Colour Science & Perception
what the eye settles, and what it cannot
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Essays arrive in groups rather than one at a time. The most recent group is below in full, and every earlier one after it, newest first.

Essays arrive in groups rather than one at a time, and a group usually opens up a subject not covered before. Between one group and the next nothing changes, so a reader who has seen the most recent group has seen everything.

23 September 2026

12 essays on what it takes to deliver it, what a camera does, what a scene does, what the brain does, difference and uniformity, what the eye does and matching and measuring

Where a sharpened E errs, per pixel and as seen: black type on paper, 10 point. The letter E at 10 point on a 300-dot-an-inch page, black type on paper, sharpened by an unsharp mask on stored values and on light; the two maps show the colour difference between the results, pixel by pixel on the left and after the eye's three spatial channels at 40 centimetres on the right, on one scale. The thin line is the letter's outline and the dashed circles mark two pixels round each corner — 8 outer corners and stroke ends, 4 inside angles. The circled zones are 31% of the outline and hold 28% of the per-pixel error and 25% of the seen error. What it takes to deliver it

Sharpened type errs on its dark side

A sharpened square hides its halo along its edges and shows it at its corners, so a sharpened page of type was predicted to show its error at the corners of its letters, several times out of proportion to their length. Black type does the opposite: its outer corners and stroke ends hold between two thirds and nine tenths of their share. As the eye leaves it, the error lies on the dark side of every edge, and a corner holds as much of it as it has dark ground around it — a quarter of a disc where a black corner points out into paper, three quarters where black wraps round a pale one.

7 figures A four-ink inverse table's error along the grey axis, 9 nodes, black from L* 60. The colour difference between a grey asked for and the grey printed, from L 92 to 14, for a 9-node inverse table whose separation strategy begins black generation at L 60 (dashed line). Three tables: filled exactly from the strategy, mean 0.073; refitted with each node sliding along the strategy, 0.050; refitted freely, 0.036. To the left of the dashed line the strategy-bound refit lies close to the filled table; to the right it lies close to the free refit. Every table is exact at its nodes, marked on the axis. What it takes to deliver it

A strategy keeps the refit only where black prints

Refitting an inverse table's nodes against their own error halves it, and in a four-ink table the refit has to leave the separation strategy's choice of black alone. Held to the strategy, it keeps the whole of its gain wherever the strategy prints black and almost none of it where the strategy does not — and the share it keeps equals the share of the grey ramp printed with black, to within three hundredths. The start of black generation, predicted to be where the refit would fail, is where the table needs it least.

6 figures The calibration error a narrow fourth channel survives, by where it is placed. For a red, green and blue ambient sensor with one more channel 10 nm wide, centred from 450 to 640 nm: the first calibration error at which some lamp of fourteen is misclassified. Dashed: the channel pooled into the whole residual, as the ambient sensor's disagreement was read; its best is ±1.50 per cent. Solid: the channel read on its own, as its departure from what the camera's white predicts for it; its best is ±4.0 per cent, at 450 nm. Crosses mark centres where the channel read alone does not separate the lamps at all. The two horizontal lines are the red, green and blue design (±1 per cent) and the design with a clear channel (±4 per cent). What a camera does

A narrow channel has to be read on its own

An ambient sensor with a clear channel tells structured lamps from smooth ones by reading deep red, and one without it reads structure but breaks at one per cent of calibration error. A narrow fourth channel between the camera's peaks was proposed to have both. Pooled into the sensor's disagreement with the camera, it reads structure and breaks at one and a quarter per cent — no better than the design it was meant to rescue. Read on its own, as its departure from what the camera predicts for it, a channel at 450 nm holds to four per cent, the clear channel's figure, and far red does not move it.

6 figures Four ways to correct the corner, under each of four lamps, at 25°. The mean colour error left on the chart's coloured patches at the corner of the frame, under each lamp, after: the red row fitted under that lamp; one red row fitted on the chart under all four lamps with the grey held under daylight; a grey-card gain map calibrated under daylight; and the worst of the other lamps' rows used by mistake. daylight: 0.93, 1.33, 1.86, 4.91; tungsten: 0.99, 1.45, 1.87, 3.26; white LED: 0.36, 1.39, 3.28, 1.77; fluorescent: 0.37, 1.56, 3.09, 2.45. The pooled row holds every lamp between 1.33 and 1.56. What a camera does

One row for every lamp costs the lamps that lose least

A corner correction fitted under one lamp is right under that lamp and can be badly wrong under another, so a converter unsure of its lamp was offered a single row fitted under several at once. Pooled over four lamps, one row holds every lamp's corner between 1.33 and 1.56 colour differences — no lamp worse than a grey-card map, and none near the 4.91 a wrong row can leave. The price falls on the white LED and the fluorescent tube, which it leaves four times worse than their own rows, because they lose the least red at the corner and the pooled row is built to repair the lamps that lose the most. Two rows, one per class of lamp, keep almost all of both.

7 figures Where chroma stops protecting a wall, in five rooms. The seventy-two paints in each of five rooms, sorted by how much light the wall returns and read in overlapping windows of eighteen: the rank correlation of the share of colour a satin finish takes with the wall's chroma, lightness held. Below zero a more saturated paint loses less; above, more. The dots are where each room's curve crosses: cube at 0.36, corridor at 0.37, low room at 0.38, one wall open at 0.29, two walls open at 0.24. Solid lines are closed rooms of three shapes; dashed are the cube with one and two walls opened. What a scene does

An open room hands over sooner

A gloss finish takes the least colour from a saturated dark wall and the most from a saturated pale one, and in a closed cube the sign changes at a wall returning about a third of the light. The prediction was that a less enclosed room would move that point up the lightness scale and that a room with a window would have no pale end. Opening one wall moves it down, from a luminance factor of 0.36 to 0.29, and opening a second to 0.24; stretching the room into a corridor or flattening it nudges it slightly up. The ambient does whiten, as predicted. A whiter ambient does not delay the colour term — it weakens it, so the other term takes over sooner.

5 figures The lamp's white, six walls and the light arriving at each. On the 1976 chromaticity diagram, in the closed cube under daylight: the lamp's white (centre), six saturated walls with bands centred from 450 to 650 nm (open circles), and the light arriving at each wall from the rest of the room, lamp included (filled). Each ambient lies on the line from the white to its wall, a fraction of the way along it: 450 nm 10 per cent, 490 nm 12 per cent, 530 nm 19 per cent, 570 nm 19 per cent, 610 nm 13 per cent, 650 nm 5 per cent. What a scene does

A probe at the wall prices the finish

The light arriving at a painted wall from the rest of its room is what a gloss finish hands back, and a small probe held against the wall reads it. It lies on the line from the lamp's white to the wall's own colour, a fraction of the way along, and the fraction is set by how much light the wall returns, not by how colourful it is — as predicted. It is not the fixed fraction the prediction said: it runs from 2 to 46 per cent across seventy-two paints in one room. That variation is what makes it useful. Read in the matt room, it orders what a satin finish would cost more tightly than the paint's own lightness does, in every room tried.

6 figures 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.

6 figures 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.

6 figures The appearance model's lightness-to-chroma balance, as the room takes a share of the adaptation. The median lightness pair's reading over the median chroma pair's, for twelve base colours, against the display's white, in a room of 20 cd/m². Solid: CAM16-UCS, with the viewer taking all, three quarters, half, a quarter and none of the adaptation from the display — darker lines take more from the display. Dashed: ΔEITP, which no room enters. With the display alone the model's balance falls 23 per cent; with half from the room, 13; with none from the display it does not move. Difference and uniformity

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.

5 figures How wrong a declared veil makes the unit, for four true veils. On a 100 cd/m² display, the worst error over grey steps from L 2 to L 90 — the size of the natural logarithm of the declared reading over the true one — against the veil declared, for rooms putting 0.1, 0.3, 1 and 3 cd/m² on the screen. Each curve reaches nought at its own true veil and rises on both sides. The flat stretch at the left is declaring almost nothing, which is declaring none: 0.22 for a true veil of 0.1, 0.54 for a true veil of 0.3, 1.14 for a true veil of 1, 1.89 for a true veil of 3. Difference and uniformity

A guessed veil halves the error

A colour difference that takes a display's absolute luminance leaves out the light a room reflects off the screen, and on an ordinary display in an ordinary room that makes it wrong about the darkest greys by a factor of three. Giving the unit the veil as a declared argument fixes that when the veil is known. The worry was that it never would be — that a guessed argument is no better than none. It is better: any declared veil up to about twice the true one beats declaring none, and one middling guess for every room halves the worst error. What a guess cannot do is reach ten per cent; that needs the veil known within a sixth, which is what a luminance meter aimed at a black screen gives.

5 figures How far a mesopic match moves as the S weight opens: two rooms against one field. For every pair of the five lamps, the median over forty-two surfaces of how far a match moves as the rod signal's weight into the S channel goes from nothing to equal: pale for the two-room match, each half adapted to its own lamp; dark for a bipartite field whose two halves share one adaptation. The field's signal is larger for every pair, by ×1.5 to ×7.7. What the eye does

One field keeps what two rooms divide out

An asymmetric match can measure how strongly the rods feed the blue-yellow pathway, but set with the observer adapted to each lamp in turn it needs seventy-five settings on the best pair of lamps and hours of waiting between them. Putting the two lamps on the two halves of one field was proposed as the quick version, at the cost of a weaker signal. The signal is not weaker. Under one shared adaptation it is three times stronger for daylight against a white LED, and the best pair needs six settings. The adaptation that makes the slow version slow is also what was dividing the rods' contribution out of each half.

5 figures How much of a coated press is left at each margin inside its boundary. The share of a coated press's printable volume in CIELAB that lies at least a given distance inside its boundary, for margins from half a unit to 32. A margin of one unit keeps 88%, two keep 80%, four 66% and eight 45%. At every margin up to 30 what is left is a single connected piece; at 31 units, with 0.14% of the volume left, it first splits, into a core of 623 cells and 2 fragments of one or two cells — the deepest point is 32.7 units inside, so what splits is the last crumb of the core, not a waist. Matching and measuring

A margin costs a press its corners

A gradient held inside a coated press by projection was predicted to tear if the press were first shrunk by a safety margin, at any pinch narrow enough for the shrinking to cut. The press has no such pinch: shrunk by any margin up to thirty CIELAB units it stays in one piece, and projected routes on it are neither trapped nor torn. What a margin costs is concentrated at the corners — the solid yellow moves nearly four times the margin to get inside, like the tip of a 31-degree spike.

7 figures

Before that

Everything published earlier, newest first. Titles only — the cards are on the full listing.

20 September 2026

11 essays on where the model breaks, what light is, what the eye does, what a scene does, difference and uniformity, what the brain does and matching and measuring

17 September 2026

16 essays on what a scene does, where the model breaks, what it takes to deliver it, what the eye does, what the brain does, difference and uniformity, what a camera does, what light is and matching and measuring

15 September 2026

20 essays on what the brain does, difference and uniformity, what it takes to deliver it, what a camera does, what light is, matching and measuring and what a scene does

14 September 2026

20 essays on what a camera does, what light is, what a scene does, what it takes to deliver it, matching and measuring, difference and uniformity, where the model breaks and what the brain does

12 September 2026

14 essays on matching and measuring, difference and uniformity, what the brain does, what a camera does, what it takes to deliver it, what light is and what a scene does

10 September 2026

20 essays on matching and measuring, what a camera does, what the brain does and what it takes to deliver it

6 September 2026

50 essays on what light is, difference and uniformity, where the model breaks, what the eye does, matching and measuring, what a scene does, what it takes to deliver it, what a camera does and what the brain does

1 September 2026

20 essays on where the model breaks, what a scene does, what it takes to deliver it, what light is, what a camera does, difference and uniformity, matching and measuring, what the eye does and what the brain does

31 August 2026

20 essays on where the model breaks, what light is, difference and uniformity, matching and measuring, what it takes to deliver it, what a camera does, what the brain does, what a scene does and what the eye does

30 August 2026

20 essays on what a scene does, difference and uniformity, what light is, where the model breaks, what the eye does, matching and measuring, what the brain does, what a camera does and what it takes to deliver it

28 August 2026

20 essays on what the eye does, difference and uniformity, what the brain does, where the model breaks, what light is, what a camera does, what a scene does, matching and measuring and what it takes to deliver it

27 August 2026

15 essays on where the model breaks, difference and uniformity, what the eye does, matching and measuring, what the brain does, what a scene does, what it takes to deliver it and what a camera does

26 August 2026

15 essays on what the eye does, what the brain does, difference and uniformity, what light is, what it takes to deliver it, matching and measuring, what a camera does, what a scene does and where the model breaks

24 August 2026

15 essays on what the eye does, matching and measuring, difference and uniformity, what a scene does, what a camera does, what light is, where the model breaks, what it takes to deliver it and what the brain does

23 August 2026

15 essays on what light is, what the eye does, matching and measuring, what a scene does, what it takes to deliver it, difference and uniformity, what a camera does, where the model breaks and what the brain does

21 August 2026

30 essays on what the eye does, what light is, matching and measuring, difference and uniformity, what the brain does, what a camera does, what it takes to deliver it, what a scene does and where the model breaks

19 August 2026

15 essays on what the brain does, matching and measuring, difference and uniformity, what the eye does, where the model breaks and what light is

18 August 2026

15 essays on what the eye does, what light is, difference and uniformity, matching and measuring, what the brain does and where the model breaks

16 August 2026

15 essays on what light is, what the eye does, matching and measuring, difference and uniformity, what the brain does and where the model breaks

15 August 2026

15 essays on what it takes to deliver it

14 August 2026

15 essays on what a camera does

11 August 2026

15 essays on what a scene does

4–10 August 2026

46 essays on what light is, difference and uniformity, matching and measuring, where the model breaks, what the brain does and what the eye does

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