Order-Randomized Laplacian Mesh Smoothing

Conference paper
First Online:
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10521)

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.

Keywords

Laplacian smoothing Graph Laplacian matrix Voter processes Triangle meshes Regular grids Taubin smoothing 
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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Ying Yang
    • 1
    • 2
  • Holly Rushmeier
    • 2
  • Ioannis Ivrissimtzis
    • 3
  1. 1.Fujian Provincial Key Laboratory of Information Processing and Intelligent ControlMinjiang UniversityFuzhouChina
  2. 2.Yale UniversityNew HavenUSA
  3. 3.Durham UniversityDurhamUK

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