Forced Random Sampling: fast generation of importance-guided blue-noise samples

In computer graphics, stochastic sampling is frequently used to efficiently approximate complex functions and integrals. The error of approximation can be reduced by distributing samples according to an importance function, but cannot be eliminated completely. To avoid visible artifacts, sample distributions are sought to be random, but spatially uniform, which is called blue-noise sampling. The generation of unbiased, importance-guided blue-noise samples is expensive and not feasible for real-time applications. Sampling algorithms for these applications focus on runtime performance at the cost of having weak blue-noise properties. Blue-noise distributions have also been proposed for digital halftoning in the form of precomputed dither matrices. Ordered dithering with such matrices allows to distribute dots with blue-noise properties according to a grayscale image. By the nature of ordered dithering, this process can be parallelized easily. We introduce a novel sampling method called forced random sampling that is based on forced random dithering, a variant of ordered dithering with blue noise. By shifting the main computational effort into the generation of a precomputed dither matrix, our sampling method runs efficiently on GPUs and allows real-time importance sampling with blue noise for a finite number of samples. We demonstrate the quality of our method in two different rendering applications.