Color Control Functions for Multiprimary Displays I: Robustness Analysis and Optimization Formulations.

Color management for a multiprimary display requires, as a fundamental step, the determination of a color control function (CCF) that specifies control values for reproducing each color in the display's gamut. Multiprimary displays offer alternative choices of control values for reproducing a color in the interior of the gamut and accordingly alternative choices of CCFs. Under ideal conditions, alternative CCFs render colors identically. However, deviations in the spectral distributions of the primaries and the diversity of cone sensitivities among observers impact alternative CCFs differently, and, in particular, make some CCFs prone to artifacts in rendered images. We develop a framework for analyzing robustness of CCFs for multiprimary displays against primary and observer variations, incorporating a common model of human color perception. Using the framework, we propose analytical and numerical approaches for determining robust CCFs. First, via analytical development, we: (a) demonstrate that linearity of the CCF in tristimulus space endows it with resilience to variations, particularly, linearity can ensure invariance of the gray axis, (b) construct an axially linear CCF that is defined by the property of linearity over constant chromaticity loci, and (c) obtain an analytical form for the axially linear CCF that demonstrates it is continuous but suffers from the limitation that it does not have continuous derivatives. Second, to overcome the limitation of the axially linear CCF, we motivate and develop two variational objective functions for optimization of multiprimary CCFs, the first aims to preserve color transitions in the presence of primary/observer variations and the second combines this objective with desirable invariance along the gray axis, by incorporating the axially linear CCF. A companion Part II paper, presents an algorithmic approach for numerically computing optimal CCFs for the two alternative variational objective functions proposed here and presents results comparing alternative CCFs for several different 4,5, and 6 primary designs.