Colour Science & Perception
what the eye settles, and what it cannot
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The thread: Matching is not appearance — page 6

CIE XYZ predicts when two lights will match 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.
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. What the brain does

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.

 How far the answer for the average is from the average answer, over eight spreads. For each spread of inputs, the distance between the mean of the model's answers and its answer for the mean input, as a share of the spread of the answers. Over a population of observers it is 1.4 per cent. Over surfaces it is 21 on smooth natural reflectances, 27 on a banded family with lightness in it, and 9 on a set of pale surfaces. Over the light one room sees in a day it is 59. What the brain does

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 soft proof exact for one observer, as two hundred others see it. Each display is driven to match each of thirty printed patches exactly for the reference observer, so for that observer screen and print are the same colour to fourteen decimal places. The bars are what two hundred observers drawn from the population make of the same pairs: the median observer's difference, median over the patches, and the ninety-fifth percentile observer's: 1.8 and 4.8 on the wide-gamut LCD, 2.0 and 5.4 on the OLED, 3.1 and 7.5 on the laser projector. The narrower a display's primaries, the larger both become. What it takes to deliver it

A soft proof is exact for one reader

A display can be driven to match a printed patch exactly for the standard observer — three equations, three unknowns, agreement to fourteen decimal places. Two hundred observers drawn from a realistic population see the same screen and print a median of 2.1 colour differences apart on an OLED panel and 5.4 apart at the ninety-fifth percentile. On a laser projector the ninety-fifth percentile is 7.5. The patch that fails worst is unprinted paper, and in the chain's own unit the ninety-fifth percentile reader's stage is larger than every one of the four stages a delivery chain is budgeted for.

 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. What a scene does

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.

 A gloss finish's loss of colour, read by the light and by a viewer in the room. Four changes against the matt room as the coloured walls are made glossier, from roughness 0.8 to 0.15: the chroma of the room's reflected light as a colorimeter reads it; the mean chroma of the six faces as CIECAM16 sees them adapted to the lamp and adapted to the room's own average light; and how far the faces sit from that average in the model's uniform space. At roughness 0.2 the light loses 8.3 per cent, the faces 8.6 per cent to the lamp-adapted viewer and 13.9 to the room-adapted one, and the spread 11.0 per cent against 11.2 read against the lamp. What a scene does

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.

 A soft proof exact for one observer, and three proofs tuned for readers. For each display, the median over printed patches of the 95th percentile reader's mismatch between screen and print, for four ways of choosing the display's three drive levels: exact for the reference observer; least squares over a population of a hundred; tuned on that population's 95th percentile; and tuned on the two hundred readers it is scored on, which no workflow could do. On a wide-gamut LCD the four give 4.57, 4.99, 4.74, 4.39, and the three tuned proofs cost the reference observer 0.70, 0.82, 0.69. On an OLED panel the four give 5.12, 5.72, 4.99, 4.86, and the three tuned proofs cost the reference observer 1.35, 0.95, 0.67. On a laser projector the four give 7.54, 7.00, 6.81, 6.50, and the three tuned proofs cost the reference observer 1.88, 1.23, 1.14. What it takes to deliver it

A proof cannot be tuned for readers who disagree

A soft proof matched exactly for the standard observer is five colour differences wrong for one reader in twenty. Giving up that exactness to tune the display's three drives for a population instead moves the ninety-fifth percentile reader by 4 to 14 per cent even when the tuning is done on the very readers it is scored against — because what readers see is mostly each other's disagreement, and three drives act on every reader at once.

 The metamerism index, computed three ways, as the reference match loosens. The special metamerism index of 6 metameric pairs under an incandescent test light, against how well each pair matches under the reference light. Uncorrected, the index absorbs the reference mismatch and rises from 2.86 to 3.76. Corrected multiplicatively it rises to 3.31 and additively to 3.87. All three are the same number when the pair matches exactly, which is the only case the definition covers. Matching and measuring

The metamerism index has two corrections

The index for a metameric pair is defined for a pair that matches exactly under the reference light, and no real pair does. The standard's remedy is to correct the sample first, and it names two corrections — scale the tristimulus values, or add the difference. On six pairs matched to one colour difference, the two answers differ by a tenth to four tenths of an index unit; at two, by a whole one.

 How much of a display's gamut each observer names differently. Each of 60 observers names every colour of the displayable gamut that the panel can make — 823 of them — and the histogram is how much of that gamut each observer names differently from the standard observer. On an OLED panel the median observer renames 8.1 per cent and the furthest 13.1 per cent. Nobody agrees with the standard observer about all of it. What the brain does

A name moves with the reader

Three earlier essays have moved a colour's name by changing the distance function, the room and the space. All three held the observer fixed. Handed the same light from the same display, sixty observers rename between 3.5 and 13.1 per cent of the gamut against the standard observer, a quarter of its colours have a dissenter in twenty, and the narrower the display's primaries the worse it gets.

 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. What the brain does

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.

 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. What the brain does

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.

 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. What the brain does

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.

 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. What the brain does

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.

 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. What the brain does

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.

 Three stored-value defects, before the eye and after it, a print at 40 cm. Each defect's largest colour difference between the version computed on stored values and the version computed on light, read twice: as a pixel carries it, and after both images have been through the visual system's three channels at 83 pixels a degree. The two rankings are not the same. The unsharp mask has the largest error per pixel — 16.62 — and keeps only 38 per cent of it; the corner has the smallest at 7.14 and comes out at 9.87. The filter is not a blur applied to a difference: it is applied to each image, and the difference is taken after. What it takes to deliver it

The eye keeps the lightness errors

Four essays have priced what a resize taken on stored values costs, in colour differences between pixels. A reader does not see a pixel. Put the two versions of each image through the visual system's own three channels and the ranking reverses: the unsharp mask, the largest error per pixel at 16.6, is seen at 6.3 on a printed page, while the corner's 7.1 is seen at 9.9. What decides it is not the size of an error but how much of it is colour.

 An orange ink's tints on three papers: which way the hue turns. The hue of each tint of an orange ink, from the solid to a tenth coverage, against the solid on the same paper, in degrees of Oklab hue: on a coated sheet, an unbrightened uncoated sheet and a newsprint. Solid lines are read against daylight's white, as an instrument reads them; dashed lines against the paper's own white, as a reader adapted to the page. At a tenth coverage, read against daylight, the coated sheet's tint has turned -8.7 degrees and the newsprint's 21.8; read against each paper's white, -8.7 and -1.1. What the brain does

Newsprint turns a tint with its colour, not its gain

A halftone tint turns its hue the way a mixture of light does, by less, because optical dot gain carries it part of the way towards a paint tint. The straight line through a coated sheet's gain predicted that an uncoated sheet's larger gain would carry the orange past the crossing at a factor of 3.2, so that the same ink would turn opposite ways on two papers. It does turn opposite ways — on newsprint the orange's pale tints swing 13 degrees one way where a coated sheet's swing 8 the other. But the gain is not what does it. The road towards paint bends and stops at 60 to 70 per cent of the way, the orange needs a factor of 5.4 to cross, and newsprint's reversal comes almost entirely from the paper being yellow. Read against the paper's own white, as a reader looking at the page is adapted, it goes away.

 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'. What the brain does

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.

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