Blue Noise Sampling with Controlled Aliasing

Daniel Heck1       Thomas Schlömer1       Oliver Deussen1      

1University of Konstanz, Germany


In this paper we revisit the problem of blue noise sampling with a strong focus on the spectral properties of the sampling patterns. Starting from the observation that oscillations in the power spectrum of a sampling pattern can cause aliasing artifacts in the resulting images, we synthesize two new types of blue noise patterns: step blue noise with a power spectrum in the form of a step function and single-peak blue noise with a wide zero-region and no oscillations except for a single peak. We study the mathematical relationship of the radial power spectrum to a spatial statistic known as the radial distribution function to determine which power spectra can actually be realized and to construct the corresponding point sets. Finally, we show that both proposed sampling patterns effectively prevent structured aliasing at low sampling rates and perform well at high sampling rates.


Final Paper

PDF (9.1 MB)

Source Code
ZIP (6 kB)

Additional Material

Analysis Tool
Open source analysis
tool at Google Code
Daniel's PhD Thesis
Includes an extended discussion of the material
PDF (24 MB)


  author =       {Daniel Heck and Thomas Schl{\"o}mer and Oliver Deussen},
  title =        {Blue Noise Sampling with Controlled Aliasing},
  journal =      {ACM Trans. Graph.},
  year =         2013,
  volume =       32,
  number =       3,
  pages =        {25:1--25:12},
  month =        jun