Inverse display characterization: A two-step parametric model for digital displays Laurent Blondé Jürgen Stauder Bongsun Lee Abstract — A simple additivity model is often used as a basic model for digital-display charac- terization. However, such a simple model cannot satisfy the needs of demanding color-management applications all the time. On the other hand, systematic sampling of the color space and 3-D interpo- lation is an expensive method in terms of measurement and computation time when precision is needed. This paper presents an enhanced method to characterize the XYZ-to-RGB transform of a digi- tal display. This parametric method exploits the independence between the luminance variation of the electro-optic response and the colorimetric responses for certain display types. The model is gen- erally applicable to digital displays, including 3-DMD projectors, single DMDs, CRTs, LCDs, etc., if the independence condition is satisfied. While the problem to solve is a 3-D–to–3-D transformation (from XYZ to RGB), the proposed parametric model is the composition of a 2-D transform followed by a 1-D transform. The 2-D transform manages the chromatic aspects and, in succession, the 1-D transform manages the luminance variations. This parametric digital model is applicable in the field of color management, with the objective of characterizing digital displays and applying a reference look such as a film look. Keywords — Display characterization, inverse display characterization, parametric model color, display, color management, device profiling, liquid-crystal display, digital light processing, digital micromirror device. DOI # 10.1889/JSID17.1.13 1 Introduction 1.1 Application context In cinematographic post-production, the digital processing of images, called digital intermediates (DI), is replacing more and more (and in some contexts has replaced) the con- ventional film workflow. Digital post-production requires the preview of DIs with a reproduction of colors, contrast, details, and resolution comparable to the final film projec- tion. 1 During the reproduction of colors on digital displays, the most commonly used simple additivity a model has revealed its limits, and therefore more elaborated models need to be developed to satisfy the application requirements in terms of color quality. For example, some signal processing in the display may infringe the “simple additivity” model hypothe- sis and prevent its use. More elaborate 3-D interpolation models can satisfy- ing results, but often at the expense of many color measure- ments and complex computation. This paper presents a parametric model, which is based on display physics, and compares it to the simple additivity model (3 × 3 matrix) 2,3 as well as to a more-com- plex 3-D interpolation model (non-linear Splines and Tetra- hedral) 3,4 for different display configurations. 1.2 Technical problems to solve The technical problem to be solved is to find a reliable trans- form between the digital domain (e.g., RGB Values) and the visual domain (e.g., XYZ b values) for an entire color space. Typically when R, G, and B have a dynamic of n = 8, 10, or 12 bits, a correspondence must be found between RGBs and XYZs for N = (2 n ) 3 triplets (N is greater than 10 9 for n = 10 bits). For each candidate XYZ, the corresponding RGB must be estimated. This RGB value used as input to the digital display shall generate the required XYZ color with a suffi- cient accuracy for the application. The problem to solve is to find a parametric model that allows the efficient computation of a RGB triplet for each candidate XYZ, using (RGB–XYZ) measurements on a restricted set of colors. 1.3 Goal of the parametric digital model The goal of a characterization model is to approximate a color transform between the signal input and the visual out- Revised extended version of a paper presented at the 15th Color Imaging Conference (CIC 15) held November 5–9, 2007, in Albuquerque, New Mexico, U.S.A. The authors are with THOMSON R&D, 1 avenue de Belle Fontaine, CS 17616, Cesson-Sévigné, 35576 France; telephone +33-(0)-2-99-27-30-42, fax –01, e-mail: Laurent.Blonde@thomson.net. © Copyright 2009 Society for Information Display 1071-0922/09/1701-0013$1.00 a Simple additivity: adding up weighted light contributions of color pri- maries as in the combination of a 3 × 3 matrix with an electro-optic curve (often referred to as a gamma curve). b XYZ: CIE1931 standard observer tristimulus coordinates. Journal of the SID 17/1, 2009 13