CIECAM16 — where it appears
Named by 61 essays across 7 fields — each of them below, with the objects they name alongside it.
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.
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.
Why there are four unique hues
Observers agree that four hues are elementary and that no colour is reddish green. Nothing in the three receptors predicts either fact, and the axes of every standard colour space miss the four by tens of degrees.
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.
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.
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.
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.
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.
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.
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.
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.
The index is one observer's opinion
A colour rendering index is printed to a tenth of a point and computed for a single set of colour-matching functions that no standard names as a choice. Scored by two hundred eyes instead, one lamp's spread is wider than the whole range the standard observer puts five lamps in — and two lamps the standard separates by four tenths of a point come out the other way round for every member of the population.
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.
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.
A corner moves both terms
The interreflection essays compute what a corner does to a spectrum, which is one of the two things a corner does. It is also a brighter place with a differently coloured background — a viewing condition, not a stimulus — and adaptation removes most of the first and none of the second. At an enclosure of six tenths that is 63 per cent of seven units gone and a further unit arriving from the extra light alone.
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.
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.
A difference needs a basis too
A linear change of coordinates leaves every colour match exactly where it was. A cube root does not commute with one — so a lightness–chroma space, and every colour difference computed in it, is a property of the basis that happened to be in place before the nonlinearity. CIELAB's basis was chosen in 1931 for reasons that had nothing to do with difference.
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.
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.
The surround is three rows of a table
An appearance model takes the room as three constants, and the standard tabulates three rooms. Every appearance figure in this collection is drawn at one of them. The parameter they are three points of is continuous, and the middle row is not in the middle.
A discount nobody measured
Every adaptation number in this collection assumes an observer who adapts completely. The appearance model's own formula says they do not — it puts the degree at 0.94 in an ordinary room — and the difference is not a rounding. It is a factor of 1.7 on the residual every one of those figures reports.
A delivery tolerance is three tolerances
A colour reaches a reader through a profile, a gamut mapping and a room, and each has a number somebody chose. Each has an essay of its own here, and none of those essays had put the three costs in one column. Put there, the stage nobody controls carries ninety-seven per cent of the total.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
Which mixture bows most depends on the ruler
The physical half-and-half mixture of two lights misses the midpoint of their two readings in any unit a person is shown, and the share it misses by is about the same in ΔE₀₀ and in the appearance model's own space — 12.8 and 14.6 per cent at the median. Which mixtures miss most is not. The rank correlation between the two units is 0.57, a display's blue and yellow is the worst pair in one and the mildest in the other, and the smaller number usually quoted for the appearance model is its power correction rather than a straighter line.
A distance raised to a power has no length
CAM16-UCS's colour difference is its Euclidean distance raised to the power 0.63 and multiplied by 1.41. That is still a metric — the triangle inequality holds on every one of four thousand random triples — and it has no length. A grey ramp from black to white measures 25 units in one step, 137 in a hundred and 755 in ten thousand, growing as the number of steps to the power 0.37, and halving the size of a step triples the number of steps that fit.
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.
The average surface does not look average
Over a population of observers the appearance model is so nearly linear that the mean of its answers is its answer for the mean, to 1.4 per cent of the spread. Over the surfaces in a scene it is not. On 240 smooth reflectances the gap is 21 per cent of the spread, and the mean surface looks 4.2 units lighter than the surfaces look on average. The grey that matches the average light is a 47 per cent reflectance; the grey that matches the average look is a 43 per cent one.
A chain measured in a unit that cannot add
A delivery chain's four stages, measured in the power-corrected appearance difference, sum to 7.66 while the chain end to end measures 5.05, and the shortfall was read as the stages partly cancelling. A chain whose four stages lay in a straight line and added exactly would still read 0.74 of its sum in that unit, because a distance raised to the power 0.63 cannot add. Measured in the model's own Euclidean space the same chain reaches 0.84 of its sum. Three quarters of the published shortfall was the exponent.
A gloss room looks less colourful than it measures
A gloss finish takes 8.3 per cent of the chroma out of a green room's reflected light, and a viewer adapted to the room should discount a loss that affects everything alike. The appearance model says the opposite. Adaptation removes the colour the whole room shares, leaves the colour that differs from face to face, and the finish takes as large a share of that as of anything — so to a viewer standing in the room the faces lose 13.9 per cent of their chroma, not 8.6.
Two filters cancel only in a bright enough room
An older lens and a denser macular pigment cancel each other once an eye has adapted — and that result belongs to the end of a dial nobody stands at. Read at the degree of adaptation CIECAM16 gives an ordinary room, the two barely cancel; in a living room they add, and in a cinema they cost six times what they cost under the sky. The room has to be about as bright as an office before the cancelling begins at all.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
The hue disagreement is the quantiser's
As a display brightens, the appearance model shifts every colour's balance between lightness and chroma by one factor, and ΔEITP shifts violets towards lightness and yellow-greens towards chroma. The proposed source was the perceptual quantiser acting on three cone-like signals at unequal levels. Replacing the quantiser with a pure power law and changing nothing else removes the disagreement exactly: every colour moves by a factor of one. With the quantiser, how far a colour moves follows the spread of its three signals, and which way follows where its S signal sits — above the other two, towards lightness; below, towards chroma.
The blue resists through the model's denominator
CIECAM16 says a saturated blue is nearly impervious to added white: at equal luminance and an equal dose it loses a sixteenth of what an orange loses, where CIELAB and Oklab say a quarter. The model has two obvious places for that to come from — a hue factor fitted to make colourfulness equal across hues, and the sum of cone signals it divides its opponent signals by. Setting the hue factor to one changes nothing. Replacing the sum with the model's own achromatic signal makes the blue lose 0.233 of the orange's loss, beside CIELAB's 0.221 and Oklab's 0.223. The disagreement is one denominator.
The blue's hue turn was lost with a matrix
Add white to a saturated blue and its hue turns — sixteen degrees by the constant-hue data Oklab was fitted to, four by CIECAM16. The obvious suspect was the model's compressive response, acting on a very large blue signal. It is not: removing the compression's saturation moves no hue by half a degree, and a cube root instead of its exponent moves the blue by one. What decides it is the cone space the compression happens in. Computed in Hunt–Pointer–Estévez, the space CIECAM02 compressed in, the same model turns the blue 15.6 degrees; CIECAM02's own front end turns it 16.1. CIECAM16 merged CIECAM02's two spaces into one sharpened for adaptation, and that one gives a display's blue almost as much long-wave signal as white has.
At the gamut's edge the reds move as far as the violets
As a display brightens, ΔEITP shifts a saturated colour's balance between lightness and chroma by an amount set by its three quantised signals, and CAM16-UCS shifts every colour alike. The largest shifts found so far were a yellow-green at ×0.63 and a dark blue at ×1.62, both at the census's edge — and the blue turns out to be a colour no BT.2020 display can show. Walked out to the display's real boundary, the yellow-greens go lower, to ×0.54, and the dark blues never pass ×1.35, because BT.2020's blue edge is at low chroma. The top of the range goes to the reds and red-purples at ×1.6: at the edge the L-minus-M term grows to two thirds of the S term. Pairing the two extremes still needs a third of the observers the violet experiment needs.
A display's red takes the reds' move and leaves the pair
At BT.2020's edge ΔEITP moved a dark red's balance between lightness and chroma furthest of any colour, ×1.64 from a dim display to a bright one, and the reason offered was BT.2020's red primary, a line far out at 630 nanometres. Moving that primary in along the spectral locus confirms it: the reds fall faster than any other hue, to ×1.40 at 615 nanometres and ×1.25 at 605, and Display P3, whose red is a 615 nm line to three ten-thousandths, gives the reds the same. The top of the range goes to a red-purple, which rises as the red moves in because BT.2020 had pushed it past its own peak. And the forced-choice pair the experiment needs is the same two colours on every display.
Two matrices fail under a warm white
Compressing in Hunt–Pointer–Estévez after adapting in CIECAM16's own space restores the blue's Abney turn, and the reason CIECAM16 stopped using two spaces was that converting between them sends some colours to negative signals. Where it does depends on the white. Adapted to a daylight display's white, only spectral lights past 560 nm fail, in their short-wave signal, by thousandths of their luminance, and nothing on sRGB's boundary fails at all. Adapted to a tungsten white, every spectral light from 380 to 474 nm fails in its long-wave signal, some by several times their luminance, and so do points on every display's boundary; there the display blue's restored turn becomes a swing of fifty degrees.
Two matrices hold to almost tungsten, and the blue turns long before
An appearance model that adapts in CIECAM16's space and compresses in Hunt–Pointer–Estévez gets the blue's hue turn right under daylight and sends the display's blue to a negative signal under illuminant A. The prediction was that the failure reaches sRGB's blue near 3500 K, a warm-white LED, and that the blue's turn holds its daylight value down to about 4000 K. Walked down the radiator and daylight loci, sRGB's boundary holds to 2872 K — fifteen kelvin short of illuminant A — while BT.2020's fails at 3626. There is a neutral window, 4700 to 5700 K, where no colour at all goes negative. But the blue's turn does not wait for the failure: it is five degrees above its daylight value by 4500 K and nearly three times it before anything breaks, because it follows the blue's long-wave signal down towards nought.
An appearance model flattens the blue by its hue
A safety margin moves a corner of a display's gamut inward by a multiple of itself set by the corner's shape, and the unit the margin is written in decides the shape. In ΔE₀₀ the yellow is the sharpest corner of an sRGB and a BT.2020 display, because its sharpness lies across hue where ΔE₀₀'s chroma compression cannot reach it. CAM16-UCS compresses colourfulness less steeply, and the prediction was that it would leave the blue sharper than the yellow. It leaves the yellow sharpest, at 1.66 times a margin on both displays, and flattens the blue to 1.17 and 1.10 — the bluntest corner of all twelve. Its colourfulness does what the prediction said: on its own it would sharpen the blue past the yellow. Its hue scale undoes that. At a display's blue one degree of CIELAB hue is three and a half degrees of the appearance model's, and a unit that counts hue that finely there spreads the blue's directions apart until the corner is nearly a face.
A quantiser keeps the blue a spike
A gamut margin moves a display's corners inward by multiples set by the unit it is written in. ΔE₀₀ and CAM16-UCS both blunt an sRGB or BT.2020 display's blue, CAM16-UCS to nearly a face, and the prediction was that ΔEITP — the difference built on ICtCp for high-dynamic-range television — would blunt it too. It does the opposite. With the white at 320 cd/m² the blue is ΔEITP's sharpest corner on both displays, moving 3.12 and 3.24 times a margin, about as far as in CIELAB; at the green, cyan, magenta and yellow the three tolerance units agree within a quarter, and at the blue they span a factor of three. ΔEITP's lengths alone would blunt the blue as ΔE₀₀ does. What keeps it sharp is the perceptual quantiser: ICtCp's chroma rows sum to nought, so under a response that compresses like a logarithm, dimming the blue primary is a step in intensity and nothing else. Replace the quantiser by a linear response and the blue falls to 2.15; by a logarithm, it rises to 3.39. A brighter display sharpens it further.
Adapting to a warm room deepens the shadows' tint
A warm room's light reflected off a local-dimming screen tints the shadows of every dark picture when the screen's black is declared in grey — by up to 17.7 ΔEITP — and ΔEITP has no viewer in it. A viewer who has sat in a 2,700 K room all evening is adapted partly to the room, and adaptation to a warm white discounts warm light. The prediction was that a viewer adapted a third of the way to the room would see under half the tint, and one adapted two thirds of the way would see the darkest greys turn blue. Read through CIECAM16, the opposite happens in a dark picture. The tint the viewer sees grows at every step of adaptation: in the moon picture's darkest grey from 2.7 CAM16-UCS units for a viewer adapted to the display to 3.3, 3.9 and 4.4. The darkest greys never turn blue; they stay orange and fade. What turns blue is the mid-greys, whose light is the display's own and now looks cool. In the bright window picture the tint shrinks, and declaring the floor in the room's colour still removes it for every viewer.
Named alongside it
The objects these essays reach for when they reach for this one.
Colour appearanceViewing conditionSurroundChromatic adaptationLightnessSpecificationAdaptationColour differenceChromaColourfulnessΔEModelling assumption