Tensor Valuations and Their Applications in Stochastic Geometry and Imaging

1. Auflage 2017
ISBN: 978-3-319-51950-0
Verlag: Springer International Publishing

Buch, Englisch, Band 2177, 462 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 7139 g

Reihe: Lecture Notes in Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Kiderlen, Markus

Jensen, Eva B. Vedel

Fachgebiete

• Mathematik | Informatik Mathematik Geometrie Differentialgeometrie
• Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung
• Mathematik | Informatik Mathematik Topologie Analytische Topologie
• Mathematik | Informatik Mathematik Stochastik Stochastische Prozesse

Inhaltsverzeichnis

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.