Convex Programming Colour Constancy with a Diagonal Offset Model

Gamut mapping colour constancy algorithms attempt to map image RGBs captured under an unknown light to corresponding RGBs under a reference light so as to render images colour constant. While the approach often works well, for a significant number of real images the algorithm delivers a solution. We show that the solution problem arises because of a failure of the diagonal model of illumination change on which the algorithm is based. We address the problem by proposing a new diagonal-offset model which has 6 rather than 3 parameters and which is able therefore to deal with a wider range of imaging conditions. Based on this model we formulate a convex programming solution to colour constancy and we show (by testing on real images) that the new algorithm is robust to the failures of the diagonal model and is capable of delivering very good colour constancy.