Solving for colour constancy using a constrained dichromatic reflection model

Statistics-based colour constancy algorithms work well as long as there are many colours in a scene, they fail however when the encountering scenes co mprise few surfaces. In contrast, physics-based algorithms, based on an und erstanding of physical processes such as highlights and interreflections, a re theoretically able to solve for colour constancy even when there are as few as two surfaces in a scene. Unfortunately, physics-based theories rarel y work outside the lab. In this paper we show that a combination of physica l and statistical knowledge leads to a surprisingly simple and powerful col our constancy algorithm, one that also works well for images of natural sce nes. From a physical standpoint we observe that given the dichromatic model of i mage formation the colour signals coming from a single uniformly-coloured s urface are mapped to a line in chromaticity space. One component of the lin e is defined by the colour of the illuminant (i.e. specular highlights) and the other is due to its matte, or Lambertian, reflectance. We then make th e statistical observation that the chromaticities of common light sources a ll follow closely the Planckian locus of black-body radiators. It follows t hat by intersecting the dichromatic line with the Planckian locus we can es timate the chromaticity of the illumination. We can solve for colour consta ncy even when there is a single surface in the scene. When there are many s urfaces in a scene the individual estimates from each surface are averaged together to improve accuracy. In a set of experiments on real images we show our approach delivers very g ood colour constancy. Moreover, performance is significantly better than pr evious dichromatic algorithms.