1. A computer-implemented method for generating a deposterized image, comprising: for a posterized image including pixels that have color values that belong to a set of posterized color values, calculating constraints for each posterized color value in the form of a minimum bound and a maximum bound, wherein the minimum bound and the maximum bound for a given posterized color value are selected so that any corresponding deposterized color value between the minimum bound and the maximum bound will be rounded to the given posterized color value during a reposterization process; and calculating color values for pixels in the deposterized image by solving a partial differential equation (PDE) for each pixel in the deposterized image subject to the calculated constraints on the minimum bound and the maximum bound associated with the corresponding posterized color value; wherein each of said calculating constraints and said calculating color values is performed by one or more computer systems.