test chart's saturation changes, with the camera and its matrix untouched. The elasticity is 0.67 — the same figure, to two per cent, that an entirely unrelated measurement over an entirely unrelated set of surfaces gives.

imaging · Capture 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 The census along the line from ΔE76 to ΔE94, and past it. ΔE94 is ΔE76 with two weighting constants in it, and at zero those constants make every weight exactly one, so the two formulae are joined by a line rather than separated by a choice. The horizontal axis is how much of the published weighting is applied: 0 is exactly ΔE76, 1 is exactly ΔE94, and 3 is three times more weighting than anybody has proposed. The falling curve is the census's mean elasticity to how saturated its test set is, which drops from 1.11 to 0.74 — most of the fall happening before the published value is reached. The other curve is Kendall's τ against ΔE2000's ranking, and it peaks at w = 0.5, not at 1: the weighting that best reproduces the published ordering is about half the published weighting. There is no value of this dial that reaches ΔE2000, whose rotation term is not on this line at all.

A dial through a discrete menu

ΔE*94 is ΔE*ab with two weighting constants in it, and at zero those constants make every weight exactly one — so the two ends of the oldest disagreement in colour difference are joined by a line rather than separated by a choice. Walking it gives a derivative where a menu gives only a spread, and the derivative says the published weighting is on the far side of the interesting part.

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 Two sensitivities from two libraries, under every unit. Two quantities that share no code, no test set and no physical question: how much the adaptation census's residual depends on how saturated its surfaces are, and how much a camera profile's reported error depends on how saturated its test chart is. The first is a mean over fourteen changes of light built from cosine combinations; the second is one number about one silicon sensor scored on Gaussian bumps. Under the published unit they sit at 0.687 and 0.656. Across the whole menu they move together, from about 0.5 under the appearance unit to about 1.15 under plain CIELAB, staying within 12 per cent of each other at the worst point. Two numbers agreeing once is a coincidence; two curves agreeing at six points across a factor of two and a half is a shared mechanism, and the mechanism is the compression the unit applies to a chroma difference.

The coincidence was a mechanism

Two sensitivities from two libraries with no shared code came out two per cent apart, and the claim made about them was that they share a mechanism rather than a number. That claim has a colour-difference formula inside it, so it can be tested by changing the formula — and both curves move together across the whole menu, from 0.5 to 1.15.

imaging · Capture The share of a sample's reflectance an aperture recovers, by how wide it is. Six materials, and the fraction of each one's true reflectance that a measurement recovers through an aperture of the stated radius. The horizontal axis is logarithmic in millimetres; the vertical is a share, so 1.0 is the whole of it. The dashed line is a 4-millimetre radius, which is about what a hand-held spectrophotometer has. At that aperture coated paper reads 98 per cent of its own reflectance and candle wax reads 48. Every curve approaches one from below and none of them reaches it: the kernel's tail is what is being cut, and it falls as one over the aperture rather than exponentially.

An aperture is a filter

A measuring aperture throws away the light that came back outside it, and the light that comes back furthest is the light at the wavelengths the sample absorbs least. So an aperture does not attenuate a translucent sample evenly — it attenuates its peaks more than its troughs, which is a filter whose transmission curve the sample itself decides.

applied · Delivery Where a sample's colour goes as the aperture closes. The a and b of three translucent materials as the measuring aperture narrows from forty millimetres to one. Each track starts at the open circle, which is the colour the model says the sample has, and ends at the filled one. The axes cross at the neutral point. pale marble passes through neutral at a radius of 5.32 millimetres and comes out on the other side; candle wax passes through neutral at a radius of 7.07 millimetres and comes out on the other side; skin passes through neutral at a radius of 0.76 millimetres and comes out on the other side. Nothing about the sample changed: the aperture is a filter with a colour of its own, and the colour is decided by how the sample scatters rather than by what it absorbs.

The hue the hole decides

A piece of pale marble measured through a wide aperture is faintly yellow. Measured through a narrow one it is faintly blue, and between the two there is an aperture at which it is exactly neutral. Nothing about the stone changes; the aperture is a filter with a colour, and what decides that colour is the size of the particles rather than the pigment between them.

scene · Scene A departure against how far the sample sits from the light. The sample is mixed with a flat reflectance, from the flat one at the left to its own at the right, and two observers differing in the macular pigment look at each mixture. The straight line is the distance between their relative cone excitations, and it is straight to 0.0 per cent: the departure is a pairing, and scaling one factor scales the product. The curved line is the same sequence in ΔE₀₀, which is not a linear function of the excitations and cannot be — it has cube roots in it and a chroma weighting underneath. The identity is about the eye; the curvature belongs to the unit.

A departure is straight in the excitations

Walk a sample a quarter of the way from the light towards its own reflectance and exactly a quarter of the observer disagreement remains — in cone excitations, to two parts in a hundred. In ΔE₀₀ the same quarter leaves 0.347 where proportionality wants 0.428, and the discrepancy belongs entirely to the unit.

difference · Metric What the floor receives, matt walls against walls of roughness 0.2. The spectral radiance leaving the floor towards the front of the room, computed twice. The matt curve peaks at 530 nanometres, where the walls' pigment is. The glossy curve is higher everywhere and higher by relatively more away from that peak, because the extra light is a Fresnel return and a Fresnel return has the lamp's spectrum rather than the paint's. That difference in shape is the desaturation, drawn before it is reduced to a number, and it is the reason the two lines cannot be brought together by any exposure change.

A lobe takes colour out of a bounce

A gloss wall sends more light to the floor and less colour. The extra light is a Fresnel reflection at the interface, it carries the lamp's spectrum rather than the paint's, and it arrives at the next surface white — so a green room in satin paint is less green than the same room in flat paint by nearly a colour difference of chroma.

scene · Scene Two ways of putting a lobe on a wall, and the sign they disagree about. The chroma of the floor's return against the wall's roughness, computed twice. In one the interface's return is taken out of the body term — light reflected at the boundary never reaches the pigment, which is what a real finish does. In the other it is added beside the body term, which is what a microfacet model does if nobody couples the two. The first says a gloss wall makes the room less coloured and the second says more, and the gap at the glossiest end is 2.87 units of chroma. Neither is a numerical error; the difference is a modelling decision that is usually made by omission.

Two ways to put a lobe on a wall

Take the interface's return out of the body term and a gloss wall makes the room less colourful. Add it beside the body term and the same wall makes the room more colourful. Same solver, same room, one line of energy accounting, and the two answers differ by nearly three units of chroma at the glossy end.

scene · Scene The lobe's share of what leaves a surface of body reflectance 0.5. For light arriving at 45°, the fraction of what leaves the surface that is the interface's Fresnel return rather than the pigment's. It runs from about 9.1 per cent at an eggshell finish down to 4.2 at a matt one. That is a small share, and it is the whole of the effect: a tenth of the return arriving white is enough to move the room's colour by units of ΔE₀₀, because the bounce is what a room's colour is made of and every bounce is multiplied by the next.

A tenth of the return arriving white

Nine per cent of what leaves a satin wall is a Fresnel reflection carrying no pigment. That nine per cent moves the room's colour by 4.89 ΔE₀₀ and its chroma by five per cent, because an interreflection multiplies and a small contribution with a different spectrum compounds into a large one.

scene · Scene A hue circle through a per-channel curve. 28 colours on a circle of constant lightness 55 and chroma 38, each put through the tone curve one channel at a time and read back. The curve is a function of a single number and has no idea what hue is, and it rotates the circle by up to 4.4 degrees — largest at hue 260 — while raising chroma by a factor of 1.27 and lightness by about 1 units.

A contrast control is three controls

A tone curve is a function of one number at a time and knows nothing about hue. Applied to each channel separately it rotates a hue circle by up to seventeen degrees, raises chroma by a factor of 1.27 at ordinary strength, and lifts lightness — so a photographer who moves a contrast slider has moved three things and the interface names one of them. All three scale with the curve's strength, monotonically, and the hue rotation depends on which hue it is.

imaging · Capture A stop taken in raw, and the same lightness reached afterwards. Each row is a stop of exposure applied to the raw values, against a gain applied after the whole pipeline and solved so that an eighteen per cent grey comes out at the same lightness. The two are then the same brightness by construction and differ by 4.2 colour differences at the mean and 11.1 at the worst patch. A stop is a scalar in front of the curve and is not a scalar behind it.

A stop is not a stop afterwards

Doubling the light is exactly a factor of two in raw values and in tristimulus values, which is the one thing about exposure everybody is sure of. A stop taken after the tone curve is a factor of something else, and matching the two on an eighteen per cent grey leaves the rest of the frame between three and four colour differences apart at the mean and up to eleven at the worst patch. The gain that matches one stop is 2.47 rather than 2.

imaging · Capture Out to the device and back, once and again. Each intent applied 3 times in succession to the same ramp. The upper bar is what the first pass moves and the lower is what the second moves. relative-colorimetric is idempotent — the second pass moves nothing, to the floating-point floor — and the other two are not: perceptual moves another 2.73 and saturation moves another 3.09. A file converted twice is not a file converted once.

A second conversion is not a repeat

A colour converted to a device and back is described as lossy where the device cannot hold it and exact where it can, which suggests that a colour surviving one round trip survives any number. One of the four intents is idempotent to the floating-point floor. The other two are not — a perceptual conversion moves a ramp 3.70 colour differences on its first pass and another 2.73 on its second, and after three passes it is still moving by 2.42.

applied · Delivery The room's reflected light and its colour, against how glossy the walls are. Four changes against the matt room as the coloured walls are made glossier, from roughness 0.8 on the left to 0.15 on the right. The room's reflected light rises by up to 19 per cent and its chroma falls by up to 9.1 per cent. The walls' own outgoing chroma falls fastest, by 14.6 per cent, and the floor's follows the room's. A lobe does not move colour from one face to another: the room as a whole has less of it.

A gloss finish takes colour out of the whole room

A gloss wall makes the floor's return less colourful seen from the front of a room and more colourful seen from the coloured walls, which leaves open whether the lobe removes colour or only moves it. A ledger of every flux between the room's faces answers it. At an eggshell finish the room's reflected light gains 16 per cent in quantity and loses 8.3 per cent of its chroma, and the loss is nearly the same for blue, green and orange walls while the walls' own losses range from 13 to 25 per cent. Only the painted walls receive light as colourful as before.

scene · Scene 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 What is left of one colour difference when the two colours alternate. 23 pairs built at exactly ΔE₀₀ 1.000, alternated at a rate, with each part of the difference scaled by its own temporal channel and the formula then applied unchanged. At rest every pair is the flat line at one. By 7 hertz the median is 1.11 and the pairs run from 0.57 to 3.04 — a factor of 5.3 between pairs the formula calls identical. By sixty hertz the largest of them is 0.15.

A difference has no rate

A colour difference formula answers for two patches that are both there and stay. Alternate the same two colours and the difference is not scaled but taken apart: the colour half is gone by fifteen hertz and the lightness half is four times louder at eight, so twenty-three pairs the formula calls identical run over a factor of six at the rate the eye is best at, and are worth nothing at all above sixty.

difference · Metric The pairs that change places in chroma are a wedge with two straight edges. Every pair of samples, plotted by the log ratio of the two samples' background-free responses across and the log ratio of their chroma at a background of 2 up. A pair changes places between that background and one of 80 exactly when its chroma ratio and its response ratio point in opposite directions and the chroma ratio is the smaller — which is the wedge between the horizontal axis and a line of slope -0.2598, half the change in the lightness exponent. 754 of 14028 pairs are inside it, and the condition names every one of them and nothing else: 0 disagreements between the line and the model. The pale dots are one pair in eleven of those outside; the filled ones are every pair inside.

The reversals have a straight edge

Twenty-one of 276 pairs change places in chroma between a dark background and a light one, and the reason given was that chroma is a product of a term carrying the exponent and a term that does not. That is true and it is not a description of which pairs. Chroma at one background is a single common factor times a power of lightness at another, so a pair reverses exactly when its chroma ratio and its lightness ratio point opposite ways and the first is the smaller — a wedge with two straight edges, which names every reversal and nothing else.

brain · Appearance One lightness scale, drawn as a contour across the rooms. Three surrounds up the page and the background's luminance factor across it, on a square-root scale so that the model's own exponent base is linear in the axis. Each curve joins the rooms whose lightness exponent is the same, and every room on one curve returns the same lightness for every sample. The marked curve is the one through a television in a lit living room against a mid grey: it also passes through a print on a desk against a background of 2.8 and a projection in a dark room against 47.0. A curve that leaves the plot has no member in that surround, because each surround multiplies a base that runs only from 1.48 to 2.48.

Two rooms with one lightness scale

CIECAM16's surround and its background both reach lightness, and they reach it through one product. So the rooms fall into classes: a television in a lit living room against a mid grey returns exactly the lightness a print on a desk against a background of 2.8 does, for every sample, to the last bit of a double. It returns 0.76 of its chroma and 0.81 of its brightness. Two of the model's four viewing-condition parameters are one parameter, and only colour tells them apart.

brain · Appearance A satin finish pulls each room towards the lamp's white — a 3000 K radiator. Six rooms lit by a 3000 K radiator, on the ab plane of an instrument referenced to daylight, whose own white is the cross at the centre. Each open circle is a matt room and the arrow runs to the same room with satin walls. The filled diamond is the lamp's own white on that plane. Every arrow points within 9.2 degrees of the diamond and covers between 8.1 and 11.5 per cent of the distance to it. Whether the daylight instrument then reads more chroma or less depends only on whether the room was nearer the cross than the diamond is.

A finish adds colour only to a daylight meter

Measured against daylight's white, a satin finish under six lamps and six wall colours takes anything from −6 to 42 per cent of a room's colour, and one room reads as more colourful glossy than matt. Measured against the white of the lamp each room is actually lit by, the same thirty-six rooms lose between 7.7 and 12.9 per cent and none gains. The whole spread was the lamp's own colour, and the finish does one simple thing to every room: it pulls the room's colour a tenth of the way towards the lamp's white.

scene · Scene Thirty-six rooms as a viewer adapted to each would see them. Each cell is one room at a satin finish: wall colour down, lamp across. The large number is the share of the faces' chroma a viewer adapted to the room's own light loses, read through CIECAM16; the small number under it is what the room's light loses against the lamp's white. The viewer loses between 12.8 and 30.9 per cent, always more than the light, and the rows differ far more than the columns: a deep red room loses about twice what a green one does under every lamp.

What an adapted viewer loses is set by the wall

A satin finish takes about a tenth of a room's colour, measured on the room's light against its lamp's white. Read through an appearance model by a viewer adapted to the room, the same thirty-six rooms lose between 12.8 and 30.9 per cent — 1.4 to 2.4 times as much — and the wall colour decides the multiplier: a deep red room loses twice what a green one does, under every lamp. A test on the bare wall predicts it. Add a little of the lamp's white to the wall's own colour and ask the model what that costs: the answer orders the thirty-six multipliers at 0.95.

scene · Scene The share a finish takes falls with how much light the wall returns. Seventy-two rooms under daylight, each with a different paint on two opposite walls — six hues, four band widths, three peak reflectances — at a satin finish. Across is the wall's luminance factor, the share of the lamp's light it returns; up is the share of the room's chroma the finish takes. The losses fall with the luminance factor at a rank correlation of −0.89, from 15.5 per cent on the darkest walls to 2.5 on the palest. The two ringed paints make rooms of the same matt chroma and lose 14.7 and 2.5 per cent.

A dark wall pays for a finish

A satin finish takes about a tenth of a room's colour, and the tenth varies. The natural explanation is that a weak colour loses a larger share of itself to the white light a glossy surface adds. Over seventy-two paints under one lamp that explanation orders nothing: the loss runs from 2.5 to 15.5 per cent, it follows how much light the wall returns at a rank correlation of −0.89, and it follows how colourful the wall is at −0.04. Two rooms equally colourful matt lose shares nearly six times apart, and the one that loses more is the darker.

scene · Scene How far each model turns a display colour's hue as white is added. The twenty-four most saturated colours an sRGB display makes, one every 15° of HSV hue across, each mixed with the display's white at the same luminance down to a fifth of its purity. Up, how far that mixture's hue angle turns in CIECAM16, CIELAB and Oklab. From red to a fifth of its purity CIECAM16 turns −9.4° and Oklab −10.2°; CIELAB −18.1°. From the display's blue, Oklab turns +16.3°, CIECAM16 +3.6° and CIELAB −8.9°.

White turns a hue, and the models part at blue

Mix a saturated light with white and its hue changes as well as its saturation — the Abney effect, and the reason lines of constant perceived hue curve in a chromaticity diagram. Asked what adding white does to the twenty-four most saturated colours a display makes, CIECAM16, CIELAB and Oklab all turn the hue. About reds they agree: CIECAM16 turns within a degree of Oklab, whose hue was fitted to observers' constant-hue judgements. About the display's blue they do not: Oklab turns sixteen degrees, CIECAM16 four, and CIELAB nine the other way.

brain · Appearance Which way a tint turns a pigment's hue, made in paint and made in light. For eight pigments tinted nineteen parts white to one of colour, the Oklab hue turn from the pure pigment: of the tint made in paint (upper bar) and of the additive mixture with white at the same luminance (lower bar). For seven of the eight the two point in opposite directions. The orange turns +13.5° in paint and −13.9° in light.

A tint in paint turns the other way

A pale colour can be made two ways: by stirring white pigment into a coloured one, or by adding white light to it — which is what a halftone on white paper and a display both do. At the same luminance the two tints are not the same colour. For seven of eight pigments they turn the hue in opposite directions, an orange by +13.5 degrees in paint and −13.9 in light, and the paint tint is the more colourful of the two every time. The cause is in the reflectance: diluting a pigment moves its absorption edge, and adding light does not.

brain · Appearance What survives holding the lightness still. For each of five groups of rooms sorted by how much light the wall returns, the rank correlation of the finish's share with three properties of the paint, taken with the wall's luminance factor held. The wall's chroma runs from -0.90 among the darkest walls to 0.81 among the palest, crossing zero in the middle — the reversal. The band's width, which was the predicted mechanism, never leaves the range -0.15 to 0.22, and the census already contains four families whose bands are all the same width.

The finish adds the room's own colour

Among dark walls a more saturated paint loses a smaller share of its colour to a gloss finish, and among pale walls a larger one. The mechanism proposed for that reversal was spectral concentration — a narrow tall band — and the census that found it already contained four families of paints whose bands are all the same width. Holding lightness still, the band's width orders the losses at a rank correlation of 0.01. What does order them is that the light a finish adds has already bounced off the walls.

scene · Scene How each unit balances lightness against chroma, as a display brightens. Twelve pairs built to differ in lightness alone and twelve built to differ in chroma alone, each at exactly one ΔE₀₀, read in both units at nine display levels. Up is the median lightness pair's reading divided by the median chroma pair's, so a falling curve means chroma differences becoming relatively more visible. Both fall. ΔEITP's median runs from 0.91 at a 1.5-candela white to 0.81 at 10,000, a fall of 11 per cent; CAM16-UCS's from 1.13 to 0.87, a fall of 23 per cent. Neither turns: both units say chroma differences gain on lightness differences as a display brightens, and CAM16-UCS says it twice as strongly.

The units part by hue, not by light level

Two colour differences with a light level in them were compared on a display running from 5 to 5,000 cd/m², and a prediction was drawn from how each divided a difference between lightness and chroma. Built into pairs that differ in lightness alone and in chroma alone, both units say the same thing about light level: as a display brightens, chroma differences gain on lightness differences — ΔEITP by a tenth, CAM16-UCS by a quarter. Where they part is hue. The appearance model moves every colour's balance by the same factor; ΔEITP moves the violets, reds and cyan-blues the other way, and at nine of twelve base colours the two units disagree about the direction.

difference · Metric A four-ink inverse table's error along the grey axis, 9 nodes, black from L* 60. The colour difference between a grey asked for and the grey printed, from L 92 to 14, for a 9-node inverse table whose separation strategy begins black generation at L 60 (dashed line). Three tables: filled exactly from the strategy, mean 0.073; refitted with each node sliding along the strategy, 0.050; refitted freely, 0.036. To the left of the dashed line the strategy-bound refit lies close to the filled table; to the right it lies close to the free refit. Every table is exact at its nodes, marked on the axis.

A strategy keeps the refit only where black prints

Refitting an inverse table's nodes against their own error halves it, and in a four-ink table the refit has to leave the separation strategy's choice of black alone. Held to the strategy, it keeps the whole of its gain wherever the strategy prints black and almost none of it where the strategy does not — and the share it keeps equals the share of the grey ramp printed with black, to within three hundredths. The start of black generation, predicted to be where the refit would fail, is where the table needs it least.

applied · Delivery Where chroma stops protecting a wall, in five rooms. The seventy-two paints in each of five rooms, sorted by how much light the wall returns and read in overlapping windows of eighteen: the rank correlation of the share of colour a satin finish takes with the wall's chroma, lightness held. Below zero a more saturated paint loses less; above, more. The dots are where each room's curve crosses: cube at 0.36, corridor at 0.37, low room at 0.38, one wall open at 0.29, two walls open at 0.24. Solid lines are closed rooms of three shapes; dashed are the cube with one and two walls opened.

An open room hands over sooner

A gloss finish takes the least colour from a saturated dark wall and the most from a saturated pale one, and in a closed cube the sign changes at a wall returning about a third of the light. The prediction was that a less enclosed room would move that point up the lightness scale and that a room with a window would have no pale end. Opening one wall moves it down, from a luminance factor of 0.36 to 0.29, and opening a second to 0.24; stretching the room into a corridor or flattening it nudges it slightly up. The ambient does whiten, as predicted. A whiter ambient does not delay the colour term — it weakens it, so the other term takes over sooner.

scene · Scene The lamp's white, six walls and the light arriving at each. On the 1976 chromaticity diagram, in the closed cube under daylight: the lamp's white (centre), six saturated walls with bands centred from 450 to 650 nm (open circles), and the light arriving at each wall from the rest of the room, lamp included (filled). Each ambient lies on the line from the white to its wall, a fraction of the way along it: 450 nm 10 per cent, 490 nm 12 per cent, 530 nm 19 per cent, 570 nm 19 per cent, 610 nm 13 per cent, 650 nm 5 per cent.

A probe at the wall prices the finish

The light arriving at a painted wall from the rest of its room is what a gloss finish hands back, and a small probe held against the wall reads it. It lies on the line from the lamp's white to the wall's own colour, a fraction of the way along, and the fraction is set by how much light the wall returns, not by how colourful it is — as predicted. It is not the fixed fraction the prediction said: it runs from 2 to 46 per cent across seventy-two paints in one room. That variation is what makes it useful. Read in the matt room, it orders what a satin finish would cost more tightly than the paint's own lightness does, in every room tried.

scene · Scene 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 The appearance model's lightness-to-chroma balance, as the room takes a share of the adaptation. The median lightness pair's reading over the median chroma pair's, for twelve base colours, against the display's white, in a room of 20 cd/m². Solid: CAM16-UCS, with the viewer taking all, three quarters, half, a quarter and none of the adaptation from the display — darker lines take more from the display. Dashed: ΔEITP, which no room enters. With the display alone the model's balance falls 23 per cent; with half from the room, 13; with none from the display it does not move.

A lit room brings the units' medians together

As a display brightens, CAM16-UCS says chroma differences gain a quarter on lightness differences and ΔEITP says a tenth. All of the appearance model's movement comes from what the viewer is adapted to, and every calculation had the viewer adapted to the display alone. Give the room its share of the adaptation and the model's movement shrinks at every step: with a 20 cd/m² room supplying two thirds of it, the two units' medians fall by the same amount. What does not shrink is their disagreement about direction. The model still moves every colour the same way, ΔEITP still moves violets, reds and cyan-blues the other way, and in a lit room that becomes the whole of what separates them.

difference · Metric

Named alongside it

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

SpecificationLightnessCIEDE2000Colour differenceInterreflectionSpecularCIECAM16FresnelPerceptual uniformityRank correlationReflectanceAppearance model

All concepts