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

Every essay — page 3

Page 3 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

SeriesObserversNamed objectsRefutationsSearch

What the brain does

Constancy, adaptation and simultaneous contrast — the reasons a patch of known radiance still has no determined appearance.

The cheapest direction to give ground in is the flattest one. Six bars, one per direction the adaptation objective can see, showing how much of the other objective a fixed budget of adaptation buys if it is spent along that direction. The rate is the slope of the second objective divided by the square root of the first's curvature, so it rewards a direction the second objective wants and punishes one the first is stiff in. The flattest direction wins at 10.68 against 3.29 for the next best and 0.54 for the stiffest — a factor of 20. Spending 1 per cent of the adaptation optimum there moves the anisotropy from 7.70 to 5.02.

The trade only runs one way

Standing at the basis that adapts best, one per cent of adaptation buys forty-four per cent of the way to the discrimination floor. Standing at the basis that discriminates best, the same one per cent buys under two. The scatter that shows two objectives pulling apart looks symmetric and is not, and the asymmetry is what a committee choosing between them would most want to know.

7 figures 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.

7 figures A mid-grey's lightness across a continuum of rooms. The lightness a mid-grey is predicted to have, plotted along the continuous surround parameter running from an average room to a dark one. The three rooms the standard tabulates are marked on it: average at the left, dark at the right, and dim 61% of the way between them rather than halfway. The whole span is 9.71 units of lightness and the step from average to dim is 5.64 of it — 58% — so choosing one of the three rows is a decision worth most of the range.

The surround is three rows of a table

An appearance model takes the room as three constants, and the standard tabulates three rooms. Every appearance figure in this collection is drawn at one of them. The parameter they are three points of is continuous, and the middle row is not in the middle.

5 figures Every adaptation number here assumes a complete adaptation. Three curves and their mean: the colour difference an adapted observer is left with after a change of light, against the degree of adaptation from zero — no adaptation at all — to one. Every adaptation figure in this collection is computed at one, the right-hand end. The appearance model's own formula puts the degree at 0.941 for an average surround at a hundred candelas, marked, where the residual is 2.21 ΔE00 rather than 1.27 — larger by a factor of 1.74. The left-hand end is exactly the unadapted change, which is not an approximation but an identity, and is what says the curve interpolates between the two things it claims to.

A discount nobody measured

Every adaptation number in this collection assumes an observer who adapts completely. The appearance model's own formula says they do not — it puts the degree at 0.94 in an ordinary room — and the difference is not a rounding. It is a factor of 1.7 on the residual every one of those figures reports.

5 figures 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.

Five transforms and the space between them

Every appearance prediction here chooses one of five published adaptation transforms, and the five disagree about where a protanope's confusion lines meet by more than the distance between the two pigments the disagreement is about. That spread is itself a scale, and using it needs no population model at all.

6 figures What six of this collection's published numbers do when the unit changes. Six quantities, from six calculations that share nothing: a change of light after an observer has adapted, a camera profile's error, the gap between the two standard observers, a metameric pair under the lamp that breaks it, the same image on two papers, and an observer two seconds into a new room. Each is recomputed under all six units and every unit is calibrated onto ΔE2000's scale first, so the bar is not a change of units in the ordinary sense. The bar is the ratio of the largest reading to the smallest, and it runs from 1.71 to 2.30. Five of the six are printed in ΔE2000 by the essays that report them; the sixth is printed in CAM16-UCS, because the model it comes out of defines that unit.

A model judged in another model's unit

An appearance shift is a change in what an observer would report, not a change in a stimulus, so measuring one with a matching difference means first asking what stimulus a settled observer would need to be shown to give the same report. That step is not bookkeeping — it is the whole distinction the field rests on, and it costs a factor of 1.7 across the menu.

9 figures Two slabs with one reflectance, and two colours through an aperture. Two constructed media whose bulk reflectance agrees at every wavelength to fifteen figures, and whose diffusion lengths differ by a factor of four. The upper curve is that shared reflectance — both slabs lie on it exactly. The two patches on the right are what a 4 millimetre radius returns from each, and they are 6.3 ΔE₀₀ apart. This is a metamerism with no observer in it: the two samples are the same colour to anybody under any light, and the instrument separates them because it is measuring a kernel through a hole rather than measuring a reflectance.

The appearance model has no slot for it

Two slabs with identical reflectance and different kernels come out of CIECAM16 with identical lightness, chroma and hue — to six decimal places, because the model's input is a stimulus and their stimuli are the same. Translucency is a recognised appearance attribute with no correlate in any appearance model, and the reason is structural rather than an oversight.

7 figures Each departure over forty-two surfaces rather than one. The same six departures measured over a family of forty-two analytic reflectances — an absorption band of stated centre, width and depth — with the smallest, the median, the ninety-fifth percentile and the largest marked. Every one of them spans more than a factor of three, and the ranking between them is not stable across the family: what decides a departure's size is which sample it is asked about, because a departure is a pairing and the sample is one of the two factors. Quoting any single number for what an observer's age is worth is quoting a choice of example.

The census under another observer

This collection's largest computed result is an adaptation census — fourteen changes of light judged over a hundred and twenty-five constructed surfaces. Every number in it was computed through one observer, and the observer's own departures are between one and two and a half units on the same surfaces, which is the size of the effects the census reports.

5 figures What choosing a space to divide the white out in is worth. Three pairs of routes to the same colour, over forty-two surfaces: dividing the white out in tristimulus values, in a published cone space, and in the observer's own cones. The first two agree to 0.59 ΔE₀₀ at the median. Either of them differs from the observer's own cones by more than fifteen. That is why the two exact conditions in this round are exact only in the eye's own coordinates: the identity belongs to the receptors, and every published arithmetic works in a basis somebody else chose.

The appearance model takes XYZ

CIECAM16 predicts how a colour looks, and its input is three tristimulus values computed through a standard observer. Everything this round measures happens before the model is called, so an appearance prediction inherits six observer departures and a choice of cone space before it begins.

6 figures The two tabulation choices over forty-two surfaces, under a 6500 K thermal radiator. Each column is one choice, measured over a family of forty-two analytic reflectances rather than on a single example: an absorption band of stated centre, width and depth. The four marks are the smallest, the median, the ninety-fifth percentile and the largest cost in ΔE₀₀, logarithmically. Under a smooth light the range is worth 9.1 times the step at the median, so a collection wanting one repair should widen its range rather than refine its step — and under a fluorescent tube the ranking reverses outright.

The grid under the census

The adaptation census is computed on eighty-one wavelengths from 380 to 780 nanometres. Under the daylight and blackbody sources it uses, the range is worth about half a colour difference on ordinary surfaces and the step about a twentieth — so the census carries a tabulation term as well as an observer one, and they are not the same size.

5 figures Where a stated appearance has no stimulus under it. The chroma the inverse can still return a light for, at lightness 50, all the way round the hue circle. Below the curve a stated appearance corresponds to a stimulus; above it the formula still returns three numbers and one of them is negative. Over a lattice of 10488 appearances spanning the whole space a specification is written in, 10.8 per cent are of that kind, and only 44 per cent are colours a display could show.

An appearance is not always a stimulus

CIECAM16's inverse is a closed form that returns three numbers for every lightness, chroma and hue it is handed. Whether those three numbers are a light it does not ask, and over a lattice spanning the space a specification is written in, 10.8 per cent of them are not — one tristimulus value negative, or a relative luminance above the white's. Only 43.8 per cent are colours a display could show at all.

8 figures The model's hue scale, and the four numbers it is built from. Hue quadrature against hue angle. The four anchors are the unique hues, each with its own weight, and between them the scale is a hyperbolic interpolation rather than a straight line. The quadrant from blue back to red spans 143 degrees of hue angle for its hundred units of quadrature, against 70 for red to yellow.

The hue scale has four corners

CIECAM16 reports hue twice — as an angle in its own opponent plane, and as a quadrature interpolated through four unique hues with four fitted weights. The second is the one hue tolerances and hue-preserving mappings are written in, and it is piecewise — its slope jumps at each of the four anchors, by a factor of 1.74 at green and by 0.41 at blue, and it runs 4.1 times faster near yellow than near blue.

8 figures