Tensor Valuations and Their Applications in Stochastic Geometry and Imaging

• Corporate Author: SpringerLink (Online service)
• Other Authors: Jensen, Eva B. Vedel (Editor), Kiderlen, Markus (Editor)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2017.
• Series: Lecture Notes in Mathematics, 2177
• Subjects: Mathematics.; Geometry.; Probabilities.; Manifolds (Mathematics).; Complex manifolds.; Manifolds and Cell Complexes (incl. Diff.Topology).; Probability Theory and Stochastic Processes.
• Physical Description: XIV, 462 p. 25 illus., 16 illus. in color. online resource.
• ISBN: 9783319519517
• ISSN: 0075-8434 ;

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.