Neugebauer-type models for reflectance factor spectra produced by halftone-based color hardcopy rely on the spectra of the so-called Neugebauer primaries, an invertible function of reflectance, and a weight, or scalar, for each Neugebauer primary. This paper discusses the calculation of the third factor.

Research has, until now, relied heavily, perhaps exclusively, on just three parameter-less sets of equations to compute these scalars. In the previous paper in this series, it was shown how the scalar for each Neugebauer primary could be computed from the function governing the scalar of the primary consisting of all colorants, the so-called final scalar. In this paper, conditions necessary and sufficient for a function to provide the final scalar are recited. Copulas, an entire class of functions from probability theory, also satisfy these conditions, and therefore may be used for final scalar calculation.

Halftone patterns generated by a raster image processor were used to assess potential improvement in final scalar accuracy in two-colorant dot-on-dot printing with a slight amount of misregistration. Using a copula new to this application resulted in a nearly ten-fold improvement in accuracy over the best-performing overlap models in the prior art, indicating significant increases in accuracy are to be expected with actual printed artifacts.