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

Population — where it appears

A modelled distribution of observers rather than a single standard one, built by drawing each of the reported sources of variation from its own spread. It turns a quantity computed for one pair of eyes into a distribution, and the width of that distribution is what says whether the quantity is a property of a person.

Named by 11 essays across 5 fields — each of them below, with the objects they name alongside it.

What the confusion points charge, across a population. A histogram of 200 members of a population of eyes, each scored by what the adaptation basis their own confusion points determine leaves after the gain. It runs from 1.22 to 2.24 ΔE00 with a median of 1.78. Vertical marks show the unconstrained floor at 0.97, the published transforms, and the single observer this site quotes at 1.65. The distribution straddles Hunt–Pointer–Estévez and reaches below CAT16: 18 per cent of members are better served by their own receptors than by a matrix built to make a gain behave, and 2 per cent than by the current recommendation.

The price is also the person

The receptor construction costs seventy per cent above the unconstrained floor, which is a number usually quoted as a property of the construction. Propagated across a population of eyes it runs from a quarter above the floor to a hundred and thirty per cent above it, and the population's own spread is wider than the entire gap between the published transforms the seventy per cent was being compared against.

limits · Limits How far a fitted transform is from anybody's eyes. Five groups of three bars: for each published adaptation transform, the distance from the population's own cloud to the confusion point that transform is committed to, measured in the population's standard deviations on that point. On the protanope's point every one of them is between 2.2 and 14.4 out, and on the deuteranope's between 3.7 and 11.8. On the tritanope's, 5 of the five are within three standard deviations — indistinguishable from a member of the population. The claim that these matrices are not cone responses is safe, and the evidence for it is two points out of three.

Two points out of three

Every published adaptation transform implies three dichromat confusion points, whether or not it was fitted to any. Measured in the population's own standard deviations they are two to fourteen out on the protanope's point and four to twelve on the deuteranope's — and between half a standard deviation and two and a half on the tritanope's, which is inside the population. The claim that these matrices are not cone responses is safe. The evidence for it is two points.

matching · Gamut A population of receptor bases, in the plane the published ones live in. The two axes this collection scores an adaptation basis on — the residual across the illumination census on the horizontal, ellipse anisotropy on the vertical, lower better on both — with 200 extra points on it. Each is the basis a member of the population's own confusion points determine. The cloud is not a point: it runs from 1.22 to 2.24 ΔE00 horizontally, which is wider than the whole spread of the published transforms marked on it. The observer this site quotes sits inside the cloud and near one edge of it, and the sentence "the receptor basis costs seventy per cent" is a sentence about that one point rather than about the construction.

A trade between matrices, not people

Across the space of possible bases, adapting well and discriminating well pull in opposite directions — the two optima sit at the ends of an empty diagonal. Across a population of actual observers the same two costs move weakly together, at a correlation of +0.29. The trade-off is a property of the set of matrices somebody could choose, not of the eyes anybody has. One measurement inside the population does trade, and it is the macular pigment.

brain · Appearance The same claim in nanometres of pigment, where no declared width can reach it. Five horizontal bars on a scale of nanometres, one per published chromatic-adaptation transform, each showing how far the medium-wave cone pigment's absorption peak would have to move for the receptors' own protan confusion point to land where that transform puts it. Zero is the measured peak. The bars run from -10.5 to 18.2 nanometres — in both directions, so two of the transforms want the pigment shorter and two want it longer. Drawn across them is the 25 nm separation between the L and M pigment peaks, which is the whole basis of red-green vision and is not a number this collection declared. The nearest transform asks for a displacement of 30 per cent of that separation, and the span across the table is 28.7 nanometres — larger than the separation itself. No population, cloud or standard deviation appears anywhere in the statement.

The claim, in nanometres

For four rounds the claim here has been that every published adaptation transform puts the protanope's confusion point outside any real population of eyes, stated in standard deviations of a population whose widths were declared rather than measured. Restated as a pigment displacement it needs no population at all — and the nearest transform asks the medium-wave cone to move thirty per cent of the way to the long-wave one.

eye · Cones How far this site's median observer sits from the 1931 standard, by template. Twenty-four natural reflectances under D65, each given a tristimulus value twice: once by the 1931 colour-matching functions and once by this site's median member, with each judged against its own white. The bar is the mean difference, which is the residual this collection bounds and calls inescapable. It is inescapable, and it is smallest for the simpler template: Lamb's 1995 nomogram gives 0.9006 against Govardovskii's 0.9522, and removing Govardovskii's secondary band brings it down again to 0.9354. Neither is an argument for changing template — a nomogram is fitted to measurements of individual receptors, not to colour matches, so agreement with the standard observer is not what either was trying to achieve. What it says is that the residual is a mismatch between two kinds of observer rather than a shortfall a better pigment model would close. The number after each bar is the template's tail ratio: how far the L cone's half-maximum reaches below its peak against how far it reaches above.

The population rests on a template

Two hundred observers here are built from one formula fitted to microspectrophotometry in 2000. The obvious alternative — the tabulated cone fundamentals — is not available, and the reason is the finding. A tabulated fundamental has no peak wavelength to move, so the moment it is used the population collapses to a single observer.

eye · Cones The three cone absorptances at two settings of the age of the lens. Solid and dashed are the same construction at the two ends of twenty years old against seventy. The curves are built from one pigment template through its ocular media, which is the same model its population of two hundred eyes is drawn from. The largest difference between the two sets is 25.5 per cent of the peak, and where it sits along the wavelength axis is what decides which stimuli the two observers disagree about — a departure concentrated in the blue is invisible on a sample with no blue in it.

The observer has no age

Five of the six arguments in this round are spreads — a population differs about them and the mean is a reasonable summary. The lens is not. Everybody's lens yellows in the same direction at about the same rate, so a standard observer with no age is not an average over a population; it is a snapshot of one moment in every reader's life.

eye · Cones The same white, matched at six primary widths. At every width the three primaries are solved to match D65 exactly for the reference member; the bands are what the population sees. A broad primary integrates the observer differences over a band and averages them away; a narrow one samples them at a point and passes them straight through. From 40 nm to 2 the ninety-fifth percentile rises from 11.3 to 17.9 ΔE00, monotonically, and the technology has been moving from left to right for thirty years.

A narrow primary buys a disagreement

The observer audit decomposes what a display costs a population. Narrowing the primaries raises the pigment-peak departure monotonically, moving one raises or lowers the macular departure, and the two respond to different design variables — so a wide gamut and an observer-robust display are bought with the same money.

matching · Gamut Where averaging the model's answers is and is not averaging its argument. Each row takes a spread of situations, averages the model's predictions across them, and compares that against the model's prediction for the average situation. The bar is the gap as a share of the spread itself. Over the differences between observers it is 1.4 per cent — the model is very nearly linear there. Over the range of adapting luminance one room covers in a day it is 59 per cent, and from indoors to outdoors 74.

Where the model's curve does not matter

This round has been about what a nonlinearity does to an average, and CIECAM16 is the most nonlinear thing in the collection. Over the spread a population of observers produces, the average of its predictions is its prediction for the average to within 1.4 per cent — the nonlinearity is there and the excursion is too small to reach it. Over the range of adapting luminance one room covers in a day, the same gap is 59 per cent of the spread, and from indoors to outdoors 74.

brain · Appearance 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.

applied · Delivery 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.

applied · Delivery How much of a display's gamut each observer names differently. Each of 60 observers names every colour of the displayable gamut that the panel can make — 823 of them — and the histogram is how much of that gamut each observer names differently from the standard observer. On an OLED panel the median observer renames 8.1 per cent and the furthest 13.1 per cent. Nobody agrees with the standard observer about all of it.

A name moves with the reader

Three earlier essays have moved a colour's name by changing the distance function, the room and the space. All three held the observer fixed. Handed the same light from the same display, sixty observers rename between 3.5 and 13.1 per cent of the gamut against the standard observer, a quarter of its colours have a dissenter in twenty, and the narrower the display's primaries the worse it gets.

brain · Appearance

Named alongside it

The objects these essays reach for when they reach for this one.

Cone fundamentalsIndividual variationMacular pigmentObserver metamerismStandard observerBasisChromatic adaptationObserver variabilitySpecificationConfusion pointNarrow band displaysPrimaries

All concepts