國立虎尾科技大學 |

Rotational integral geometry and its applications

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Rotational integral geometry and its applications/ by 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

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

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

672316
Integral geometry.

LC Class. No.: QA672

Dewey Class. No.: 516.362

Rotational integral geometry and its applications
LDR:02748nam a2200373 a 4500 001 1159677
003 DE-He213
005 20250613131650.0
006 m d
007 cr nn 008maaau
008 251029s2025 sz s 0 eng d
020 $a 9783031870477 $q (electronic bk.)
020 $a 9783031870460 $q (paper)
024 7 $a 10.1007/978-3-031-87047-7 $2 doi
035 $a 978-3-031-87047-7
040 $a GP $c GP
041 0 $a eng
050 4 $a QA672
072 7 $a PBM $2 bicssc
072 7 $a PBD $2 bicssc
072 7 $a MAT012020 $2 bisacsh
072 7 $a PBM $2 thema
072 7 $a PBD $2 thema
082 0 4 $a 516.362 $2 23
090 $a QA672 $b .J54 2025
100 1 $a Jensen, Eva B. Vedel. $3 1173246
245 1 0 $a Rotational integral geometry and its applications $h [electronic resource] / $c by Eva B. Vedel Jensen, Markus Kiderlen.
260 $a Cham : $c 2025. $b Springer Nature Switzerland : $b Imprint: Springer,
300 $a ix, 263 p. : $b ill. (some col.), digital ; $c 24 cm.
338 $a online resource $b cr $2 rdacarrier
490 1 $a Springer monographs in mathematics, $x 2196-9922
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.
650 0 $a Integral geometry. $3 672316
650 1 4 $a Convex and Discrete Geometry. $3 672138
650 2 4 $a Probability Theory. $3 1366244
650 2 4 $a Measure and Integration. $3 672015
700 1 $a Kiderlen, Markus. $3 1173247
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
830 0 $a Springer monographs in mathematics. $3 882184
856 4 0 $u https://doi.org/10.1007/978-3-031-87047-7
950 $a Mathematics and Statistics (SpringerNature-11649)