Color device calibration is the process of achieving and maintaining a desired color response. For printers, calibration is typically achieved via 1-D tone reproduction `curves (TRCs) applied to each of C, M, Y and K colorant channels. This however, can be severely restrictive in the amount of control. For example, 1-D TRCs can be designed for either gray-balance or smooth rendition of individual color ramps, but not both. To enable complete control, 3- D/4-D color transforms may be used but they are at odds with the goal of calibration being a lightweight transform with respect to measurement and computation. In 2004, Bala et al. proposed two-dimensional (2-D) calibration to facilitate a superior cost vs. control trade-off. In this paper, we view the design of cost-effective calibration transforms as a dimensionality reduction problem. We observe that the quality of the transform, i.e. its ability to match a true higher-dimensional (4-D) transform, depends on both the projection operator applied to high-dimensional device inputs, and the functional approximation built out of the reduced dimension variables. With that view, we develop techniques to significantly enhance the accuracy of previously proposed 2-D calibration transforms. In particular, we develop 2-D color transforms that allow complete control of cleverly selected 2-D planes in the 3-D CMY cube. We also develop a novel 2-D calibration LUT for the K channel which exploits the knowledge of printer GCR strategy to improve rendition of dark colors. Experimental results show vastly improved calibration ability particularly for the case of calibrating multiple devices to a common colorimetric aim.
Vishal Monga, Raja Bala, "Two-dimensional color correction: Recent advances" in Proc. IS&T 15th Color and Imaging Conf., 2007, pp 48 - 53, https://doi.org/10.2352/CIC.2007.15.1.art00010