LEADER 03579nam 2200517 450 001 9910484219003321 005 20230421124342.0 010 $a3-030-75452-9 024 7 $a10.1007/978-3-030-75452-5 035 $a(CKB)4100000011951207 035 $a(DE-He213)978-3-030-75452-5 035 $a(MiAaPQ)EBC6635764 035 $a(Au-PeEL)EBL6635764 035 $a(OCoLC)1255219459 035 $a(PPN)258852178 035 $a(EXLCZ)994100000011951207 100 $a20220125d2021 uy 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aMorphological models of random structures /$fDominique Jeulin 205 $a1st ed. 2021. 210 1$aCham, Switzerland :$cSpringer,$d[2021] 210 4$dŠ2021 215 $a1 online resource (XXXII, 919 p. 291 illus., 89 illus. in color.) 225 1 $aInterdisciplinary Applied Mathematics,$x0939-6047 ;$v53 311 $a3-030-75451-0 327 $a1. 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. 330 $aThis book covers methods of Mathematical Morphology to model and simulate random sets and functions (scalar and multivariate). The introduced models concern many physical situations in heterogeneous media, where a probabilistic approach is required, like fracture statistics of materials, scaling up of permeability in porous media, electron microscopy images (including multispectral images), rough surfaces, multi-component composites, biological tissues, textures for image coding and synthesis. The common feature of these random structures is their domain of definition in n dimensions, requiring more general models than standard Stochastic Processes.The main topics of the book cover an introduction to the theory of random sets, random space tessellations, Boolean random sets and functions, space-time random sets and functions (Dead Leaves, Sequential Alternate models, Reaction-Diffusion), prediction of effective properties of random media, and probabilistic fracture theories. 410 0$aInterdisciplinary Applied Mathematics,$x0939-6047 ;$v53 606 $aRandom sets 606 $aModels matemātics$2thub 608 $aLlibres electrōnics$2thub 615 0$aRandom sets. 615 7$aModels matemātics 676 $a519.2 700 $aJeulin$b D$g(Dominique),$01076319 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910484219003321 996 $aMorphological models of random structures$92586700 997 $aUNINA