Deterministic Importance Sampling with Error Diffusion

Abstract

This paper proposes a deterministic importance sampling algorithm that is based on the recognition that delta-sigma modulation is equivalent to importance sampling. We propose a generalization for delta-sigma modulation in arbitrary dimensions, taking care of the curse of dimensionality as well. Unlike previous sampling techniques that transform low-discrepancy and highly stratified samples in the unit cube to the integration domain, our error diffusion sampler ensures the proper distribution and stratification directly in the integration domain. We also present applications, including environment mapping and global illumination rendering with virtual point sources.