How to color a checkerboard with a given distribution - Matrix rounding achieving low 2 × 2-discrepancy

Abstract

Motivated by a digital halftoning application to convert a continuous-tone image into a binary image, we discusses how to round a [0, 1]-valued matrix into a 0, 1 binary matrix achieving lowdi screpancy with respect to the family of all 2×2 square submatrices (or regions). A trivial upper bound of the discrepancy is 2 and the known lower bound is 1. In this paper we shall show howto achieve a new upper bound 5/3 using a newpro of technique based on modified graph matching. © 2001 Springer Berlin Heidelberg.