What an adapted viewer loses is set by the wall

A gloss room looks less colourful than it measures read one room through an appearance model: green walls, daylight, a satin finish. The room’s light lost 8.3 per cent of its chroma to the finish. A viewer adapted to the room’s own light saw its faces lose 13.9 per cent, because adaptation discounts the colour the whole room shares and leaves the colour that differs from face to face, and the finish takes as large a share of that as of anything.

A finish adds colour only to a daylight meter then measured the light in thirty-six rooms — six wall colours by six lamps — and found every one losing between 7.7 and 12.9 per cent, once each room was measured against its own lamp’s white. So there are now two measurements of the same finish that disagree about its size, one of them in thirty-six rooms and the other in one.

The natural expectation is that the viewer loses about 1.7 times the light in every room, since that is the ratio the one room gave. It is not what happens, and what does happen says more about the appearance model than about the rooms.

Twice the light’s loss, and the wall decides how many times #

Read through CIECAM16 by a viewer adapted to each room’s own light, a satin finish takes between 12.8 and 30.9 per cent of the faces’ chroma — between 1.4 and 2.4 times what the room’s light loses. The wall colour sets the multiplier far more than the lamp does.

• A deep red room loses 27 per cent on average over the six lamps, and a green one 13.5 — twice as much, with the light losing 12.0 and 8.3.
• The spread between wall colours is 13.5 points; the most any wall colour spreads across the six lamps is 8.4.
• The light’s own loss orders the viewer’s loosely, at 0.73, and orders the multiplier hardly at all, at 0.24.
• A test on the bare wall orders the multiplier at 0.95. Add five per cent of the lamp’s white to the wall’s own colour and read the chroma it costs in the appearance model: blue gives up 6.7 per cent, deep red 25.6.
• Adapting to the room rather than the lamp adds three to nine points to every room; the ordering is already set before that step.

Thirty-six rooms, read twice #

The rooms are the ones the light was measured in: the unit cube with a lamp in its ceiling, two opposite walls carrying a paint whose reflectance is a band centred at 450, 490, 530, 570, 610 or 650 nanometres, the other faces grey, every face with the same satin lobe. The appearance reading takes each face’s reflected light, scales all six together so that the average face has a luminance factor of 20, and passes each through CIECAM16 with the adopted white set to the room’s own average reflected light — which is what a person who has been standing in the room for a minute is adapted to in the model’s terms. Four ways to move a white point is the reminder that this step is itself a choice among transforms that disagree.

The quantity is the faces’ mean chroma, matt and satin, and the loss is the fall between them.

The table above is the result. Down each column the numbers change a great deal and along each row they change a little. Every cell is larger than the light’s loss printed under it, from the blue row, where the viewer loses 14 to 16 per cent against a light loss of ten, to the red row, where the viewer loses 22.5 to 30.9 against a light loss of eleven to thirteen.

That is not the shape the single daylight room suggested. Scaling the light’s loss by a fixed factor would make the rows differ in the same proportions the light’s losses do, and they do not: the green row’s light loses 8.3 per cent and the red row’s 12.0, a ratio of 1.4, while their viewers lose 13.5 and 27.1, a ratio of two.

The light’s loss is not the viewer’s, scaled #

The direct comparison is the light’s loss against the viewer’s, room by room.

The rooms scatter between a viewer losing 1.4 and 2.4 times the light’s loss, and the two dashed lines that bound them fan out rather than coinciding. The rank correlation is 0.73: rooms whose light loses more do tend to lose more to the viewer, which is expected, since both are measuring the same white light added to the same walls. But the multiplier between them is not a constant and is not ordered by the light’s loss, and at the top of the plot the red rooms sit well above where any single multiplier would put them.

So the viewer’s loss has an ingredient the light’s does not, and it varies strongly between wall colours. Matching is not appearance is the general case of that gap; here it has a size in every room. The obvious candidates are the two things the appearance reading adds to a colorimeter’s: a different unit — CIECAM16’s chroma rather than CIELAB’s — and a different white, the room’s own light rather than the lamp’s.

Two steps, and the first one sorts the walls #

The two can be separated by reading the rooms a third way, through CIECAM16 with the adopted white set to the lamp’s rather than the room’s. That is the appearance model’s unit with the colorimeter’s white.

The first step — changing only the unit — is where the wall colours separate. A viewer adapted to the lamp loses less than the light in the blue rooms, 7.4 per cent against 10.3; the same in the green rooms, 8.3 against 8.3; and nearly twice as much in the red rooms, 23.2 against 12.0. The ordering of the walls is already the final ordering.

The second step — adapting to the room — adds a few points everywhere, between 3.2 and 8.4 across the thirty-six rooms. It is the mechanism the daylight essay found: a coloured pair of walls tints the room’s light, adapting to that light discounts the tint, and what remains is the difference between faces, which the finish shrinks. It raises every row. It does not reorder them.

So the question of what sets the multiplier becomes a question about the unit. Something about how CIECAM16 measures chroma makes a satin finish cost a red room far more than CIELAB says and a blue room less.

The test that needs no room #

A satin finish, seen from the point of view of one wall, does one thing: it adds some of the lamp’s white to what the wall returns. The simplest question to ask the appearance model is therefore what adding white to a wall’s colour does to its chroma, with no room, no interreflection and no adaptation to anything but the lamp.

The six walls give up their chroma to added white at very different rates. At five per cent of the lamp’s luminance, the blue wall loses 6.7 per cent of its chroma and the deep red wall 25.6 — nearly four times as much. The ordering is the same at every amount tried, from one per cent to forty, and at forty the blue wall has lost a third of its chroma and the red two thirds.

That one-patch test orders the thirty-six multipliers at a rank correlation of 0.95. It orders the viewer’s losses themselves at 0.89 and the lamp-adapted viewer’s at 0.96. A computation on one wall’s colour, under one lamp, with no geometry at all, predicts how many times the light’s loss a person standing in the finished room will lose — to the extent the model describes that person.

The mechanism is therefore a property of the appearance model rather than of the room. CIECAM16 treats a saturated dark blue as resisting added white and a deep red as yielding to it, and a satin finish is a way of adding white; the rooms inherit the ordering, and adaptation to the room then adds its few points on top.

The two units disagree about blue and red #

The same one-patch test can be read in CIELAB, and the disagreement is the clearest statement of what the appearance model is contributing.

At the greens, yellows and oranges the two units come within about three points of each other. At the ends of the spectrum they part. On the dark blue wall CIELAB says the dab costs 17.1 per cent of the chroma and CIECAM16 says 6.7; on the deep red wall CIELAB says 21.6 and CIECAM16 24.9. CIELAB’s test orders the rooms’ losses less well, at 0.84, and it gets the blue rooms wrong in the direction that matters: it predicts them among the heaviest losers, where the viewer puts them among the lightest.

The two units are built differently in every step that matters here. CIELAB takes a cube root of each tristimulus channel against the white and measures chroma as a plain distance from the neutral axis. CIECAM16 first transforms to cone-like channels, compresses each with a response that behaves like a 0.42 power at low levels and saturates at high ones, divides its opponent signals by a quantity that grows with all three channels, and weights the result by a factor that depends on hue. Any of those could make a dab of white cost a dark blue less and a deep red more, and nothing here separates them. What the figure establishes is that the two constructions make different claims about how fast colour drains from a dark saturated patch as white is added — a patch is not a scene is the general warning about which of the two has earned trust — and that they differ most at the two ends of the spectrum.

Where in the room the loss is #

The room-level average hides which faces carry the loss, and the red room is worth opening up because it is the extreme.

The two red walls carry most of the chroma and most of the loss: from 66.2 to 44.2 to the adapted viewer, a third of their colour. The grey faces, which the viewer sees faintly tinted away from the walls’ red because the room’s light is reddish and the grey reflects it evenly, lose between an eighth and a fifth of their small chroma. The ceiling, lit directly by the lamp and seen as nearly neutral, barely moves.

So the room’s loss is mostly the walls’ own loss, and the walls’ loss is the one-patch test with a room around it — which is why the test predicts the room so closely. The interreflections that a bounce is a multiplication described are present and shape the grey faces, but they are second-order here.

What a specifier can take from it #

The size of what a finish costs a room depends on which reading is meant, and the readings disagree about which walls pay most. On the light, a dark wall pays for a finish: the loss follows how much light the wall returns. To an adapted viewer, according to CIECAM16, the loss follows hue as well, and a deep red room pays twice what a green one does even at similar lightness. A dark blue wall, which the light-based reading says should pay heavily, pays lightly to the viewer.

For a red or orange accent wall the model’s warning is severe: a satin finish costs a quarter to nearly a third of the room’s colour, to a viewer, under every lamp. For a green one it costs about an eighth. For a blue one, about a seventh.

And the prediction can be made without modelling the room. The one-patch test is a sum over one reflectance and one lamp, and any colour tool that includes an appearance model can run it on a paint before it is chosen. Whether it should be believed is a separate question, and the next section is about that.

How the rooms were read #

The rooms are those of the earlier light measurement, solved directionally in eighty-one bands with a satin lobe (roughness 0.2, refractive index 1.5) on every face and the lamp’s emission removed from the ceiling. For the appearance reading the six faces’ reflected fluxes are scaled by one common factor so that their average luminance factor is 20, then passed through CIECAM16 at an adapting luminance of 100 cd/m², a background of 20 and an average surround, which gives a degree of adaptation of 0.94. The adopted white is the room’s average reflected light, or the lamp’s, as stated.

The one-patch test takes the wall’s reflectance times the lamp, normalised so that the lamp has a luminance factor of 100, adds the stated share of the lamp’s own tristimulus values, and reads the chroma before and after in CIECAM16 adapted to the lamp and in CIELAB against the lamp’s white. Correlations are Spearman’s over the thirty-six rooms.

What this leaves out #

Everything here is what CIECAM16 predicts, not what a person reports. The model was fitted to judgements of colourfulness and hue on patches in controlled surrounds, and the property this essay rests on — how fast its chroma falls when white is added, by hue — is a property of its construction that nothing here tests against observers. It is closely related to the question of what happens to a colour’s appearance as it is diluted with white, which has its own experimental literature, and the model’s ordering of hues under dilution is exactly what that literature could confirm or refute.

The adopted white is the room’s average reflected light, fully weighted. A person in a real room adapts partly to the lamp, partly to the room and partly to whatever they looked at last, and a discount nobody measured is the argument that the share is not known. The two whites computed here bracket the range, and the ordering of the walls is the same at both.

The losses are in CIECAM16’s chroma, at one adapting luminance. Its colourfulness is the chroma times a factor set by the light level, and brighter looks more colourful is what that factor does; at a fixed level it multiplies the matt and the satin room alike, so every share here is the same in colourfulness. A dimmer or brighter room changes how colourful both look, not the share the finish takes.

And the rooms are single-hue with grey faces, at one finish. A room of several colours adapts its viewer to a mixture, and a glossier finish adds more white; both would change the sizes and neither should change the ordering, since the ordering comes from the one-patch test.

Still open: whether people give up colour to white the way the model does #

The whole result reduces to one claim about the appearance model: that added white drains a deep red’s colourfulness about four times as fast as a dark blue’s. That is testable without a room.

The experiment is a colourfulness matching or scaling task on patches: a set of saturated patches at the six hues, each shown pure and with increasing amounts of a white light added, observers judging colourfulness against a fixed reference. If people’s judgements fall with added white in the model’s hue order — red fastest, blue slowest — then the rooms’ multipliers follow and a specifier can trust them. If people’s judgements are closer to CIELAB’s, the blue rooms are underpriced here and the red rooms overpriced.

The literature on colour appearance under dilution with white points in a relevant direction without settling it, because it was mostly conducted to study how hue shifts under dilution rather than how fast colourfulness falls, and a model can get one right and the other wrong. The two tables — hue shift and colourfulness loss by hue — are one session’s work, and the second is the one this result needs.

A multiplier is a model until it has a mechanism #

The habit is about a ratio that looks like a constant.

The daylight room gave a ratio of 1.7 between what the eye loses and what the light loses, and a ratio like that invites being used as a conversion: measure the light, multiply, report what a viewer sees. Across thirty-six rooms it would have overstated the viewer’s loss by a quarter in some and understated it by two fifths in others, and nothing about the one room it came from would have said so.

The move is to ask what the ratio is made of before using it — here, by reading the same rooms a third way, which split the multiplier into a unit step that sorts the walls and an adaptation step that raises them all. Once the first step was isolated, the one-patch test found what it was measuring.

The failure mode is a conversion factor derived from one case and applied to others, where the factor is a property of the case. A ratio between two measurements is only constant if the two measure the same thing, and the way to find out is to vary the case until it moves.