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 Huang4,5 Oliver Deussen1,5
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.
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