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Projective Blue-Noise Sampling, Computer Graphics Forum 2015 and presented at EGSR 2016

Projective Blue-Noise Sampling

Bernhard Reinert1     Tobias Ritschel1, 2, 3     Hans-Peter Seidel1     Iliyan Georgiev4

MPI Informatik1, MMCI2, Saarland University3, Solid Angle4

Our projective blue-noise distributions (a, bottom) have blue-noise spectra in 2D as well as in their 1D projections, while classic 2D blue noise (a, top) has an almost white-noise spectrum in 1D. Applications include Monte Carlo rendering (b), reconstruction (c), as well as placement of primitives (d) such that they are well distributed both in 3D and when projected to 2D.


We propose projective blue-noise patterns that retain their blue-noise characteristics when undergoing one or multiple projections onto lower dimensional subspaces. These patterns are produced by extending existing methods, such as dart throwing and Lloyd relaxation, and have a range of applications. For numerical integration, our patterns often outperform state-of-the-art stochastic and low-discrepancy patterns, which have been specifically designed only for this purpose. For image reconstruction, our method outperforms traditional blue-noise sampling when the variation in the signal is concentrated along one dimension. Finally, we use our patterns to distribute primitives uniformly in 3D space such that their 2D projections retain a blue-noise distribution.



Paper (7.7 MB)
Video (60 MB)
Rendering comparisons: Bench scene, Helicopter scene, Desert scene, Desert stones scene, Dragon scene, Quad scene
EGSR 2016 presentation slides (178 MB, please see Notes section for comments and script).


Bernhard Reinert, Tobias Ritschel, Hans-Peter Seidel, Iliyan Georgiev
Projective Blue-Noise Sampling
Computer Graphics Forum 2015.

  author = { 
	Bernhard Reinert and
	Tobias Ritschel and 
	Hans-Peter Seidel and
	Iliyan Georgiev},
  title = {Projective Blue-Noise Sampling},
  journal = {Computer Graphics Forum},
  issn = {1467-8659},
  year = {2015}


We would like to thank the anonymous reviewers for helpful comments.