Tensor valuations and their applications in stochastic geometry and imaging / [edited by] Eva B. Vedel Jensen and Markus Kiderlen.

Include index and bibliographical references and index.

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.

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.