Book Details


Morphological Models of Random Structures

Publication year: 2021

ISBN: 978-3-030-75452-5

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This book covers methods of Mathematical Morphology to model and simulate random sets and functions (scalar and multivariate). The introduced models concern many physical situations in heterogeneous media, where a probabilistic approach is required, like fracture statistics of materials, scaling up of permeability in porous media, electron microscopy images (including multispectral images), rough surfaces, multi-component composites, biological tissues, textures for image coding and synthesis. The common feature of these random structures is their domain of definition in n dimensions, requiring more general models than standard Stochastic Processes.The main topics of the book cover an introduction to the theory of random sets, random space tessellations, Boolean random sets and functions, space-time random sets and functions (Dead Leaves, Sequential Alternate models, Reaction-Diffusion), prediction of effective properties of random media, and probabilistic fracture theories.

Subject: Mathematics and Statistics, Probability Theory and Stochastic Processes, Computational Science and Engineering, Geometry, Mathematical Modeling and Industrial Mathematics, Applications of Mathematics, mathematical morphology, random closed sets, random functions, random media, sequential models, stochastic processes, multi-scale random media, numerical simulations, materials sciences, homogenization, fracture statistics, percolation