The ICC profile — where it appears
Named by 37 essays across 4 fields — each of them below, with the objects they name alongside it.
A hex code is not a colour
Six hexadecimal digits identify three numbers. Turning three numbers into a colour needs a colour space, a transfer function, a white point and a display, and leaving any of them unstated is the everyday version of every confusion in colour management.
Raw is not a picture
A raw file is three integrals per site and a list of decisions nobody has taken yet. Every one of those decisions has a defensible answer and none of them has a correct one, which is why two converters open the same file and disagree.
A camera profile is a fit
Since no matrix is exact, the one a manufacturer ships is a least-squares compromise over a set of surfaces somebody chose. Fitted on desaturated patches it is excellent on desaturated patches — and the sample set is a hidden argument to every camera profile in existence.
No matrix is right everywhere
The best three-by-three this sensor admits, fitted and tested on the same twenty-four surfaces, leaves a worst case of ΔE00 2.85. A control sensor built to satisfy Luther's condition reaches ten to the minus seven under the identical computation, which is what makes the first number a measurement.
A profile is a table
An ICC profile does not contain a model of the device it describes. It contains a lattice of patches that were printed and measured, and everything between them is interpolation — which is exactly zero at every patch, so a profile checked against its own target reports perfection for ever.
The paper is the white point
A printed colour is reported against the sheet it sits on rather than against the light in the room, and the choice is a switch in every colour engine. Flipped one way, the same separation on coated stock and on newsprint is a 3.04 colour difference; flipped the other, it is 0.13 — and the two answers are about different questions.
The separation is not unique
A four-ink press has one more control than a colour has numbers, so most colours can be printed several ways. The alternatives agree to a hundredth of a colour difference under the light the match was made in — and they are metamers of one another, so under a tungsten lamp the same eleven separations of one colour spread by nearly seven.
No mapping preserves everything
More than half the sRGB solid is outside a press's gamut, so something has to be done with it, and there are two things that can be done. One leaves every reproducible colour exactly where it was and delivers a gradient as a flat area. The other keeps the gradient and moves every colour that needed no help by about three.
The proof is a different object
A soft proof can be made colorimetrically exact and still not match the print, because the print is in a booth at two thousand lux with an average surround and the screen is in a dim room at a fifth of the luminance. The appearance model puts four CAM16-UCS units between them, with no change of stimulus anywhere — larger than the error any rendering intent is arguing about.
A mean is not a difference
A specification for a proof, a profile or a print run is written against a set of colours and has to reduce that set to one number. The mean and the ninety-fifth percentile disagree about which of two reproductions is better in thirty per cent of cases, and both numbers are honest.
Dividing by the paper
Media-relative colorimetry divides tristimulus values by the substrate's, which is a von Kries adaptation applied in XYZ — the one basis the table here describes as the oldest mistake still shipping. On a paper-mill white it costs a few hundredths of a unit. On a tinted sheet it costs ten times what the same rule costs in a cone basis.
A proof cannot glow
A proof is a different sheet of paper pretending to be the production one, and the pretence works by adding ink until the two agree. It cannot work for a brightened stock, because the direction the proof has to travel is towards more blue at the same lightness and every ink a proofer owns moves it towards less light instead.
A matrix is fitted under one light
A camera's colour matrix is nine numbers determined by a chart photographed under a particular illuminant, and the error it quotes is the error under that illuminant. Fitted under a tungsten lamp and used under a cold sky it delivers eight times as much — and the two-matrix scheme every real profile uses turns out not to be a compromise at all.
A profile is a fit between its nodes
A printer profile is a table, exact at every patch that was printed and interpolated everywhere else — and everywhere else is where every job lives. Going from a hundred and thirty-five patches to three and a half thousand is twenty-seven times the work for eight times the accuracy, and the exponents say that is as good as it gets.
Best on the average, undefined at the edge
Bradford has the lowest mean residual of any adaptation transform over the census of illumination changes, which is why colour management uses it. Inside the family that census was drawn from, its middle row's reading of the white passes through zero — so the gain is a division by nothing, and the model stops being defined rather than merely doing badly. CAT16, which exists because its predecessor did this, does not.
The slope arrives before the bowl
The adaptation transforms colour management actually uses are not optima of anything. At every one of them the objective has a slope, and the slope is the larger term over almost the whole distance to the best matrix — so a table of curvatures taken there describes a bowl nobody meets on the way anywhere.
A delivery tolerance is three tolerances
A colour reaches a reader through a profile, a gamut mapping and a room, and each has a number somebody chose. Each has an essay of its own here, and none of those essays had put the three costs in one column. Put there, the stage nobody controls carries ninety-seven per cent of the total.
The order is not in the documentation
A raw converter performs a white balance, a colour matrix, a tone curve and a clip, and every account of the process lists them in that order without saying the order decides anything. Exchanging the first two moves the picture by nine colour differences at the mean and thirteen at the worst patch. The twenty-four arrangements collapse into five outcomes running out to sixty-five, and nothing a converter ships says which of them it is.
The budget adds two units
This collection publishes a three-stage error budget for a colour-management chain and prints its sum. Two of the three stages are colour differences between stimuli and the third is a distance between appearances, and the conversion between those is not a constant. Re-measured in one unit over the same colours the chain has four stages rather than three, its end-to-end error is 5.05 against a sum of 7.66, and the profile's contribution where a job actually lands is 3.2 times its published average.
An intent is not a function of the colour
A rendering intent is chosen per job and applied per pixel, which suggests it is a function of the colour. The colorimetric ones are, exactly — the same colour from two documents comes out identical to the floating-point floor. The perceptual one is not — it compresses the whole source solid into the destination, so the same colour delivered from a wide document and from a muted one lands 2.6 colour differences apart, on colours the destination could hold either way.
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.
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.
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.
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.
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.
A little black ends the cast
A four-ink inverse table errs by a warm cast along the grey axis wherever the separation strategy prints only three inks, and almost only in lightness wherever it prints black. Real strategies start black gently, and the gentle start was expected to keep the cast until black carried much of the grey. It does not. The cast falls to a tenth of its three-ink size once black supplies a tenth to a sixth of the grey's darkening, at every toe from nothing to thirty units wide — because inside the toe the table's chord runs along the trade of black against the other three inks, which errs in lightness. What the toe does cost is the segment where black begins, which goes from the table's best to its worst.
The cast returns where black is steep
Below a black-generation toe a four-ink table's grey picks up a small cast again, up to a third of the three-ink cast at the widest toe, and the explanation offered was the jump in black's curvature where the toe ends. It is not. A toe whose curvature is nothing at its end returns exactly the same cast, segment for segment, and a kink put into straight black casts in its own segment once in twelve tries. What the returned cast follows is how steep black has to be once the toe is done — how far the chromatic inks climbed while black was held back, and how fast they then have to come down.
A knee in the ink limit quiets the shadow
A cap on total ink coverage quiets a four-ink table's shadow, and the one segment where the cap is first reached is quiet or loud depending on where the binding point falls among the table's nodes: inside a segment it is quiet, within a quarter of a segment of a node it is not. A real cap is approached through a knee. The prediction was that a knee as wide as a segment would make the binding segment quiet wherever it fell, and that a knee much wider would turn the cap into a steep straight black that casts like the heavy-black strategy. The first half holds only in part: a five-unit knee halves the binding segment's cast and quiets three of the nine loud ones, but those whose binding point sits within a quarter of a segment of a node stay louder than a neighbour. The second half is wrong in sign. A wider knee leaves the whole capped shadow quieter at every step — its mean cast falls from 11.5 thousandths to 3.0 at fifteen units — because a knee spreads the chromatic inks' forced descent, and a slower descent is one the table's straight lines between nodes can follow.
Off the grey axis a knee trades hue for chroma
Along the grey axis a total-ink cap approached through a knee quiets the cast a four-ink table prints between its nodes, because the knee slows the chromatic inks' retirement where black takes over. In a saturated shadow the chromatic inks carry the colour, and the prediction was that a knee would quiet the hue error there in the same way, a fifteen-unit knee halving the worst segment's. On two rays of dark colours, a deep blue and a brown, it does quiet the hue — every wider knee lowers it on both — and halves the worst segment's on the blue, to 0.28 of the hard cap's, but not on the brown, at 0.68, whose inks the knee slows far less. And the hue was never the main error. Between nodes the table prints these colours duller than asked, its chroma error five to eight times its hue error, and every wider knee makes that loss slightly worse, so the table's total error rises as its hue error falls. The cap itself, met hard, halves the blue's error, as it removed the grey's cast; on the brown it changes almost nothing.
More nodes quarter the dulling and leave the knee a larger share
A four-ink table printing a dark saturated colour between its nodes prints it a little duller than asked, and a knee in the ink limit, which quiets the hue error, deepens that dulling by about a hundredth of a unit. The prediction was that doubling the table's nodes quarters the dulling — the square of the spacing — and the knee's added cost with it, so that on a dense table the knee's hue gain is all that remains. On tables of 9, 17, 33 and 65 nodes along a deep-blue and a brown ray, the dulling does fall about fourfold with each doubling, capped or not, to under a hundredth at 65 nodes. The knee's added dulling does not keep pace: on the blue it is 13 per cent of the hard cap's at seventeen nodes, 23 at 33 and 35 at 65, and the knee's whole error, an eighth more than the hard cap's at seventeen nodes, is a quarter more at 65. The knee keeps its hue gain at every density. A denser table shrinks every error and makes the knee's trade worse.
Three nodes at the cap's corner cut the dulling by a third
A four-ink table printing a dark saturated colour between its nodes prints it duller than asked, and at 65 nodes a fifteen-unit knee in the ink limit carries 35 per cent of that dulling on a deep-blue ray. The prediction was that the knee's added dulling sits in the two or three segments just below where the cap binds, and that three nodes placed there take its share back under a tenth. The first half holds: the knee's addition peaks one unit of lightness below the binding point and four fifths of it lies within seven. The second does not. Three nodes placed one, two and three units below the bind cut the hard cap's dulling by a third, 0.0097 to 0.0064, and the knee's by nearly two fifths, where three more evenly spaced nodes cut each by under a tenth — but the knee keeps a quarter of the dulling. The hard cap has a corner, which one node can catch; the knee has a bend spread over a dozen units, which three nodes split but do not straighten. A node at the binding point alone helps only the hard cap, and leaves the knee 41 per cent.
Shared nodes belong in the deep shadow
Three nodes placed just below where each dark colour's ink reaches the press's cap cut a four-ink table's dulling of that colour by a third — but a profile's nodes along lightness are shared by every colour, and the colours' caps bind anywhere from L* 15 to 31. The prediction was that one shared placement keeps two thirds of the own-placement gain on a deep-blue ray and all of it on a brown. Placed once, one to three units below the median binding point, the nodes keep 63 per cent of the blue's hard-cap gain and 92 of the brown's — and the averages hide a split. Every colour whose cap binds more than two and a half units below the shared nodes keeps under a twentieth of its own gain; every colour whose cap binds more than two units above them keeps more than all of it, up to four times. For those colours most of the dulling was never at the cap's corner: it lies in the deep shadow, where black keeps climbing under the cap, and the shared nodes sit there. Spreading the three nodes across the binding points buys nothing three even nodes would not.
Easing the cap reaches the deep shadow and no higher
A four-ink table prints dark saturated colours duller than asked between its nodes, and for colours whose ink reaches the press's total-ink cap high up the dulling lies mostly in the deep shadow below L* 20, where black climbs under a held total. The proposal was to let the total fall below the cap there, and the prediction was that easing the cap by a tenth or a fifth between L* 20 and the floor halves those colours' dulling on even nodes — more than three shared nodes do — at a cost of a unit or two of L* in the darkest colour the press can reach. There is no cost: every eased table still prints the floor at L* 14. Eased by a fifth, the deep-blue ray's dulling halves and the brown's falls to an eighth. But the eight colours that bind above L* 26 keep three fifths of theirs: the ease removes two thirds of their deep-shadow dulling and none of what lies between their binding point and L* 20. And the eased cap does not let black rise less steeply — it makes black rise faster.
A higher ramp trades one shadow for another
Easing a four-ink table's total-ink cap by a fifth on a ramp from L* 20 to the floor halves the dulling of dark colours whose cap binds low, and leaves the colours that bind high with three fifths of theirs, because most of what is left lies between their binding point and L* 20, above the ramp. The prediction was that a ramp starting at L* 32 halves the high binders' dulling, at a small cost to the low binders. It does neither. Started at L* 26, the same fifth's ease does cut the high binders' upper dulling by more than half — the cap was its cause after all — but their deep-shadow dulling comes back to more than twice what the L* 20 ramp left, and their total is unchanged at 0.0052. The low binders give back nearly everything: on the brown ray from almost nothing to 0.0084 with the ramp at L* 32. Every ray, knee and group does best, or within a fiftieth of best, with the ramp at L* 20.
A bent ramp takes more ink and dulls more
Easing a four-ink table's total-ink cap by a fifth on a straight ramp from L* 20 to the floor straightens the deep shadow's bend and halves the dulling of dark colours, and a ramp started higher trades the deep shadow's cure for the upper stretch's. The prediction for a ramp bent at L* 20 — a quarter of the ease spent between L* 32 and 20, the rest below — was that it keeps nearly all of the deep shadow's cure while taking a third off the high-binding colours' upper stretch, their total falling by a fifth. The bent ramp takes at least as much ink as the straight one at every lightness. It dulls every group more. The high binders' upper stretch improves by a sixth; their deep shadow loses half its cure, and their total rises from 0.0052 to 0.0060; the brown's low binders, left with almost nothing by the straight ramp, keep 0.0039. The deep shadow's cure follows how steeply the cap falls below L* 20 — a fifth of the cap over six units, not three twentieths — and not how much ink is taken there.
A steeper ramp cures the shadow by overshooting it
A four-ink press's total-ink cap dulls the deepest colours it binds, and easing the cap by a fifth on a straight ramp from L* 20 to the floor halves the deep blue's dulling. A ramp bent to take more ink above L* 20 dulled every group more, so the cure seemed to follow how steeply the cap falls below L* 20. The prediction was that a ramp steeper still — the whole fifth spent from L* 17 — cures more. Read as the census has read every ramp, by the mean chroma lost, it does: every group dulls less at each step from L* 20 to 18.5 to 17. But the brown's low binders cross nought: their prints come out more chromatic than the colour asked, by as much as 0.07, and read by the error's size the brown ray's mean error more than doubles. The measure that ranked every earlier ramp was signed, and a signed measure cannot see an overshoot. Eased by a tenth, the steep ramp is no worse anywhere and better on three cases of four.
Each dark ray wants its own ease
Easing a four-ink press's total-ink cap below L* 20 cures the dulling of the deepest colours it binds, and a steeper ramp — the whole ease spent from L* 17 — cures more on the signed mean, but eased by a fifth it prints the brown ray's low binders up to 0.07 more chromatic than asked and more than doubles the brown's error read by size. The prediction was that three twentieths from L* 17 is the ease the steep ramp wants: below every earlier setting on both rays. The brown still overshoots, by 0.039, and errs nearly twice as much as on the gentle ramp. The overshoot follows one number — how fast the eased cap gives ink back per unit of lightness — and the two rays want that number set differently. Hard, the blue errs least on three twentieths from L* 17 and the brown on three twentieths from L* 20; the brown's best costs the blue a fifteenth more error, the blue's best costs the brown four fifths more.
Named alongside it
The objects these essays reach for when they reach for this one.
InterpolationColour managementProcess inksSeparationSpecificationInk limitGrey component replacementGamut mappingChromaDeclared inputLightnessChromatic adaptation