Tensor Valuations and Their Applications in Stochastic Geometry and Imaging

  • Eva B. Vedel Jensen
  • Markus Kiderlen

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

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Daniel Hug, Rolf Schneider
    Pages 27-65
  3. Semyon Alesker
    Pages 67-78
  4. Daniel Hug, Jan A. Weis
    Pages 111-156
  5. Eva B. Vedel Jensen, Markus Kiderlen
    Pages 185-212
  6. Károly J. Böröczky, Monika Ludwig
    Pages 213-234
  7. Joseph H. G. Fu
    Pages 261-299
  8. Julia Schulte, Wolfgang Weil
    Pages 301-338
  9. Daniel Hug, Michael A. Klatt, Günter Last, Matthias Schulte
    Pages 339-383
  10. Michael A. Klatt, Günter Last, Klaus Mecke, Claudia Redenbach, Fabian M. Schaller, Gerd E. Schröder-Turk
    Pages 385-421
  11. Astrid Kousholt, Johanna F. Ziegel, Markus Kiderlen, Eva B. Vedel Jensen
    Pages 423-434
  12. Anne Marie Svane
    Pages 435-454
  13. Back Matter
    Pages 455-462

About this book

Introduction

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.

Keywords

Minkowski tensors valuation theory convex body integral geometry stochastic geometry curvature measures valuations on manifolds normal cycle stereology

Editors and affiliations

  • Eva B. Vedel Jensen
    • 1
  • Markus Kiderlen
    • 2
  1. 1.Department of MathematicsAarhus UniversityAarhus CDenmark
  2. 2.Department of MathematicsAarhus UniversityAarhus CDenmark

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-51951-7
  • Copyright Information Springer International Publishing AG 2017
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-51950-0
  • Online ISBN 978-3-319-51951-7
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site