Importance Sampling with Floyd-Steinberg Halftoning

This paper proposes a deterministic importance sampling algorithm for complex integrands. The idea is based on the recognition that halftoning algorithms are equivalent to importance sampling if the gray-scale image and a resulting white pixel are considered as the target importance function and the sampling position, respectively. We adopt the Floyd-Steinberg halftoning algorithm, extend it to higher dimensions, and rephrase it as a sampling method. As the Floyd-Steinberg halftoning places a sample also considering where other samples are located, our sampling algorithm distributes samples in a stratified way. In order to demonstrate the power of the method, we present an environment mapping application where the sampling mimics the product of the cosine weighted BRDF, environment radiance, and the environment visibility.