Quasi-Monte Carlo Algorithms (not only) for Graphics Software

TL;DR

This paper discusses advanced quasi-Monte Carlo algorithms used in computer graphics, focusing on efficient low discrepancy sequences, practical numerical issues, and parallel image synthesis applications with optimized point sets.

Contribution

It introduces optimized low discrepancy sequences for graphics, analyzes numerical pitfalls, and explores parallel quasi-Monte Carlo methods for improved image synthesis.

Findings

Low discrepancy sequences improve uniformity in rendering

Numerical pitfalls can affect quasi-Monte Carlo performance

Parallel algorithms enhance efficiency in image synthesis

Abstract

Quasi-Monte Carlo methods have become the industry standard in computer graphics. For that purpose, efficient algorithms for low discrepancy sequences are discussed. In addition, numerical pitfalls encountered in practice are revealed. We then take a look at massively parallel quasi-Monte Carlo integro-approximation for image synthesis by light transport simulation. Beyond superior uniformity, low discrepancy points may be optimized with respect to additional criteria, such as noise characteristics at low sampling rates or the quality of low-dimensional projections.