STOCHASTIC GEOMETRY AND ITS APPLICATIONS PDF
View Table of Contents for Stochastic Geometry and its Applications Stochastic geometry and spatial statistics play a fundamental role in. An extensive update to a classic text. Stochastic geometry and spatial statistics play a fundamental role in many modern branches of physics, materials sciences, . Request PDF on ResearchGate | Stochastic Geometry and Its Applications | An extensive update to a classic text Stochastic geometry and spatial statistics play a .
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An extensive update to a classic text Stochastic geometry and spatial statistics play a fundamental role in many modern branches of physics, materials sciences, . is required for the applications to stochastic geometry. First, the necessary definitions and concepts related to geometric point processes and from convex. Mathematical morphology and stochastic geometry provide efficient tools for both phology finds most of its applications in the field of image.
A complete answer to this question requires the theory of random closed sets , which makes contact with advanced concepts from measure theory. The key idea is to focus on the probabilities of the given random closed set hitting specified test sets. There arise questions of inference for example, estimate the set which encloses a given point pattern and theories of generalizations of means etc.
Connections are now being made between this latter work and recent developments in geometric mathematical analysis concerning general metric spaces and their geometry.
Good parametrizations of specific random sets can allow us to refer random object processes to the theory of marked point processes; object-point pairs are viewed as points in a larger product space formed as the product of the original space and the space of parametrization.
Stochastic Geometry and Its Applications, 3rd Edition
Line and hyper-flat processes[ edit ] Suppose we are concerned no longer with compact objects, but with objects which are spatially extended: lines on the plane or flats in 3-space. This leads to consideration of line processes, and of processes of flats or hyper-flats. There can no longer be a preferred spatial location for each object; however the theory may be mapped back into point process theory by representing each object by a point in a suitable representation space.
For example, in the case of directed lines in the plane one may take the representation space to be a cylinder.
A complication is that the Euclidean motion symmetries will then be expressed on the representation space in a somewhat unusual way. Moreover, calculations need to take account of interesting spatial biases for example, line segments are less likely to be hit by random lines to which they are nearly parallel and this provides an interesting and significant connection to the hugely significant area of stereology , which in some respects can be viewed as yet another theme of stochastic geometry.
It is often the case that calculations are best carried out in terms of bundles of lines hitting various test-sets, rather than by working in representation space. Line and hyper-flat processes have their own direct applications, but also find application as one way of creating tessellations dividing space; hence for example one may speak of Poisson line tessellations.
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Chiu S.N. et al. Stochastic Geometry and its Applications
Stochastic Geometry and its Applications Editor s: Kendall Joseph Mecke. First published: Print ISBN: Book Series: Wiley Series in Probability and Statistics.
About this book 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. This editi on: Presents a wealth of models for spatial patterns and related statistical methods.
Provides a great survey of the modern theory of random tessellations, including many new models that became tractable only in the last few years. Includes new sections on random networks and random graphs to review the recent ever growing interest in these areas.
Provides an excellent introduction to theory and modelling of point processes, which covers some very latest developments.
Illustrate the forefront theory of random sets, with many applications. Adds new results to the discussion of fibre and surface processes. Offers an updated collection of useful stereological methods. Includes new references.
Is written in an accessible style enabling non-mathematicians to benefit from this book.Request Username Can't sign in?
Adds new results to the discussion of fibre and surface processes.
Offers an updated collection of useful stereological methods. Permissions Request permission to reuse content from this site. Random object[ edit ] What is meant by a random object?
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