Colour Science & Perception
what the eye settles, and what it cannot
What the brain does

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.
13 min read 6 figures Identical, and assertedThe instrument is the reader

Two large regions of identical luminance, joined by a narrow band in which one side ramps up and the other ramps down. The whole left region looks lighter than the whole right region. Cover the band with a finger and the two halves become obviously identical.

The Cornsweet edge, with its luminance profileThe 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.one value on the left, the same value on the rightluminance profileboth plateaux are #898989asserted equal
Fig. 1 The Cornsweet edge with its luminance profile beneath. The two plateaux carry exactly the same value and are flat — everything that differs lies inside a narrow band at the centre. The difference in appearance extends across regions where nothing differs at all.

This is a stronger demonstration than simultaneous contrast, and the reason is worth being precise about. In simultaneous contrast the two patches have different surrounds, so something in the neighbourhood really does differ. Here, the two plateaux are identical and so is everything near them. The only difference in the entire figure is confined to a band neither region touches.

What the effect implies

If the visual system reported luminance region by region, the two plateaux would look the same, because they are the same. They do not, so it does not.

What appears to happen instead is that the system detects edges — places where the signal changes rapidly — and then reconstructs the surfaces between them by, in effect, integrating outward from the edges. The Cornsweet profile contains a step-like edge at the centre; the reconstruction propagates that step across both plateaux; and the gradual ramps either side of it, being gradual, are discounted as illumination rather than as changes in the surface.

That last part is the important half. The visual system is not merely detecting edges; it is deciding which changes are the object and which are the lighting. Sharp changes are usually where one surface meets another. Gradual changes are usually a shadow or a falloff in illumination. The system treats them differently on purpose, and the Cornsweet stimulus is constructed so that its gradual part gets discounted and its sharp part gets believed.

Why this is a good design

It is worth resisting the framing in which these effects are errors.

The problem the visual system is solving is to recover the properties of surfaces — how reflective they are — from a signal that confounds reflectance with illumination. A surface’s reflectance is a stable, useful thing to know: it identifies materials, it stays constant as the light changes, it is what “the colour of” an object means. The luminance arriving at the eye is the product of that reflectance with an illumination that varies by orders of magnitude and carries little useful information.

Separating the two from a single measurement is formally impossible — one equation, two unknowns. The system solves it with assumptions, and the assumptions are sound ones about the world: illumination usually varies smoothly, surfaces usually have sharp boundaries, and the brightest thing in view is usually white.

Every figure in this essay is a stimulus engineered to violate one of those assumptions. The results are then called illusions, which is a slightly unfair name for a system giving the right answer to the question it was designed for.

The checkerboard

The most famous version puts the assumption about illumination on display directly.

A checkerboard under a shadow, with two squares markedThe two marked squares are both #797979. One is a dark square in full light; the other is a light square inside the shadow. Nothing about the drawing enforces the illusion — the two values are set equal in code and asserted before drawing.ABA and B are both #797979asserted equal
Fig. 2 A checkerboard under a cast shadow. The two marked squares carry the same value: A is a dark square in full light, B is a light square in shadow. The equality is set in code and asserted before drawing.

The appearance is not close. The two squares look plainly different, and no amount of staring resolves it. What the visual system has done is entirely reasonable: it has identified a shadow, discounted the illumination inside it, and reported the reflectances — and as reflectances the two squares genuinely are different. One is a dark square and one is a light square. The report is correct about the world and wrong about the image.

Because this figure is generated rather than reproduced from a bitmap, the bar that destroys the illusion can be drawn from the same coordinates as the squares:

The same checkerboard with the two squares joinedThe two marked squares are both #797979. One is a dark square in full light; the other is a light square inside the shadow. The connecting bar is the same value again, and joining them makes the equality obvious.ABA and B are both #797979asserted equal
Fig. 3 The same board with a connecting bar of the same value laid between the two squares. Joining them removes the interpretation as two separate surfaces under different illumination, and the equality becomes obvious.

The bar works by defeating the parsing. A continuous region of one value cannot be two surfaces at different illuminations, so the scene interpretation that produced the effect is no longer available, and the raw equality comes through.

White’s illusion, again

The stripe figure belongs here too, because it is the cleanest evidence that local mechanisms are insufficient.

White's illusion: identical bars on a square-wave gratingBoth grey bars are #909090. The bar sitting in a dark stripe looks darker, not lighter — the opposite of what contrast with the immediate surround predicts, which is why this figure is the standard objection to explaining brightness by lateral inhibition alone.in a dark stripein a light stripeboth bars are #909090asserted equal
Fig. 4 Both bars carry the same value. The bar lying in a dark stripe looks darker — the reverse of what contrast with the immediate surround predicts, and the standard counter-example to explaining lightness by lateral inhibition.

Lateral inhibition predicts that a patch with more black around it should look lighter. Measure the adjacency and the bar in the dark stripe has more black neighbours; it looks darker. Whatever the visual system is doing, it is not counting adjacent luminances.

The leading account is that the bar is grouped with the stripe it lies along — treated as part of that stripe’s surface — and its lightness is judged relative to that grouping rather than to everything it touches. Which is a claim about mid-level vision, about how the scene is carved into objects, and not about retinal filtering at all.

Anchoring: what counts as white

There is one more ingredient, and it is the piece that makes the whole system work.

Ratios alone do not determine lightness. Knowing that patch A is twice patch B does not say whether they are white and grey or grey and black. Something has to anchor the scale, and the evidence is that the visual system anchors it roughly to the highest luminance in the scene, which it treats as white.

This is why a photograph of a dimly lit room looks like a dimly lit room rather than like a set of dark surfaces, and why the same photograph brightened looks like a normally lit room. It is also why a projected image can contain convincing blacks despite the projector emitting light everywhere — the black is the darkest thing available, and it anchors accordingly.

Anchoring is what makes lightness a relative quantity in a way brightness is not, and it is where a good deal of the current disagreement in the field sits — scenes with several illumination regions can have several anchors, and how the system chooses between them is not settled.

The same logic in colour

Everything above concerns lightness, and the chromatic version behaves the same way.

Two identical grey patches on different surroundsBoth inner squares are #868686. The one on the dark field looks lighter. The values are asserted equal in code before the figure is drawn, so the claim is a fact about the drawing rather than a promise.on a dark fieldon a light fieldboth patches are #868686asserted equal
Fig. 5 The lightness case for reference. The chromatic version substitutes coloured surrounds and shifts the apparent hue of the patch away from the surround’s hue — a grey patch on a red field takes on a greenish cast, which is the opponent axis appearing directly.

That the shift runs along opponent axes rather than arbitrary directions is evidence for the opponent recoding sitting between the cones and everything downstream. A red surround does not make a patch look yellow or blue; it makes it look green, because red and green are the two ends of one channel.

The chromatic and achromatic effects are usually treated together because they appear to share a mechanism: local normalisation against an estimate of the surround, computed separately on each opponent channel.

What this does to specification

The practical consequence runs through the whole of applied colour.

A colour cannot be specified in isolation and expected to behave, because appearance is a function of the arrangement. A palette assessed as a row of swatches has been assessed in a configuration it will never appear in — swatches beside one another influence each other, and the same swatches separated by white space do not.

A single grey bar lying on a gradientThe horizontal bar is #959595 from end to end. Against the dark end of the ramp it looks light; against the light end it looks dark. This is the easiest figure here to verify — one bar, one value, and an eyedropper will confirm it anywhere along its length.the bar is one valuethe bar is #959595 throughoutasserted equal
Fig. 6 The simplest possible statement of the problem. One bar, one value, an appearance that varies continuously along its length. Any specification of this bar by its value is complete and says nothing about what it looks like.

This is why colorimetry stops where it does, and why colour appearance models take the viewing situation as an argument rather than deriving it. It is also why this site’s page chrome is exactly neutral: coloured furniture would shift every swatch on every page, by an amount depending on where in the layout it happened to sit.

What was computed here

Every figure in this family is generated from parameters, and every identity claim is asserted.

The Cornsweet construction carries an additional check the others do not need. Its caption depends on the plateaux being genuinely flat and genuinely equal — if the ramp leaked even slightly into them, the figure would be an ordinary brightness difference in disguise. So the assertion measures the spread of luminance across each plateau separately and requires it to be zero, and then requires the two plateaux to be equal to each other. Both come out exactly zero rather than merely small, because the profile is constructed piecewise with the cusp confined to a stated interval.

All the greys are specified by relative luminance rather than code value, since these figures are about luminance relationships and the transfer function is not linear.

Every grey here is specified by relative luminance and converted through the sRGB transfer function, because these figures are about luminance relationships and the code value is not the luminance. Specifying them by code value would have made the captions wrong in a way no amount of looking would reveal.

Why the generated version is weaker, and better

There is a trade-off in building these figures from code rather than reproducing photographs, and it runs against the illusions.

Adelson’s original checkerboard is a rendered three-dimensional scene with a cylinder casting the shadow, depth cues, a soft penumbra and consistent perspective. All of that strengthens the illumination interpretation, and the illusion is correspondingly stronger. The version here is flat rectangles with a plausible shadow region, and it works less well.

It is nonetheless the version this site draws, because every value in it is known, computed and asserted. The photograph is more convincing and the reader has to take its claim on trust; the generated figure is less convincing and its claim is checked. Given that the entire point of the exercise is that the identity cannot be verified by looking, the weaker and checkable version is the right trade.

The same reasoning applies across the fleet these sites belong to. A picture that is convincing and unverified is worth less than a picture that is plain and asserted, because the failures that matter have no visual signature.

Where the account is still unsettled

Edge integration and anchoring are well supported and they are not a complete theory, and it is worth marking the boundary.

Anchoring in scenes with several illumination regions is genuinely open — how the visual system decides which regions share an anchor, and what happens at the boundaries, remains a matter of competing models. White’s illusion has at least three current explanations, appealing to grouping, to filling-in and to spatial filtering at multiple scales, and the experimental evidence does not cleanly separate them.

So the mechanisms described here are the best available account rather than a settled one. What is settled is the data: the figures reproduce, the identities hold, and any theory has to accommodate them.

The reader as instrument

Every figure here is an experiment the reader runs rather than a result reported to them, which is unusual and worth naming.

The Cornsweet effect can be tested by covering the centre band with a finger. The checker-shadow can be tested by comparing the connected and unconnected versions. White’s illusion can be tested by cropping mentally to one stripe at a time. In each case the reader’s visual system is the measuring device, and the measurement is repeatable.

That is available on this subject and almost nowhere else in this fleet of sites. It also carries the corresponding limitation: an instrument that cannot be calibrated, in conditions that cannot be controlled, reporting to the person operating it.

One consequence for anyone building figures of this kind: the more convincing the illusion, the more the reader is being asked to trust. A rendered scene with depth cues and soft shadows produces a much stronger effect than the flat construction here, and it also produces a claim the reader has no way to check. Between a compelling picture whose identity is promised and a plain one whose identity is asserted, the plain one is worth more, and this site takes that trade every time.

One more consequence, for anyone designing with contrast. Because lightness is inferred from edges rather than from areas, a boundary carries more perceptual weight than the regions either side of it. A thin dividing rule can separate two regions more effectively than a large difference in fill, and a soft boundary between two different fills can read as a single surface under uneven lighting. Both are the same mechanism doing what it does, and both are usable rather than merely avoidable.

What the pictures cannot show

The effects vary considerably between viewers and viewing conditions. Screen brightness, ambient light, viewing distance and the physical size the figure renders at all matter, and the checker-shadow in particular is weaker at small sizes because the shadow reads less convincingly as a shadow.

More interestingly, none of these figures can show what the visual system is doing. They show its output under engineered conditions, and every mechanism described above is inferred from patterns of such outputs. The edge-integration account is a model with substantial evidence behind it, not something anyone has watched happen.

And there is a limit specific to a generated figure. The checkerboard here is a flat arrangement of rectangles with a plausible shadow region. A photograph of a real scene carries depth cues, texture gradients and shadow penumbrae that make the illumination interpretation far more compelling. The generated version is more honest — every value is known and asserted — and it is a weaker illusion for exactly that reason.

Who found it, and when

The luminance profile is named for Tom Cornsweet, who described it in his 1970 textbook, though related observations go back to Mach in the 1860s. The effect is sometimes called the Craik–O’Brien–Cornsweet illusion, after all three who worked on it independently.

The checkerboard is Edward Adelson’s, published in 1995, and has become the single most reproduced figure in visual perception. Adelson’s own commentary on it makes the point this essay is built around: the visual system is not a light meter, and judging it as a failed one is the wrong frame.

Alan Gilchrist’s work from the 1970s onward established the anchoring problem and much of what is known about how scenes with several illumination levels are handled.

Where this goes next

The purpose behind all of it is constancy is the default, which takes up the illumination-discounting directly. The measurement-versus-appearance distinction underneath is matching is not appearance. And the simpler starting case is these two patches are identical.

Where this goes next

on a dark fieldon a light fieldboth patches are #818181asserted equal These two patches are identical It is the most repeated and least checkable sentence in visual perception, because the whole point is that it does not look true. Every instance on this site is an assertion in code that stops the build if it ever stops being the case. 400450500550600650700wavelength / nmunder D650.428, 0.474under A0.500, 0.467reflectance is a fraction, 0 to 1CIE 1931 2° observer Constancy is the default A sheet of paper looks white in daylight and white under a tungsten lamp, although the light reaching the eye differs enormously. The visual system is solving one equation with two unknowns, and it solves it by assumption. on a dark fieldon a light fieldboth patches are #868686asserted equal Matching is not appearance CIE XYZ predicts when two lights will look the same under identical viewing conditions. It was never a model of how anything looks, and most of the confusion in applied colour comes from using it as one.