Blue-noise halftoning for hexagonal grids

Daniel L. Lau, Robert Ulichney

Research output: Contribution to journalArticlepeer-review

24 Scopus citations


In this paper, we closely scrutinize the spatial and spectral properties of aperiodic halftoning schemes on rectangular and 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. Along with a thorough Fourier analysis of blue-noise dither patterns on both rectangular and hexagonal sampling grids, this paper also demonstrates the construction of a blue-noise dither array for hexagonal grids. EDICS: 4-QUAN Quantization and Halftoning.

Original languageEnglish
Pages (from-to)1270-1284
Number of pages15
JournalIEEE Transactions on Image Processing
Issue number5
StatePublished - May 2006


  • Blue-noise
  • Green-noise
  • Halftoning
  • Printing

ASJC Scopus subject areas

  • Software
  • Computer Graphics and Computer-Aided Design


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