Display characterization, deriving the relationship between the digital input values and the corresponding CIEXYZ tri-stimulus values, is necessary to reproduce accurate colors in a color management system. For colorimetric reproduction in a display device, an inverse characterization process is needed to input RGB corresponding to the desired tri-stimulus values. However, inverse display characterization using nine channel tone response curves (TRCs) cannot be directly inverted because the CIEXYZ values corresponding to each RGB value are inseparable. Inverse display characterization is usually implemented using the three-dimensional (3D)-look-up table (LUT) method, yet this requires a lot of memory space and a considerable amount of measurement data, although it provides a relatively accurate estimation. Accordingly, this paper proposes an inverse characterization method based on modeling channel-dependent values and a nine-channel inverse process using the gain-offset-gamma (GOG) model. First, the initially normalized luminance values for each RGB channel are computed using the inverse matrix. These normalized luminance values are then used to compensate the corresponding nine channel TRCs, thereby modifying the TRCs into input linearized values for the inverse process. Thereafter, each of the nine channel digital RGB values is estimated using the inverse GOG model based on the pre-determined parameters from the forward characterization. Finally, three digital RGB values are deduced for each RGB channel based on the ratio of the maximum CIEXYZ values to reduce the interpolation error. Consequently, the proposed method enhances the accuracy of the display characterization and reduces both the complexity and the number of measurement data required.
Yang-Ho Cho, Hye-Bong Im, Yeong-Ho Ha, "Inverse Characterization Method of Alternate Gain-Offset-Gamma Model for Accurate Color Reproduction in Display Device" in Journal of Imaging Science and Technology, 2006, pp 139 - 148, https://doi.org/10.2352/J.ImagingSci.Technol.(2006)50:2(139)