Original title:
Zobecněné náhodné mozaiky, jejich vlastnosti, simulace a aplikace
Translated title:
Generalized random tessellations, their properties, simulation and applications
Authors:
Jahn, Daniel ; Beneš, Viktor (advisor) ; Rataj, Jan (referee) Document type: Master’s theses
Year:
2019
Language:
eng Abstract:
The past few years have seen advances in modelling of polycrystalline materi- als using parametric tessellation models from stochastic geometry. A promising class of tessellations, the Gibbs-type tessellation, allows the user to specify a great variety of properties through the energy function. This text focuses solely on tetrahedrizations, a three-dimensional tessellation composed of tetrahedra. The existing results for two-dimensional Delaunay triangulations are extended to the case of three-dimensional Laguerre tetrahedrization. We provide a proof of existence, a C++ implementation of the MCMC simulation and estimation of the models parameters through maximum pseudolikelihood. 1
Keywords:
Gibbs generalized tessellation; incremental-decremental algorithm; properties of stochastic models; algoritmus přidání a odebrání; Gibbsova zobecněná mozaika; vlastnosti stochastických modelů
Institution: Charles University Faculties (theses)
(web)
Document availability information: Available in the Charles University Digital Repository. Original record: http://hdl.handle.net/20.500.11956/105167