ACM Trans. Graph. (Proceedings of SIGGRAPH Asia 2022)

Gaussian Blue Noise

Abdalla G. M. Ahmed1       Jing Ren1,2       Peter Wonka1
1 KAUST, KSA
2 ETH, Zurich

Point distributions (1K sets) and power spectra (1K realizations) of different blue-noise optimization techniques including: (a) BNOT [de Goes et al. 2012], (b) KDM [Fattal 2011], (c) VnC [Ulichney 1993], (d) FPO [Schlömer 2011], (e) BlueNets [Ahmed and Wonka 2021], (f) SOT [Paulin et al. 2020], and (g) GBN (Ours). While the frequency power spectral plots may look similar, a closeup view reveals that the low-frequency disc in the middle is perfectly black in GBN, indicating very low low-frequency noise. (h) A log-log plot of the radial power spectra, using 1K realizations of 4K point sets. Stratified sets are also included for comparison. We may distinguish two families of spectral profiles: polynomial (BNOT, SOT, and Stratified), appearing as straight lines in the log-log scale, and exponential for GBN, VNC, KDM, and notably FPO. The shaded area is the noise reduction of GBN relative to BNOT.

Abstract

Among the various approaches for producing point distributions with blue noise spectrum, we argue for an optimization framework using Gaussian kernels. We show that with a wise selection of optimization parameters, this approach attains unprecedented quality, provably surpassing the current state of the art attained by the optimal transport (BNOT) approach. Further, we show that our algorithm scales smoothly and feasibly to high dimensions while maintaining the same quality, realizing unprecedented high-quality high-dimensional blue noise sets. Finally, we show an extension to adaptive sampling.


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Bibtex

@article{Ahmed2022Gaussian,
    author      = {Ahmed, Abdalla G. M. and Ren, Jing and Wonka, Peter},
    title       = {{Gaussian Blue Noise}},
    year        = {2022},
    issue_date  = {December 2022},
    publisher   = {ACM},
    volume      = {41},
    number      = {6},
    issn        = {0730-0301},
    url         = {https://doi.org/10.1145/3550454.3555519},
    doi         = {10.1145/3550454.3555519},
    journal     = {ACM Trans. Graph.},
    month       = nov,
    articleno   = {260},
    numpages    = {15},
    keywords    = {sampling, kernel density, blue noise}
}

Acknowledgments

Thanks to the anonymous reviewers for the valuable comments.
Thanks to Mohanad Ahmed for his insightful discussions.