Tensor Valuations and Their Applications in Stochastic Geometry and Imaging
Published on 12. June 2017
Book
Paperback/Softback
XIV, 462 pages
978-3-319-51950-0 (ISBN)
Description
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.
More details
Series
Edition
1st ed. 2017
Language
English
Place of publication
Cham
Switzerland
Publishing group
Springer International Publishing
Target group
Professional and scholarly
Illustrations
16 farbige Abbildungen, 9 s/w Abbildungen
XIV, 462 p. 25 illus., 16 illus. in color.
Dimensions
Height: 235 mm
Width: 155 mm
Thickness: 26 mm
Weight
715 gr
ISBN-13
978-3-319-51950-0 (9783319519500)
DOI
10.1007/978-3-319-51951-7
Schweitzer Classification
Other editions
Additional editions
Eva B. Vedel Jensen | Markus Kiderlen
Tensor Valuations and Their Applications in Stochastic Geometry and Imaging
E-Book
06/2017
Springer
€69.54
Available for download
Content
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.