Hierarchical graph color dither

摘要

Suppose a dispersed-dot dither matrix is treated as a collection of numbers, each number having a position in space; when the numbers are visited in increasing order, what is the distance in space between pairs of consecutive numbers visited? In Bayer's matrices, this distance is always large. We hypothesize that this large consecutive distance is important for good dispersed-dot threshold matrices. To study the hypothesis, matrices that have this quality were generated by solving a more general problem: given an arbitrary set of points on the plane, sort them into a list where consecutive points are far apart. Our solution colors the nearest-neighbor graph, hierarchically. The method does reproduce Bayer's dispersed-dot dither matrices under some settings and, furthermore, can produce matrices of arbitrary dimensions. Multiple similar matrices can be created to minimize repetitive artifacts that plague Bayer dither while retaining its parallelizability. The method can also be used for halftoning with points on a hexagonal grid, or even randomly placed points. It can also be applied to artistic dithering, which creates a dither matrix from a motif image. Unlike in the artistic dither method of Ostromoukhov and Hersch, the motif image can be arbitrary and need not be specially constructed.