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Order-randomized Laplacian mesh smoothing

Yang, Ying; Rushmeier, Holly; Ivrissimtzis, Ioannis

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Authors

Ying Yang

Holly Rushmeier



Contributors

Michael S. Floater
Editor

Tom Lyche
Editor

Marie-Laurence Mazure
Editor

Knut Mørken
Editor

Larry L. Schumaker
Editor

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.

Citation

Yang, Y., Rushmeier, H., & Ivrissimtzis, I. (2017). Order-randomized Laplacian mesh smoothing. In M. S. Floater, T. Lyche, M. Mazure, K. Mørken, & L. L. Schumaker (Eds.), Mathematical methods for curves and surfaces : 9th International Conference, MMCS 2016, Tønsberg, Norway, June 23 - June 28, 2016. Revised selected papers (312-323). https://doi.org/10.1007/978-3-319-67885-6_17

Conference Name 9th International Conference on Mathematical Methods for Curves and Surfaces
Conference Location Tønsberg, Norway
Start Date Jun 23, 2016
End Date Jun 28, 2016
Acceptance Date Mar 7, 2017
Online Publication Date Oct 18, 2017
Publication Date Oct 18, 2017
Deposit Date Aug 15, 2017
Publicly Available Date Oct 18, 2018
Pages 312-323
Series Title Lecture notes in computer science
Series Number 10521
Series ISSN 0302-9743,1611-3349
Book Title Mathematical methods for curves and surfaces : 9th International Conference, MMCS 2016, Tønsberg, Norway, June 23 - June 28, 2016. Revised selected papers.
ISBN 9783319678849
DOI https://doi.org/10.1007/978-3-319-67885-6_17
Public URL https://durham-repository.worktribe.com/output/1146570

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