Accounting from Inks Interaction in the Yule Nielsen Spectral Neugebauer Model

Multispectral printer characterization requires an effec- tive model to map the inputs to the printer (i.e., the digital counts of the inks) into reflectance spectra and vice versa. Most of the meth- ods for printer modeling are based on the color mixing model of Neugebauer, but this model, in its original formulation, is a rather poor predictor of the printer's output, since it fails to take into ac- count many of the relevant phenomena that take place in the print- ing process. These phenomena, which include light scattering within the substrate, internal and surface reflection, and ink spreading, de- termine an enlargement of ink drops called dot gain, which differs on the basis of the substrate condition. This paper presents a novel strategy to model dot gain and interaction among inks in the defini- tion of a printer model based on the Yule-Nielsen spectral Neuge- bauer equation. The method proposed has been designed for a four-ink ink jet printer, but its formulation is general and may be extended to the characterization of devices having more than four inks. Our method requires the definition of a relatively large number of parameters, that we estimate using genetic algorithms. The model has been tested on two different printers: An Epson Stylus- ColorTM 740 ink jet printer and an Epson StylusPhotoTM 890 ink jet printer. Using a data set consisting of 777 samples, regularly distrib- uted in the HSV color space, we have obtained an accuracy in terms of mean root mean squared error of 0.59% and of 1.5 deltaE*ab for the first printer and of 1.02% and of 2.0 deltaE*ab for the second printer. With respect to an approach based on a single dot gain function for each ink, our approach based on many dot gain functions reduced the average root mean square error on the test set of about 40% on average.