Graph-order dithering

This paper presents a generalization of dispersed-dot dithering. While existing methods such as Bayer’s assume that color dots are arranged in a square matrix, this method works with arbitrarily-placed color points. To create a good dither pattern for arbitrarily-placed points, they must be ordered so that consecutive pairs are maximally separated. In this papre, the ordering is obtained by hierarchically coloring the vertices of the points’ adjacency graph. Each level in the coloring hierarchy adds a color digit to each graph vertex’s label, and sorting the resulting multi-digit labels produces the desired consecutive-point separation. The method can reproduce Bayer’s dispersed-dot dither matrices, but can also produce many similar matrices. Multiple matrices can be used to minimize repetitive artifacts that plague Bayer dither, while retaining its parallelizability. The method can also be applied to artistic dithering: given a repeatable motif image, its pixels can be grouped into subsets, one for each gray level, and each subset ordered. Concatenating the subsets yields a dither matrix that reproduces a motif while displaying an overall image. Unlike in previous artistic dither methods, the motif image can be arbitrary, and need not be specially constructed.