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

Abstract
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.

Citation
Ahmed, A. G. M., & Wonka, P. (2020). Screen-space blue-noise diffusion of monte carlo sampling error via hierarchical ordering of pixels. ACM Transactions on Graphics, 39(6), 1–15. doi:10.1145/3414685.3417881

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.

Publisher
Association for Computing Machinery (ACM)

Journal
ACM Transactions on Graphics

DOI
10.1145/3414685.3417881

Additional Links
https://dl.acm.org/doi/10.1145/3414685.3417881

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