Computational Color Constancy

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Background

A generic image acquired by a digital camera is mainly characterized by three physical factors: the illuminant spectral power distribution I(λ), the surface spectral reflectance S(λ) and the spectral sensitivities C(λ) of the sensor. Using this notation, the sensor responses at the spatial point with coordinates (x,y) can be then described as:

(1) where ω is the wavelength range of the visible spectrum, ρ and C(λ) are three-component vectors (Figure 1). Since the three spectral sensitivities of the sensor C(λ) are usually respectively more sensitive to low, medium and high wavelengths, the three-component vector of the sensor response ρ = (ρ₁, ρ₂, ρ₃)is also referred to as the sensor or camera raw RGB = (R, G, B) triplet.

Assuming that the color I of the illuminant in the scene observed by the camera only depends on the illuminant spectral power distribution I(λ) and on the spectral sensitivities C(λ) of the sensor, color constancy is equivalent to the estimation of I by:

(2) given only the sensor responses ρ(x,y) across the image. This is an under-determined problem and therefore cannot be solved without further assumptions and/or knowledge, such as some information about the camera being used, and/or assumptions about the statistical properties of the expected illuminants and surface reflectances. From a computational perspective, once the illuminant has been estimated, the image colors can be corrected on the basis of this estimate. The correction generates a new image of the scene as if it was taken under a known canonical illuminant (see Figure 2). The estimation of the color of the illuminant could be performed if an achromatic patch is present in the image. This is because the spectral reflectance S(λ) of an achromatic surface is approximately constant over a wide range of wavelengths, and thus the sensor response 𝛒 is proportional to I, i.e. the RGB of the achromatic patch is proportional to that of the incident light.