  In this work, we present a new method for generating a threshold structure.
This kind of structure can be advantageously used in various halftoning
algorithms such as clustered-dot or dispersed-dot dithering, error diffusion
with threshold modulation, etc. The proposed method is based on rectifiable
polyominoes -- a non-periodic hierarchical structure, which tiles the Euclidean
plane with no gaps. Each polyomino contains a fixed number of discrete
threshold values. Thanks to its inherent non-periodic nature combined with
off-line optimization of threshold values, our polyomino-based threshold
structure shows blue-noise spectral properties. The halftone images produced
with this threshold structure have high visual quality. Although the proposed
method is general, and can be applied on any polyomino tiling, we consider one
particular case: tiling with G-hexominoes. We compare our polyomino-based
threshold structure with the best known state-of-the-art methods for generation
threshold matrices, and conclude considerable improvement achieved with our
method.
