A pattern that is to be formed by a colorant on a substrate is defined in terms of the halftone image that instructs a printing system. This image contains information at each pixel as to which colorants to use at which drop states, i.e., Neugebauer Primaries (NPs) such as CC (two drops of cyan ink) or CM (a drop of cyan and a drop of magenta ink). However, the transformation from this digital input to a final printed pattern involves other steps as well as physical, colorant and substrate interaction effects. An important contributor to the final output is the partitioning of a halftone image into its complementary sub-images that are printed in each pass of a multi-pass or multi-bar printing system (common in inkjet). Typically, great attention is given to the goodness of a halftone image – good pattern distribution, good NP and ink choices – however, partitioning can also have a significant impact on the output both in terms of avoiding unwanted physical interactions (e.g., coalescence, alignment artifacts) and exercising control over the pattern. This can lead to closer correspondence to the halftone and improved print properties (such as grain and robustness) and can be achieved by co-optimizing halftoning (responsible for the spatial distribution of the halftone image) and partitioning (responsible for distributing it among the N passes or bars of a given printing system). The results are not only good overall halftone images as has been the case already, but also good partial halftone sub-images whose gradual printing in different passes results in maximized NP control and thereby its effect on the printed color.