Screen-space blue-noise diffusion of monte carlo sampling error via hierarchical ordering of pixels

We present a novel technique for diffusing Monte Carlo sampling error as a blue noise in screen space. We show that automatic diffusion of sampling error can be achieved by ordering the pixels in a way that preserves locality, such as Morton's Z-ordering, and assigning the samples to the pixels from successive sub-sequences of a single low-discrepancy sequence, thus securing well-distributed samples for each pixel, local neighborhoods, and the whole image. We further show that a blue-noise distribution of the error is attainable by scrambling the Z-ordering to induce isotropy. We present an efficient technique to implement this hierarchical scrambling by defining a context-free grammar that describes infinite self-similar lookup trees. Our concept is scalable to arbitrary image resolutions, sample dimensions, and sample count, and supports progressive and adaptive sampling.