A simple push-pull algorithm for blue-noise sampling

Abdalla G.M. Ahmed, Jianwei Guo, Dong Ming Yan*, Jean Yves Franceschia, Xiaopeng Zhang, Oliver Deussen

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

38 Scopus citations


We describe a simple push-pull optimization (PPO) algorithm for blue-noise sampling by enforcing spatial constraints on given point sets. Constraints can be a minimum distance between samples, a maximum distance between an arbitrary point and the nearest sample, and a maximum deviation of a sample's capacity (area of Voronoi cell) from the mean capacity. All of these constraints are based on the topology emerging from Delaunay triangulation, and they can be combined for improved sampling quality and efficiency. In addition, our algorithm offers flexibility for trading-off between different targets, such as noise and aliasing. We present several applications of the proposed algorithm, including anti-aliasing, stippling, and non-obtuse remeshing. Our experimental results illustrate the efficiency and the robustness of the proposed approach. Moreover, we demonstrate that our remeshing quality is superior to the current state-of-the-art approaches.

Original languageEnglish (US)
Article number7790842
Pages (from-to)2496-2508
Number of pages13
JournalIEEE Transactions on Visualization and Computer Graphics
Issue number12
StatePublished - Dec 1 2017

Bibliographical note

Funding Information:
We would like to thank Zhonggui Chen, Fernando de Goes, Raanan Fattal, Mohamed S. Ebeida and Daniel Heck for providing the data and executables, Liyi Wei and Rui Wang for sharing the DDA tool. This project was supported by the Deutsche Forschungsgemeinschaft Grant (DE-620/22-1), the National Natural Science Foundation of China (61372168, 61620106003, and 61331018), the National Foreign 1000 Plan (WQ201344000169) and the Leading Talents of Guangdong Program (00201509). Dong-Ming Yan is the corresponding author. Abdalla G. M. Ahmed and Jianwei Guo are joint first authors.

Publisher Copyright:
© 1995-2012 IEEE.


  • Blue-noise sampling
  • Push-pull
  • Remeshing
  • Stippling
  • Surface sampling

ASJC Scopus subject areas

  • Software
  • Signal Processing
  • Computer Vision and Pattern Recognition
  • Computer Graphics and Computer-Aided Design


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