Fast Tile-Based Adaptive Sampling with User-Specified Fourier Spectra

Florent Wachtel 1   Adrien Pilleboue 1   David Coeurjolly 2   Katherine Breeden 3   Gurprit Singh 1   Gaël Cathelin 1   Fernando de Goes 4   Mathieu Desbrun 4   Victor Ostromoukhov 1,2

1 Université de Lyon   2 CNRS-LIRIS   3 Stanford University   4 Caltech

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We introduce a novel tile-based method for adaptive two-dimensional sampling with user-specified spectral properties. Our approach achieves several orders of magnitude speed improvement over current spectrum-controlled sampling methods through a deterministic, hierarchical construction of self-similar, equi-area tiles whose spatial distribution is free of spurious spectral peaks. A lookup table of sample points, computed offline using any existing procedure that optimizes point sets to shape their Fourier spectrum, is then used to populate the tiles. The result is a linear-time, adaptive, and high-quality sampling of arbitrary density functions that conforms to the desired spectral distribution.


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author = {Wachtel, Florent and Pilleboue, Adrien and Coeurjolly, David and Breeden, Katherine and Singh, Gurprit and Cathelin, Gaël and de Goes, Fernando and Desbrun, Mathieu and Ostromoukhov, Victor},
title = {Fast Tile-Based Adaptive Sampling with User-Specified Fourier Spectra},
journal = {ACM Trans. Graph.}, volume = {33}, number = {4}, year = {2014},
publisher = {ACM}, address = {New York, NY, USA},
keywords = {sampling, tile-based methods, blue-noise distribution, general-noise distribution, fourier spectrum},