The ColorChecker dataset is one of the most widely used image sets for evaluating and ranking illuminant estimation algorithms. However, this single set of images has at least 3 different sets of ground-truth (i.e., correct answers) associated with it. In the literature it is often asserted that one algorithm is better than another when the algorithms in question have been tuned and tested with the different ground-truths. In this short correspondence we present some of the background as to why the 3 existing ground-truths are different and go on to make a new single and recommended set of correct answers. Experiments reinforce the importance of this work in that we show that the total ordering of a set of algorithms may be reversed depending on whether we use the new or legacy ground-truth data.

A robust and accurate hue descriptor that is useful in modeling human color perception and for computer vision applications is explored. The hue descriptor is based on the peak wavelength of a Gaussian-like function (called a wraparound Gaussian) and is shown to correlate as well as CIECAM02 hue to the hue designators of papers from the Munsell and Natural Color System color atlases and to the hue names found in Moroney's Color Thesaurus. The new hue descriptor is also shown to be significantly more stable under a variety of illuminants than CIECAM02. The use of wraparound Gaussians as a hue model is similar in spirit to the use of subtractive Gaussians proposed by Mizokami et al., but overcomes many of their limitations.

Illumination estimation is an important component of color constancy and automatic white balancing. A number of methods of combining illumination estimates obtained from multiple subordinate illumination estimation methods now appear in the literature. These combinational methods aim to provide better illumination estimates by fusing the information embedded in the subordinate solutions. The existing combinational methods are surveyed and analyzed here with the goals of determining: 1) the effectiveness of fusing illumination estimates from multiple subordinate methods; 2) the best method of combination; 3) the underlying factors that affect the performance of a combinational method; and 4) the effectiveness of combination for illumination estimation in multiple-illuminant scenes. The various combinational methods are categorized in terms of whether or not they require supervised training and whether or not they rely on high-level scene content cues (e.g., indoor versus outdoor). Extensive tests and enhanced analyzes using three data sets of real-world images are conducted. For consistency in testing, the images were labeled according to their high-level features (3D stages, indoor/outdoor) and this label data is made available on-line. The tests reveal that the trained combinational methods (direct combination by support vector regression in particular) clearly outperform both the non-combinational methods and those combinational methods based on scene content cues.

A new algorithm for calculating the metamer mismatch volumes that arise in colour vision and colour imaging is introduced. Unlike previous methods, the proposed method places no restrictions on the set of possible object reflectance spectra. As a result of such restrictions, previous methods have only been able to provide approximate solutions to the mismatch volume. The proposed new method is the first to characterize precisely the metamer mismatch volume for any possible reflectance.

A new multilinear constraint on the color of the scene illuminant based on the dichromatic reflection model is proposed. The formulation avoids the problem, common to previous dichromatic methods, of having to first identify pixels corresponding to the same surface material. Once pixels from two or more materials have been identified, their corresponding dichromatic planes can be intersected to yield the illuminant color. However, it is not always easy to determine which pixels from an arbitrary region of an image belong to which dichromatic plane. The image region may cover an area of the scene encompassing several different materials and, hence, pixels from several different dichromatic planes. The new multilinear constraint accounts for this multiplicity of materials and provides a mechanism for choosing the most plausible illuminant from a finite set of candidate illuminants. The performance of this new method is tested on a database of real images.

A new multilinear constraint on the color of the scene illuminant based on the dichromatic reflection model is proposed. The formulation avoids the problem, common to previous dichromatic methods, of having to first identify pixels corresponding to the same surface material. Once pixels from two or more materials have been identified, their corresponding dichromatic planes can be intersected to yield the illuminant color. However, it is not always easy to determine which pixels from an arbitrary region of an image belong to which dichromatic plane. The image region may cover an area of the scene encompassing several different materials and hence pixels from several different dichromatic planes. The new multilinear constraint accounts for this multiplicity of materials and provides a mechanism for choosing the most plausible illuminant from a finite set of candidate illuminants. The performance of this new method is tested on a database of real images. 1

A new color correction method is introduced which predicts how changing the color of the scene illuminant will affect a camera's RGB response. Like diagonal transformation color correction methods, the new method requires only 3-parameters. It therefore requires only the RGB color of the two illuminants be known. The method models the 9-parameters of a 3-by-3 linear transformation using a 3-dimensional linear model composed of 3 basis transformations. Experiments show that the method works better than the standard diagonal model unless the camera sensors are very sharply peaked, in which case the performance is essentially unchanged.

We introduce a context for testing computational color constancy, specify our approach to the implementation of a number of the leading algorithms, and report the results of three experiments using synthesized data. Experiments using synthesized data are important because the ground truth is known, possible confounds due to camera characterization and pre-processing are absent, and various factors affecting color constancy can be efficiently investigated because they can be manipulated individually and precisely. The algorithms chosen for close study include two gray world methods, a limiting case of a version of the Retinex method, a number of variants of Forsyth's gamut-mapping method, Cardei et al.'s neural net method, and Finlayson et al.'s color by correlation method. We investigate the ability of these algorithms to make estimates of three different color constancy quantities: the chromaticity of the scene illuminant, the overall magnitude of that illuminant, and a corrected, illumination invariant, image. We consider algorithm performance as a function of the number of surfaces in scenes generated from reflectance spectra, the relative effect on the algorithms of added specularities, and the effect of subsequent clipping of the data. All data is available on-line at http://www.cs.sfu.ca/(tilde)color/data, and implementations for most of the algorithms are also available (http://www.cs.sfu.ca/(tilde)color/code).

We test a number of the leading computational color constancy algorithms using a comprehensive set of images. These were of 33 different scenes under 11 different sources representative of common illumination conditions. The algorithms studied include two gray world methods, a version of the Retinex method, several variants of Forsyth's gamut-mapping method, Cardei et al.'s neural net method, and Finlayson et al.'s Color by Correlation method. We discuss a number of issues in applying color constancy ideas to image data, and study in depth the effect of different preprocessing strategies. We compare the performance of the algorithms on image data with their performance on synthesized data. All data used for this study are available online at http://www.cs.sfu.ca/(tilde)color/data, and implementations for most of the algorithms are also available (http://www.cs.sfu.ca/(tilde)color/code). Experiments with synthesized data (part one of this paper) suggested that the methods which emphasize the use of the input data statistics, specifically color by correlation and the neural net algorithm, are potentially the most effective at estimating the chromaticity of the scene illuminant. Unfortunately, we were unable to realize comparable performance on real images. Here exploiting pixel intensity proved to be more beneficial than exploiting the details of image chromaticity statistics, and the three-dimensional (3-D) gamut-mapping algorithms gave the best performance.

Color casts occur in all forms of digital color imagery. Although they usually arise from a mismatch between the chromaticity of the scene illumination and the illumination for which the imaging system was color balanced some situations provide more of a challenge for color constancy methods than others. In the case of digital cameras, for example, the spectral sensitivity of the camera can be measured and hence taken into account when color balancing its images. Also the camera data can be linearized. On the other hand, for digitally scanned film many things are likely to be unknown, including film type, film dye lot, spectral response of the film, film exposure, and film nonlinearity. In addition, many of the relevant scanner characteristics may be hard to ascertain. For an image obtained on the Web, generally nothing is known about its origin; nonetheless, a human observer will quickly notice any error in color balance. This paper discusses the problems of correcting the color in digital color images of various origins and the color constancy methods developed in response to them.

Illumination is rarely constant in intensity or color throughout a scene. Multiple light sources with different spectra-sun and sky, direct and interreflected light-are the norm. Nonetheless, almost all color constancy algorithms assume that the spectrum of the incident illumination remains constant across the scene. We assume the converse, that illumination does vary, in developing a new algorithm for color constancy. Rather than creating difficulties, varying illumination is in fact a very powerful constraint. Indeed tests of our algorithm using real images of an office scene show excellent results.>

Objects can be recognized on the basis of their color alone by color indexing, a technique developed by Swain-Ballard (1991) which involves matching color-space histograms. Color indexing fails, however, when the incident illumination varies either spatially or spectrally. Although this limitation might be overcome by preprocessing with a color constancy algorithm, we instead propose histogramming color ratios. Since the ratios of color RGB triples from neighboring locations are relatively insensitive to changes in the incident illumination, this circumvents the need for color constancy preprocessing. Results of tests with the new color-constant-color-indexing algorithm on synthetic and real images show that it works very well even when the illumination varies spatially in its intensity and color.>

Many standard computer vision algorithms for shape from shading, optical flow, color constancy or surface reconstruction depend upon the solution of Poisson equations. Using retinex lightness computation as an example, it is shown how these algorithms can be dramatically sped up using a varying resolution sensor, so long as the sensor architecture is based on a conformal mapping. The varying resolution lightness algorithm is developed by the technique of using a conformal transplant. In the final analysis, very little of the algorithm needs to be changed, but a speed up in running time of roughly 50 times is obtained, even though the total amount of data is reduced by only a factor of 28. The speed increases at the expense of peripheral resolution.>

The main result is to show that under the conditions imposed by the Maloney-Wandell color constancy algorithm, color constancy can be expressed in terms of a simple independent adjustment of the sensor responses, so long as the sensor space is first transformed to a new basis. The overall goal is to present a theoretical analysis connecting many established theories of color constancy. For the case where surface reflectances are two-dimensional and illuminants are three-dimensional, it is proved that perfect color constancy can always be solved for by an independent adjustment of sensor responses, which means that the color constancy transform can be expressed as a diagonal matrix. In addition to purely theoretical arguments, results from simulations of diagonal-matrix-based color constancy, in which the spectra of real illuminants and reflectances along with the human cone sensitivity functions were used, are presented. The simulations demonstrate that when the cone sensor space is transformed to its new basis in the appropriate manner, a diagonal matrix supports close to optimal color constancy.>

Mutual illumination occurs when light reflected from one surface impinges on a second one. The resulting additional illumination incident on the second surface affects both the color and intensity of the light reflected from it. As a consequence, the image of a surface in the presence of mutual illumination differs from what it otherwise would have been in the absence of mutual illumination. Unaccounted for mutual illumination can easily confuse methods that rely on intensity or color such as shape-from-shading or color-based object recognition. In this correspondence, we introduce an algorithm that removes mutual illumination effects from images. The domain is that of previously-segmented images of convex surfaces of uniform color and diffuse reflectance where for each surface the interreflection occurs mainly from one other surface and can be accurately accounted for within a one-bounce model. The algorithm is based on a singular value decomposition of the colors coming from each surface. Geometrical information about where on the surface the colors emanate from is not required. The RGB triples from a single convex surface experiencing interreflection fall in a plane; intersecting the planes generated from two interreflecting surfaces results in a unique interreflection color. Each pixel can then be factored into its interreflection and no-interreflection components so that a complete no-interreflection image is produced.>

Light reflected from one surface onto a second surface changes both the intensity and spectral power distribution of light leaving the second surface. Similarly, light from the second surface illuminates the first. This mutual reflection effect can be exploited by examining pixels where interreflection is and is not present. From these measurements several intrinsic properties can be determined: the reflectance of each surface, the spectral power distribution of the incident illumination, and some constraints on the physical configuration of the two surfaces. The authors use finite dimensional linear models for the ambient illumination and for surface spectral reflectance, with m basis functions for illumination and n for surfaces. Examining p sensor values (e.g. RGB values) they find that if p satisfies the condition p>or=(2n+m)/3 they can solve for finite dimensional model descriptors of both surfaces and of the ambient illumination, as well as for a form-factor stemming from the surface configuration. With n=m=3, p can also be 3. A single-bounce model of mutual reflection accounts for the most important contribution to light intensity in an interreflecting geometry.>

A separation algorithm for achieving color constancy and theorems concerning its accuracy are presented. The algorithm requires extra information, over and above the usual three values mapping human cone responses, from the optical system. However, with this additional information-specifically, a sampling across the visible range of the reflected, color-signal spectrum impinging on the optical sensor-the authors are able to separate the illumination spectrum from the surface reflectance spectrum contained in the color-signal spectrum which is, of course, the product of these two spectra. At the heart of the separation algorithm is a general statistical method for finding the best illumination and reflectance spectra, within a space represented by finite-dimensional linear models of statistically typical spectra, whose product closely corresponds to the spectrum of the actual color signal. Using this method, the authors are able to increase the dimensionality of the finite-dimensional linear model for surfaces to a realistic value. One method of generating the spectral samples required for the separation algorithm is to use the chromatic aberration effects of a lens. An example of this is given. The accuracy achieved in a large range of tests is detailed, and it is shown that agreement with actual surface reflectance is excellent.>

The authors combine an alternate version of B.K.P. Horn's computation (1974) for recovering lightness from Land's retinex scheme, as modified by A. Blake (1985), with a finite-dimensional linear model for color images. The authors recover surface spectral reflectance from images of near-Mondrian scenes by using edge detection and derivatives to screen out slowly changing illumination from color scene images. They first develop a model for lightness recovery, based on Horn's, because a similar treatment is needed for the FDM case (a particular finite-dimensional linear model). Based on the equations for the one-dimensional case, they develop a model of surface reflectance recovery for near-Mondrian images by extending the basic approach to the vector model of illumination, reflectance, and receptors.>

Color constancy can be achieved by analyzing the chromatic aberration in an image.Chromatic aberration spatially separates light of different wavelengths and this allows the spectral power distribution of the light to be extracted.This is more information about the light than is registered by the cones of the human visual system or by a color television camera; and, using it, we show how color constancy, the separation of reflectance from illumination, can be achieved.As examples, we consider grey-level images of(a) a colored dot under unknown illumination, and (b) an edge between two differently colored regions under unknown illumination.Our first result is that in principle we can determine completely the spectral power distribution of the reflected light from the dot or, in the case of the color edge, the difference in the spectral power distributions of the light from the two regions.By employing a finite-dimensional linear model of illumination and surface reflectance, we obtain our second result, which is that the spectrum of the reflected light can be uniquely decomposed into a component due to the illuminant and another component due to the surface reflectance.This decomposition provides the complete spectral reflectance function, and hence color, of the surface as well as the spectral power distribution of the illuminant.Up to the limit of the accuracy of the finite-dimensional model, this effectively solves the color constancy problem.

Abstract Parallel processing algorithms have been developed which approach real‐time in displaying raster graphics images of a single rotating three‐dimensional object. The hardware required consists of a large number of individual processors with inter‐processor communication restricted to immediate neighbours. The overall structure is as if the processors were spread uniformly over the surface of a sphere. The objects for display are modelled as if they were inside this sphere of processors. Each processor stores the following information: the intersection points of the object's surface with a radial line extended from the sphere's centre along with the surface normals at those intersection points, and pixels representing a small section of the screen. The algorithm involves an organised message‐passing scheme to accomplish rotations of the object description and the subsequent display of the image. A simulation of a system involving several hundred processors indicates that its performance improves as a near‐linear function of the number of processors.