The two-by-two dot centering model enables predicting the spectral reflectance of color halftones and does not
depend on a specific halftoning algorithm. It requires measuring the reflectances of a large number of two-by-two
calibration tile patterns. Spectral measurement of hundreds or thousands of tile patterns is cumbersome and time
consuming. In order to limit the number of measurements, we estimate the reflectances of a large majority of two-by-
two calibration tile patterns from a small subset comprising less than 10% of all tile patterns. Using this subset
of measured two-by-two calibration tile patterns, we perform a linear regression in the absorptance space and
derive a transformation matrix converting tile pattern colorant surface coverages to absorptances. This
transformation matrix enables calculating the absorptance of all remaining two-by-two tile patterns. For a cyan,
magenta and yellow print, with 72 two-by-two measured calibration tile patterns, we are able to create a two-by-two
dot centering model having an accuracy only slightly below the accuracy of the model with the fully measured
set of 1072 two-by-two tile patterns.
The Yule-Nielsen modified spectral Neugebauer model enhanced for accounting for ink spreading in the
different ink superposition conditions (EYNSN) requires measuring the reflectances of halftone calibration
patches in order to compute the ink spreading curves mapping nominal ink surface coverages to effective ink
surface coverages. Spectral measurements of dozens of halftone patch reflectance spectra for each considered
halftoning method, screen shape or screen frequency variant is cumbersome and time consuming. As an
alternative, we compute automatically the reflectance of the calibration patches necessary to establish the ink
spreading curves by making use of the two-by-two dot centering model (abbreviated "2-by-2"). The two-bytwo
dot centering model requires its own set of calibration patches, among which a very small subset is
necessary for predicting the reflectance of the EYNSN calibration patches. For a given combination of printer,
paper and inks, using only 68 two-by-two calibration patches for the three CMY inks, respectively 118 two-
by-two calibration patches for the four CMYK inks, we are able to predict the reflection spectra of most
classical halftone screens and at many different frequencies. We compare the results of predictions where the
EYNSN model calibration patches are measured or are predicted with the two-by-two dot centering model.
For 125 (CMY) and 625 (CMYK) uniformly distributed patches printed with an ink-jet printer at three
different screen frequencies (75lpi, 100lpi and 125lpi), the mean reflectance prediction accuracy is similar, i.e.
the decrease in accuracy due to the two-by-two prediction of EYNSN calibration patch reflectance is less than
ΔE94=0.4.
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