Tensor valuations and their applications in stochastic geometry and imaging
著者
書誌事項
Tensor valuations and their applications in stochastic geometry and imaging
（Lecture notes in mathematics, 2177）
Springer, c2017
- : pbk
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注記
Includes bibliographical references and index
内容説明・目次
内容説明
The purpose of this volume is to give an up-to-date introduction to tensor valuations and their applications. Starting with classical results concerning scalar-valued valuations on the families of convex bodies and convex polytopes, it proceeds to the modern theory of tensor valuations. Product and Fourier-type transforms are introduced and various integral formulae are derived. New and well-known results are presented, together with generalizations in several directions, including extensions to the non-Euclidean setting and to non-convex sets. A variety of applications of tensor valuations to models in stochastic geometry, to local stereology and to imaging are also discussed.
目次
1 Valuations on Convex Bodies - the Classical Basic Facts: Rolf Schneider.- 2 Tensor Valuations and Their Local Versions: Daniel Hug and Rolf Schneider.- 3 Structures on Valuations: Semyon Alesker.- 4 Integral Geometry and Algebraic Structures for Tensor Valuations: Andreas Bernig and Daniel Hug.- 5 Crofton Formulae for Tensor-Valued Curvature Measures: Daniel Hug and Jan A. Weis.- 6 A Hadwiger-Type Theorem for General Tensor Valuations: Franz E. Schuster.- 7 Rotation Invariant Valuations: Eva B.Vedel Jensen and Markus Kiderlen.- 8 Valuations on Lattice Polytopes: Karoly J. Boeroeczky and Monika Ludwig.- 9 Valuations and Curvature Measures on Complex Spaces: Andreas Bernig.- 10 Integral Geometric Regularity: Joseph H.G. Fu.- 11 Valuations and Boolean Models: Julia Hoerrmann and Wolfgang Weil.- 12 Second Order Analysis of Geometric Functionals of Boolean Models: Daniel Hug, Michael A. Klatt, Gunter Last and Matthias Schulte.- 13 Cell Shape Analysis of Random Tessellations Based on Minkowski Tensors: Michael A. Klatt, Gunter Last, Klaus Mecke, Claudia Redenbach, Fabian M. Schaller, Gerd E. Schroeder-Turk.- 14 Stereological Estimation of Mean Particle Volume Tensors in R3 from Vertical Sections: Astrid Kousholt, Johanna F. Ziegel, Markus Kiderlen.- 15 Valuations in Image Analysis: Anne Marie Svane.
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