Extending The Branch-path Clapper-Yule Model With Irregular Ink Dot For Color Halftone

The color prediction model is one of the most important research topics in image reproduction field, and the relationship between the dot area fraction and the spectral reflections of halftone prints has always been the core issue that many researchers concern. However, in the actual printing progress, the physical phenomena which affect the real restoration of the originals by halftone prints are very complicated. The existing color prediction models have been established on the basis of integrally incorporating all kinds of physical phenomena. Although the classical Clapper-Yule color prediction models have laid the important theoretical foundation for our follow-up researches, the defect of this model that the prediction values are lower than the measurement, is one of the dilemmas that people have always tried to tackle. Based on the extended Clapper-Yule model, this paper has introduced the factor of the dot edge ink spreading leading to the ink layer transmittance variations, modifying the branch-path Clapper-Yule color prediction model.The branch-path Clapper-Yule color prediction model is established on the assumption of the ideal bi-level ink dot which has sharp edge and no feather. But in actual prints, due to the mechanical printing pressure during the ink shifting and the rheological characteristic of ink, the ink will spread out at the edge, which leads to the ink irregularity and the ink density decreasing from the ink center to ink edge. According to the Lambert-Bill law, the ink layer transmittance will have corresponding variations, which affects the spectral reflection of halftone prints. This paper put attention on the ink irregularity, assuming that the surface morphology of ink dot can be simulated by the two-dimensional Gaussian function. According to the ink volume constancy before or after the ink spreading, the dot area refraction which has added into the physical dot gain is derived as formula; at the same time the function of ink layer transmittance variations has been derived. By introducing the effective dot fraction added the mechanical dot gain and the effective ink transmittance to the branch-path Clapper-Yule model to modify the dot irregularity and incorporating the effective dot area refraction of multi-colors overlap, the new spectral prediction model has been established.Comparing the color difference of the new model, the extended Clapper-Yule model and the classical Clapper-Yule model with the experimental measurements, the rationality and feasibility of our new model has been verified. Numerical simulation shows that the new model has not only modified the defects of classical Clapper-Yule model being darker but also made up the branch-path Clapper-Yule model not considering the problem of ink edge spreading out. The color difference of our new model is 2.6 around, which reveals higher prediction accuracy.So our new model can be used to predict the relationship between the input of dot area refraction and the output of spectral reflectance, which has provided a theoretical guidance to the research and development of the color management in actual printing.