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Fast electrostatic halftoning

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Abstract

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 of an hour for about 50,000 particles, to a day for 1 million particles. Our contributions to remedy this problem are threefold: we design the first GPU-based NFFT algorithm without special structural assumptions on the positions of nodes, we introduce a novel nearest-neighbour identification scheme for continuous point distributions, and we optimise the whole algorithm for n-body problems such as electrostatic halftoning. For 1 million particles, this new algorithm runs 50 times faster than the most efficient technique on the CPU, and even yields a speedup of 7,000 over the original algorithm.

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Acknowledgments

The authors thank the Cluster of Excellence ‘Multimodal Computing and Interaction’ for partly funding this work, and Thomas Schlömer from the University of Constance for providing images for comparison.

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Authors and Affiliations

  1. Mathematical Image Analysis Group, Faculty of Mathematics and Computer Science, Saarland University, Campus E1.1, 66041, Saarbrücken, Germany

    Pascal Gwosdek, Christian Schmaltz & Joachim Weickert

  2. Mathematical Image Processing and Data Analysis, Department of Mathematics, Technical University of Kaiserslautern, Erwin-Schrödinger-Straße, 67663, Kaiserslautern, Germany

    Tanja Teuber

Authors
  1. Pascal Gwosdek
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  2. Christian Schmaltz
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  3. Joachim Weickert
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  4. Tanja Teuber
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Correspondence to Pascal Gwosdek.

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Gwosdek, P., Schmaltz, C., Weickert, J. et al. Fast electrostatic halftoning. J Real-Time Image Proc 9, 379–392 (2014). https://doi.org/10.1007/s11554-011-0236-3

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  • DOI: https://doi.org/10.1007/s11554-011-0236-3

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