Illuminant Estimation using constrained Minkowski norms

Colour constancy algorithms attempt to estimate and then remove the colour of the prevailing illuminant. Since, only when this is done, can image colour be used as a cue for reflectance and so usefully subserve tasks such as tracking and recognition. Broadly speaking, there are two ways to estimate the illuminant. First, we might calculate a simple statistic, such as the mean, from the image and argue that this should correlate with light colour. Second, we incorporate physical knowledge and probabilistic inference to arrive at the estimate. The latter approach results in significantly better performance though, often at significant computational cost. In this paper we present a simple statistical approach which, given only knowledge of the RGBs of typical lights, results in performance close to that delivered by more complex algorithms. The paper begins with the observation that the two simplest statistical estimators, the mean and max RGB responses, are respectively the L1 and Linfinity norms. We show then that an LP norm might also be used as an estimator. The theory is then developed to allow a prior constraint to be placed on the illuminant (natural and artificial lights are often bluish, whitish and yellowish but are rarely purple). Experiments on the Simon Fraser calibrated data set show that the illuminant can be reliably estimated using a constrained L4 norm. Moreover, performance is comparable to the most advanced methods