Exploration of Gibbs-Laguerre tessellations for three-dimensional stochastic modeling
| Autor: | Lukas Petrich, Carl E. Krill, F. Seitl, Jakub Staněk, Volker Schmidt, Viktor Beneš |
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| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
FOS: Computer and information sciences
Statistics and Probability Tessellation General Mathematics Image and Video Processing (eess.IV) 010102 general mathematics Probabilistic logic Markov chain Monte Carlo Function (mathematics) Electrical Engineering and Systems Science - Image and Video Processing 01 natural sciences Statistics - Computation Point process 010104 statistics & probability symbols.namesake Stochastic simulation FOS: Electrical engineering electronic engineering information engineering symbols Laguerre polynomials Statistical physics 0101 mathematics 60D55 Computation (stat.CO) Energy (signal processing) Mathematics |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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