Morphological models of random structures / Dominique Jeulin.

Format:

Book

Author/Creator:

Jeulin, D. (Dominique), author.

Series:

Interdisciplinary Applied Mathematics, 0939-6047 ; 53

Language:

English

Subjects (All):

Random sets.

Physical Description:

1 online resource (XXXII, 919 p. 291 illus., 89 illus. in color.)

Edition:

1st ed. 2021.

Place of Publication:

Cham, Switzerland : Springer, [2021]

Summary:

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.

Contents:

1. Introduction

Part I Tools for Random Structures

2 Introduction to Random Closed Sets and to Semi-continuous Random Functions

3 Quantitative Analysis of Random Structures

Part II Models of Random Structures

4 Excursion sets of Gaussian RF

5 Stochastic Point Processes and Random Trees

6 Boolean Random Sets

7 Random Tessellations

8 The Mosaic Model

9 Boolean Random Functions

10 Random Tessellations and Boolean Random Functions

11 Dead Leaves Models: from Space Tessellations to Random Functions

12 Sequential Cox Boolean and Conditional Dead Leaves Models

13 Sequential Alternate Random Functions

14 Primary Grains and Primary Functions

15 Dilution Random Functions

16 Reaction-Diffusion and Lattice Gas Models

17 Texture Segmentation by Morphological Probabilistic Hierarchies

Part III Random Structures and Change of Scale

18 Change of Scale in Physics of Random Media

19 Digital Materials

20 Probabilistic Models for Fracture Statistics

21 Crack Paths in Random Media.

Notes:

Description based on print version record.

ISBN:

3-030-75452-9

OCLC:

1255219459