Halftone patterns for arbitrary screen periodicities

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Abstract
Ordered dither has long been considered to be a simple and effective method of image binarization. If ft is the two-dimensional continuous signal to be halftoned, then ordered dither consists of thresholding the discrete space signal fn against a periodic spatial screen σn whose periodicity is defined by a periodicity matrix N. Although in some dithering schemes used in practice, N is not assumed to be a diagonal matrix, most theory on dithering does include this assumption. Consequently, the majority of optimal dither patterns are designed for rectangularly periodic screen functions. In this paper the benefits of altering N are analyzed in an effort to improve the ordered dither algorithm. Optimal dither patterns for several representative nonrectangular screen periodicities are derived. It is shown that the optimal pattern sequences for these periodicities have gray-scale-rendition capabilities superior to those of previously considered dither patterns, resulting in substantially improved image fidelity.

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