| Description |
1 online resource (583 pages) |
| Contents |
Stochastic Geometry and its Applications; Contents; Foreword to the first edition; From the preface to the first edition; Preface to the second edition; Preface to the third edition; Notation; 1 Mathematical foundations; 1.1 Set theory; 1.2 Topology in Euclidean spaces; 1.3 Operations on subsets of Euclidean space; 1.4 Mathematical morphology and image analysis; 1.5 Euclidean isometries; 1.6 Convex sets in Euclidean spaces; 1.7 Functions describing convex sets; 1.7.1 General; 1.7.2 Set covariance; 1.7.3 Chord length distribution; 1.7.4 Erosion-dilation functions; 1.8 Polyconvex sets |
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1.9 Measure and integration theory2 Point processes I -- The Poisson point process; 2.1 Introduction; 2.2 The binomial point process; 2.2.1 Introduction; 2.2.2 Basic properties; 2.2.3 Simulation; 2.3 The homogeneous Poisson point process; 2.3.1 Definition and defining properties; 2.3.2 Characterisation of the homogeneous Poisson point process; 2.3.3 Moments and moment measures; 2.3.4 The Palm distribution of a homogeneous Poisson point process; 2.4 The inhomogeneous and general Poisson point process; 2.5 Simulation of Poisson point processes |
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2.5.1 Simulation of a homogeneous Poisson point process2.5.2 Simulation of an inhomogeneous Poisson point process; 2.6 Statistics for the homogeneous Poisson point process; 2.6.1 Introduction; 2.6.2 Estimating the intensity; 2.6.3 Testing the hypothesis of homogeneity; 2.6.4 Testing the Poisson process hypothesis; 3 Random closed sets I -- The Boolean model; 3.1 Introduction and basic properties; 3.1.1 Model description; 3.1.2 Applications; 3.1.3 Stationarity and isotropy; 3.1.4 Simulation; 3.1.5 The capacity functional; 3.1.6 Basic characteristics; 3.1.7 Contact distribution functions |
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3.2 The Boolean model with convex grains3.2.1 The simplified formula for the capacity functional; 3.2.2 Intensities or densities of intrinsic volumes; 3.2.3 Contact distribution functions; 3.2.4 Morphological functions; 3.2.5 Intersections with linear subspaces; 3.2.6 Formulae for some special Boolean models with isotropic convex grains; 3.3 Coverage and connectivity; 3.3.1 Coverage probabilities; 3.3.2 Clumps; 3.3.3 Connectivity; 3.3.4 Percolation; 3.3.5 Vacant regions; 3.4 Statistics; 3.4.1 General remarks; 3.4.2 Testing model assumptions; 3.4.3 Estimation of model parameters |
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3.5 Generalisations and variations3.6 Hints for practical applications; 4 Point processes II -- General theory; 4.1 Basic properties; 4.1.1 Introduction; 4.1.2 The distribution of a point process; 4.1.3 Notation; 4.1.4 Stationarity and isotropy; 4.1.5 Intensity measure and intensity; 4.1.6 Ergodicity and central limit theorem; 4.1.7 Contact distributions; 4.2 Marked point processes; 4.2.1 Fundamentals; 4.2.2 Intensity and mark distribution; 4.3 Moment measures and related quantities; 4.3.1 Moment measures; 4.3.2 Factorial moment measures; 4.3.3 Product densities; 4.3.4 The Campbell measure |
| Summary |
An extensive update to a classic text Stochastic geometry and spatial statistics play a fundamental role in many modern branches of physics, materials sciences, engineering, biology and environmental sciences. They offer successful models for the description of random two- and three-dimensional micro and macro structures and statistical methods for their analysis. The previous edition of this book has served as the key reference in its field for over 18 years and is regarded as the best treatment of the subject of stochastic geometry, both as a subject with vital a |
| Notes |
4.3.5 The mark correlation function |
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Print version record |
| Subject |
Stochastic geometry.
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Stochastic geometry
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| Form |
Electronic book
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| Author |
Stoyan, Dietrich
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Kendall, W. S.
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Mecke, Joseph
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| ISBN |
9781118658253 |
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1118658256 |
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