Abstract
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 socalled 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 nonlinear methods. However, the derivation of this result leads to some interesting mathematical insights which point to how a maximumignorance type approach can be followed.
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 nonlinear methods. However, the derivation of this result leads to some interesting mathematical insights which point to how a maximumignorance type approach can be followed.
Original language  English 

Title of host publication  Proceedings of 13th AIC Congress 2017 
Place of Publication  Jeju, Korea 
Publisher  Korea Society of Color Studies 
ISBN (Print)  9788957082768 
Publication status  Published  16 Oct 2017 
Profiles

Graham Finlayson
 School of Computing Sciences  Professor of Computing Science
 Colour and Imaging Lab  Member
Person: Research Group Member, Academic, Teaching & Research