Introducing ink spreading within the cellular Yule-Nielsen modified Neugebauer model

We propose an extension of the cellular Yule-Nielsen spectral Neugebauer model accounting for ink spreading of each ink within each subdomain. Characterization of the ink spreading within a given subdomain is performed by fitting the mid-range weights of subdomain node reflectances with the goal of minimizing the sum of square differences between predicted and measured mid-range reflectances. We show that the mid-range weights within a subdomain can be either separately fitted on three halftones or jointly fitted on a single halftone. Accounting for ink spreading considerably improves the prediction accuracy and requires only one additional measurement per subdomain. These additional measurements do not necessarily require spectral measurements. Instead, ink spreading can also be characterized with red, green and blue sensor responses without decreasing the model reflectance prediction accuracy. Introduction A printer is characterized by the relationship between the printer’s input in terms of nominal surface coverages of the inks and the resulting output color. This relationship is often obtained by printing hundreds of color halftones at different combinations of ink surface coverages. Another approach consists in modeling the interaction of the light and the print according to a spectral prediction model [1] [2] such as the Yule-Nielsen modified spectral Neugebauer model (YNSN). The colorants contributing to the halftone reflectance, also called Neugebauer primaries, are formed by the paper white, the inks and their superpositions. The predicted spectral reflectance of color halftones at given ink surface coverages is obtained by the sum of the colorant spectral reflectances weighted by their corresponding area coverages, where a scalar exponent (n-value) is used to model the non linear relationship between the colorant spectral reflectances and the resulting halftone reflectance. Thanks to a spectral prediction model, the printer can be characterized with a small number of measurements. In order to provide a higher prediction accuracy, Heuberger et al. [3] proposed the Cellular Neugebauer model. Subdomains are created by dividing the CMY surface coverage unit cube into 8 subcubes, called subdomains, formed by combinations of 0%, 50% and 100% surface coverages of the cyan, magenta and yellow inks. With such a subdivision, the number of primary reflectances increases from 8 to 27. Each subdomain, for example the one formed by ink coverages varying between 0% and 50%, forms itself a spectral Neugebauer model formed by 8 of the 27 primary reflectances. Balasubramanian [4] has shown that the cellular subdivision is also applicable to the Yule-Nielsen spectral Neugebauer model (name: CYNSN or simply "cellular Yule-Nielsen"). Due to the printing process, the deposited ink dot surface coverage is generally larger than the nominal surface coverage, yielding a “physical” dot gain responsible for the ink spreading phenomenon [4]. An extension of the YNSN model [5] has therefore been proposed to account for ink spreading (name: IS-YNSN). Ink spreading functions are computed by taking into account the respective physical dot gains of an ink halftone printed in different superposition conditions, i.e. in superposition with the different underlying colorants: alone on paper, in superposition with a second solid ink and in superposition with the second and a third solid ink. This yields, for each ink halftone in each superposition condition, an ink spreading curve mapping nominal to effective surface coverages [5]. For predicting the spectral reflectance of a color halftone, effective surface coverages are obtained from nominal surface coverages by weighting the effective surface coverages deduced from the ink spreading curves according to the area coverages of the underlying colorants. Both the ink spreading and the cellular subdivision enhancements of the Yule-Nielsen model require additional measurements. For CMY prints, the IS-YNSN model requires at least the spectral reflectance of the 50% ink halftones in each superposition condition (3 ink halftones, each in 4 superposition conditions = 12 halftones) plus the spectral reflectance of the 8 Neugebauer primaries, yielding 20 spectral measurements. In case of the cellular Yule-Nielsen model (CYNSN), a single level subdivision requires 3 3 = 27 spectral primary measurements and a finer level subdivision obtained with combination of 0%, 25%, 50%, 75% and 100% ink surface coverages requires 5 3 = 125 measurements of spectral primaries. In prior work, the cellular Yule-Nielsen model was further improved along the following lines: a) Optimization of the Neugebauer primary reflectances according to the color halftone patches forming the learning set [4]. b) Octtree like hierarchical subdivision of the surface coverage cube and subcubes until the desired prediction accuracy is reached within each leaf subcube [12]. c) Introducing for each ink a single function relying on single ink halftone ramps mapping nominal to effective surface coverages [4] [13]. d) Optimization of the positions for the non-uniform cellular subdivision of the surface coverage unit cube [13]. In the present contribution, we propose an extension of the cellular Yule-Nielsen model accounting for ink spreading 18th Color Imaging Conference Final Program and Proceedings 295 either by fitting the ink spreading curves with one halftone per ink and per subdomain (name: IS-CYNSN) or by fitting them with a single halftone (name: ISsingle-CYNSN) per subdomain. For both an inkjet print and a laser print, there is a remarkable improvement of the prediction accuracies offered by the proposed IS-CYNSN and ISsingle-CYNSN model extensions compared with the stand-alone CYNSN model (Sect. 4). In addition, we show that ink spreading can be characterized by measurements from 3 color sensors instead of full spectral measurements without reducing the prediction accuracies (Sect. 3). Ink spreading for the Cellular Yule-Nielsen model The Yule-Nielsen modified Neugebauer spectral model Eq. (1) is used to predict the spectral reflectance R(λ) of a color halftone as a weighted sum of Neugebauer primary reflectances Ri(λ), where ai is the area coverage of the i th primary, Ri(λ) its reflection spectrum and n the Yule-Nielsen value accounting for the lateral propagation of light (in general, 1<n<100).