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

Scene interpretation — where it appears

The step where a set of measured radiances is turned into an account of surfaces and a light, which is what constancy requires. It is underdetermined — the same radiances arise from many scenes — so any algorithm doing it is making an assumption about the world.

Named by 4 essays across 2 fields — each of them below, with the objects they name alongside it.

The Cornsweet edge, with its luminance profile. The two plateaux are both #898989 and are flat to exactly — the profile below shows that everything which differs lies within a narrow band at the boundary. Cover the centre line and the two halves become obviously identical.

Brightness is inferred from edges

The Cornsweet effect makes two identical regions look different by altering nothing except a narrow band at the boundary between them. Cover the boundary and the difference vanishes, which says the visual system is reconstructing surfaces rather than reading off intensities.

brain · Appearance five greens, no neutral, under D65 — four guesses at the illuminant. The scene's surfaces as they reach the eye, and each estimator's angular error in degrees against the illuminant that actually lit them. Grey-world 43.1°, Max-RGB 27.7°, Shades-of-grey (p = 6) 31.4°, Grey-edge 34.4°. The best here is Max-RGB, which is best because this scene happens to satisfy its assumption — something reflects fully in every band — and not because it is the better algorithm. Any hatched patch is a surface this display cannot show under this light.

The algorithms that guess the light

What reaches a sensor is an illuminant multiplied by a reflectance, and no arithmetic separates a product into its factors. Every white-balance algorithm therefore works by assuming something about the world — and the interesting content of each is not its formula but the assumption, because a scene can violate it.

brain · Appearance How short of determining the light a photograph is, as the scene grows. Each cell is the number of unknowns left over after every equation the image supplies: three sensors, a three-dimensional illuminant, and reflectances confined to a linear model of the dimension on the left. At one and two dimensions more surfaces close the gap. At three the gap never closes, because each further surface adds three equations and three unknowns; at four it widens. The count is arithmetic and has no algorithm in it.

An image does not determine the light

A photograph of a scene under one illuminant gives three numbers per surface and asks for the illuminant plus three numbers per surface. The count closes only if reflectances lie in a two-dimensional model, and no number of surfaces helps — at three dimensions the alternative scenes can be written down, and they reproduce every sensor response exactly.

scene · Scene 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.

brain · Appearance

Named alongside it

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

ReflectanceColour constancyThe grey-world assumptionIlluminant estimationWhite balanceAdaptationAnchoringAppearance modelCIECAM16Colour appearanceColour appearance modelThe Cornsweet effect

All concepts