Tensor Valuations and Their Applications in Stochastic Geometry and Imaging / edited by Eva B. Vedel Jensen, Markus Kiderlen.

Format:

Book

Contributor:

Jensen, Eva B. Vedel, Editor.

Kiderlen, Markus, Editor.

Series:

Lecture Notes in Mathematics, 0075-8434 ; 2177

Language:

English

Subjects (All):

Geometry.

Manifolds (Mathematics).

Complex manifolds.

Probabilities.

Manifolds and Cell Complexes (incl. Diff.Topology).

Probability Theory and Stochastic Processes.

Local Subjects:

Geometry.

Manifolds and Cell Complexes (incl. Diff.Topology).

Probability Theory and Stochastic Processes.

Physical Description:

1 online resource (XIV, 462 p. 25 illus., 16 illus. in color.)

Edition:

1st ed. 2017.

Place of Publication:

Cham : Springer International Publishing : Imprint: Springer, 2017.

Summary:

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.

Contents:

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.

Notes:

Includes index.

Description based on publisher supplied metadata and other sources.

ISBN:

3-319-51951-4

OCLC:

990143424