The maximum ignorance assumption with positivity

Abstract

Color devices are not colorimetric. It follows then that some color correction must be done to map device RGBs to XYZ's. One common correction method involves finding the linear transform which takes device spectral sensitivities as close to the XYZ color matching curves as possible (in the least-squares sense). Thereafter, this transform is used to map device RGBs to XYZs. It is well known that this procedure is statistically justified so long as one assumes that all spectra with positive and negative power are equally likely to occur i.e., so long as one is maximally ignorant about the world. In this paper we point out that the maximally ignorant stance is unjustified since spectra with negative power cannot physically occur. This leads us to develop the notion of maximal ignorance with positivity i.e., we assume that all spectra which are everywhere all positive are equally likely. We demonstrate that this new maximal ignorance stance delivers considerable benefits in terms of improved color correction.