Low-Discrepancy Blue Noise Sampling

ACM Transactions on Graphics (Proceedings of SIGGRAPH ASIA 2016)

Abdalla G. M. Ahmed¹            Hélène Perrier²             David Coeurjolly²            Victor Ostromoukhov²

 Jianwei Guo³            Dongming Yan³             Hui Huang^4,5             Oliver Deussen^1,5

¹University of Konstanz         ²Université de Lyon, CNRS/LIRIS          ³Institute of Automation            ⁴Shenzhen University               ⁵SIAT

Starting from a template low-discrepancy (LD) point set (a), we use a segmented table of permutations to rearrange the LD set to match a reference set with the desired target spectrum (b). The permutations are localized and carefully constructed in such a way that they have minimal impact on the discrepancy of the underlying template set. The resulting set (c) inherits the spectral profile of the target set, while still retaining the discrepancy profile of the template set (d).

Abstract
We present a novel technique that produces two-dimensional low-discrepancy (LD) blue noise point sets for sampling. Using one-dimensional binary van der Corput sequences, we construct two-dimensional LD point sets, and rearrange them to match a target spectral profile without loosing their low discrepancy. We store the rearrangement information in a compact lookup table that can be used to produce arbitrarily large point sets. To the best of our knowledge, our construction is the first one that combines blue-noise and low-discrepancy properties at the same time. We evaluate our technique and compare it to the state-of-the-art sampling approaches.

Data & Code
Note that the DATA and CODE are free for Research and Education Use ONLY.
Please cite our paper (add the bibtex below) if you use any part of our ALGORITHM, CODE, DATA or RESULTS in any publication.

Interactive Demo

Results
This html bundle contains all the data that was collected while performing tests and comparisons between the LDBN sampler and various other samplers from the state of the art. You can click on any sampler to see all its associated data, discrepancy results, integration variance results, point distribution, behaviour relatively to aliasing (zoneplate tests), and spectral behaviour.

Video

Acknowledgment 
We thank the anonymous reviewers for their detailed feedback to improve the paper. Thanks to Jean-Yves Franceschi and Jonathan Dupuy for reviewing an earlier version of the paper. This project was supported in part by Deutsche Forschungsgemeinschaft Grant (DE-620/22-1), French ANR Excellence Chair (ANR-10-CEXC-002-01) and CoMeDiC (ANR-15-CE40-0006), 973 Program (2015CB352501), National Foreign 1000 Plan (WQ201344000169), National Natural Science Foundation of China (61372168, 61620106003, 61331018), GD Leading Talents Plan (00201509), GD Science and Technology Program (2014B050502009, 2014TX01X033, 2015A030312015, 2016A050503036), and SZ Innovation Program (JCYJ20151015151249564).

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