Cost function analysis for stochastic clustered-dot halftoning based on direct binary search

Most electrophotographic printers use periodic, clustered-dot screening for rendering smooth and stable prints. However, periodic, clustered-dot screening suffers from the problem of periodic moir´e resulting from interference between the component periodic screens superposed for color printing. There has been proposed an approach, called CLU-DBS for stochastic, clustered-dot halftoning and screen design based on direct binary search. This method deviates from conventional DBS in its use of different filters in different phases of the algorithm. In this paper, we derive a closed-form expression for the cost metric which is minimized in CLU-DBS. The closed-form expression provides us with a clearer insight on the relationship between input parameters and processes, and the output texture, thus enabling us generate better quality texture. One of the limitations of the CLU-DBS algorithm proposed earlier is the inversion in the distribution of clusters and voids in the final halftone with respect to the initial halftone. In this paper, we also present a technique for avoiding the inversion by negating the sign of one of the error terms in the newly derived cost metric, which is responsible for clustering. This not only simplifies the CLU-DBS screen design process, but also significantly reduces the number of iterations required for optimization.