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Rotational integral geometry and its applications

Record Type:	Electronic resources : Monograph/item
Title/Author:	Rotational integral geometry and its applicationsby Eva B. Vedel Jensen, Markus Kiderlen.
Author:	Jensen, Eva B. Vedel.
other author:	Kiderlen, Markus.
Published:	Cham :Springer Nature Switzerland :2025.
Description:	ix, 263 p. :ill. (some col.), digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Integral geometry.
Online resource:	https://doi.org/10.1007/978-3-031-87047-7
ISBN:	9783031870477$q(electronic bk.)

Rotational integral geometry and its applications
Jensen, Eva B. Vedel.

Rotational integral geometry and its applications[electronic resource] /by Eva B. Vedel Jensen, Markus Kiderlen. - Cham :Springer Nature Switzerland :2025. - ix, 263 p. :ill. (some col.), digital ;24 cm. - Springer monographs in mathematics,2196-9922. - Springer monographs in mathematics..

- 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.

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.

ISBN: 9783031870477$q(electronic bk.)

Standard No.: 10.1007/978-3-031-87047-7doiSubjects--Topical Terms:

306357
Integral geometry.

LC Class. No.: QA672

Dewey Class. No.: 516.362

Rotational integral geometry and its applications
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505 0 $a - 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.
520 $a 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.
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