To accurately predict the response of colour devices such as digital cameras to spectral stimuli their spectral sensitivities need to be known. In this paper we present a simple, flexible method for characterising such devices, based on a single image of aMacbeth Color Checker Chart.We begin by showing that device RGBs are linearly related to the Macbeth reflectances and that this linear relationship is defined by the spectral sensitivities of the device. It follows then that it should be possible to solve for these sensitivities by linear regression. However, this simple idea does notwork well in practice - recovered sensitivities are very different from the actual device sensitivities.The simple regression fails because the Macbeth reflectance set has limited dimensionality and so the regression is highly sensitive to image noise. To overcome this problem we incorporate a number of natural constraints: positivity, modality, and band-limitedness into the regression formulation. Each constraint can be written as a linear inequality and so solving for device sensitivities by this constrained regression is a quadratic programming problem. Posing the problem in this form, we can search for the sensors which best fit the data, quickly and efficiently, by trying different combinations of the linear constraints.The results of performing this constrained regression on a number of colour devices are presented here. In all cases our new technique recovers sensors which are very close to the actual device sensitivities and we are confident that these results will extrapolate to other colour devices.
Graham D. Finlayson, Steven Hordley, Paul M. Hubel, "Recovering Device Sensitivities with Quadratic Programming" in Proc. IS&T 6th Color and Imaging Conf., 1998, pp 90 - 95, https://doi.org/10.2352/CIC.1998.6.1.art00020