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Exploration of Gibbs-Laguerre Tessellations for Three-Dimensional Stochastic Modeling

Author

Listed:
  • F. Seitl

    (Charles University Prague)

  • L. Petrich

    (Ulm University)

  • J. Staněk

    (Charles University Prague)

  • C. E. Krill

    (Ulm University)

  • V. Schmidt

    (Charles University Prague)

  • V. Beneš

    (Charles University Prague)

Abstract

Random tessellations are well suited for probabilistic modeling of three-dimensional (3D) grain microstructures of polycrystalline materials. The present paper is focused on so-called Gibbs-Laguerre tessellations, in which the generators of the Laguerre tessellation form a Gibbs point process. The goal is to construct an energy function of the Gibbs point process such that the resulting tessellation matches some desired geometrical properties. Since the model is analytically intractable, our main tool of analysis is stochastic simulation based on Markov chain Monte Carlo. Such simulations enable us to investigate the properties of the models, and, in the next step, to apply the knowledge gained to the statistical reconstruction of the 3D microstructure of an aluminum alloy extracted from 3D tomographic image data.

Suggested Citation

  • F. Seitl & L. Petrich & J. Staněk & C. E. Krill & V. Schmidt & V. Beneš, 2021. "Exploration of Gibbs-Laguerre Tessellations for Three-Dimensional Stochastic Modeling," Methodology and Computing in Applied Probability, Springer, vol. 23(2), pages 669-693, June.
    • Handle: RePEc:spr:metcap:v:23:y:2021:i:2:d:10.1007_s11009-019-09757-x
    DOI: 10.1007/s11009-019-09757-x
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    References listed on IDEAS

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    1. Tscheschel, A. & Stoyan, D., 2006. "Statistical reconstruction of random point patterns," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 859-871, November.
    2. Dereudre, D. & Lavancier, F., 2011. "Practical simulation and estimation for Gibbs Delaunay-Voronoi tessellations with geometric hardcore interaction," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 498-519, January.
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