Tensor Valuations and Their Applications in Stochastic Geometry and Imaging [Paperback]

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.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: K?roly J. B?r?czky 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 H?rrmann and Wolfgang Weil.- 12 Second Order Analysis of Geometric Functionals of Boolean Models: Daniel Hug, Michael A. Klatt, G?nter Last and Matthias Schulte.- 13 Cell Shape Analysis of Random Tessellations Based on Minkowski Tensors: Michael A. Klatt, G?nter Last, Klaus Mecke, Claudia Redenbach, Fabian M. Schalls