ACM Trans. Graph. (Proceedings of SIGGRAPH Asia 2023)

ART-Owen Scrambling

Abdalla G. M. Ahmed¹       Matt Pharr²       Peter Wonka¹

¹ KAUST, KSA
² NVIDIA, USA

With geometric details at the scale of a few pixels, unscrambled Sobol sampling points may give structured artifacts. This is a typical example of aliasing artifacts [Shannon 1948] where frequencies beyond the sampling rate manifest as low-frequency structures. Owen-scrambling the points causes the error to be higher-frequency, which is more visually pleasing. Our approach, ART-Owen Scrambling, efficiently generates Owen-scrambled sample points using a grammar based on adaptive regular tiles (ART).

Abstract

We present a novel algorithm for implementing Owen-scrambling, combining the generation and distribution of the scrambling bits in a single self-contained compact process. We employ a context-free grammar to build a binary tree of symbols, and equip each symbol with a scrambling code that affects all descendant nodes. We nominate the grammar of adaptive regular tiles (ART) derived from the repetition-avoiding Thue-Morse word, and we discuss its potential advantages and shortcomings. Our algorithm has many advantages, including random access to samples, fixed time complexity, GPU friendliness, and scalability to any memory budget. Further, it provides two unique features over known methods: it admits optimization, and it is invertible, enabling screen-space scrambling of the high-dimensional Sobol sampler.s

Stippling and Adaptive Reconstruction Demo

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