Tensor Valuations and Their Applications in Stochastic Geometry and Imaging
Nonfiction, Science & Nature, Mathematics, Topology, Geometry
| Author: | ISBN: | 9783319519517 | |
| Publisher: | Springer International Publishing | Publication: | June 10, 2017 |
| Imprint: | Springer | Language: | English |
| Author: | |
| ISBN: | 9783319519517 |
| Publisher: | Springer International Publishing |
| Publication: | June 10, 2017 |
| Imprint: | Springer |
| Language: | English |
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.
