  Blue noise error patterns are well suited to human perception, and when
applied to stochastic rendering techniques, blue noise masks (blue noise
textures) minimize unwanted low-frequency noise in the final image. Current
methods of applying blue noise masks at each frame independently produce white
noise frequency spectra temporally. This white noise results in slower
integration convergence over time and unstable results when filtered
temporally. Unfortunately, achieving temporally stable blue noise distributions
is non-trivial since 3D blue noise does not exhibit the desired 2D blue noise
properties, and alternative approaches degrade the spatial blue noise
qualities.
  We propose novel blue noise patterns that, when animated, produce values at a
pixel that are well distributed over time, converge rapidly for Monte Carlo
integration, and are more stable under TAA, while still retaining spatial blue
noise properties. To do so, we propose an extension to the well-known void and
cluster algorithm that reformulates the underlying energy function to produce
spatiotemporal blue noise masks.
  These masks exhibit blue noise frequency spectra in both the spatial and
temporal domains, resulting in visually pleasing error patterns, rapid
convergence speeds, and increased stability when filtered temporally. We
demonstrate these improvements on a variety of applications, including
dithering, stochastic transparency, ambient occlusion, and volumetric
rendering.
  By extending spatial blue noise to spatiotemporal blue noise, we overcome the
convergence limitations of prior blue noise works, enabling new applications
for blue noise distributions.
