Maximum Ignorance Polynomial Colour Correction

In colour correction, we map the RGBs captured by a camera to human visual system referenced colour coordinates including sRGB and CIE XYZ. Two of the simplest methods reported are linear and polynomial regression. However, to obtain optimal performance using regression – especially for a polynomial based method - requires a large corpus of training data and this is time consuming to obtain. If one has access to device spectral sensitivities, then an alternative approach is to generate RGBs synthetically (we numerically generate camera RGBs from measured surface reflectances and light spectra). Advantageously, there is no limit to the number of training samples we might use. In the limit – under the so-called maximum ignorance with positivity colour correction - all possible colour signals are assumed.

In this work, we revisit the maximum ignorance idea in the context of polynomial regression. The formulation of the problem is much trickier, but we show – albeit with some tedious derivation – how we can solve for the polynomial regression matrix in closed form. Empirically, however, this new polynomial maximum ignorance regression delivers significantly poorer colour correction performance compared with a physical target based method. So, this negative result teaches that the maximum ignorance technique is not directly applicable to non-linear methods. However, the derivation of this result leads to some interesting mathematical insights which point to how a maximum-ignorance type approach can be followed.