Colour Reproduction

The problem of printer calibration

Colour prediction models are useful for populating the color calibration tables of printing devices. These tables convert input colors, for instance calibrated RGB or CIE-XYZ, into coverages of Cyan, Magenta, Yellow and Black inks. Without prediction model, one needs to measure the CIE-XYZ colorimetric values of a large number of patches (several hundreds) in order to fill the calibration tables by interpolating between the acquired pairs of XYZ-CMY values. The relation between colorimetric values and amounts of cyan, magenta, yellow inks is highly non-linear and depends on many different parameters: the spectra of the inks, the properties of the paper, the halftoning method, ink spreading, etc.. Hence, new calibrations needs to be performed whenever any of these parameters is changed, e.g. when printing with a different paper, a different ink cartridge or a different halftoning algorithm. Color prediction models allow to populate printer calibration tables by measuring just a few patches and therefore greatly facilitate the calibration process. Next generation of printers will be equipped with sensors for the acquisition of reflection spectra or of colorimetric values. This will enable printers to perform automatic recalibration. A similar approach may be applied for the calibration of printers printing with custom inks (inks which are different from standard cyan, magenta and yellow inks).

New spectral prediction model relying on an extension of the Clapper-Yule model (2005)

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 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 (Clapper-Yule component). We also propose models for taking into account ink spreading, a phenomenon which 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 printers.

Improved YNSN predictions with new ink spreading model (2005)

Dot gain is different when dots are printed alone, printed in superposition with one ink or printed in superposition with two inks. In addition, the dot gain may also differ depending on which solid ink the considered halftone layer is superposed. In a previous research project, we developed a model for computing the effective surface coverage of a dot according to its superposition conditions. In the present contribution, we improve the Yule-Nielsen modified Neugebauer model by integrating into it our effective dot surface coverage computation model. Calibration of the reproduction curves mapping nominal to effective surface coverages in every superposition condition is carried out by fitting effective dot surfaces which minimize the sum of square differences between the measured reflection density spectra and reflection density spectra predicted according to the Yule-Nielsen modified Neugebauer model. In order to predict the reflection spectrum of a patch, its known nominal surface coverage values are converted into effective coverage values by weighting the contributions from different reproduction curves according to the weights of the contributing superposition conditions. The improved YNSN yields excellent predictions for clustered dot haltones in the case of offset, thermal transfer, ink-jet technologies.

Unified spectral prediction model (1999)

We developed a unified spectral prediction model relying on a two flux approach (Kubelka-Munk), describing in a single mathematical expression the reflection of light on one or several uniform ink layers, both for transparent and partially opaque inks.This model takes into account the surface reflection at the interface between the air and the paper, light absorption in the ink layers, light scattering and reflection within the paper bulk and the internal reflections at the print-air interface. The model is extended to halftone ink layers by modeling lateral light scattering with a convolution function. The presented approach unifies the classical models within a new mathematical framework based on matrices.

Color Gamut Reduction

Printing with custom inks is of interest both for artistic purposes and for printing security documents such as banknotes. However, in order to create designs with only a few custom inks, a general purpose high-quality gamut reduction technique is needed. Most existing gamut mapping techniques map an input gamut such as the gamut of a CRT display into the gamut of an output device such as a CMYK printer. In the present contribution, we are interested in printing with up to three custom inks, which in the general case define a rather narrow color gamut compared with the gamut of standard CMYK printers. The proposed color gamut reduction techniques should work for any combination of custom inks and have a smooth and predictable behavior [Chosson02, Chosson03]. When the black ink is available, the lightness levels present in the original image remain nearly identical. Original colors with hues outside the target gamut are projected onto the gray axis or onto desaturated colors. Original colors with hues inside the target gamut hues are rendered as faithful as possible. When the black ink is not available, we map the gray axis G into a colored curve G' connecting in the 3D color space the paper white and the darkest available color formed by the superposition of the 3 inks. The mapped gray axis curve G' is given by the Neugebauer equations when enforcing equal amounts of custom inks. After lightness mapping, hue and saturation mappings are carried out. When the target gamut does not incorporate the gray axis, we divide it into two volumes, one on the desaturated side of the mapped gray axis curve G' and the other on the saturated side of the G' curve. Colors whose hues are not part of the target color gamut are mapped to colors located on the desaturated side of the G' curve. Colors within the set of printable hues remain within the target color gamut and retain as much as possible their original hue and saturation.

Original image mapped
onto 4 different target color gamuts :

two custom inks
and the black ink

three custom inks
and the black ink

three custom inks
without black

three custom inks
without black

<basile.schaeli@epfl(add: .ch)>

Last modified: 2007/09/26 21:22:01