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Blue-Noise Halftoning for Hexagonal Grids

Lau, Daniel L.; Ulichney, Robert


Keyword(s): halftoning; printing; blue-noise; green-noise

Abstract: In this paper, we closely scrutinize the spatial and spectral properties of aperiodic halftoning schemes on hexagonal sampling grids. Traditionally, hexagonal sampling grids have been shunned due to their inability to preserve the high frequency components of blue-noise dither patterns at gray-levels near one- half, but as will be shown, only through the introduction of diagonal correlations between dots can even rectangular sampling grids preserve these frequencies. And by allowing the sampling grid to constrain the placement of dots, a particular algorithm may introduce visual artifacts just as disturbing as excess energy below the principal frequency. If, instead, the algorithm maintains radial symmetry by introducing a minimum degree of clustering, then that algorithm can maintain its grid defiance illusion fundamental to the spirit of the blue-noise model. As such, this paper shows that hexagonal grids are preferrable because they can support gray-levels near one-half with less required clustering of minority pixels and a higher principal frequency. Furthermore, hexagonal grids allow for improved radial symmetry in the size and shape of clusters. Finally, the world's first blue-noise dither array for hexagonal grids will be demonstrated. Notes:

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