Error-less colour correction

Colour correction is the problem of mapping device dependent RGBs to standard CIE XYZs. Traditionally it is solved for by an error minimising one-to-one linear transform. However this problem is ill-posed. There exist multiple reflectances, known as metamers, which induce the same RGB but different XYZs (and vice versa). In this paper, we propose that this ill-posedness might be viewed positively. Indeed, that it leads to an error-less transform for colour correction. We propose that a mapping is error-less if it takes an RGB to an XYZ such that there exists a real reflectance spectrum which integrates to this RGB-XYZ pair. We show how we can solve for a mapping which satisfies this error-less criterion. As in previous studies, we seek a linear transform that is error-less. We show that we can solve for such a transform by quadratic programming. Experiments demonstrate 3 important results. First, that a linear least squares transform is not error-less. Specifically, saturated RGB-XYZ pairs do not correspond to a plausible reflectance. Second, there exists a linear transform that is error-less. Finally, that the best error-less transform performs almost as well as least-squares, but substantially better for saturated colours. It is possible to map RGB to XYZ with zero error.