One aspect of the method/apparatus finds, for each input-image pixel, an “offset weighted average” of neighboring-pixel interactions—and uses the averages to make a final image. Another aspect assumes a value for each pixel, to use in a final rendered image form—and, at each in a series of approximations, determines whether to change the value, and finds a probabilistic weight to help determine. Yet another finds, for each pixel, a numerical representation of neighboring-pixel interactions—and establishes a distance cutoff for use in defining “neighbor”, and uses the representation to decide whether to change color values. Still another finds a desired or ideal number of print passes, and adapts the number of passes actually used to the found number. Another combines halftoning and printmasking into one procedure and prints images prepared thereby. Another integrates halftoning and image filtering, to obtain esthetic visual effects, into one procedure—and prints images thus prepared.