Does colour constancy exist?

Color constancy in real-world settings

Color constancy denotes the ability to assign a particular and stable color percept to an object, irrespective of its surroundings and illumination. The light reaching the eye confounds illumination and spectral reflectance of the object, making the recovery of constant object color an ill-posed problem. How good the visual system is at accomplishing this task is still a matter of heated debate, despite more than a 100 years of research. Depending on the laboratory task and the specific cues available to observers, color constancy was found to be at levels ranging between 15% and 80%, which seems incompatible with the relatively stable color appearance of objects around us and the consistent usage of color names in real life. Here, we show close-to-perfect color constancy using real objects in a natural task and natural environmental conditions, chosen to mimic the role of color constancy in everyday life. Participants had to identify the color of a (non-present) item familiar to them in an office room under five different experimental illuminations. They mostly selected the same colored Munsell chip as their match to the absent object, even though the light reaching the eye in each case differed substantially. Our results demonstrate that color constancy under ideal conditions in the real world can indeed be exceptionally good. We found it to be as good as visual memory permits and not generally compromised by sensory uncertainty.

A true color palette: binary metastable photonic pigments

Different from the traditional concept that binary photonic crystals can only reproduce mixed colors due to the simple superposition of the photonic band gaps, precisely addressable "true colors" obtained from volume fraction deviation of binary photonic crystals with metastable structures are reported here. Inspired by the mussels' adhesion and longhorn beetles' photonic scales, a binary metastable amorphous photonic crystal was obtained by enhancing the driving forces and customizing the surface roughness of building blocks to regulate the thermodynamic and dynamic factors simultaneously. By controlling the volume fraction of two building blocks, the tunable photonic bandgap varies linearly in the visible region. Furthermore, the "true violet" that cannot be obtained by conventional color mixing is reproduced with the particular ultraviolet characteristics of red photonic pigment's metastable structures, which complement the palette effect of "true colors". Meanwhile, due to the self-adhesion and post-modification of building blocks, the stability of photonic pigments is further improved. The binary photonic pigments not only solve the dilemma of mixed colors, but also realize the tunability and multiplicity of "true colors", offering a new choice for the color palette of the world.

On the evaluation of temporal and spatial stability of color constancy algorithms

Computational color constancy algorithms are commonly evaluated only through angular error analysis on annotated datasets of static images. The widespread use of videos in consumer devices motivated us to define a richer methodology for color constancy evaluation. To this extent, temporal and spatial stability are defined here to determine the degree of sensitivity of color constancy algorithms to variations in the scene that do not depend on the illuminant source, such as moving subjects or a moving camera. Our evaluation methodology is applied to compare several color constancy algorithms on stable sequences belonging to the Gray Ball and Burst Color Constancy video datasets. The stable sequences, identified using a general-purpose procedure, are made available for public download to encourage future research. Our investigation proves the importance of evaluating color constancy algorithms according to multiple metrics, instead of angular error alone. For example, the popular fully convolutional color constancy with confidence-weighted pooling algorithm is consistently the best performing solution for error evaluation, but it is often surpassed in terms of stability by the traditional gray edge algorithm, and by the more recent sensor-independent illumination estimation algorithm.

ARC: Angle-Retaining Chromaticity diagram for color constancy error analysis

Color constancy algorithms are typically evaluated with a statistical analysis of the recovery angular error and the reproduction angular error between the estimated and ground truth illuminants. Such analysis provides information about only the magnitude of the errors, and not about their chromatic properties. We propose an Angle-Retaining Chromaticity diagram (ARC) for the visual analysis of the estimated illuminants and the corresponding errors. We provide both quantitative and qualitative proof of the superiority of ARC in preserving angular distances compared to other chromaticity diagrams, making it possible to quantify the reproduction and recovery errors in terms of Euclidean distances on a plane. We present two case studies for the application of the ARC diagram in the visualization of the ground truth illuminants of color constancy datasets, and the visual analysis of error distributions of color constancy algorithms.

Reconciling the statistics of spectral reflectance and colour

The spectral reflectance function of a surface specifies the fraction of the illumination reflected by it at each wavelength. Jointly with the illumination spectral density, this function determines the apparent colour of the surface. Models for the distribution of spectral reflectance functions in the natural environment are considered. The realism of the models is assessed in terms of the individual reflectance functions they generate, and in terms of the overall distribution of colours which they give rise to. Both realism assessments are made in comparison to empirical datasets. Previously described models (PCA- and fourier-based) of reflectance function statistics are evaluated, as are improved versions; and also a novel model, which synthesizes reflectance functions as a sum of sigmoid functions. Key model features for realism are identified. The new sigmoid-sum model is shown to be the most realistic, generating reflectance functions that are hard to distinguish from real ones, and accounting for the majority of colours found in natural images with the exception of an abundance of vegetation green and sky blue.

Chips in the sunshine: color constancy with real versus simulated Munsell chips under illuminants adjacent to the daylight locus

Accurate color judgments rely on a powerful cognitive component. Here we compare the performance of color constancy under real and simulated conditions. Shifts in the u^'v^' color plane induced by illuminant A (2750 K) and illuminant S (>20,000  K) were measured using asymmetric color matching. A general linear model was used to predict performance from the following dependent variables: chroma ("4" and "6"), illuminant ("A" and "S"), presentation mode ("Real" and "Monitor"), and hue zone ("blue," "green," "yellow," "red," and "purple"). There was a strong overall effect [F(7,264)=78.65, p<0.001]. Post hoc analysis showed that performance was substantially superior under real [chromatic constancy index (cCI)=0.76] compared with simulated cCI=0.55) conditions.

Effect of Scene Complexity on Colour Constancy with Real Three-Dimensional Scenes and Objects

The effect of scene complexity on colour constancy was tested with a novel technique in which a virtual image of a real 3-D test object was projected into a real 3-D scene. Observers made discriminations between illuminant and material changes in simple and complex scenes. The extent of colour constancy achieved varied little with either scene structure or test-object colour, suggesting a dominant role of local cues in determining surface-colour judgments.

Organic Photodiodes: The Future of Full Color Detection and Image Sensing

Major growth in the image sensor market is largely as a result of the expansion of digital imaging into cameras, whether stand-alone or integrated within smart cellular phones or automotive vehicles. Applications in biomedicine, education, environmental monitoring, optical communications, pharmaceutics and machine vision are also driving the development of imaging technologies. Organic photodiodes (OPDs) are now being investigated for existing imaging technologies, as their properties make them interesting candidates for these applications. OPDs offer cheaper processing methods, devices that are light, flexible and compatible with large (or small) areas, and the ability to tune the photophysical and optoelectronic properties - both at a material and device level. Although the concept of OPDs has been around for some time, it is only relatively recently that significant progress has been made, with their performance now reaching the point that they are beginning to rival their inorganic counterparts in a number of performance criteria including the linear dynamic range, detectivity, and color selectivity. This review covers the progress made in the OPD field, describing their development as well as the challenges and opportunities.

Why the "stimulus-error" did not go away

Psychologists in the early years of the discipline were much concerned with the stimulus-error. Roughly, this is the problem encountered in introspective experiments when subjects are liable to frame their perceptual reports in terms of what they know of the stimulus, instead of just drawing on their perceptual experiences as they are supposedly felt. "Introspectionist" psychologist E. B. Titchener and his student E. G. Boring both argued in the early 20th century that the stimulus-error is a serious methodological pit-fall. While many of the theoretical suppositions motivating Titchener and Boring have been unfashionable since the rise of behaviourism, the stimulus-error brings our attention to one matter of perennial importance to psychophysics and the psychology of perception. This is the fact that subjects are liable to give different kinds of perceptual reports in response to the same stimulus. I discuss attempts to control for variable reports in recent experimental work on colour and lightness constancy, and the disputes that have arisen over which kinds of reports are legitimate. Some contemporary psychologists do warn us against a stimulus-error, even though they do not use this terminology. I argue that concern over the stimulus-error is diagnostic of psychologists' deep theoretical commitments, such as their conception of sensation, or their demarcation of perception from cognition. I conclude by discussing the relevance of this debate to current philosophy of perception.

Test illuminant location with respect to the Planckian locus affects chromaticity shifts of real Munsell chips

The asymmetric sequential color-matching technique was used to determine the shifts in chromaticity of real Munsell chips induced by four test illuminants. The reference illuminant was C. Illuminants green (G) and purple (P) induced shifts orthogonal to the Planckian locus, while illuminants S and A induced shifts along the Planckian locus. Vectors describing the shifts induced by A and S were quantitatively and qualitatively different from those due to G and P. The data suggest that physiological factors, influenced by the proximity of the Planckian locus, affect chromatic constancy under nonsimulated viewing conditions.

Rethinking Colour Constancy

Colour constancy needs to be reconsidered in light of the limits imposed by metamer mismatching. Metamer mismatching refers to the fact that two objects reflecting metameric light under one illumination may reflect non-metameric light under a second; so two objects appearing as having the same colour under one illuminant can appear as having different colours under a second. Yet since Helmholtz, object colour has generally been believed to remain relatively constant. The deviations from colour constancy registered in experiments are usually thought to be small enough that they do not contradict the notion of colour constancy. However, it is important to determine how the deviations from colour constancy relate to the limits metamer mismatching imposes on constancy. Hence, we calculated metamer mismatching’s effect for the 20 Munsell papers and 8 pairs of illuminants employed in the colour constancy study by Logvinenko and Tokunaga and found it to be so extensive that the two notions—metamer mismatching and colour constancy—must be mutually exclusive. In particular, the notion of colour constancy leads to some paradoxical phenomena such as the possibility of 20 objects having the same colour under chromatic light dispersing into a hue circle of colours under neutral light. Thus, colour constancy refers to a phenomenon, which because of metamer mismatching, simply cannot exist. Moreover, it obscures the really important visual phenomenon; namely, the alteration of object colours induced by illumination change. We show that colour is not an independent, intrinsic attribute of an object, but rather an attribute of an object/light pair, and then define a concept of material colour in terms of equivalence classes of such object/light pairs. We suggest that studying the shift in material colour under a change in illuminant will be more fruitful than pursuing colour constancy’s false premise that colour is an intrinsic attribute of an object.

Estimating information from image colors: an application to digital cameras and natural scenes

The colors present in an image of a scene provide information about its constituent elements. But the amount of information depends on the imaging conditions and on how information is calculated. This work had two aims. The first was to derive explicitly estimators of the information available and the information retrieved from the color values at each point in images of a scene under different illuminations. The second was to apply these estimators to simulations of images obtained with five sets of sensors used in digital cameras and with the cone photoreceptors of the human eye. Estimates were obtained for 50 hyperspectral images of natural scenes under daylight illuminants with correlated color temperatures 4,000, 6,500, and 25,000 K. Depending on the sensor set, the mean estimated information available across images with the largest illumination difference varied from 15.5 to 18.0 bits and the mean estimated information retrieved after optimal linear processing varied from 13.2 to 15.5 bits (each about 85 percent of the corresponding information available). With the best sensor set, 390 percent more points could be identified per scene than with the worst. Capturing scene information from image colors depends crucially on the choice of camera sensors.

Color constancy by category correlation

Finding color representations that are stable to illuminant changes is still an open problem in computer vision. Until now, most approaches have been based on physical constraints or statistical assumptions derived from the scene, whereas very little attention has been paid to the effects that selected illuminants have on the final color image representation. The novelty of this paper is to propose perceptual constraints that are computed on the corrected images. We define the category hypothesis, which weights the set of feasible illuminants according to their ability to map the corrected image onto specific colors. Here, we choose these colors as the universal color categories related to basic linguistic terms, which have been psychophysically measured. These color categories encode natural color statistics, and their relevance across different cultures is indicated by the fact that they have received a common color name. From this category hypothesis, we propose a fast implementation that allows the sampling of a large set of illuminants. Experiments prove that our method rivals current state-of-art performance without the need for training algorithmic parameters. Additionally, the method can be used as a framework to insert top-down information from other sources, thus opening further research directions in solving for color constancy.

Synaesthesia and colour constancy

Grapheme-colour synaesthesia is an atypical condition characterized by the perception of colours when reading achromatic text. We investigated the level of colour processing responsible for these experiences. To do so, we tapped a central characteristic of colour perception. In different lighting conditions the same wavelength of light can prompt the perception of different colours. This helps humans recognize distinctive coloured objects despite changes in illumination. We wanted to see if synaesthetic colours were generated at a neural locus that was susceptible to colour constancy analyses. We used colour matching and naming tasks to examine interactions between simulated coloured illuminants and synaesthetic colours. Neither synaesthetic colour matching or naming was impacted. This contrasted with non-synaesthetic control participants, who performed the colour-matching task with graphemes physically coloured to mimic synaesthesia. Our data suggest that synaesthetic colour signals are not generated at lower-levels of colour processing, but are introduced at higher levels of analysis and are therefore not impacted by the processes responsible for perceptual constancy.

Context-dependent judgments of color that might allow color constancy in scenes with multiple regions of illumination

For a color-constant observer, a change in the spectral composition of the illumination is accompanied by a corresponding change in the chromaticity associated with an achromatic percept. However, maintaining color constancy for different regions of illumination within a scene implies the maintenance of multiple perceptual references. We investigated the features of a scene that enable the maintenance of separate perceptual references for two displaced but overlapping chromaticity distributions. The time-averaged, retinotopically localized stimulus was the primary determinant of color appearance judgments. However, spatial separation of test samples additionally served as a symbolic cue that allowed observers to maintain two separate perceptual references.

Slow updating of the achromatic point after a change in illumination

For a color constant observer, the color appearance of a surface is independent of the spectral composition of the light illuminating it. We ask how rapidly color appearance judgments are updated following a change in illumination. We obtained repeated binary color classifications for a set of stimuli defined by their reflectance functions and rendered under either sunlight or skylight. We used these classifications to derive boundaries in color space that identify the observer's achromatic point. In steady-state conditions of illumination, the achromatic point lay close to the illuminant chromaticity. In our experiment, the illuminant changed abruptly every 21 s (at the onset of every 10th trial), allowing us to track changes in the achromatic point that were caused by the cycle of illuminant changes. In one condition, the test reflectance was embedded in a spatial pattern of reflectance samples under consistent illumination. The achromatic point migrated across color space between the chromaticities of the steady-state achromatic points. This update took several trials rather than being immediate. To identify the factors that governed perceptual updating of appearance judgments, we used two further conditions, one in which the test reflectance was presented in isolation and one in which the surrounding reflectances were rendered under an inconsistent and unchanging illumination. Achromatic settings were not well predicted by the information available from scenes at a single time point. Instead, the achromatic points showed a strong dependence on the history of chromatic samples. The strength of this dependence differed between observers and was modulated by the spatial context.

Generalization of color-difference formulas for any illuminant and any observer by assuming perfect color constancy in a color-vision model based on the OSA-UCS system

The most widely used color-difference formulas are based on color-difference data obtained under D65 illumination or similar and for a 10° visual field; i.e., these formulas hold true for the CIE 1964 observer adapted to D65 illuminant. This work considers the psychometric color-vision model based on the Optical Society of America-Uniform Color Scales (OSA-UCS) system previously published by the first author [J. Opt. Soc. Am. A 21, 677 (2004); Color Res. Appl. 30, 31 (2005)] with the additional hypothesis that complete illuminant adaptation with perfect color constancy exists in the visual evaluation of color differences. In this way a computational procedure is defined for color conversion between different illuminant adaptations, which is an alternative to the current chromatic adaptation transforms. This color conversion allows the passage between different observers, e.g., CIE 1964 and CIE 1931. An application of this color conversion is here made in the color-difference evaluation for any observer and in any illuminant adaptation: these transformations convert tristimulus values related to any observer and illuminant adaptation to those related to the observer and illuminant adaptation of the definition of the color-difference formulas, i.e., to the CIE 1964 observer adapted to the D65 illuminant, and then the known color-difference formulas can be applied. The adaptations to the illuminants A, C, F11, D50, Planckian and daylight at any color temperature and for CIE 1931 and CIE 1964 observers are considered as examples, and all the corresponding transformations are given for practical use.

Working memory is related to perceptual processing: a case from color perception

We explored the relation between individual differences in working memory (WM) and color constancy, the phenomenon of color perception that allows us to perceive the color of an object as relatively stable under changes in illumination. Successive color constancy (measured by first viewing a colored surface under a particular illumination and later recalling it under a new illumination) was better for higher WM individuals than for lower WM individuals. Moreover, the magnitude of this WM difference depended on how much contextual information was available in the scene, which typically improves color constancy. By contrast, simple color memory, measured by viewing and recalling a colored surface under the same illumination, showed no significant relation to WM. This study reveals a relation between WM and a low-level perceptual process not previously thought to operate within the confines of attentional control, and it provides a first account of the individual differences in color constancy known about for decades.

Hue manifold

It is generally accepted that hues can be arranged so as to make a circle. The circular representation of hue has been supported by multidimensional scaling, which allows for the representation of a set of colored papers as a configuration in a Euclidean space where the distances between the papers correspond to the perceptual dissimilarities between them. In particular, when papers of various hues are evenly illuminated, they are arranged in a one-dimensional circular configuration. However, under variegated illumination we show that the same papers in fact make a two-dimensional configuration that resembles a torus.

Color constancy

A quarter of a century ago, the first systematic behavioral experiments were performed to clarify the nature of color constancy-the effect whereby the perceived color of a surface remains constant despite changes in the spectrum of the illumination. At about the same time, new models of color constancy appeared, along with physiological data on cortical mechanisms and photographic colorimetric measurements of natural scenes. Since then, as this review shows, there have been many advances. The theoretical requirements for constancy have been better delineated and the range of experimental techniques has been greatly expanded; novel invariant properties of images and a variety of neural mechanisms have been identified; and increasing recognition has been given to the relevance of natural surfaces and scenes as laboratory stimuli. Even so, there remain many theoretical and experimental challenges, not least to develop an account of color constancy that goes beyond deterministic and relatively simple laboratory stimuli and instead deals with the intrinsically variable nature of surfaces and illuminations present in the natural world.

Colour constancy: influence of viewing behaviour on grey settings

In numerous studies on colour constancy or colour induction subjects have to adjust a test field so that it looks achromatic. Their viewing behaviour during these settings is often not controlled or reported. Here I show that the results of grey settings depend on whether subjects visually explore the stimulus by looking around or fixate their gaze exclusively on the test field. Two different viewing instructions are compared with regard to the degree of constancy as measured by the shift of grey settings in coloured surrounds. In variegated surrounds (but not in uniform surrounds) there is a robust effect of viewing condition for all subjects and all surround chromaticities tested, in that exploration increases colour constancy compared to fixating the test field. Values of a colour constancy index are increased by as much as 20% (where 100% colour constancy means that the subject chooses as grey the mean chromaticity of the surround) with an average across all subjects and surrounds of 12.6%. Thus, if this factor is not experimentally controlled, it could inflate variance, reduce comparability between different studies, and even lead to unwarranted conclusions if viewing behaviour unpredictably differs between experimental conditions.

Effect of Scene Dimensionality on Colour Constancy with Real Three-Dimensional Scenes and Objects

The effect of scene dimensionality on colour constancy was tested with real scenes and objects. Observers viewed a three-dimensional (3-D) scene, or its two-dimensional (2-D) planar projection, through a large beam-splitter that projected the virtual image of a real test object (a cube or its 2-D projection) so that it appeared part of the scene. Test object and scene could be illuminated independently with high chromatic precision. In each trial, the illuminance of the scene changed abruptly from 25 000 K to 6700 K and the illuminant of the test object changed either consistently or inconsistently with it by a variable quantifiable amount. Observers had to decide whether the test object underwent a change in its materials. The extent of constancy obtained in the experiment was not influenced by scene dimensionality and varied significantly with the colour of the test object. These results suggest that color constancy in the conditions tested here may be determined by local spectral quantities.

Color strategies for object identification

We measured accuracy of object identification across illuminations on the basis of color cues. Four similarly shaped real objects, three of the same reflectance, were separated into pairs under distinct colored real lights. Observers were asked to pick the odd object. Correct and incorrect identifications formed systematic patterns that could not be explained by color-constancy, contrast-constancy, inverse-optics or neural-signal matching algorithms. The pattern of results were simulated by an algorithm that purposely made the incorrect assumption that color constancy holds, and used similarity between perceived object colors, along the difference vector between illuminant colors, to identify objects of the same reflectance across illuminants. The visual system may use this suboptimal strategy because the computational costs of an optimal strategy outweigh the benefits of more accurate performance.

Color constancy: phenomenal or projective?

Naive observers viewed a sequence of colored Mondrian patterns, simulated on a color monitor. Each pattern was presented twice in succession, first under one daylight illuminant with a correlated color temperature of either 16,000 or 4000 K and then under the other, to test for color constancy. The observers compared the central square of the pattern across illuminants, either rating it for sameness of material appearance or sameness of hue and saturation or judging an objective property-that is, whether its change of color originated from a change in material or only from a change in illumination. Average color constancy indices were high for material appearance ratings and binary judgments of origin and low for hue-saturation ratings. Individuals' performance varied, but judgments of material and of hue and saturation remained demarcated. Observers seem able to separate phenomenal percepts from their ontological projections of mental appearance onto physical phenomena; thus, even when a chromatic change alters perceived hue and saturation, observers can reliably infer the cause, the constancy of the underlying surface spectral reflectance.

Brightness and darkness as perceptual dimensions

A common-sense assumption concerning visual perception states that brightness and darkness cannot coexist at a given spatial location. One corollary of this assumption is that achromatic colors, or perceived grey shades, are contained in a one-dimensional (1-D) space varying from bright to dark. The results of many previous psychophysical studies suggest, by contrast, that achromatic colors are represented as points in a color space composed of two or more perceptual dimensions. The nature of these perceptual dimensions, however, presently remains unclear. Here we provide direct evidence that brightness and darkness form the dimensions of a two-dimensional (2-D) achromatic color space. This color space may play a role in the representation of object surfaces viewed against natural backgrounds, which simultaneously induce both brightness and darkness signals. Our 2-D model generalizes to the chromatic dimensions of color perception, indicating that redness and greenness (blueness and yellowness) also form perceptual dimensions. Collectively, these findings suggest that human color space is composed of six dimensions, rather than the conventional three.

Vision scientists have long adhered to the classic opponent-coding theory of vision, which states that bright–dark, red–green, and blue–yellow form mutually exclusive color pairs. According to this theory, it is not possible to see both brightness and darkness at a single spatial location, or an extended set of locations, such as a uniform surface. One corollary of this statement is that all perceivable grey shades vary along a continuum from bright to dark. At first glance, the notion that brightness and darkness cannot coexist on a single surface accords with our common-sense notion that a given grey shade cannot be simultaneously both brighter and darker than any other grey shade. The results presented here suggest that this common-sense notion is not supported by experimental data. Our results imply that a given grey shade can indeed be simultaneously brighter and darker than another grey shade. This seemingly paradoxical conclusion arises naturally if one assumes that brightness and darkness constitute the dimensions of a two-dimensional perceptual space in which points represent grey shades. Our results may encourage scientists working in related fields to question the assumption that perceptual variables, rather than sensory variables, are encoded in opponent pairs.

The relation between color discrimination and color constancy: when is optimal adaptation task dependent?

Color vision supports two distinct visual functions: discrimination and constancy. Discrimination requires that the visual response to distinct objects within a scene be different. Constancy requires that the visual response to any object be the same across scenes. Across changes in scene, adaptation can improve discrimination by optimizing the use of the available response range. Similarly, adaptation can improve constancy by stabilizing the visual response to any fixed object across changes in illumination. Can common mechanisms of adaptation achieve these two goals simultaneously? We develop a theoretical framework for answering this question and present several example calculations. In the examples studied, the answer is largely yes when the change of scene consists of a change in illumination and considerably less so when the change of scene consists of a change in the statistical ensemble of surface reflectances in the environment.

Color constancy in natural scenes explained by global image statistics

To what extent do observers' judgments of surface color with natural scenes depend on global image statistics? To address this question, a psychophysical experiment was performed in which images of natural scenes under two successive daylights were presented on a computer-controlled high-resolution color monitor. Observers reported whether there was a change in reflectance of a test surface in the scene. The scenes were obtained with a hyperspectral imaging system and included variously trees, shrubs, grasses, ferns, flowers, rocks, and buildings. Discrimination performance, quantified on a scale of 0 to 1 with a color-constancy index, varied from 0.69 to 0.97 over 21 scenes and two illuminant changes, from a correlated color temperature of 25,000 K to 6700 K and from 4000 K to 6700 K. The best account of these effects was provided by receptor-based rather than colorimetric properties of the images. Thus, in a linear regression, 43% of the variance in constancy index was explained by the log of the mean relative deviation in spatial cone-excitation ratios evaluated globally across the two images of a scene. A further 20% was explained by including the mean chroma of the first image and its difference from that of the second image and a further 7% by the mean difference in hue. Together, all four global color properties accounted for 70% of the variance and provided a good fit to the effects of scene and of illuminant change on color constancy, and, additionally, of changing test-surface position. By contrast, a spatial-frequency analysis of the images showed that the gradient of the luminance amplitude spectrum accounted for only 5% of the variance.

Frequency of metamerism in natural scenes

Estimates of the frequency of metameric surfaces, which appear the same to the eye under one illuminant but different under another, were obtained from 50 hyperspectral images of natural scenes. The degree of metamerism was specified with respect to a color-difference measure after allowing for full chromatic adaptation. The relative frequency of metameric pairs of surfaces, expressed as a proportion of all pairs of surfaces in a scene, was very low. Depending on the criterion degree of metamerism, it ranged from about 10(-6) to 10(-4) for the largest illuminant change tested, which was from a daylight of correlated color temperature 25,000 K to one of 4000 K. But, given pairs of surfaces that were indistinguishable under one of these illuminants, the conditional relative frequency of metamerism was much higher, from about 10(-2) to 10(-1), sufficiently large to affect visual inferences about material identity.

Color constancy in natural scenes with and without an explicit illuminant cue

Observers can generally make reliable judgments of surface color in natural scenes despite changes in an illuminant that is out of view. This ability has sometimes been attributed to observers' estimating the spectral properties of the illuminant in order to compensate for its effects. To test this hypothesis, two surface-color-matching experiments were performed with images of natural scenes obtained from high-resolution hyperspectral images. In the first experiment, the sky illuminating the scene was directly visible to the observer, and its color was manipulated. In the second experiment, a large gray sphere was introduced into the scene so that its illumination by the sun and sky was also directly visible to the observer, and the color of that illumination was manipulated. Although the degree of color constancy varied across this and other variations of the images, there was no reliable effect of illuminant color. Even when the sky was eliminated from view, color constancy did not worsen. Judging surface color in natural scenes seems to be independent of an explicit illuminant cue.

The proximity structure of achromatic surface colors and the impossibility of asymmetric lightness matching

In asymmetric lightness matching tasks, observers sometimes report that they cannot achieve satisfactory matches between achromatic surfaces under different neutral illuminants. The surfaces appear different, yet no further adjustment of either surface improves the match. There are evident difficulties in interpreting data from a task that the observer cannot always do, and these difficulties likely affect the interpretation of a large number of previous studies. We investigated, as an alternative to asymmetric matching, the direct use of proximity judgments in the study of surface lightness perception. We asked observers to rate the perceived dissimilarity of pairs of achromatic surfaces that were placed in identical scenes and viewed under different neutral illuminants. We develop a parametric model that accurately predicts perceived dissimilarity in terms of physical light intensities and surface albedos. The parameters of this model are readily interpretable. In particular, the ratio of the influence of changes in illuminant intensity and changes in surface albedo is a measure of the extent to which the observer discounts the illuminant. Asymmetric lightness matching can be interpreted as an unachievable limiting case of proximity judgment.

Do common mechanisms of adaptation mediate color discrimination and appearance? Uniform backgrounds

Color vision is useful for detecting surface boundaries and identifying objects. Are the signals used to perform these two functions processed by common mechanisms, or has the visual system optimized its processing separately for each task? We measured the effect of mean chromaticity and luminance on color discriminability and on color appearance under well-matched stimulus conditions. In the discrimination experiments, a pedestal spot was presented in one interval and a pedestal + test in a second. Observers indicated which interval contained the test. In the appearance experiments, observers matched the appearance of test spots across a change in background. We analyzed the data using a variant of Fechner's proposal, that the rate of apparent stimulus change is proportional to visual sensitivity. We found that saturating visual response functions together with a model of adaptation that included multiplicative gain control and a subtractive term accounted for data from both tasks. This result suggests that effects of the contexts we studied on color appearance and discriminability are controlled by the same underlying mechanism.

Minimalist surface-colour matching

Some theories of surface-colour perception assume that observers estimate the illuminant on a scene so that its effects can be discounted. A critical test of this interpretation of colour constancy is whether surface-colour matching is worse when the number of surfaces in a scene is so small that any illuminant estimate is unreliable. In the experiment reported here, observers made asymmetric colour matches between pairs of simultaneously presented Mondrian-like patterns under different daylights. The patterns had either 49 surfaces or a minimal 2 surfaces. No significant effect of number was found, suggesting that illuminant estimates are unnecessary for surface-colour matching.

Information limits on identification of natural surfaces by apparent colour

By adaptational and other mechanisms, the visual system can compensate for moderate changes in the colour of the illumination on a scene. Although the colours of most surfaces are perceived to be constant ('colour constancy'), some are not. The effect of these residual colour changes on the ability of observers to identify surfaces by their apparent colour was determined theoretically from high-resolution hyperspectral images of natural scenes under different daylights with correlated colour temperatures 4,300 K, 6,500 K, and 25,000 K. Perceived differences between colours were estimated with an approximately uniform colour-distance measure. The information preserved under illuminant changes increased with the number of surfaces in the sample, but was limited to a relatively low asymptotic value, indicating the importance of physical factors in constraining identification by apparent colour.

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.

Minimum-variance cone-excitation ratios and the limits of relational color constancy

Relational color constancy refers to the constancy of the perceived relations between the colors of surfaces of a scene under changes in the spectral composition of the illuminant. Spatial ratios of cone excitations provide a natural physical basis for this constancy, as, on average, they are almost invariant under illuminant changes for large collections of natural surfaces and illuminants. The aim of the present work was to determine, computationally, for specific surfaces and illuminants, the constancy limits obtained by the application of a minimum-variance principle to cone-excitation ratios and to investigate its validity in predicting observers' surface-color judgments. Cone excitations and their changes due to variations in the color of the illuminant were estimated for colored surfaces in simulated two-dimensional scenes of colored papers and real three-dimensional scenes of solid colored objects. For various test surfaces, scenes, and illuminants, the estimated levels of relational color constancy mediated by cone-excitation ratios varied significantly with the test surface and only with certain desaturated surfaces corresponded to ideal matches. Observers' experimental matches were compared with predictions expressed in CIE 1976 (u′,v′) space and were found to be generally consistent with minimum-variance predictions.

Colour constancy under simultaneous changes in surface position and illuminant

Two kinds of constancy underlie the everyday perception of surface colour: constancy under changes in illuminant and constancy under changes in surface position. Classically, these two constancies seem to place conflicting demands on the visual system: to both take into account the region surrounding a surface and also discount it. It is shown here, however, that the ability of observers to make surface-colour matches across simultaneous changes in test-surface position and illuminant in computer-generated 'Mondrian' patterns is almost as good as across changes in illuminant alone. Performance was no poorer when the surfaces surrounding the test surface were permuted, or when information from a potential comparison surface, the one with the highest luminance, was suppressed. Computer simulations of cone-photoreceptor activity showed that a reliable cue for making surface-colour matches in all experimental conditions was provided by the ratios of cone excitations between the test surfaces and a spatial average over the whole pattern.

Ecology and evolution of primate colour vision

More than one hundred years ago, Grant Allen suggested that colour vision in primates, birds and insects evolved as an adaptation for foraging on colourful advertisements of plants--fruits and flowers. Recent studies have shown that well developed colour vision appeared long before fruits and flowers evolved. Thus, colour vision is generally beneficial for many animals, not only for those eating colourful food. Primates are the only placental mammals that have trichromatic colour vision. This may indicate either that trichromacy is particularly useful for primates or that primates are unique among placental mammals in their ability to utilise the signals of three spectrally distinct types of cones or both. Because fruits are an important component of the primate diet, primate trichromacy could have evolved as a specific adaptation for foraging on fruits. Alternatively, primate trichromacy could have evolved as an adaptation for many visual tasks. Comparative studies of mammalian eyes indicate that primates are the only placental mammals that have in their retina a pre-existing neural machinery capable of utilising the signals of an additional spectral type of cone. Thus, the failure of non-primate placental mammals to evolve trichromacy can be explained by constraints imposed on the wiring of retinal neurones.

Protanopic observers show nearly normal color constancy with natural reflectance spectra

The ability of color-deficient observers to discriminate between illuminant changes and surface-reflectance changes in a scene was tested with natural and Munsell reflectance spectra. To avoid the confounding effects of spatial structure, stimuli were simulations of Mondrian-like colored patterns, presented on a computer-controlled color monitor. Protanopes performed less well than normal trichromats, regardless of the type of reflectance spectra, but they were least disadvantaged with patterns comprising reflectance spectra drawn from urban and rural scenes, more characteristic of the natural environment.