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Tensor Valuations and Their Applications in Stochastic Geometry and Imaging

  • Book
  • © 2017

Overview

Editors:
  1. Eva B. Vedel Jensen

    1. Department of Mathematics, Aarhus University, Aarhus C, Denmark

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    You can also search for this editor in PubMed   Google Scholar

  2. Markus Kiderlen

    1. Department of Mathematics, Aarhus University, Aarhus C, Denmark

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    You can also search for this editor in PubMed   Google Scholar

  • 15 chapters written by experts in their fields give a comprehensive overview of the modern theory of tensor valuations
  • Includes new yet unpublished results that make this volume an up-to-date survey of valuation theory
  • Chapters on applications of tensor valuations deepen understanding and emphasize the usefulness of theoretical concepts

Part of the book series: Lecture Notes in Mathematics (LNM, volume 2177)

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Table of contents (15 chapters)

  1. Front Matter

    Pages i-xiv
    Download chapter PDF

  2. Valuations on Convex Bodies: The Classical Basic Facts

    • Rolf Schneider
    Pages 1-25

  3. Tensor Valuations and Their Local Versions

    • Daniel Hug, Rolf Schneider
    Pages 27-65

  4. Structures on Valuations

    • Semyon Alesker
    Pages 67-78

  5. Integral Geometry and Algebraic Structures for Tensor Valuations

    • Andreas Bernig, Daniel Hug
    Pages 79-109

  6. Crofton Formulae for Tensor-Valued Curvature Measures

    • Daniel Hug, Jan A. Weis
    Pages 111-156

  7. A Hadwiger-Type Theorem for General Tensor Valuations

    • Franz E. Schuster
    Pages 157-183

  8. Rotation Invariant Valuations

    • Eva B. Vedel Jensen, Markus Kiderlen
    Pages 185-212

  9. Valuations on Lattice Polytopes

    • Károly J. Böröczky, Monika Ludwig
    Pages 213-234

  10. Valuations and Curvature Measures on Complex Spaces

    • Andreas Bernig
    Pages 235-260

  11. Integral Geometric Regularity

    • Joseph H. G. Fu
    Pages 261-299

  12. Valuations and Boolean Models

    • Julia Schulte, Wolfgang Weil
    Pages 301-338

  13. Second Order Analysis of Geometric Functionals of Boolean Models

    • Daniel Hug, Michael A. Klatt, Günter Last, Matthias Schulte
    Pages 339-383

  14. 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
    Pages 385-421

  15. Stereological Estimation of Mean Particle Volume Tensors in \(\mathbb{R}^{3}\) from Vertical Sections

    • Astrid Kousholt, Johanna F. Ziegel, Markus Kiderlen, Eva B. Vedel Jensen
    Pages 423-434

  16. Valuations in Image Analysis

    • Anne Marie Svane
    Pages 435-454

  17. Back Matter

    Pages 455-462
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Keywords

About this book

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.

Editors and Affiliations

  • Department of Mathematics, Aarhus University, Aarhus C, Denmark

    Eva B. Vedel Jensen, Markus Kiderlen

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