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

Colour appearance model — where it appears

A model predicting what an observer in a stated viewing situation would report about a stimulus, rather than which stimuli match. Its inputs are a stimulus and a few numbers describing the surroundings, which is what makes it blind to anything carried by an image rather than by a patch.

Named by 8 essays across 2 fields — each of them below, with the objects they name alongside it.

The same claim in nanometres of pigment, where no declared width can reach it. Five horizontal bars on a scale of nanometres, one per published chromatic-adaptation transform, each showing how far the medium-wave cone pigment's absorption peak would have to move for the receptors' own protan confusion point to land where that transform puts it. Zero is the measured peak. The bars run from -10.5 to 18.2 nanometres — in both directions, so two of the transforms want the pigment shorter and two want it longer. Drawn across them is the 25 nm separation between the L and M pigment peaks, which is the whole basis of red-green vision and is not a number this collection declared. The nearest transform asks for a displacement of 30 per cent of that separation, and the span across the table is 28.7 nanometres — larger than the separation itself. No population, cloud or standard deviation appears anywhere in the statement.

Five transforms and the space between them

Every appearance prediction here chooses one of five published adaptation transforms, and the five disagree about where a protanope's confusion lines meet by more than the distance between the two pigments the disagreement is about. That spread is itself a scale, and using it needs no population model at all.

brain · Appearance 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 How far below nought the two-matrix model's smallest signal goes, along the locus. For every spectral light from 380 to 700 nm, the smallest of its three Hunt–Pointer–Estévez signals after CIECAM16's adaptation, divided by the light's luminance, adapted to the display white and to illuminant A, drawn down to −2. Adapted to the display white the smallest signal dips below nought only past 560 nm, and by at most 0.0037; adapted to A it is below nought from 380 to 474 nm and reaches −6.7 of its luminance at the violet end.

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.

brain · Appearance Where each display's boundary and the spectrum fail, as the adapting white warms. For radiators from 6500 K down to 2700 K, the temperatures at which the two-matrix front end sends some point of each display's boundary, or some spectral light, negative: shaded where it fails. sRGB and Display P3 first fail at 2871 K, just above illuminant A; BT.2020 at 3626 K. P3 and BT.2020 also fail at their red corners under whites cooler than 5700 K, and no spectral light fails between 5700 and 4700 K. The dashed line is the 3500 K the prediction named.

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.

brain · Appearance Per channel, a tenth of green lands where a half was graded. Each mixture's CIECAM16 hue quadrature on the master and through the per-channel curve, between unique green at 200 and unique blue at 300. On the master a tenth of green sits at 312.9 and a half at 277.5; per channel on the 100 cd/m² display the tenth lands at 260.9, past the master's half.

An appearance model sees the per-channel sky turn twice as far

BT.2390's tone curve, applied to each channel of a 1,000 cd/m² master shown on a 100 cd/m² display, raises a sky-blue's green share from a tenth to 69 per cent of its blue and turns its ICtCp hue 23°, where the same curve applied to the largest channel with all three scaled keeps the hue within 3°. ICtCp's hue is not an appearance, and the prediction was that CIECAM16, read under the display's own white, still shows the per-channel turn as more than twenty hue-quadrature units and more than ten ΔEITP, the scaled curve under three of each. The appearance model sees it as fifty-two units, more than half the way from unique blue to unique green, and its lightness more than doubles. The scaled curve keeps hue and lightness to a quarter of a unit. And ΔEITP between master and display ranks the two curves backwards: in absolute light the per-channel sky is the nearer one.

matching · Gamut A blue's intensity sits below where the curve compresses. BT.2390's curve from the 1,000 cd/m² master to displays of 100 and 300 cd/m², with the level a pure blue, a tenth-green and a half-green sky present to it when the curve is applied to ICtCp intensity, and the level their blue channel presents when it is applied per channel or to the largest channel. The skies' intensity corresponds to 79 to 387 cd/m², against knees of 27.9 and 161.4; their blue channel sits at 1,000, the top of the curve.

A curve on intensity cannot see a blue's brightness

ITU-R BT.2390's tone curve applied to each channel of a bright master turns a tone-mapped sky's appearance fifty-two hue-quadrature units towards green on a 100 cd/m² display; applied to the largest channel with all three scaled, it keeps hue and lightness to a quarter of a unit. BT.2390 also describes applying the curve to ICtCp's intensity and scaling its chroma, which keeps ICtCp's hue by construction, and the prediction was that it keeps the appearance's hue within three units and its lightness within two. It keeps the hue, within 2.3 units. It cannot keep anything on the display: a saturated blue's intensity is the PQ level of 79 cd/m², under the 300 cd/m² display's knee, so the curve barely touches it and every sky asks for two to seven times the blue the display has. Clipped channel by channel, the sky turns as far as the per-channel curve turned it; scaled back into the gamut, it lands where the scaled curve put it. The step back into the gamut decides the appearance, not the curve.

matching · Gamut Holding ICtCp's hue and lightening the chroma still turns the sky. Each mixture mapped by BT.2390 on ICtCp intensity on the 100 cd/m² display and brought into its gamut three ways — clipped channel by channel, scaled until the largest drive is full, and by its ICtCp chroma alone at fixed intensity and hue — read as the change in CIECAM16 hue quadrature from the master's. The chroma-only return moves −16.8, −14.4, −12.6, −17.0, −9.2 units at no green to half green; scaled into gamut, −1.3, −1.6, −1.8, −1.6, −2.2.

Lowering only the chroma turns the sky white and its hue with it

A tone curve applied to ICtCp's intensity keeps a high-dynamic-range sky's hue, but a saturated blue's intensity lies under the curve's knee, so the colour it asks for lies outside every display's gamut. The prediction was that bringing it back by lowering its chroma alone — intensity and ICtCp hue held — keeps the CIECAM16 hue within three units, lifts the lightness by ten and halves the chroma: a paler blue of the right hue. The ICtCp hue and intensity are kept to a hundredth. Everything else fails. The chroma must fall to a fifth or less on a 100 cd/m² display, the sky rises from a lightness of 22 to 76 and higher, and its hue quadrature moves eight to seventeen units toward green — a pure blue's by 17. Holding ICtCp's hue while lowering chroma does not hold the hue a viewer sees, and the intensity the curve chose was never a blue's.

matching · Gamut Holding the true hue saves one or two units of seventeen. Each mixture's CAM16-UCS distance from the master on the 100 cd/m² display: mapped on intensity and returned by ICtCp chroma, returned along CIECAM16's hue at the same lightness, scaled into the gamut, and the master's drives shown unmapped. The CIECAM16 return lies 16.7, 17.2, 17.3, 16.8, 15.7 from the master, against 18.9, 18.7, 18.5, 17.6, 16.8 for ICtCp's; the master's own drives 4.14, 4.10, 4.07, 4.02, 4.05.

The sky a dim display can show best is the master's own

A tone curve applied to ICtCp's intensity maps a saturated high-dynamic-range sky to a colour no display can show, and bringing it back by lowering only its ICtCp chroma turns it pale and toward green. The prediction was that a return along CIECAM16's own hue line, at the lightness the curve chose, holds the hue by construction, needs a deeper chroma cut, and still lies at least twice as far from the master as simply scaling the drives. It holds the hue to a hundredth, keeps more chroma than ICtCp's return rather than less, and lies two and a half to four times as far as scaling — because holding the true hue removes only one or two of seventeen units of difference. The rest is the lightness the curve held. And the nearest a dimmer display can come to the master's appearance turns out to be the master's drives, shown unmapped.

matching · Gamut

Named alongside it

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

Hue quadratureTone curveChromatic adaptationCIECAM16Dynamic rangeGamut mappingTransfer functionAbney effectCAT16Display gamutHueSpectral locus

All concepts