Four issues concerning colour constancy and relational colour constancy

Colour expectations across illumination changes

This study investigates human expectations towards naturalistic colour changes under varying illuminations. Understanding colour expectations is key to both scientific research on colour constancy and applications of colour and lighting in art and industry. We reanalysed data from asymmetric colour matches of a previous study and found that colour adjustments tended to align with illuminant-induced colour shifts predicted by naturalistic, rather than artificial, illuminants and reflectances. We conducted three experiments using hyperspectral images of naturalistic scenes to test if participants judged colour changes based on naturalistic illuminant and reflectance spectra as more plausible than artificial ones, which contradicted their expectations. When we consistently manipulated the illuminant (Experiment 1) and reflectance (Experiment 2) spectra across the whole scene, observers chose the naturalistic renderings significantly above the chance level (>25 %) but barely more often than any of the three artificial ones, collectively (>50 %). However, when we manipulated only one object/area's reflectance (Experiment 3), observers more reliably identified the version in which the object had a naturalistic reflectance like the rest of the scene. Results from Experiments 2-3 and additional analyses suggested that relational colour constancy strongly contributed to observer expectations, and stable cone-excitation ratios are not limited to naturalistic illuminants and reflectances but also occur for our artificial renderings. Our findings indicate that relational colour constancy and prior knowledge about surface colour shifts help to disambiguate surface colour identity under illumination changes, enabling human observers to recognise surface colours reliably in naturalistic conditions. Additionally, relational colour constancy may even be effective in many artificial conditions.

Temporal dynamics of daylight perception: Detection thresholds

Temporal changes in illumination are ubiquitous; natural light, for example, varies in color temperature and irradiance throughout the day. Yet little is known about human sensitivity to temporal changes in illumination spectra. Here, we aimed to determine the minimum detectable velocity of chromaticity change of daylight metamers in an immersive environment. The main stimulus was a continuous, monotonic change in global illumination chromaticity along the daylight locus in warmer (toward lower correlated color temperatures [CCTs]) or cooler directions, away from an adapting base light (CCT: 13,000 K, 6500 K, 4160 K, or 2000 K). All lights were generated by spectrally tunable overhead lamps as smoothest-possible metamers of the desired chromaticities. Mean detection thresholds (for 22 participants) for a fixed duration of 10 seconds ranged from 15 to 2 CIELUV ΔE units, depending significantly on base light CCT and with a significant interaction between CCT and direction of change. Cool changes become less noticeable for progressively warmer base lights and vice versa. For the two extreme base lights, sensitivity to changes toward neutral is significantly lower than for the opposite direction. The results suggest a “neutral bias” in illumination change discriminability, and that typical temporal changes in daylight chromaticity are likely to be below threshold detectability, at least where there are no concomitant overall illuminance changes. These factors may contribute to perceptual stability of natural scenes and color constancy.

Determinants of Colour Constancy and the Blue Bias

We investigated several sensory and cognitive determinants of colour constancy across 40 illumination hues. In the first experiment, we measured colour naming for the illumination and for the colour induced by the illumination on the colorimetric grey. Results confirmed that the induced colours are approximately complementary to the colour of the illumination. In the second experiment, we measured colour constancy using achromatic adjustments. Average colour constancy was perfect under the blue daylight illumination and decreased in colour directions away from the blue daylight illumination due to undershooting and a strong blue bias. Apart from this blue bias, colour constancy was not related to illumination discrimination and to chromatic detection measured previously with the same setup and stimuli. We also observed a strong negative relationship between the degree of colour constancy and the consensus of naming the illumination colour. Constancy coincided with a low naming consensus, in particular because bluish illumination colours were sometimes seen as achromatic. Blue bias and category consensus alone explained >68%, and all determinants together explained >94% of the variance of achromatic adjustments. These findings suggest that colour constancy is optimised for blue daylight.

Spectral sharpening of color sensors: diagonal color constancy and beyond

It has now been 20 years since the seminal work by Finlayson et al. on the use of spectral sharpening of sensors to achieve diagonal color constancy. Spectral sharpening is still used today by numerous researchers for different goals unrelated to the original goal of diagonal color constancy e.g., multispectral processing, shadow removal, location of unique hues. This paper reviews the idea of spectral sharpening through the lens of what is known today in color constancy, describes the different methods used for obtaining a set of sharpening sensors and presents an overview of the many different uses that have been found for spectral sharpening over the years.

Basic color terms use by aged observers: lens aging and perceptual compensation

Basic Color Terms (BCTs) use by aged people (normal and tritanomalous) was analysed on the basis of the results provided by two visual search tasks. One task (mapping) required participants to select every stimulus that could be included in a specific BCT. Another task (best representative) required participants to select the stimulus that most accurately identified a BCT. Both tasks' results were used for two different goals. First (descriptive level), to specify the main differences between aged and young people in their use of BCTs (dimensions provided by multidimensional scaling, confusions between specific pairs of BCTs). Second (explicative level), to compare the accuracy of three models for predicting aged people's performance. Model A (filtering without compensation) assumed that aged people must use BCTs as young people do when responding to stimuli similar to the ones produced by lens aging. On the contrary, model B (filtering with compensation) assumed that lens aging effects were partially compensated by a von Kries-type mechanism (white normalisation). Finally, model C (tritan lines) assumed that ocular aging only influences S cone responses (tritan responses). Results showed that model B was the most accurate with the percentage of explained variance over 90% for both aged groups.

Temporal properties of perceptual calibration to local and broad spectral characteristics of a listening context

The auditory system calibrates to reliable properties of a listening environment in ways that enhance sensitivity to less predictable (more informative) aspects of sounds. These reliable properties may be spectrally local (e.g., peaks) or global (e.g., gross tilt), but the time course over which the auditory system registers and calibrates to these properties is unknown. Understanding temporal properties of this perceptual calibration is essential for revealing underlying mechanisms that serve to increase sensitivity to changing and informative properties of sounds. Relative influence of the second formant (F(2)) and spectral tilt was measured for identification of /u/ and /i/ following precursor contexts that were harmonic complexes with frequency-modulated resonances. Precursors filtered to match F(2) or tilt of following vowels induced perceptual calibration (diminished influence) to F(2) and tilt, respectively. Calibration to F(2) was greatest for shorter duration precursors (250 ms), which implicates physiologic and/or perceptual mechanisms that are sensitive to onsets. In contrast, calibration to tilt was greatest for precursors with longer durations and higher repetition rates because greater opportunities to sample the spectrum result in more stable estimates of long-term global spectral properties. Possible mechanisms that promote sensitivity to change are discussed.

Auditory color constancy: calibration to reliable spectral properties across nonspeech context and targets

Brief experience with reliable spectral characteristics of a listening context can markedly alter perception of subsequent speech sounds, and parallels have been drawn between auditory compensation for listening context and visual color constancy. In order to better evaluate such an analogy, the generality of acoustic context effects for sounds with spectral-temporal compositions distinct from speech was investigated. Listeners identified nonspeech sounds-extensively edited samples produced by a French horn and a tenor saxophone-following either resynthesized speech or a short passage of music. Preceding contexts were "colored" by spectral envelope difference filters, which were created to emphasize differences between French horn and saxophone spectra. Listeners were more likely to report hearing a saxophone when the stimulus followed a context filtered to emphasize spectral characteristics of the French horn, and vice versa. Despite clear changes in apparent acoustic source, the auditory system calibrated to relatively predictable spectral characteristics of filtered context, differentially affecting perception of subsequent target nonspeech sounds. This calibration to listening context and relative indifference to acoustic sources operates much like visual color constancy, for which reliable properties of the spectrum of illumination are factored out of perception of color.

Perceiving colour at a glimpse: The relevance of where one fixates

We used classification images to examine whether certain parts of a surface are particularly important when judging its colour, such as its centre, its edges, or where one is looking. The scene consisted of a regular pattern of square tiles with random colours from along a short line in colour space. Targets defined by a square array of brighter tiles were presented for 200ms. The colours of the tiles within the target were biased by an amount that led to about 70% of the responses being correct. Subjects fixated a point that fell within the target's lower left quadrant and reported each target's colour. They tended to report the colour of the tiles near the fixation point. The influence of the tiles' colour reversed at the target's border and was weaker outside the target. The colour at the border itself was not particularly important. When coloured tiles were also presented before (and after) target presentation they had an opposite (but weaker) effect, indicating that the change in colour is important. Comparing the influence of tiles outside the target with that of tiles at the position at which the target would soon appear suggests that when judging surface colours during the short "glimpses" between saccades, temporal comparisons can be at least as important as spatial ones. We conclude that eye movements are important for colour vision, both because they determine which part of the surface of interest will be given most weight and because the perceived colour of such a surface also depends on what one looked at last.

Combining local and global contributions to perceived colour: An analysis of the variability in symmetric and asymmetric colour matching

Are surfaces' colours judged from weighted averages of the light that they reflect to the eyes and the colour contrast at their borders? To find out we asked subjects to set the colour and luminance of test disks to match reference disks, on various backgrounds, and analysed the variability in their settings. Most of the variability between repeated settings was in luminance. The standard deviations in the set colour were smallest when the disk and background were the same colour, irrespective of the colour itself. Matches were equally precise for greenish or reddish disks on a grey background, as for grey disks on a greenish or reddish background. The precision was less dependent on the colour contrast at the disks' borders when the backgrounds were more complex and when there was a large luminance contrast at the disks' borders. Subjects were less precise when different colours surrounded the two disks. These findings are consistent with the perceived colour at any position being a weighted average of the local cone excitation ratio and the change in the cone excitation ratio at the borders of the surface in question. However, the involved weights must be variable and depend systematically on parameters such as the luminance contrast at the surface's borders and other chromatic contrasts within the scene.

Sensory, computational and cognitive components of human colour constancy

When the illumination on a scene changes, so do the visual signals elicited by that scene. In spite of these changes, the objects within a scene tend to remain constant in their apparent colour. We start this review by discussing the psychophysical procedures that have been used to quantify colour constancy. The transformation imposed on the visual signals by a change in illumination dictates what the visual system must 'undo' to achieve constancy. The problem is mathematically underdetermined, and can be solved only by exploiting regularities of the visual world. The last decade has seen a substantial increase in our knowledge of such regularities as technical advances have made it possible to make empirical measurements of large numbers of environmental scenes and illuminants. This review provides a taxonomy of models of human colour constancy based first on the assumptions they make about how the inverse transformation might be simplified, and second, on how the parameters of the inverse transformation might be set by elements of a complex scene. Candidate algorithms for human colour constancy are represented graphically and pictorially, and the availability and utility of an accurate estimate of the illuminant is discussed. Throughout this review, we consider both the information that is, in principle, available and empirical assessments of what information the visual system actually uses. In the final section we discuss where in our visual systems these computations might be implemented.

Olive green or chestnut brown?

Reflectance and spectral power functions are poor predictors of color experiences. Only in completely relativized conditions (single observer, non-metameric set of stimuli, and single set of viewing conditions) is the relationship close. Variation in reflectance of Munsell chips experienced by color-normal observers as having a unique green hue encompasses approximately sixty percent of the complete range of hues falling under the category “green”; and in recent determinations of unique hues, ranges of yellow and green as well as green and blue unique hues overlap.

Why not color physicalism without color absolutism?

We make three points. First, the concept of productance value that the authors propose in their defense of color physicalism fails to do the work for which it is intended. Second, the authors fail to offer an adequate physicalist account of what they call the hue-magnitudes. Third, their answer to the problem of individual differences faces serious difficulties.

Color realism and color illusions

As demonstrated by several example displays, color illusions challenge color realism, because they involve a one-to-many reflectance-to-color mapping. Solving this problem by differentiating between veridical and illusory colors corresponding to the same reflectance is hampered because of the lack of an appropriate criterion. However, the difference between veridical and illusory color perception can still be maintained.

Have Byrne & Hilbert answered Hardin's challenge?

I argue that Byrne & Hilbert (B&H) have not answered Hardin's objection to physicalism about color concerning the unitary-binary structure of the colors for two reasons. First, their account of unitary-binary structure seems unsatisfactory. Second, pace B&H, there are no physicalistically acceptable candidates to be the hue-magnitudes. I conclude with a question about the justification of physicalism about color.

Perceptual variation, realism, and relativization, or: How I learned to stop worrying and love variations in color vision

In many cases of variation in color vision, there is no nonarbitrary way of choosing between variants. Byrne & Hilbert insist that there is an unknown standard for choosing, whereas eliminativists claim that all the variants are erroneous. A better response relativizes colors to perceivers, thereby providing a color realism that avoids the need to choose between variants.

Can a physicalist notion of color provide any insight into the nature of color perception?

Byrne & Hilbert (B&H) conceive of color perception as the representation of a physical property “out there.” In our view, their approach does not only have various internal problems, but is also apt to becloud both the intricate and still poorly understood role that “color” plays within perceptual architecture, and the complex coupling to the “external world” of the perceptual system as an entirety. We propose an alternative perspective, which avoids B&H's misleading dichotomy between a purely subjective and a realist conception of “color.”

An account of color without a subject?

While color realism is endorsed, Byrne & Hilbert's (B&H's) case for it stretches the notion of “physical property” beyond acceptable bounds. It is argued that a satisfactory account of color should do much more to respond to antirealist intuitions that flow from the specificity of color experience, and a pointer to an approach that does so is provided.

Color realism redux

Our reply is in three parts. The first part concerns some foundational issues in the debate about color realism. The second part addresses the many objections to the version of physicalism about color (“productance physicalism”) defended in the target article. The third part discusses the leading alternative approaches and theories endorsed by the commentators.

Orange laser beams are not illusory: The need for a plurality of “real” color ontologies

Reflectance physicalism only provides a partial picture of the ontology of color. Byrne & Hilbert’ account is unsatisfactory because the replacement of reflectance functions by productance functions is ad hoc, unclear, and only leads to new problems. Furthermore, the effects of color contrast and differences in illumination are not really taken seriously: Too many “real” colors are tacitly dismissed as illusory, and this for arbitrary reasons. We claim that there cannot be an all-embracing ontology for color.

Color nominalism, pluralistic realism, and color science

Byrne & Hilbert are right that it might be an objective fact that a particular tomato is unique red, but wrong that it cannot simultaneously be yellowish-red (not only objectively, but from somebody else's point of view). Sensory categorization varies among organisms, slightly among conspecifics, and sharply across taxa. There is no question of truth or falsity concerning choice of categories, only of utility and disutility. The appropriate framework for color categories is Nominalism and Pluralistic Realism.

Perceptual variation and access to colors

To identify the set of reflectances that constitute redness, the authors must first determine which surfaces are red. They do this by relying on widespread agreement among us. However, arguments based on the possible ways in which humans would perceive colors show that mere widespread agreement among us is not a satisfactory way to determine which surfaces are red.

Chromatic induction and the layout of colours within a complex scene

A target's apparent colour is influenced by the colours in its surrounding. If the surrounding consists of a single coloured surface, the influence is a shift 'away' from the surface's colour. If the surface is more than 1 degrees from the target area the shift is very small. If there are many surfaces, then not only the average luminance and chromaticity of the surfaces matters, but also the chromatic variability. It is not yet clear whether it makes any difference where the chromatic variability is within the scene, so we constructed stimuli in which the chromatic variability was restricted to certain regions. We found that it made very little difference where the chromatic variability was located. The extent to which the average colour of nearby surfaces influences the apparent colour of the target seems to depend on the average chromatic variability of the whole scene.

Parallels between hearing and seeing support physicalism

There are 2,000 hair cells in the cochlea, but only three cones in the retina. This disparity can be understood in terms of the differences between the physical characteristics of the auditory signal (discrete excitations and resonances requiring many narrowly tuned receptors) and those of the visual signal (smooth daylight excitations and reflectances requiring only a few broadly tuned receptors). We argue that this match supports the physicalism of color and timbre.

Surreptitious substitution

In this commentary I argue that Byrne & Hilbert commit a number of philosophical solecisms: They beg the question of “realism,” they take the phenomenon and the theoretical model to be the same thing, and they surreptitiously substitute data sets for the life-world.

Clarifying the problem of color realism

“The problem of color realism” as defined in the first section of the target article, is crucial to the argument laid out by Byrne & Hilbert. They claim that the problem of color realism “does not concern, at least in the first instance, color language or color concepts” (sect. 1.1). I argue that this claim is misconceived and that a different characterisation of the problem, and some of their preliminary assumptions makes their positive proposal less appealing.

Ecological considerations support color physicalism

We argue that any theory of color physicalism must include consideration of ecological interactions. Ecological and sensorimotor contingencies resulting from relative surface motion and observer motion give rise to measurable effects on the spectrum of light reflecting from surfaces. These contingencies define invariant manifolds in a sensory-spatial space, which is the physical underpinning of all subjective color experiences.

Confusion of sensations and their physical correlates

The authors favor a “color realism” theory that considers colors to be physical properties residing in objects that reflect, emit, or transmit light. It is opposed to the theory that colors are sensations or visual experiences. This commentary suggests that both theories are correct, and that context usually indicates which of these dual aspects is being considered.

True color only exists in the eye of the observer

The colors we perceive are the outcome of an attempt to meaningfully order the spectral information from the environment. These colors are not the result of a straightforward mapping of a physical property to a sensation, but arise from an interaction between our environment and our visual system. Thus, although one may infer from a surface’ reflectance characteristics that it will be perceived as “colored,” true colors only arise by virtue of the interaction of the reflected light with the eye (and brain) of an observer.

Color and content

Those who identify colours with physical properties need to say how the content of colour experiences relate to their favoured identifications. This is because it is not plausible to hold that colour experiences represent things as having the physical properties in question. I sketch how physical realists about colour might tackle this item of unfinished business.

“Color realism” shows a subjectivist' mode of thinking

Byrne & Hilbert (B&H) assert that reflectances embody the reality of color, but metamerism smears the authors' “real” color categories into uselessness. B&H ignore this problem, possibly because they implicitly adopt a sort of subjectivism, whereby an object is defined by the percepts (or more generally by the measurements) it engenders. Subjectivism is unwieldy, and hence prone to such troubles.

Spatial position and perceived color of objects

Visual percepts are called veridical when a “real” object can be identified as their cause, and illusions otherwise. The perceived position and color of a flashed object may be called veridical or illusory depending on which viewpoint one adopts. Since “reality” is assumed to be fixed (independent of viewpoint) in the definition of veridicality (or illusion), this suggests that “perceived” position and color are not properties of “real” objects.

Reflectance-to-color mappings depend critically on spatial context

In visual science, color is usually regarded as a subjective phenomenon. The relationship between the specific color experiences that are evoked by a visual scene and the physical properties of the surfaces viewed in that scene are complex and highly dependent on spatial context. There is no simple correspondence between experienced color and a stable class of physical reflectances.

Byrne and Hilbert's chromatic ether

Because our only access to color qualities is through their appearance, Byrne & Hilbert's insistence on a strict distinction between apparent colors and real colors leaves them without a principled way of determining when, if ever, we see colors as they really are.

Beautiful red squares

The reflectance types that Byrne & Hilbert identify with colors count as types only in a way that is more dependent on, and more relative to color perceivers, than their account suggests. Their account of perceptual content may be overly focused on input conditions and distal causes.

Perceptual objects may have nonphysical properties

Byrne & Hilbert defend color realism, which assumes that: (a) colors are properties of objects; (b) these objects are physical; hence, (c) colors are physical properties. I accept (a), agree that in a certain sense (b) can be defended, but reject (c). Colors are properties of perceptual objects – which also have underlying physical properties – but they are not physical properties.

Color as a material, not an optical, property

For all animals, color is an indicator of the substance and state of objects, for which purpose reflectance is just one among many relevant optical properties. This broader meaning of color is confirmed by linguistic evidence. Rather than reducing color to a simple physical property, it is more realistic to embrace its full phenomenology.

Productance physicalism and a posteriori necessity

The problem of nonreflectors perceived as colored is the central problem for Byrne & Hilbert's (B&H's) physicalism. Vision scientists and other interested parties need to consider the motivation for their account of “productance physicalism.” Is B&H's theory motivated by scientific concerns or by philosophical interests intended to preserve a physicalist account of color as a posteriori necessary?

In favor of an ecological account of color

Byrne & Hilbert understate the difficulties facing their version of color realism. We doubt that they can fix reflectance types and magnitudes in a way that does not invoke relations to perceivers. B&H's account, therefore, resembles the dispositional or ecological accounts that they dismiss. This is a good thing, for a dispositional account is promising if understood in an ecological framework.

Color as a factor analytic approximation to Nature

Color vision provides accurate measures of the phase and intensity of daylight, and also a means of discriminating between objects. Neither property implies that objects are colored.

Hue magnitudes and Revelation

Revelation, the thesis that the full intrinsic nature of colors is revealed to us by color experiences, is false in Byrne & Hilbert's (B&H's) view, but in an interesting and nonobvious way. I show what would make Revelation true, given B&H's account of colors, and then show why that situation fails to obtain, and why that is interesting.

Surface color perception in constrained environments

Byrne & Hilbert propose that color can be identified with explicit properties of physical surfaces. I argue that this claim must be qualified to take into account constraints needed to make recovery of surface color information possible. When these constraints are satisfied, then a biological visual system can establish a correspondence between perceived surface color and specific surface properties.

Color: A vision scientist's perspective

Vision scientists are interested in three diverse entities: physical stimuli, neural states, and consciously perceived colors, and in the mapping rules among the three. In this worldview, the three kinds of entities have coequal status, and views that attribute color exclusively to one or another of them, such as color realism, have no appeal.

Do metamers matter?

Metamerism is a rather common feature of objects. The authors see it as problematic because they are concerned with a special case: metamerism in standard conditions. Such metamerism does not, however, pose a problem for color realists. There is an apparent problem in cases of metameric light sources, but to see such metamers as problematic is to fail to answer Berkeley's challenge.

Imprecise color constancy versus color realism

Byrne & Hilbert's thesis, that color be associated with reflectance-type, is questioned on the grounds that it is far from clear that the human visual system is able to determine a surface's reflectance-type with sufficient accuracy. In addition, a (friendly) suggestion is made as to how to amend the definition of reflectance-type in terms of CIE (Commission Internationale de l'Eclairage) coordinates under a canonical illuminant.

Cone contributions to colour constancy

Colour constancy refers to the stable perception of object colour under changing illumination conditions. This problem has been reformulated as relational colour constancy, or the ability of the observer to discriminate between material changes and changes in illumination. It has been suggested that local cone excitation ratios play a prominent role in achieving such constancy. Here we show that perceptual colour constancy measured by achromatic adjustments is to a large part complete after 25 ms. This speaks against a prominent role for receptor adaptation, which takes significantly longer. We also found no difference in colour constancy between colour changes that were compatible with a change of illuminant, and between colour changes where local cone ratios were uncorrelated between the two illuminants. Our results show that constant cone ratios are not necessary for colour constancy.

Is lightness induction a pictorial illusion?

Lightness induction, or simultaneous lightness contrast (we prefer the term lightness induction since contrast has another meaning in the visual literature, namely, the relative intensity of the stimulation), was studied for a 3-D object (Adelson's wall of blocks) and its 2-D pictorial representations. A statistically significant lightness induction effect was found only for the pictures but not for the 3-D object. No lightness induction effect was found for the 3-D object under either monocular or binocular viewing conditions.

Detecting changes of spatial cone-excitation ratios in dichoptic viewing

Spatial ratios of cone excitations produced by light reflected by different surfaces in a scene may provide the cue for discriminating changes in illuminant from changes in surface reflectances. To test whether these ratios can be computed across the two eyes, observers were presented with simulations on a computer-controlled monitor of pairs of juxtaposed or separated Munsell surfaces undergoing an illuminant change with a small change in cone-excitation ratios or a change with constant cone-excitation ratios. Surfaces were viewed either binocularly or dichoptically. Observers reliably discriminated the two changes in both viewing conditions, although less well dichoptically. Cone-excitation ratios, which may in principle be computed retinally, may also be computed cortically.

When is a background equivalent? Sparse chromatic context revisited

Jenness and Shevell (Vision Res 1995;35:797-805) reported that a red background with white dots scattered on it has a different influence on a target's apparent colour than an equivalent uniform background. We show that this finding depends on what one considers an equivalent background. Jenness and Shevell averaged the chromaticity and luminance of the background with the dots, and 'superimposed' the target onto this new background. This changed the luminance and chromaticity of both the target and the surround. We show that if only the surround is changed, it is irrelevant whether the latter is red with white dots scattered over it, or a uniform field with the same space averaged chromaticity and luminance. Our findings are consistent with a local contrast mechanism that has a limited spatial resolution.

Detecting natural changes of cone-excitation ratios in simple and complex coloured images

Ratios of excitations in each cone-photoreceptor class produced by light reflected from pairs of surfaces in a scene are almost invariant under natural illuminant changes. The stability of these spatially defined ratios may explain the remarkable ability of human observers to efficiently discriminate illuminant changes from changes in surface reflectances. Spatial cone-excitation ratios are not, however, exactly invariant. This study is concerned with observers' sensitivity to these invariance violations. Simulations of Mondrian paintings with either 49 or two natural surfaces under Planckian illuminants were presented as images on a computer-controlled display in a two-interval experimental design: in one interval, the surfaces underwent an illuminant change; in the other interval, the surfaces underwent the same change but the images were then corrected so that, for each cone class, ratios of excitations were preserved exactly. Although the intervals with corrected images corresponded individually to highly improbable natural events, observers systematically misidentified them as containing the illuminant changes, the probability of error increasing as the violation of invariance in the other interval increased. For the range of illuminants and surfaces tested, sensitivity to violations of invariance was found to depend on cone class: it was greatest for long-wavelength-sensitive cones and least for short-wavelength-sensitive cones. Spatial cone-excitation ratios, or some closely related quantities, seem to be the cues preferred by observers for making inferences about surface illuminant changes.