The surround is three rows of a table

An appearance model needs to be told about the room, and it is told in three numbers chosen from a table with three rows.

The claim #

Every appearance figure in this collection is computed at one of three tabulated rooms, the parameter those three are samples of is continuous, and where a figure sits on it is a decision worth most of the range.

• The table has three rows. Average, dim and dark, each a triple of constants: an adaptation factor, a tone-curve exponent, and a chromatic induction factor.
• The standard itself permits interpolating between them, so the continuum is not an invention of this essay — it is in the recommendation, and this collection already uses it in one place.
• A mid-grey’s predicted lightness moves 9.7 units across it, which is a large fraction of the range a lightness scale has.
• And the middle row is not in the middle. The step from average to dim is fifty-eight per cent of the whole span, so a figure drawn at dim has been placed nearer the dark end than the word suggests.
• The other appearance conclusions here move by very little across the same continuum, which is the useful half: what is decided by the choice of row is the lightness, and not the effects.

What the three rows are #

The viewing condition is an argument, and it has been since this collection built an appearance model at all. What was not obvious until it was measured is how much of that argument is carried by the three constants that describe the room rather than by the adapting luminance or the background.

The three rows are a print sample on a desk in a lit room, a television in a living room, and a projected image in a darkened cinema. Each supplies a factor for the degree of adaptation, an exponent for the tone response, and a factor for chromatic induction; they are the model’s entire account of what surrounds the thing being looked at.

The parameter behind the rows is a ratio: how luminous the surround is compared with the white in the field. Average means a surround at or above about a fifth of the white; dark means essentially nothing there; dim is between. So the three rows are three points on a one-dimensional family, and a room is a value of that ratio rather than one of three things.

There is a reason the three exist as words rather than as a slider, and it is not laziness. The ratio is awkward to measure and easy to misjudge: a reader asked whether their room is average or dim will answer confidently and often wrongly, because the eye adapts and a room that feels normally lit can be a tenth of the luminance of the screen in it. Naming three conditions is a way of giving somebody a judgement they can actually make. What it costs is that the judgement then looks like a measurement.

What moving along it does #

Sweeping the three constants linearly from the average row to the dark row — which is what the recommendation permits and what this collection’s own delivered-gamut sweep already does, because the room brightness it looks for sits between two rows — produces a smooth curve rather than three steps.

A mid-grey at twenty per cent of the white reads 41.6 in an average surround, 47.2 in a dim one, and 51.3 in a dark one. The whole span is 9.7 units of lightness, and the first step takes 5.6 of them.

The surround is one of several constants the same audit priced, and its place among them is what says whether three tabulated rows are a problem worth having.

Fifty-eight per cent of the span lies between the first two rows. That is the finding, and it has a consequence for reading any figure drawn at one of them: dim is not the midpoint of the range, so a figure drawn there is not a compromise between the other two. It is much nearer the dark end than the word suggests, and a reader who takes the three rows as evenly spaced samples of rooms is calibrating on a scale the model does not have.

It is worth being concrete about how large 9.7 units of lightness is. The scale runs from zero at black to a hundred at the white, and a step of one unit is roughly a just-noticeable difference for a large uniform patch. So the choice of row is worth about ten times the smallest difference anybody could see — not a subtlety, and not a catastrophe either. It is the size of effect that a reader would notice if the same figure were drawn twice and would never suspect from one drawing.

The mechanism is in the constants themselves. The exponent runs 0.69, 0.59, 0.525 across the three rows, so the step from average to dim is 0.10 and the step from dim to dark is 0.065. The tabulation is unevenly spaced because the effect it models is unevenly distributed, which is correct and is invisible in a three-row table.

The second thing the curve shows is that it has no kinks. A three-row table invites a suspicion that the model is piecewise — that something changes character between rows — and it does not: the constants enter smoothly and the output is smooth in them. That is worth checking rather than assuming, because a model whose behaviour did change between tabulated conditions would make interpolation meaningless, and the recommendation permits interpolation without saying so.

Which conclusions this touches, and which it does not #

The number that moves is the lightness. The effects — the differences the appearance model exists to predict — mostly do not.

Brighter looks more colourful is a statement about how colourfulness rises with adapting luminance, and the surround enters it only as a small modulation. What a second model changed compares an appearance prediction with a colorimetric one, and the comparison moves together as the surround moves. The tone curve’s steepening from dark to average is the surround effect and is therefore the thing being swept rather than a casualty of it.

So the exposure is narrow and is worth stating precisely: any figure here that quotes a lightness quotes it at a chosen row. Any figure that compares two things in the same room is unaffected, because both move together. That is most of them, which is why the choice has cost nothing so far.

It is a good illustration of a general point about sensitivity. A model parameter can be enormously influential on the values a model produces and almost irrelevant to the comparisons it is used to make, and which of those a collection depends on is a fact about the writing rather than about the model.

The check was worth running rather than assuming, and it found one place where the distinction does bite. A figure that shows a stimulus in three rooms side by side — the one at the top of this essay’s second panel — is a comparison across rows, so the spacing between them is the content. That figure is now the one place in this collection where the unevenness matters, and its caption says so: the step from the first column to the second is larger than the step from the second to the third, and a reader who reads three columns as three equal steps will read the effect as more linear than the model makes it.

Everything else compares within a room. Two paints under one light, two displays in one office, a stimulus before and after adaptation: in every case the surround constants are the same on both sides and cancel from the difference.

What was computed, and how #

The sweep interpolates the three constants linearly in a parameter that is zero at the average row and one at the dark row, evaluates the appearance model at thirteen points along it, and reads off two quantities: the lightness of a mid-grey, and the exponent of the tone curve measured between two stimuli a decade apart in luminance.

The exponent is measured rather than quoted, which matters because the constant in the table is not the exponent. It enters the model in two places and the effective exponent of the resulting lightness scale is a consequence of both. Reading the table’s number as the tone-curve exponent would be reading a coefficient as a result.

Both of those are worth having beside the sweep, because the word room is doing two jobs in this collection and they should not be confused. One is the light the room reflects onto a screen, which is physics and changes the stimulus. The other is the surround constants, which are psychophysics and change what the same stimulus looks like. This essay is entirely about the second, and a figure of the first is here so that a reader can see the difference rather than be told it.

Where the dim row falls on the continuum is computed from its own constants rather than assumed. Taking the exponent as the interpolation parameter puts it at fifty-eight per cent of the way to dark; taking the adaptation factor puts it at fifty per cent; taking the chromatic induction factor also puts it at fifty. The three constants do not agree about where dim is, which is a small and genuine untidiness in the table and is reported rather than averaged away.

What a room actually is #

The surround ratio has a definition, and following it out to a real room is instructive about how far the model reaches.

Take a screen at 200 candelas per square metre showing a white, in an office lit to 300 lux. The walls behind the screen return that illuminance diffusely at about a fifth of it, so their luminance is roughly 300 × 0.2 / π ≈ 19 candelas — under a tenth of the white. That is the dark end of the table, not the average row, in a room anybody would describe as normally lit.

The same screen in a room lit to 1000 lux against a light wall gives about 64 candelas, or a third of the white, which is squarely average. So the two ordinary offices sit at opposite ends of a parameter this collection has been treating as a single choice.

That arithmetic is not a measurement of anything and is written down here as an illustration rather than a result — the reflectance of the wall is assumed, the geometry is ignored, and a real measurement would use a luminance meter rather than a division. What it shows is the size of the gap between the vocabulary and the quantity. Two rooms a reader would call the same are two different rows.

Where the model stops #

Nothing here maps a real room onto the parameter. The surround ratio is defined against the white in the field, so measuring it requires a photometer and a decision about what counts as the surround — the wall behind the screen, the rest of the desk, the window. The model takes a number and this collection cannot tell a reader which number their room is.

That is not a criticism of the model. It is the reason the three named rows exist: they are a vocabulary for a quantity nobody measures, and a vocabulary of three words is easier to use than a ratio nobody has instrumented.

The interpolation is linear because the standard says it may be, not because anything here establishes that the underlying effect is linear in that parameter. Three points cannot distinguish a line from a gentle curve, and the recommendation’s permission to interpolate is a practical allowance rather than a claim about the psychophysics.

And the surround is one of four arguments. The adapting luminance, the background’s relative luminance and the white point are the others, and this collection has a separate essay on what the room’s own light does. Sweeping one while holding three is the right way to isolate an effect and the wrong way to describe a real change of viewing conditions, in which all four move at once.

The generalisation #

The pattern is one this phase keeps finding in different clothes. A tabulated parameter is a sample of a continuum, and a figure drawn at a table row has been placed rather than measured.

The reason it goes unnoticed is that a table looks like data. Three named rows with numbers in them read as three measured conditions, and a model that accepts only those three would make the reading correct. This one accepts anything and is documented to, which means the tabulation is a convenience that has been mistaken for the model’s domain.

The check that finds it is cheap: evaluate the model between the rows and see whether the answer is where a reader would put it. Here the answer is that dim sits at fifty-eight per cent rather than fifty, which is a small enough discrepancy to be uninteresting on its own and is exactly the kind of thing that compounds when a collection has drawn a hundred and eighty figures at one of three settings.

What it would take to do better #

The obvious repair is to stop naming a row and start computing the ratio, which the model already accepts. It is worth saying why that has not been done here and what it would cost.

Every figure in this collection is drawn from a stated rule, so a figure that took a measured surround ratio would need a measurement — and the only room that could be measured is the one the author was in, which is the least relevant room there is. The reader’s room is unknown and unknowable from inside a web page.

What could be done, and is a genuine candidate for later work, is to make the surround a dial: draw the figure at every point on the continuum and let a reader move it. This collection already does that for parameters whose variation is the argument, and the surround qualifies — it is a choice somebody made once and stopped noticing, which is the site’s own test for what deserves a handle.

The obstacle is payload rather than principle. A dial renders every frame at build time and a figure carrying appearance swatches is not small, so a surround dial on every appearance figure would multiply the weight of the heaviest pages in the collection. That is a real constraint and it is the reason this essay reports a curve rather than shipping a slider.

Who found it, and when #

The surround’s effect on apparent contrast is old and is why projection systems are given a higher gamma than displays and displays a higher one than print. Bartleson and Breneman measured the underlying effect in 1967; the constants in the current model descend from a chain of appearance models through Hunt, CIECAM97s and CIECAM02 to CIECAM16.

The permission to interpolate is in CIE 159, the report that published CIECAM02, and it exists because the three-row table was recognised as a discretisation of something continuous from the beginning. What is unusual is not the interpolation but the question: not what does the surround do, which is well established, but how much of a published number is decided by which of the three rows the author happened to pick.

Where the ladder goes next #

The surround is one of the appearance model’s constants and it is at least tabulated. The next one along is worse: the degree of adaptation is computed from a formula, every adaptation number in this collection is quoted at the value that formula does not give, and the difference is a factor of 1.7.

That is the next rung, and unlike the surround it changes numbers this collection has published rather than only the values behind them.