Disc Covering Problem with Application to Digital Halftoning
This paper considers the following geometric optimization problem: Input is a matrix R=(r (ij) ). Each entry r (ij) represents a radius of a disc with its center at (i,j) in the plane. We want to choose discs in such a way that the total area covered by exactly one disc is maximized. This problem is closely related to digital halftoning, a technique to convert a continuous-tone image into a binary image for printing. An exact algorithm is given for the one-dimensional version of the problem while approximation algorithms are given for the two-dimensional one. The approximation algorithms are verified to be satisfactory in practice through experiments in applications to digital halftoning.
digital halftoning approximation algorithm computational geometry voronoi diagram