Modeling color reproduction in halftone prints is difficult, mainly because of light scattering in the substrate, causing optical dot gain. Most available models are limited to macroscopic color measurements, averaging the reflectance over an area that is large relative the halftone dot size. The reflectance values for the full tone ink and the unprinted paper are used as input, and these values are assumed to be constant. An experimental imaging system, combining the accuracy of color measurement instruments with a high spatial resolution, allows us to measure the individual halftone dots, as well as the paper between them. Microscopic reflectance measurements reveal that the micro-reflectance of the printed dots and the paper between them is not constant, but varies with the dot area coverage. By incorporating the varying micro-reflectance values of the ink and paper in an expanded Murray-Davies model, we have previously shown that the resulting prediction errors are smaller than for the famous Yule-Nielsen model. Moreover, unlike Yule-Nielsen, the expanded Murray-Davies model takes into account the varying micro-reflectance for the printed dots and the paper, thus providing a better physical description of optical dot gain in halftone reproduction.
In this study, we further extend the methodology to handle color prints, predicting tristimulus values for prints with multiple and overlapping colorants. After converting the microscopic images of halftone prints into CIEXYZ color space, 3D histograms are computed. In the 3D histograms, the paper and the inks appear as clusters, with the transitions between the clusters corresponding to the edges of halftone dots. The tristimulus values for the paper and the different combinations of ink are computed as the centers of gravity for the clusters in the 3D histogram. From the microscopic images we can also compute the physical dot area coverage for each of the Neugebauer primaries, which typically differ from the nominal one, due to physical dot gain. The result is an expanded Neugebauer model, employing the varying tristimulus values of the paper and primary inks, as well as for overlapping, secondary colors. Experimental results confirm the accuracy of the proposed methodology, when compared to measurements using a spectrophotometer. Further, the results have shown that the variation of the micro-reflectance of the Neugebauer primaries is large, and depends strongly on the total dot area coverage.