Screen-space blue-noise diffusion of monte carlo sampling error via hierarchical ordering of pixels

Abdalla G. M. Ahmed, Peter Wonka

Research output: Contribution to journalArticlepeer-review

15 Scopus citations


We present a novel technique for diffusing Monte Carlo sampling error as a blue noise in screen space. We show that automatic diffusion of sampling error can be achieved by ordering the pixels in a way that preserves locality, such as Morton's Z-ordering, and assigning the samples to the pixels from successive sub-sequences of a single low-discrepancy sequence, thus securing well-distributed samples for each pixel, local neighborhoods, and the whole image. We further show that a blue-noise distribution of the error is attainable by scrambling the Z-ordering to induce isotropy. We present an efficient technique to implement this hierarchical scrambling by defining a context-free grammar that describes infinite self-similar lookup trees. Our concept is scalable to arbitrary image resolutions, sample dimensions, and sample count, and supports progressive and adaptive sampling.
Original languageEnglish (US)
Pages (from-to)1-15
Number of pages15
JournalACM Transactions on Graphics
Issue number6
StatePublished - Nov 26 2020

Bibliographical note

KAUST Repository Item: Exported on 2020-12-08
Acknowledgements: Thanks to the anonymous reviewers for the valuable comments. We credit reviewer #1 for pointing out the advantage of arithmetic
hashing for GPU implementation. Thanks to the scientific editing team at KAUST for proofreading the paper and to Mohanad Ahmed
for his insightful discussions.


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