Projective Blue‐Noise Sampling

Abstract

We propose projective blue‐noise patterns that retain their blue‐noise characteristics when undergoing one or multiple projections onto lower dimensional subspaces. These patterns are produced by extending existing methods, such as dart throwing and Lloyd relaxation, and have a range of applications. For numerical integration, our patterns often outperform state‐of‐the‐art stochastic and low‐discrepancy patterns, which have been specifically designed only for this purpose. For image reconstruction, our method outperforms traditional blue‐noise sampling when the variation in the signal is concentrated along one dimension. Finally, we use our patterns to distribute primitives uniformly in 3D space such that their 2D projections retain a blue‐noise distribution.We propose projective blue‐noise patterns that retain their blue‐noise characteristics when undergoing one or multiple projections onto lower dimensional subspaces. These patterns are produced by extending existing methods, such as dart throwing and Lloyd relaxation, and have a range of applications. For numerical integration, our patterns often outperform state‐of‐the‐art stochastic and low‐discrepancy patterns, which have been specifically designed only for this purpose. For image reconstruction, our method outperforms traditional blue‐noise sampling when the variation in the signal is concentrated along one dimension. Finally, we use our patterns to distribute primitives uniformly in 3D space such that their 2D projections retain a blue‐noise distribution.