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Order-Randomized Laplacian Mesh Smoothing

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Book cover Mathematical Methods for Curves and Surfaces (MMCS 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10521))

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Abstract

In this paper we compare three variants of the graph Laplacian smoothing. The first is the standard synchronous implementation, corresponding to multiplication by the graph Laplacian matrix. The second is a voter process inspired asynchronous implementation, assuming that every vertex is equipped with an independent exponential clock. The third is in-between the first two, with the vertices updated according to a random permutation of them. We review some well-known results on spectral graph theory and on voter processes, and we show that while the convergence of the synchronous Laplacian is graph dependent and, generally, does not converge on bipartite graphs, the asynchronous converges with high probability on all graphs. The differences in the properties of these three approaches are illustrated with examples including both regular grids and irregular meshes.

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Author information

Authors and Affiliations

  1. Fujian Provincial Key Laboratory of Information Processing and Intelligent Control, Minjiang University, Fuzhou, China

    Ying Yang

  2. Yale University, New Haven, USA

    Ying Yang & Holly Rushmeier

  3. Durham University, Durham, UK

    Ioannis Ivrissimtzis

Authors
  1. Ying Yang
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  2. Holly Rushmeier
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  3. Ioannis Ivrissimtzis
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Corresponding author

Correspondence to Ioannis Ivrissimtzis .

Editor information

Editors and Affiliations

  1. University of Oslo, Oslo, Norway

    Michael Floater

  2. University of Oslo, Oslo, Norway

    Tom Lyche

  3. Université Joseph Fourier, Grenoble, France

    Marie-Laurence Mazure

  4. University of Oslo, Oslo, Norway

    Knut Mørken

  5. Vanderbilt University, Nashville, Tennessee, USA

    Larry L. Schumaker

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Yang, Y., Rushmeier, H., Ivrissimtzis, I. (2017). Order-Randomized Laplacian Mesh Smoothing. In: Floater, M., Lyche, T., Mazure, ML., Mørken, K., Schumaker, L. (eds) Mathematical Methods for Curves and Surfaces. MMCS 2016. Lecture Notes in Computer Science(), vol 10521. Springer, Cham. https://doi.org/10.1007/978-3-319-67885-6_17

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  • DOI: https://doi.org/10.1007/978-3-319-67885-6_17

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-67884-9

  • Online ISBN: 978-3-319-67885-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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