Basic mathematics of color space invariants

Abstract

Color management in printing processes has been traditionally based on an analysis of the behavior of tone reproduction curves (TRC) calculated for the initial color channels. The tone curves, as well as, the color channels, are considered separately. This approach does not take into account the mutual influence of colorants when they overlap. We propose replacing two-dimensional tone reproduction curves with three-dimensional gradation trajectories in the CIE Lab metric space. When two colors overlap, one considers the space between two gradation trajectories that forms a gradation surface. These objects are described using the apparatus of differential geometry of spatial curves and surfaces, respectively, and are also invariants of color spaces. In this paper, we offer their analytical description. © 2020 World Scientific and Engineering Academy and Society. All rights reserved.