Simplified Ink Spreading Equations for CMYK Halftone Prints Thomas Bugnon, Mathieu Brichon and Roger David Hersch École Polytechnique Fédérale de Lausanne (EPFL), School of Computer and Communication Sciences, Lausanne 1015, Switzerland ABSTRACT The Yule-Nielsen modified spectral Neugebauer model enables predicting reflectance spectra from surface coverages. In order to provide high prediction accuracy, this model is enhanced with an ink spreading model accounting for physical dot gain. Traditionally, physical dot gain, also called mechanical dot gain, is modeled by one ink spreading curve per ink. An ink spreading curve represents the mapping between nominal to effective dot surface coverages when an ink halftone wedge is printed. In previous publications, we have shown that using one ink spreading curve per ink is not sufficient to accurately model physical dot gain, and that the physical dot gain of a specific ink is modified by the presence of other inks. We therefore proposed an ink spreading model taking all the ink superposition conditions into account. We now show that not all superposition conditions are useful and necessary when working with cyan, magenta, yellow, and black inks. We therefore study the influence of ink spreading in different superposition conditions on the accuracy of the spectral prediction model. Finally, we propose new, simplified ink spreading equations that better suit CMYK prints and are more resilient to noise. Keywords: color reproduction, ink spreading model, spectral prediction model, Yule-Nielsen modified Spectral Neugebauer, halftones, ink spreading curves, dot gain, ink superposition conditions, noise resilience 1. INTRODUCTION The goal of a color reproduction system is to be able to reproduce input colors as accurately as possible. This is not a trivial task since the human visual system is very sensitive to small color differences. In printing systems, there are many factors influencing the range of printable colors: the inks, the substrate (paper, plastic, glass, etc.), the illumination conditions, and the halftones. Spectral reflection prediction models are helpful in studying the influence of these factors. One of the fundamental aspects a spectral reflection prediction model has to consider is how the inks spread on the paper, a phenomenon also referred to as physical or mechanical dot gain. With an ink spreading model accounting for physical dot gain, a spectral reflection prediction model is able to accurately predict reflectance spectra in function of ink surface coverages for three or four inks 1, 2, 3 . In order to be effective, such an ink spreading model must take into account not only the interaction between an ink halftone and paper, but also the interaction between an ink halftone and superposed inks. One proposed solution is to use multiple ink spreading curves, also called tone reproduction curves, to characterize the physical dot gain of the ink halftones on paper in all solid ink superposition conditions. For CMYK halftone prints, such an approach requires the characterization of 32 ink spreading curves. The aim of this paper is to evaluate the relevance of each ink spreading curve and subsequently simplify the ink spreading model in order to use fewer curves. The relevance of an ink spreading curve depends on its impact on the spectral prediction model accuracy as well as how it is affected by noise. Section 2 introduces the Yule-Nielsen modified Spectral Neugebauer model that is used as spectral reflection prediction model. The ink spreading model and the characterization of the ink spreading curves are detailed in Section 3. Section 4 evaluates the influence of each ink spreading curve on the accuracy of the prediction model and Section 5 the influence of measurement noise on the characterization of the ink spreading curves. In Section 6, a new set of equations that reduces the number of component equations of the ink spreading model is proposed and evaluated against the existing set of equations. We finally draw the conclusions in Section 7. Proc. SPIE Vol. 6807, 680717, Color Imaging XIII: Processing, Hardcopy, and Applications; Reiner Eschbach, Gabriel G. Marcu, Shoji Tominaga; Eds., January 2008