Stochastic sampling in computer graphics
ACM Transactions on Graphics (TOG)
Digital halftoning
Spectrally optimal sampling for distribution ray tracing
Proceedings of the 18th annual conference on Computer graphics and interactive techniques
Antialiasing through stochastic sampling
SIGGRAPH '85 Proceedings of the 12th annual conference on Computer graphics and interactive techniques
Principles of Digital Image Synthesis
Principles of Digital Image Synthesis
Capacity-constrained point distributions: a variant of Lloyd's method
ACM SIGGRAPH 2009 papers
Physically Based Rendering, Second Edition: From Theory To Implementation
Physically Based Rendering, Second Edition: From Theory To Implementation
Blue-noise point sampling using kernel density model
ACM SIGGRAPH 2011 papers
Differential domain analysis for non-uniform sampling
ACM SIGGRAPH 2011 papers
Farthest-point optimized point sets with maximized minimum distance
Proceedings of the ACM SIGGRAPH Symposium on High Performance Graphics
Point sampling with general noise spectrum
ACM Transactions on Graphics (TOG) - SIGGRAPH 2012 Conference Proceedings
Least squares quantization in PCM
IEEE Transactions on Information Theory
Variational Blue Noise Sampling
IEEE Transactions on Visualization and Computer Graphics
Analysis and synthesis of point distributions based on pair correlation
ACM Transactions on Graphics (TOG) - Proceedings of ACM SIGGRAPH Asia 2012
Linear efficient antialiased displacement and reflectance mapping
ACM Transactions on Graphics (TOG)
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In this article we revisit the problem of blue noise sampling with a strong focus on the spectral properties of the sampling patterns. Starting from the observation that oscillations in the power spectrum of a sampling pattern can cause aliasing artifacts in the resulting images, we synthesize two new types of blue noise patterns: step blue noise with a power spectrum in the form of a step function and single-peak blue noise with a wide zero-region and no oscillations except for a single peak. We study the mathematical relationship of the radial power spectrum to a spatial statistic known as the radial distribution function to determine which power spectra can actually be realized and to construct the corresponding point sets. Finally, we show that both proposed sampling patterns effectively prevent structured aliasing at low sampling rates and perform well at high sampling rates.