Systems and methods for utilizing a known histogram of a particular category of images to constrain a probabilistic print-scan model in order to provide a more accurate print-scan model are described. A probability function is defined that given a two-dimensional grayscale bitmap input image provides the probability that a particular pixel of the input image will have a particular gray level in the output image after print-scan processing. Additionally, an expected target histogram is input into the system and used to constrain or modify the probabilistic print-scan model for the input image to produce a deterministic print-scan model.