Rendering along the Hilbert Curve

TL;DR

This paper introduces efficient, deterministic algorithms for image rendering using low discrepancy sequences along the Hilbert curve, achieving low-noise visual quality at low sampling rates without complex computations.

Contribution

It presents novel algorithms that combine Hilbert curves with low discrepancy sequences for improved image synthesis, avoiding randomization and costly optimization.

Findings

Achieves desirable noise characteristics at low sampling rates.

Demonstrates improved rendering quality in parallel systems.

Algorithms are simple, deterministic, and do not require lookup tables.

Abstract

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.