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

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.