Visual Computing

University of Konstanz
ACM Transactions on Graphics

Blue Noise Sampling with Controlled Aliasing

D. Heck, T. Schlömer, O. Deussen
Teaser of Blue Noise Sampling with Controlled Aliasing


Paper (.pdf, 20.8MB) Daniel's PhD Thesis (.pdf, 23.4MB) Source Code (.zip, 13.5KB) Open source analysis tool at Google Code


In this article 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.


  acmid      = {2487233},
  address    = {New York, NY, USA},
  articleno  = {25},
  author     = {D. Heck, T. Schlömer, O. Deussen},
  doi        = {10.1145/2487228.2487233},
  issn       = {0730-0301},
  issue_date = {June 2013},
  journal    = {ACM Transactions on Graphics},
  keywords   = {Sampling, anti-aliasing, blue noise, effective Nyquist frequency, power spectrum, radial distribution function},
  month      = {jul},
  number     = {3},
  numpages   = {12},
  pages      = {25:1--25:12},
  publisher  = {ACM},
  title      = {Blue Noise Sampling with Controlled Aliasing},
  url        = {},
  volume     = {32},
  year       = {2013}