Turning Grain Maps into Diagrams

Andreas Alpers, Maximilian Fiedler, Peter Gritzmann, Fabian Klemm

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


The present paper studies mathematical models for representing, imaging, and analyzing polycrystalline materials. We introduce various techniques for converting grain maps into diagram or tessellation representations that rely on constrained clustering. In particular, we show how to significantly accelerate the computation of generalized balanced power diagrams and how to extend it to allow for optimization over all relevant parameters. A comparison of the accuracy of the proposed approaches is given based on a three-dimensional real-world data set of 339 × 339 × 599 voxels.

Original languageEnglish
Pages (from-to)223-249
Number of pages27
JournalSIAM Journal on Imaging Sciences
Issue number1
StatePublished - 2023


  • coreset
  • data reduction
  • diagram
  • grain map
  • imaging
  • polycrystal


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