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Blue noise sampling with controlled aliasing

Published on Jun 1, 2013in ACM Transactions on Graphics6.495
· DOI :10.1145/2487228.2487233
Daniel Heck2
Estimated H-index: 2
(University of Konstanz),
Thomas Schlömer7
Estimated H-index: 7
(University of Konstanz),
Oliver Deussen38
Estimated H-index: 38
(University of Konstanz)
Sources
Abstract
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.
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  • References (29)
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References29
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Electrostatic halftoning is a high-quality method for stippling, dithering, and sampling, but it suffers from a high runtime. This made the technique difficult to use for most real-world applications. A recently proposed minimisation scheme based on the non-equispaced fast Fourier transform (NFFT) lowers the complexity in the particle number M from $\mathcal{O}(M^2) to \mathcal{O}(M \log M). However, the NFFT is hard to parallelise, and the runtime on modern CPUs lies still in the orders ...
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Blue noise point sampling is one of the core algorithms in computer graphics. In this paper, we present a new and versatile variational framework for generating point distributions with high-quality blue noise characteristics while precisely adapting to given density functions. Different from previous approaches based on discrete settings of capacity-constrained Voronoi tessellation, we cast the blue noise sampling generation as a variational problem with continuous settings. Based on an accurat...
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