Generalized ART-Owen Scrambling

Abdalla G. M. Ahmed; Cheng Wang

doi:10.2312/cgvc.20261017

Generalized ART-Owen Scrambling

Abdalla G. M. Ahmed
, Cheng Wang

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

Owen scrambling is a widely used randomization technique for sampling distributions in quasi-Monte Carlo applications such as rendering. ART-Owen scrambling is a flexible and scalable algorithm for implementing binary Owen scrambling, leveraging the binary structure of Adaptive Regular Tiles (ART). In this formulation, scrambling data is dynamically composed over a static ART tree. Q-ART Owen scrambling extends the approach to base 4 by factoring the 4! possible permutations into affine transformations that are easier to compose over the ART tree. We further extend the model to higher power-of-2 bases using a similar factorization into two components, and discuss a few implementation alternatives.

Original language	English
Title of host publication	Computer Graphics & Visual Computing (CGVC) 2026
DOIs	https://doi.org/10.2312/cgvc.20261017
Publication status	Published - 1 Jun 2026

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10.2312/cgvc.20261017Licence: CC BY

cgvc20261017Final published version, 7.6 MBLicence: CC BY

Cite this

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title = "Generalized ART-Owen Scrambling",

abstract = "Owen scrambling is a widely used randomization technique for sampling distributions in quasi-Monte Carlo applications such as rendering. ART-Owen scrambling is a flexible and scalable algorithm for implementing binary Owen scrambling, leveraging the binary structure of Adaptive Regular Tiles (ART). In this formulation, scrambling data is dynamically composed over a static ART tree. Q-ART Owen scrambling extends the approach to base 4 by factoring the 4! possible permutations into affine transformations that are easier to compose over the ART tree. We further extend the model to higher power-of-2 bases using a similar factorization into two components, and discuss a few implementation alternatives.",

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year = "2026",

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N2 - Owen scrambling is a widely used randomization technique for sampling distributions in quasi-Monte Carlo applications such as rendering. ART-Owen scrambling is a flexible and scalable algorithm for implementing binary Owen scrambling, leveraging the binary structure of Adaptive Regular Tiles (ART). In this formulation, scrambling data is dynamically composed over a static ART tree. Q-ART Owen scrambling extends the approach to base 4 by factoring the 4! possible permutations into affine transformations that are easier to compose over the ART tree. We further extend the model to higher power-of-2 bases using a similar factorization into two components, and discuss a few implementation alternatives.

AB - Owen scrambling is a widely used randomization technique for sampling distributions in quasi-Monte Carlo applications such as rendering. ART-Owen scrambling is a flexible and scalable algorithm for implementing binary Owen scrambling, leveraging the binary structure of Adaptive Regular Tiles (ART). In this formulation, scrambling data is dynamically composed over a static ART tree. Q-ART Owen scrambling extends the approach to base 4 by factoring the 4! possible permutations into affine transformations that are easier to compose over the ART tree. We further extend the model to higher power-of-2 bases using a similar factorization into two components, and discuss a few implementation alternatives.

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DO - 10.2312/cgvc.20261017

M3 - Conference contribution

SN - 978-3-03868-319-3

BT - Computer Graphics & Visual Computing (CGVC) 2026

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