Modeling ink spreading for color prediction

This study aims at modeling ink spreading in order to improve the prediction of the reflection spectra of three ink color prints. Ink spreading is a kind of dot gain which causes significant color deviations in ink jet printing. We have developed an ink spreading model which requires the consideration of only a limited number of cases. Using a combinatorial approach based on Pbya's counting theory, we determine a small set of ink drop configurations which allows us to deduce the ink spreading in all other cases. This improves the estimation of the area covered by each ink combination that is crucial in color prediction models. In a previous study, we developed a unified color prediction model. This model, augmented by the ink spreading model, predicts accurately the reflection spectra of halftoned samples printed on various inkjet printers. For each printer, the reflection spectra of 125 samples uniformly distributed in the CMY color cube were computed. The average prediction error between measured and predicted spectra is about ΔE = 2.5 in CIELAB. Such a model simplifies the calibration of ink jet printers, as well as their recalibrations when ink or paper is change

Towards a color prediction model for printed patches

A novel color prediction model is presented which unifies, within a framework based on matrices, the phenomena of surface reflection, light absorption, diffuse light sources, superposition of multiple ink layers, and other

A Prediction Model for Reflection on Varnished Metallic Plates

Several models predict the reflectance of a rough metallic surface. They are however not adapted to the surfaces used in the packaging industry, such as boxes made of printed metallic plates. For printing purposes, metallic surfaces need to be varnished. Light reflection properties are therefore modified. We propose methods which adapt existing reflectance models to varnished surfaces. We also present a correction capable of predicting the reflectance even if incident light is not collimated, i.e. not composed of parallel rays

Grid-based method for predicting the behaviour of colour printers

A new grid-based method is proposed for predicting the behaviour of colour printers. The method takes into account the varying density of dots as well as the light diffusion in the paper by defining at different intensity levels different colorimetric values for the printed ink as well as for the paper white. Since the model integrates both the varying density of partly overlapping ink dots and the light diffusion in the underlying substrate, the obtained predictions are more accurate than those obtained with surface based colour prediction methods described in the literature

Predicting transmittance spectra of electrophotographic color prints

For dry toner electrophotographic color printers, we present a numerical simulation model describing the color printer response based on a physical characterization of the different electrophotographic process steps. The proposed model introduces a Cross Transfer Efficiency designed to predict the color transmittance spectra of multi-color prints by taking into account the transfer influence of each deposited color toner layer upon the other layers. The simulation model leads to a better understanding of the factors that have an impact on printing quality. In order to avoid the additional optical non-linearities produced by light reflection on paper (dot-gain), we have limited the present investigation to transparency prints. The proposed model succeeded to predict the transmittance spectra of printed wedges combining two color toner layers with a mean deviation less than CIE-LAB ΔE = 2.5

Reproducing color images with embedded metallic patterns

By combining a metallic ink and standard inks, one may create printed images having a dynamic appearance: an image viewed under specular reflection may be considerably different from the same image viewed under non-specular reflection. Patterns which are either dark or hidden become highlighted under specular reflection, yielding interesting visual effects. To create such images, one needs to be able to reproduce at nonspecular reflection angles the same colors, by standard inks alone or in combination with a metallic ink. Accurate color prediction models need to be established which model the underlying physical phenomena in a consistent manner. To meet this challenge, we propose two models, one for predicting the reflection spectra of standard inks on coated paper and one for predicting the reflection spectra of a combination of standard inks and a metallic ink. They are enhancements of the classical Clapper-Yule model which models optical dot gain of halftone prints by taking into account lateral scattering within the paper bulk and multiple internal reflections. The models we propose also take into account physical dot gain and ink spreading for standard inks as well as the low reflectance of metallic inks at non-specular reflection angles and the poor adherence of standard inks printed on top of a metallic ink (trapping effect). These models open the way towards color separation of images to be reproduced by combining a metallic ink and standard inks. Several designs printed on an offset press demonstrate their applicability and their benefits for high-end design and security application

Spectral prediction and dot surface estimation models for halftone prints

We propose a new spectral prediction model as well as new approaches for modeling ink spreading which occurs when printing ink layer superpositions. The spectral prediction model enhances the classical Clapper-Yule model by taking into account the fact that proportionally more incident light through a given colorant surface is reflected back onto the same colorant surface than onto other colorant surfaces. This is expressed by a weighted mean between a component specifying the part of the incident light which exits through the same colorant as the colorant from which it enters (Saunderson corrected Neugebauer component) and a component specifying the part of the incident light whose emerging light components exit from all colorants, with a probability to exit from a given colorant equal to that colorant surface coverage (Clapper-Yule component). We also propose two models for taking into account ink spreading, a phenomenon which occurs when printing an ink halftone in superposition with one or several solid inks. Besides the physical dot gain present within a single ink halftone print, we consider in the first model the ink spreading which occurs when an ink halftone is printed on top of one or two solid inks. In the second more advanced model, we generalize this concept to ink halftones printed on top or below solid inks. We formulate for both ink spreading models systems of equations which allow to compute effective ink coverages as a combination of the individual ink coverages which occur in the different superposition cases. The new spectral prediction model combined with advanced ink spreading yields excellent spectral predictions for clustered-dot color halftone prints, both in the case of offset (75 to 150 lpi) and in the case of thermal transfer printers (50 to 75 lpi

Spectral reflection and dot surface prediction models for color halftone prints

The proposed new spectral reflection model enhances the classical Clapper-Yule model by taking into account the fact that proportionally more incident light through a given colorant surface is reflected back onto the same colorant surface than onto other colorant surfaces. It comprises a weighted mean between a component specifying the part of the incident light that exits through the same colorant as the colorant from which it enters (Saunderson corrected Neugebauer component) and a component specifying the part of the incident light whose emerging light components exit from all colorants (Clapper-Yule component). We also propose models for taking into account ink spreading, a phenomenon that occurs when printing an ink halftone in superposition with one or several solid inks. The ink-spreading model incorporates nominal-to-effective surface coverage functions for each of the different ink superposition conditions. A system of equations yields the effective ink surface coverages of a color halftone as a weighted mean of the ink surface coverages specific to the different superposition conditions. The new spectral reflection prediction model combined with the ink-spreading model yields excellent spectral reflection predictions for clustered-dot color halftones printed on an offset press or on thermal transfer printer

On the lowest eigenvalue of Laplace operators with mixed boundary conditions

In this paper we consider a Robin-type Laplace operator on bounded domains. We study the dependence of its lowest eigenvalue on the boundary conditions and its asymptotic behavior in shrinking and expanding domains. For convex domains we establish two-sided estimates on the lowest eigenvalues in terms of the inradius and of the boundary conditions

A natural Finsler--Laplace operator

We give a new definition of a Laplace operator for Finsler metric as an average with regard to an angle measure of the second directional derivatives. This definition uses a dynamical approach due to Foulon that does not require the use of connections nor local coordinates. We show using 1-parameter families of Katok--Ziller metrics that this Finsler--Laplace operator admits explicit representations and computations of spectral data.Comment: 25 pages, v2: minor modifications, changed the introductio