Most of the work in computational color recognition under varying illumination has been in the area of color constancy, the goal of which is to match object colors under varying illumination without knowing the spectral composition of either the incident light or the surface reflectance; the general approach is to recover an illuminant-invariant measure of surface reflectance by first determining the properties of the illuminant.
Depending on their assumptions and techniques, color constancy algorithms can be divided into the following six categories : (1) those which make assumptions about the statistical distribution of surface colors in the scene, (2) those which make assumptions about the types of reflection and illumination, (3) those assuming a fixed image gamut, (4) those which obtain an indirect measure of the illuminant, (5) those which require multiple illuminants, and finally, (6) those which require the presence of surfaces of known reflectance in the scene.
Among the algorithms that make assumptions about the statistical distributions of surface colors in the scene, Buchsbaum  assumes that the average of the surface reflectances over the entire scene is gray (the gray-world assumption); Gershon  assumes that the average scene reflectance matches that of another known color; Vrhel  assumes knowledge of the general covariance structure of the illuminant, given a small set of illuminants, and Freeman  assumes that the illumination and reflection in a scene follow known probability distributions. These methods are effective when the distribution of colors within the scene follows the assumed model or distribution.
The second set of color constancy algorithms make assumptions about the dimensionality of spectral basis functions  required to accurately model illumination and surface reflectance. For instance, Maloney  and Yuille  assume that the linear combination of two basis functions is sufficient. Under the assumption, the variation in surface color in a three-dimensional color space would follow a plane. Note that these assumptions are true only under specifically controlled illumination.
Among the algorithms that make assumptions about image gamuts is Forsyth's CRULE (coefficient rule) algorithm , which maps the gamut of possible image colors to another gamut of colors that is known a-priori, so that the number of possible mappings restricts the set of possible illuminants. In a variation of this algorithm, Finlayson  applies a spectral sharpening transform to the sensory data in order to relax the gamut constraints. The assumptions about gamut-mapping restrict the application of CRULE to matte Mondrian surfaces under controlled illumination and fixed orientation. Ohta  assumes a known gamut of illuminants (controlled indoor lighting that lies on some points along the CIE model), and uses multi-image correspondence to determine the specific illuminant from the known set. By restricting the illumination, this method is applied to synthetic or indoor images.
Another class of algorithms uses an indirect measure of the illumination. For instance, Shafer , Klinker  and Lee  use surface specularities (Sato  uses a similar principle, but not for color constancy); similarly, Funt  uses inter-reflections to measure the illuminant. These methods are based on the assumption of a single point-source illuminant.
In yet another approach, D'Zmura and Finlayson  require light from multiple illuminants incident upon the multiple instances of a single surface in the same scene. These approaches require identification of the same surface in two spatially distinct parts of the image that are subject to different illuminants. The methods have been shown to be effective on Mondrian images.
The final group of color constancy algorithms assumes the presence of surfaces of known reflectance in the scene and then determine the illuminant. For instance, Land's Retinex algorithm  and its many variations require the presence of a surface of maximal (white) reflectance within the scene. Similarly, Novak's supervised color constancy algorithm  requires surfaces of other known reflectances.