Rotational Integral Geometry and its Applications / by Eva B. Vedel Jensen, Markus Kiderlen.

Format:

Book

Author/Creator:

Vedel Jensen, Eva B.

Contributor:

Kiderlen, Markus.

Series:

Springer Monographs in Mathematics, 2196-9922

Language:

English

Subjects (All):

Convex geometry.

Discrete geometry.

Probabilities.

Measure theory.

Convex and Discrete Geometry.

Probability Theory.

Measure and Integration.

Local Subjects:

Convex and Discrete Geometry.

Probability Theory.

Measure and Integration.

Physical Description:

1 online resource (488 pages)

Edition:

1st ed. 2025.

Place of Publication:

Cham : Springer Nature Switzerland : Imprint: Springer, 2025.

Summary:

This self-contained book offers an extensive state-of-the-art exposition of rotational integral geometry, a field that has reached significant maturity over the past four decades. Through a unified description of key results previously scattered across various scientific journals, this book provides a cohesive and thorough account of the subject. Initially, rotational integral geometry was driven by applications in fields such as optical microscopy. Rotational integral geometry has now evolved into an independent mathematical discipline. It contains a wealth of theorems paralleling those in classical kinematic integral geometry for Euclidean spaces, such as the rotational Crofton formulae, rotational slice formulae, and principal rotational formulae. The present book presents these for very general tensor valuations in a convex geometric setting. It also discusses various applications in the biosciences, explained with a mathematical audience in mind. This book is intended for a diverse readership, including specialists in integral geometry, and researchers and graduate students working in integral, convex, and stochastic geometry, as well as geometric measure theory.

Contents:

- 1. Introduction

2. Convex Bodies and their Classical Integral Geometry

3. Integral Geometric Transformations

4. Rotational Crofton Formulae for Intrinsic Volumes

5. Rotational Crofton Formulae for Minkowski Tensors

6. Rotational Slice Formulae

7. Further Rotational Integral Geometric Formulae

8. Applications to Particle Populations

9. Implementation in Optical Microscopy.

Notes:

Description based on publisher supplied metadata and other sources.

ISBN:

3-031-87047-6

OCLC:

1524421991