Inverting Laguerre tessellations

Duan, Qibin, Kroese, Dirk P., Brereton, Tim, Spettl, Aaron and Schmidt, Volker (2014) Inverting Laguerre tessellations. The Computer Journal, 57 9: 1431-1440. doi:10.1093/comjnl/bxu029

Author Duan, Qibin
Kroese, Dirk P.
Brereton, Tim
Spettl, Aaron
Schmidt, Volker
Title Inverting Laguerre tessellations
Journal name The Computer Journal   Check publisher's open access policy
ISSN 1460-2067
Publication date 2014-09-01
Year available 2014
Sub-type Article (original research)
DOI 10.1093/comjnl/bxu029
Volume 57
Issue 9
Start page 1431
End page 1440
Total pages 10
Place of publication Oxford, United Kingdom
Publisher Oxford University Press
Formatted abstract
A Laguerre tessellation is a generalization of aVoronoi tessellation where the proximity between points is measured via a power distance rather than the Euclidean distance. Laguerre tessellations have found significant applications in materials science, providing improved modeling of (poly)crystalline microstructures and grain growth. There exist efficient algorithms to construct Laguerre tessellations from given sets of weighted generator points, similar to methods used for Voronoi tessellations. The purpose of this paper is to provide theory and methodology for the inverse construction; that is, to recover the weighted generator points from a given Laguerre tessellation. We show that, unlike the Voronoi case, the inverse problem is in general non-unique: different weighted generator points can create the same tessellation. To recover pertinent generator points, we formulate the inversion problem as a multimodal optimization problem and apply the cross-entropy method to solve it.
Keyword Cross-entropy method
Generator points
Inverse problem
Laguerre tessellation
Q-Index Code C1
Q-Index Status Confirmed Code
Institutional Status UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
Official 2015 Collection
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Citation counts: TR Web of Science Citation Count  Cited 6 times in Thomson Reuters Web of Science Article | Citations
Scopus Citation Count Cited 7 times in Scopus Article | Citations
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