Tensor Valuations and Their Applications in Stochastic Geometry and Imaging

Eva B. Vedel Jensen, Markus Kiderlen (Herausgeber)

Buch | Softcover

XIV, 462 Seiten

2017 | 1st ed. 2017
Springer International Publishing (Verlag)
978-3-319-51950-0 (ISBN)

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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: 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.

Erscheinungsdatum	21.06.2017
Reihe/Serie	Lecture Notes in Mathematics
Zusatzinfo	XIV, 462 p. 25 illus., 16 illus. in color.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
Schlagworte	analytic geometry • Analytic topology • Convex body • curvature measures • Geometry • Integral Geometry • Manifolds and Cell Complexes (incl. Diff.Topology) • Mathematics • mathematics and statistics • Minkowski tensors • normal cycle • probability and statistics • Probability theory and stochastic processes • Stereology • stochastic geometry • stochastics • valuations on manifolds • valuation theory
ISBN-10	3-319-51950-6 / 3319519506
ISBN-13	978-3-319-51950-0 / 9783319519500
Zustand	Neuware