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Tensor Valuations and Their Applications in Stochastic Geometry and Imaging

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概要 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 con...vex 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.続きを見る
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: Károly J. Böröczky 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 Hörrmann and Wolfgang Weil
12 Second Order Analysis of Geometric Functionals of Boolean Models: Daniel Hug, Michael A. Klatt, Günter Last and Matthias Schulte
13 Cell Shape Analysis of Random Tessellations Based on Minkowski Tensors: Michael A. Klatt, Günter Last, Klaus Mecke, Claudia Redenbach, Fabian M. Schaller, Gerd E. Schröder-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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本文を見る Full text available from Springer Lecture Notes in Mathematics eBooks
Full text available from Springer Mathematics and Statistics eBooks 2017 English/International

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登録日 2020.06.27
更新日 2022.07.13