Tensor Valuations and Their Applications in Stochastic Geometry and Imaging [electronic resource] / / edited by Eva B. Vedel Jensen, Markus Kiderlen.. — 1st ed. 2017.. — XIV, 462 p. 25 illus., 16 illus. in color. : online resource. — (Lecture Notes in Mathematics,) 2177 0075-8434 ;. - Lecture Notes in Mathematics, 2177 .
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.
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Анотація: 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.
9783319519517
10.1007/978-3-319-51951-7 doi
Geometry. Manifolds (Mathematics). Complex manifolds. Probabilities. Geometry. Manifolds and Cell Complexes (incl. Diff.Topology). Probability Theory and Stochastic Processes.