Department of Electrical and Computer Engineering Ph.D. Public Defense
Gamut and Color Color for Multiprimary Displays: Theory and Applications
Carlos Eduardo Rodriguez Pardo
Supervised by Professor Gaurav Sharma
Tuesday, July 13, 2021
Multiprimary displays, i.e., display systems with four or more primaries, offer two key advantages over traditional three-primary displays: multiprimary displays can enlarge the gamut, i.e., the range of colors that can be rendered using additive combinations of the primaries with modulated intensities; and multiprimary displays may render a color using multiple alternative primary combinations. Such flexibility can be exploited for optimizing display performance, motivating the characterization of the gamut and the flexibility avail- able for color control. Despite the advantages, additional primaries also bring challenges for color management. Color management for a multiprimary display requires the determination of a color control function (CCF) that specifies control vectors, i.e., vectors of the relative intensities of the primaries, for reproducing each color in the gamut. Multiprimary displays offer alternative choices of CCFs, which render colors identically under ideal conditions. 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.
This thesis advances theory required for multiprimary display modeling, design, and color management, by providing (1) a unified and comprehensive framework for the characterization of the gamut and color control for multiprimary displays and (2) a framework for analyzing and optimizing CCFs for robustness against primary and observer variations. Observing that the gamut of multiprimary displays is known to be a zonotope, we develop a complete, cohesive, and directly usable mathematical characterization of the geometry of the multiprimary gamut zonotope that immediately identifies the surface facets, edges, and vertices and provides a parallelepiped tiling of the gamut. We provide a complete characterization of the metameric control set (MCS), i.e., the set of control vectors that reproduce a given color on the display. Specifically, we show that MCS is a convex polytope whose vertices are control vectors obtained from (parallelepiped) tilings of the gamut, i.e., the range of colors that the display can produce. The mathematical framework that we develop: (a) characterizes gamut tilings in terms of fundamental building blocks called facet spans, (b) establishes that the vertices of the MCS are fully characterized by the tilings of the gamut, and (c) introduces a methodology for the efficient enumeration of gamut tilings. The framework reveals the fundamental inter-relations between the geometry of the MCS and the geometry of the gamut, and provides insight into alternative strategies for color control. We demonstrate several applications of the framework we develop and highlight how our work connects with and furthers the study of three-dimensional zonotopes, providing new approaches for describing the geometry and the tilings of broad class of zonotopes in R3, and computational results for the enumeration of tilings.
Next, 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. We develop an algorithm for numerically computing optimal CCFs under the proposed variational formulation, and use it to determine optimal CCFs for several multiprimary display systems. The variationally optimal CCFs obtained using the proposed approach offer improvements over alternatives CCFs, as assessed visually and via quantitative metrics measuring smoothness and gray-axis invariance in the presence of primary variations.