Recovery of spectral sensitivity functions from a colour chart image under unknown spectrally smooth illumination

This paper proposes a method to approximate the camera spectral sensitivity functions from a single colour image of a colour chart under an unknown illumination spectrum. Here we assume that the scene illumination has a smooth spectral variation. Although the original problem is rather ill-posed, we reformulate it as a well-posed optimisation one by introducing several constraints. The first constraint concerns with the smoothness of the illuminant power spectrum. The second one is based on the fact that the spectral sensitivity function of a digital camera should be constrained to a linear subspace according to Luther condition. The third constraint limits the influence of bands with low signal-to-noise ratios. By introducing these constraints, we can solve the problem in a coordinate-descent optimisation manner. We validate our method using data acquired from over 40 commercial camera models and compare with an alternative in the literature. We also demonstrate the utility of the estimated colour matching functions for colour simulation and colour transfer.