Multilevel Skeletonization Using Local Separators

Authors J. Andreas Bærentzen , Rasmus Emil Christensen, Emil Toftegaard Gæde , Eva Rotenberg

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Author Details

J. Andreas Bærentzen
  • Department of Applied Mathematics and Computer Science, Technical University of Denmark, Lyngby, Denmark
Rasmus Emil Christensen
  • Department of Applied Mathematics and Computer Science, Technical University of Denmark, Lyngby, Denmark
Emil Toftegaard Gæde
  • Department of Applied Mathematics and Computer Science, Technical University of Denmark, Lyngby, Denmark
Eva Rotenberg
  • Department of Applied Mathematics and Computer Science, Technical University of Denmark, Lyngby, Denmark

Cite AsGet BibTex

J. Andreas Bærentzen, Rasmus Emil Christensen, Emil Toftegaard Gæde, and Eva Rotenberg. Multilevel Skeletonization Using Local Separators. In 39th International Symposium on Computational Geometry (SoCG 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 258, pp. 13:1-13:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


In this paper we give a new, efficient algorithm for computing curve skeletons, based on local separators. Our efficiency stems from a multilevel approach, where we solve small problems across levels of detail and combine these in order to quickly obtain a skeleton. We do this in a highly modular fashion, ensuring complete flexibility in adapting the algorithm for specific types of input or for otherwise targeting specific applications. Separator based skeletonization was first proposed by Bærentzen and Rotenberg in [ACM Tran. Graphics'21], showing high quality output at the cost of running times which become prohibitive for large inputs. Our new approach retains the high quality output, and applicability to any spatially embedded graph, while being orders of magnitude faster for all practical purposes. We test our skeletonization algorithm for efficiency and quality in practice, comparing it to local separator skeletonization on the University of Groningen Skeletonization Benchmark [Telea'16].

Subject Classification

ACM Subject Classification
  • Computing methodologies → Computer graphics
  • Theory of computation → Computational geometry
  • Software and its engineering → Software design engineering
  • Algorithm engineering
  • experimentation and implementation
  • shape skeletonization
  • curve skeletons
  • multilevel algorithm


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