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

Every essay — page 39

Page 39 of 40, continuing through the fields in the same order.

What light is What the eye does Matching and measuring Difference and uniformity What the brain does What a scene does What a camera does Where the model breaks What it takes to deliver it

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What it takes to deliver it

A colour that stays where it was measured is nobody's problem. This is the apparatus that carries one to somebody else — ink on a sheet, a profile, a rendering intent, a proof, and a room — and every stage of it is a map that loses something, chosen deliberately.

Out to the device and back, once and again. Each intent applied 3 times in succession to the same ramp. The upper bar is what the first pass moves and the lower is what the second moves. relative-colorimetric is idempotent — the second pass moves nothing, to the floating-point floor — and the other two are not: perceptual moves another 2.73 and saturation moves another 3.09. A file converted twice is not a file converted once.

A second conversion is not a repeat

A colour converted to a device and back is described as lossy where the device cannot hold it and exact where it can, which suggests that a colour surviving one round trip survives any number. One of the four intents is idempotent to the floating-point floor. The other two are not — a perceptual conversion moves a ramp 3.70 colour differences on its first pass and another 2.73 on its second, and after three passes it is still moving by 2.42.

7 figures 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.

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.

6 figures How far the chain falls short of its sum, and how much of that is the unit. For each rendering intent, three ratios of the chain's end-to-end error to the sum of its four stages. The lowest bar is the published one, in the power-corrected unit. The middle bar is what that unit reports for a chain whose stages point the same way and add exactly — the exponent on its own. The top bar is the same chain measured in the model's own Euclidean space. Under the colorimetric intent the published ratio is 0.66, the exponent alone gives 0.74 and the chain in a space that can add 0.84: 77 per cent of the shortfall is the unit.

A chain measured in a unit that cannot add

A delivery chain's four stages, measured in the power-corrected appearance difference, sum to 7.66 while the chain end to end measures 5.05, and the shortfall was read as the stages partly cancelling. A chain whose four stages lay in a straight line and added exactly would still read 0.74 of its sum in that unit, because a distance raised to the power 0.63 cannot add. Measured in the model's own Euclidean space the same chain reaches 0.84 of its sum. Three quarters of the published shortfall was the exponent.

6 figures One edge magnified four times, three ways: text on a page. A step between the two colours of text on a page, magnified four times by linear interpolation, by bicubic and by a three-lobe Lanczos kernel, once on the stored values and once on the light. The curves are the stored-value result's lightness minus the light's, sample by sample across the edge; below the line the stored-value resize is darker. Linear interpolation is darker everywhere it differs. The two kernels with negative lobes swing above the line beside the edge, where their negative weights fall — bicubic by up to 1.8 colour differences and Lanczos by 3.7.

A resize with a negative weight in it

A blend taken on stored values is always darker than the blend of the light, because the encoding is concave and a convex combination of a concave function's values lies below the function of the combination. A bicubic or Lanczos resize is not a convex combination. Beside an edge its negative weights make the stored-value result lighter than the light's own — by up to 6.1 colour differences with bicubic and 12.2 with Lanczos on skin against its shadow — and on edges between full-scale values the clip hides the overshoot and the old guarantee appears to hold.

6 figures The corner of a patch of skin against its own shadow, magnified four times by Lanczos, three lobes. A map of the neighbourhood of one corner of a square patch — the patch fills the lower right, the field the rest — once it has been magnified four times by Lanczos, three lobes. Each cell is shaded by how much lighter (warm) or darker (cool) the stored-value result is than the light's, the deepest shade 18.2 units of lightness. Within three source pixels of the corner the stored-value result is up to 14.5 colour differences lighter, 14.5 outside the patch against 3.1 inside it, and up to 7.3 darker.

The corner of a resized patch is lighter than its edges

A resize taken on stored values is darker than the resize of the light wherever its weights are positive, and lighter beside an edge where a kernel's negative lobes fall. In two dimensions the kernel is a product, and just outside a patch's corner a Lanczos magnification of skin against its shadow comes out 14.5 colour differences lighter — more than along either edge. A reduction to a quarter is mostly an average and errs lighter by at most two. And an unsharp mask, whose negative weights are its whole purpose, is lighter on the stored values at every amount on every pair, and never darker.

6 figures 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.

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.

6 figures 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.

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.

7 figures The error between a profile's nodes is a bias, not a scatter. Two quantities against the lattice size: the mean colour difference between the nodes, and the mean signed lightness error. If the interpolation erred in both directions the second would be near zero while the first was not. They lie on each other — 0.136 against 0.133 at a nine-step lattice — so the whole of what a profile does between its patches is to lighten. It errs light because a press's response is convex in ink coverage: the first drop of ink removes more light than the last, and a straight line between two points on a convex curve lies above it. At three steps 400 of 400 samples err light.

A profile interpolates light

A profile is exact at its patches and wrong between them, and how wrong has been measured twice. Which way it is wrong has not. At a nine-step lattice the mean signed lightness error between the nodes is +0.136 against a mean colour difference of 0.133 — the error is not a scatter but a bias, and it lightens. The repair costs nothing measured and is forbidden by how a profile is checked: let the table be wrong at its own patches.

7 figures One instrument, one uncertainty, six places on the scale. What an absolute uncertainty of 0.001 in measured reflectance is worth in lightness, at six levels from a four-colour solid to the paper. Nothing about the instrument changes between the rows: what changes is the slope of the lightness function, which is a straight line of 903 units per unit of luminance factor below a luminance of 0.0089 and a cube root above it. At the solid the uncertainty is 0.903 lightness units and at the paper 0.043 — 21 times as much, for the same measurement.

The scale hangs from one measurement

Black point compensation is a straight line between two blacks, and the destination's is a measurement of one patch at the darkest place a spectrophotometer is ever asked to read. The lightness scale's slope is 903 units per unit of luminance factor there and 43 at the paper, so a thousandth of a reflectance is worth nine tenths of a lightness unit at the black and four hundredths at the white. That one number moves a mid grey by nearly a quarter of a delivery tolerance, and no specification names it.

7 figures Two tables, two directions of error: 5-node ramps of four inks. For each ink, the mean signed lightness error between the nodes: of the ordinary forward table, which errs light, and of four ways to fill the inverse table, all of which err dark except the one refitted against its own objective. On cyan the forward table errs by +0.206; an inverse filled from the press by -0.317; one inverted from the ordinary table by -0.554, because it inherits the forward table's error on top of its own; one inverted from the refitted table by -0.367; and one refitted in its own right by -0.002.

The inverse table errs dark

A profile's forward table predicts a print lighter than the press makes, and refitting its nodes removes the bias. The table a colour engine actually uses to separate an image is the other one — the inverse, from colour to ink — and it errs the opposite way: filled exactly from the press it asks for too much ink and prints dark, and built by inverting the ordinary forward table it prints darker still. Inverting the refitted forward table removes the inherited part and leaves the inverse's own. The round trip through both tables improves only when each is refitted against its own error, and then the two are no longer each other's inverse.

5 figures Where an unsharp mask errs, per pixel and as seen: print, 40 cm. The upper-left corner of a patch of skin against its shadow after an unsharp mask, as two maps of the colour difference between the result taken on stored values and taken on light. Left, pixel by pixel: the corner peaks at 16.8 and the middle of the edge at 16.6. Right, after the eye's three spatial channels at a print at 40 cm: the corner is seen at 17.1 and the edge at 7.1, a ratio of 2.40. Darker is larger, on one scale for both maps.

The eye counts a corner's error, not its peak

A Lanczos-magnified patch errs a fifth more at its corner than along its edges, pixel by pixel, and an unsharp mask errs almost exactly as much at its corner as along its edges. Filtered by the eye over the plane rather than along a line, the two swap: the magnified corner is seen exactly as its edge is, and on a printed page the sharpened corner is seen at 2.4 times its edge. What decides it is whether the error changes sign. Ringing averages away and a one-sided halo does not, and a corner is where two edges' halos land on the same patch of retina.

5 figures 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.

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