  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.
