Tensor Valuations and Their Applications in Stochastic Geometry and Imaging

Beschreibung

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.
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.
15 chapters written by experts in their fields give a comprehensive overview of the modern theory of tensor valuations Includes new yet unpublished results that make this volume an up-to-date survey of valuation theory Chapters on applications of tensor valuations deepen understanding and emphasize the usefulness of theoretical concepts

Autor*in

Eva B. Vedel Jensen

Themen in »Tensor Valuations and Their Applications in Stochastic Geometry and Imaging«

Minkowski tensors valuation theory convex body integral geometry stochastic geometry curvature measures valuations on manifolds normal cycle stereology

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