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

Colour appearance — where it appears

What a stimulus looks like, as opposed to which other stimuli it matches. It depends on the adapting white, the background, the light level and the surround, so it is a property of a stimulus in a situation rather than of the stimulus alone.

Named by 39 essays across 7 fields — each of them below, with the objects they name alongside it.

Two identical grey patches on different surrounds. Both inner squares are #868686. The one on the dark field looks lighter. The values are checked to be equal before the figure is drawn, so the claim is a fact about the drawing rather than a promise.

Matching is not appearance

CIE XYZ predicts when two lights will look the same under identical viewing conditions. It was never a model of how anything looks, and most of the confusion in applied colour comes from using it as one.

matching · Gamut One stimulus, three rooms, three appearances. The same XYZ in a dark, a dim and an average surround. The stimulus does not change and is drawn identically in all three panels; what changes is what CIECAM16 says it looks like. Predicted lightness runs from 65.6 to 57.5 — a spread of 8.1 — with chroma and colourfulness moving too. Colorimetry returns one answer here because it has nowhere to put the room.

A viewing condition is an argument

An appearance model takes a stimulus and a situation. The second argument is not a refinement of the first — it is the content of the claim, and a model that returns an appearance from a colour alone has assumed a room without saying which.

brain · Appearance Colourfulness rises with light level; apparent contrast does not. Predicted colourfulness M for one stimulus across four decades of adapting luminance, and the exponent of the lightness curve over the same range. M rises by a factor of 2.24 — the Hunt effect, which the model does predict. The lightness exponent changes by -2.2%, and in the wrong direction — the Stevens effect, which it does not.

Brighter looks more colourful

Colourfulness rises with light level and the model predicts it. Apparent contrast is supposed to rise too, and the model does not — which turns out to be right, because the thing that actually carries contrast is the surround.

brain · Appearance One stimulus, three rooms, three appearances. The same XYZ in a dark, a dim and an average surround. The stimulus does not change and is drawn identically in all three panels; what changes is what CIECAM16 says it looks like. Predicted lightness runs from 65.6 to 57.5 — a spread of 8.1 — with chroma and colourfulness moving too. Colorimetry returns one answer here because it has nowhere to put the room.

A patch is not a scene

A paint chip is the wrong size, on the wrong background, at the wrong luminance, in the wrong surround. Every one of those is a term in an appearance model, and the model says how much each of them moves the answer — which is the difference between a caution and a prediction.

brain · Appearance Lightness against colourfulness, in a booth and on a screen. Each arrow is one colour, from what the model predicts under a print in a 2000 lux booth to what it predicts under a display in a dim room. Every arrow points the same way, which is the content: a dimmer surround lowers predicted lightness and colourfulness together, so a proof does not merely differ from the print, it differs in a direction — and that is why proofing standards specify the room and not only the numbers.

The proof is a different object

A soft proof can be made colorimetrically exact and still not match the print, because the print is in a booth at two thousand lux with an average surround and the screen is in a dim room at a fifth of the luminance. The appearance model puts four CAM16-UCS units between them, with no change of stimulus anywhere — larger than the error any rendering intent is arguing about.

applied · Delivery Brightness against chroma, at exactly constant luminance. Seven stimuli of identical luminance and rising chroma at hue 25. The model's brightness moves by 2.2 per cent across the whole sweep, and at some hues it moves the other way. The Helmholtz–Kohlrausch effect — measured repeatedly, by several methods — is that a saturated colour looks as bright as a neutral of 1.3 to 2 times its luminance, shown as the band. The gap is the model's, and nothing here closes it: the term that would is not in CIECAM16 and is not invented for the occasion.

Brightness is not luminance

Photometry is additive because the CIE defined it that way. Brightness is not, and a saturated colour looks as bright as a neutral of one and a half times its luminance — an effect this site's appearance model moves by two per cent, in a direction that depends on the hue.

brain · Appearance One light, seven rooms. The same stimulus — fixed in XYZ, unchanged throughout — shown against whites from 12 to 800 candelas per square metre. Its lightness falls from 152 to 16 and its brightness rises, because one of those is a ratio to the white and the other is not. Brown is the low-lightness end: a colour that exists only when something brighter is present, which is why no lamp is brown and no star is.

There is no brown light

Brown is dark orange, dark is a ratio to a white, and a light in a dark room has no white to be dark against. The same stimulus, unchanged in XYZ, runs from lightness 152 to lightness 16 as the surround is raised — and only the bottom of that range has a name.

brain · Appearance One adapting colour, two answers. The left patch is what was stared at. The middle is the afterimage the cone-gain arithmetic predicts at 15 per cent adaptation; the right is the inverted code values. They are 22.1 ΔE00 apart. The gains that produced the middle patch are 0.95, 1.06, 1.69 on the long, medium and short cone classes — the reciprocal of what each class had been receiving, taken 15 per cent of the way.

An afterimage is an adaptation

The demonstration everybody gives is an inverted image, which is a statement about a file format. Running the receptoral arithmetic instead puts the afterimage of a saturated red sixty degrees of hue away from the inverse — and outside what any display can show.

brain · Appearance The colourfulness the sRGB cube reaches, against the light in the room. The display is the same display throughout and the signal is the same signal. What moves is the adapting luminance, which enters the appearance model and nothing else. The furthest colourfulness the cube reaches falls from 131 to 57, a factor of 2.29. A gamut in CIELAB cannot show this at all, because CIELAB has no light level in it — which is why every gamut percentage in circulation is quoted without one.

The gamut shrinks in the dark

Every gamut number here is a property of a device and of nothing else, which is why the same display has the same gamut in a studio and in a cinema. It does not. Turn the room down four decades and the solid loses a fifth of its reach and two thirds of its volume, with the signal unchanged.

limits · Limits How far a judgement is from the settled one, second by second. The light changed from one white to another at t = 0 and nothing else moved. The model has one degree of adaptation and no clock, so the distance plotted is what a clock adds: 3.6 CAM16-UCS units half a second in, still 1.3 after a minute, and 0.11 after five. Every appearance number on this site is the value at the right-hand end.

The model has no clock

An appearance model takes a stimulus and a situation and returns what it looks like. It does not take a time, and adaptation is not instantaneous — half a second after the light changes a judgement is three and a half CAM16-UCS units from the settled one, and a minute later it is still 1.3.

limits · Limits Colour temperature, and the number nobody quotes beside it. The Planckian locus in the 1960 UCS diagram — the only diagram on which correlated colour temperature is well defined — with four sources and the perpendicular from each to its nearest point. The temperature is where the foot of the perpendicular lands; Duv is how long the perpendicular is. halophosphate sits 0.0246 off the locus at 4513 K, which is a visible green cast that its colour temperature does not mention.

White is a region

A lamp is not sold as a chromaticity. It is sold as 4000 K, and what that means is that its chromaticity fell inside a quadrangle — which two lamps can occupy at opposite corners, eleven ΔE00 apart. In a room with either of them, the same twelve surfaces differ by one unit.

light · Light An afterimage, as the local pool coming back to equilibrium. The local pool has adapted to the patch and the global pool has not, so the gain change is exactly the local share of a full von Kries change — which is why afterimage's free strength parameter is not free here. The dwell is 20 seconds. The swatches are the predicted appearance of the test surface at four moments. They are predictions of hue and direction; there is no response compression in this model, so the chroma is a ceiling rather than an estimate.

A gain has a time constant

An afterimage and the clock on chromatic adaptation were built in different files from what the last phase said was one mechanism. Joining them removes a free parameter, reproduces both, and predicts a third thing — that two people in one room, at one moment, looking at one patch, do not agree about its colour.

brain · Appearance How much colour a display delivers, against how bright the room is. The appearance solid of the whole code cube, with the room's reflected light added to every code value and the surround ratio computed from the room's own white against the display's. A 300 cd/m² panel delivers most at 200 lux, and the curve falls on both sides: darker costs the surround, brighter costs the black. At the 32 lux the softproofing standards specify, the solid is 89 per cent of its best — which is not a criticism of the standard, since it is written for matching a screen to a print viewing booth rather than for delivering the most colour.

A display in a room is a smaller display

Two results here turn the room's light in opposite directions and neither knows about the other. A room has one light level and does both at once — so there is a brightness at which a display delivers the most colour, it is not at either end, and it scales with the panel.

limits · Limits The appearance model's three rooms, read as three moments. CIECAM16's degree of adaptation is a function of the surround and the adapting luminance and of nothing else — the model has no time in it. Solving for the moment at which an observer who will adapt completely has got that far turns each of the three tabulated surrounds into a reading on a clock. At 100 candelas per square metre they are 106, 49, 21 seconds. They are presented as three rooms. They are also one observer, in one room, at three times in the first two minutes.

A viewing condition is a moment

CIECAM16's degree of adaptation is a function of the surround and the adapting luminance and of nothing else, because the model has no time in it. Solving for when an observer who will adapt completely has got that far turns the standard's three surrounds into three clock readings — 107, 50 and 21 seconds — and the two readings are distinguishable by waiting.

brain · Appearance How much of the gamut changes name, and what changed it. The eleven basic terms are quoted as centroids in CIELAB, and a colour is named by which one it is nearest. Two things nobody records decide the answer. Changing the distance function renames 20.5 per cent of the displayable gamut. Changing the room — the same colours, the same words, a different surround, through the appearance model — renames up to 26.8 per cent. The centroids were measured in one viewing condition and are applied here in every essay as though a name were a region of a space with no room in it.

A name moves with the room

Eleven basic colour terms are quoted as centroids in CIELAB and a colour is named by which one it is nearest. Two things nobody records decide the answer — which distance function is used, which renames a fifth of the displayable gamut, and which room the colour is in, which renames more than a quarter of it.

brain · Appearance Every claim here that was computed with one model, recomputed with two. Each row is a claim one of these essays makes. The bar is how many times the two-model answer differs from the one-model answer, on a logarithmic scale. 3 of 13 have no bar at all: the first model's answer for them is exactly zero, not because it computed zero but because it has no variable for the quantity. Those are the rows where a second model did not correct an answer — it supplied one.

What a second model changed

Thirteen claims here, each computed with one model and recomputed with two. Ten of them move by half again or more. Three of them do not move at all in the ordinary sense — the first model's answer is exactly zero, not because it computed zero but because it has no variable for the quantity — and every one of those three is a join that supplied a state or a device rather than a spread.

limits · Limits How much of what a display can show each name owns. Every point on a 5-unit CIELAB lattice inside the sRGB gamut is given to its nearest centroid under ΔE00, and the shares counted. They run from 21.1 per cent for purple to 4.6 for blue, a factor of 4.6. The three terms that carry no chroma at all — black, grey and white — hold 20 per cent between them. A share here is a statement about the names and about the gamut they are counted over, and the gamut is sRGB.

A name in the model's own words

The eleven basic colour terms move when the room does, and the obvious objection is that they were being measured in a space with no room in it. Quoting them in an appearance model's own coordinates instead does not shrink the renaming — it grows it by four per cent — and the space alone renames an eighth of the gamut with the room held still.

brain · Appearance Where each published matrix puts the confusion points, whether or not it meant to. Every matrix from tristimulus values to cone responses commits itself to three confusion points, because the point is the direction the other two rows annihilate. The first row is the construction from the measured points and returns them exactly. The rest were chosen for other reasons and land elsewhere — Hunt–Pointer–Estévez, which this collection uses everywhere, misses the deuteranope's point by 1.28 in chromaticity. The worst here is 4.09.

The cones an appearance model uses

CIECAM16 adapts in three axes whose rows are labelled L, M and S, and they were fitted to corresponding-colour experiments rather than measured on receptors. Run the dichromat construction backwards on them and they commit to a deuteranope confusion point 1.45 away in chromaticity from the measured one — which is a test the axes were never asked to pass.

brain · Appearance How far from circles every basis leaves the ellipses. Eight bases ranked on the mean ratio of the long to the short axis of MacAdam's twenty-five discrimination ellipses, measured in a lightness–chroma space built on that basis. The range runs from 1.61 for best for discrimination to 7.70 for best for adaptation. The ordering is not the ordering on the other objective and is nearly its reverse.

One matrix doing two jobs

CIECAM16 adapts in CAT16 and then applies its response compression in the same axes, so a single matrix decides both how well the model handles a change of light and how uniform the space it produces is. The two jobs have different best answers, and the matrix was chosen against only one of them.

brain · Appearance The same border signal, filled in with a boundary and without one. Two fields, each 6 degrees across. The signal is injected along a ring just inside a contour and varies around it, brightest on one side and dimmest on the other. On the left the signal diffuses and the contour is impermeable: the interior settles to 1.000 against a border mean of 1.000, which is the mean-value property of a harmonic function arriving as a prediction about appearance. On the right the same signal is handed to a Gaussian pool of 0.5°, which has no notion of inside: it reaches 0.040 at the centre, because a kernel weights the near rim more than the far one and a filled region does not.

A pool with an edge

A Gaussian pool says how much of a stabilised image survives and can say nothing about what the remainder looks like, because a Gaussian has no edge. Give the pool a boundary and the interior of a faded region takes the average of its own border — exactly, by the mean value theorem, arriving as a prediction about appearance.

scene · Scene 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 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 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 model's hue scale, and the four numbers it is built from. Hue quadrature against hue angle. The four anchors are the unique hues, each with its own weight, and between them the scale is a hyperbolic interpolation rather than a straight line. The quadrant from blue back to red spans 143 degrees of hue angle for its hundred units of quadrature, against 70 for red to yellow.

The hue scale has four corners

CIECAM16 reports hue twice — as an angle in its own opponent plane, and as a quadrature interpolated through four unique hues with four fitted weights. The second is the one hue tolerances and hue-preserving mappings are written in, and it is piecewise — its slope jumps at each of the four anchors, by a factor of 1.74 at green and by 0.41 at blue, and it runs 4.1 times faster near yellow than near blue.

brain · Appearance Where averaging the model's answers is and is not averaging its argument. Each row takes a spread of situations, averages the model's predictions across them, and compares that against the model's prediction for the average situation. The bar is the gap as a share of the spread itself. Over the differences between observers it is 1.4 per cent — the model is very nearly linear there. Over the range of adapting luminance one room covers in a day it is 59 per cent, and from indoors to outdoors 74.

Where the model's curve does not matter

This round has been about what a nonlinearity does to an average, and CIECAM16 is the most nonlinear thing in the collection. Over the spread a population of observers produces, the average of its predictions is its prediction for the average to within 1.4 per cent — the nonlinearity is there and the excursion is too small to reach it. Over the range of adapting luminance one room covers in a day, the same gap is 59 per cent of the spread, and from indoors to outdoors 74.

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 stated lightness pins down, and where. A lightness quoted to 0.05 of a unit, inverted, and the luminance it fixes. Read as a fraction of the colour's own luminance the requirement is 0.90 per cent at J 10 and 0.097 at J 95, a factor of 9.3. Read in absolute luminance it is the other way round, by a factor of 6.5. Both readings are true and they answer different questions.

A stated lightness is two requirements

A specification quotes an appearance to a stated precision — a lightness to a tenth of a unit, say — and the same precision everywhere. Inverted, a twentieth of a unit of lightness fixes the luminance to nine tenths of one per cent at the bottom of the scale and to a tenth of one per cent at the top, a factor of 9.3. Read in absolute luminance it is the other way round by a factor of 6.5, and both readings are true.

brain · Appearance Which appearances a surface can have, lightness by lightness. The same lattice of lightness, chroma and hue a specification is written in, 10488 points, inverted under daylight with the observer adapted to it. Each row is one lightness, split into three shares: appearances a reflecting surface can have, appearances that are a light but that no surface can return, and appearances with no light under them at all. Over the whole lattice the first is 66 per cent, the second 23 and the third 11. At J 90 a surface can have 38 per cent of the row.

A third of the appearance box is no surface

An appearance specification is written as a lightness, a chroma and a hue, and the model's inverse turns any such triple into three numbers. A tenth of the space turns into something that is not a light at all. A further quarter turns into a light no reflecting surface can return, because a surface cannot give back more than all the light at any wavelength. So a third of the space a paint, a print or a dye is specified in cannot be made from paint, print or dye, and at lightness 90 nearly two thirds cannot.

brain · Appearance 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 What the choice of adopted white is worth, in a room lit by two lights. A room lit half by daylight and half by an incandescent lamp. The light on the surfaces is fixed; what varies is the white the model is told the observer has adapted to, running from the lamp on the left to the window on the right. The median of twelve surfaces moves 32.6 CAM16-UCS units if the lamp is adopted and 24.5 if the window is, against the room's own mixture in the middle. The model offers no way to choose, and its degree of adaptation is 0.94 at every point of the dial.

A room with two lights has no white

An appearance model takes one adapting white. A desk beside a window has two, and the mixture falling on the paper is not the same thing as the white the person reading it has adapted to. Mixing the lights is arithmetic. Choosing the white is not, and the choice is worth sixty units of appearance — most of which is a cast, and not all of which is.

brain · Appearance One grey scale, three backgrounds. CIECAM16's lightness against the luminance factor of a neutral sample, with only the background changed. A grey reflecting 19% reads 46.7 on a near-black background and 32.8 on a near-white one. The three curves are not three shapes: each is the same curve raised to a different power, because the background reaches lightness only through the exponent z, which runs 1.621 to 2.374 across the three.

A dark background moves every difference and no match

CIECAM16's background is one number, and it reaches lightness as one exponent. That is enough to change what a grey looks like and not enough to change which of two greys is lighter — so a match survives the background exactly, a corresponding colour is invariant to it, and a tolerance is not. The effect the background is usually invoked to explain is absent from the model entirely.

brain · Appearance A crispening term puts the peak where the background is. How much lightness the model returns for a small change in the sample's level, against the sample's level measured as a log ratio to the background's — so that all three backgrounds share one axis and a peak at the background is a peak at zero. The pale curves are CIECAM16 as it stands, which has no peak anywhere: they rise slowly and monotonically because a background that enters as four constants fixed before the sample arrives cannot know where the sample sits relative to it. The solid curves are the same model with a term of amplitude 6 and width 0.5 added to lightness. Each peaks at zero to within 0.000 of a log unit, and the peak's height is 12.00 lightness units per log unit of level — the amplitude divided by the width, exactly.

The cancellation is exact and cheap to lose

CIECAM16 has no crispening, and adding one was expected to be expensive: the background's exactness in a corresponding colour comes from its being a common exponent, and a function of the sample's own level is not one. It is expensive in kind and not in size. A term that raises a straddling pair's lightness difference by half moves a corresponding colour by five thousandths of a tristimulus unit — a thousandth of what stating the background differently at the two ends already costs.

brain · Appearance 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 Two uniform spaces, two answers: cyan to magenta. The gradient from above, in the a and b plane. The grey line is the straight path in CIELAB; the two coloured curves are the shortest paths under ΔE₀₀'s own local metric and under CAM16-UCS's. They are 15.7 CIELAB units apart at their furthest, against bows from the straight line of 9.9 and 12.2. Both spaces are published as uniform and both are used to decide what lies between two colours; they do not agree.

Two uniform spaces disagree about between

ΔE₀₀'s own local behaviour says which colours lie between two colours, and so does CAM16-UCS's. They do not agree. On cyan to magenta the two shortest paths run fifteen CIELAB units apart — more than either runs from the straight line — and on that gradient ΔE₀₀ would rather have the straight line than CAM16-UCS's answer. Getting the comparison at all takes noticing that one of the two has no local metric: its published difference is a Euclidean distance raised to the power 0.63, and a power below one has an infinite derivative at zero.

matching · Gamut 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 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 Three uniform spaces, three answers: red to blue. The gradient from above, in the a and b plane: CIELAB's straight line, and the shortest paths under ΔE₀₀'s local metric, under CAM16-UCS's and under Oklab's, whose shortest path is its own straight line carried back into CIELAB. They bow from CIELAB's line by 14.4, 42.5 and 42.6 units. ΔE₀₀'s and CAM16-UCS's paths run 28.3 apart at their furthest, Oklab's runs 29.0 from ΔE₀₀'s and 5.6 from CAM16-UCS's, and the space furthest from the other two here is ΔE₀₀.

A third space breaks the tie only once

ΔE₀₀ and CAM16-UCS disagree about which colours lie between two colours. Oklab was the obvious tie-breaker, and it breaks the tie on one gradient of five: on red to blue its path runs within six CIELAB units of CAM16-UCS's and twenty-nine from ΔE₀₀'s. On red to green and cyan to magenta it keeps to CIELAB's straight line while both others bow, and on blue to yellow it bows further than either. Each of the three spaces is the odd one out somewhere. Asking also exposed a CAM16-UCS path that had never converged.

matching · Gamut

Named alongside it

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

CIECAM16Viewing conditionSpecificationAdaptationSurroundLightnessChromatic adaptationCIELABModelling assumptionAssertionColourfulnessLuminance

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