2022/07/12 by Alexander Keller, Keller, Alexander, Carsten Wächter +3 · 1 citation
Computer Science · Engineering · #Advanced Numerical Analysis Techniques #Computer Graphics and Visualization Techniques #FOS: Computer and information sciences #FOS: Mathematics #Generative Adversarial Networks and Image Synthesis #Graphics (cs.GR) #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.2207.05415
openalex publication_date 2022/07/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Based on the seminal work on Array-RQMC methods and rank-1 lattice sequences by Pierre L'Ecuyer and collaborators, we introduce efficient deterministic algorithms for image synthesis. Enumerating a low discrepancy sequence along the Hilbert curve superimposed on the raster of pixels of an image, we achieve noise characteristics that are desirable with respect to the human visual system, especially at very low sampling rates. As compared to the state of the art, our simple algorithms neither require randomization, nor costly optimization, nor lookup tables. We analyze correlations of space-filling curves and low discrepancy sequences, and demonstrate the benefits of the new algorithms in a professional, massively parallel light transport simulation and rendering system.