Color Control Functions for Multiprimary Displays II: Variational Robustness Optimization.

In a companion Part I paper, we presented a framework for analyzing robustness of color control functions (CCFs) for multiprimary displays against primary and observer variations and proposed a variational minimization for obtaining robust CCFs. The objective function proposed in the Part I paper combines two nonnegative terms that serve as useful figures of merit for quantitatively characterizing CCFs. The first term measures lack of smoothness of the CCFs and characterizes how well transitions in perceptual color space are preserved in the presence of the primary/observer variations. The second term measures deviation of the CCF, in the vicinity of the gray axis, from a specific axially linear CCF that provides perceptual invariance to the variations along the gray axis. In this paper, using calculus of variations, we develop an algorithm for numerically computing optimal CCFs under the proposed variational formulation. Using the proposed algorithm, we determine optimal CCFs for a several multiprimary display designs and assess and compare their performance against alternative approaches. The variationally optimal CCFs obtained using the proposed approach offer improvements over the alternatives, as assessed visually and via quantitative metrics measuring smoothness and invariance in the presence of primary variations. The relative improvements provided by the proposed CCF increase with increasing number of primaries.