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