Overview
- Presents mathematical methods necessary for applications in medicine, material science, and image analysis
- Extends random distributions to random currents
- Stimulates new applications and research through mathematical methods
Part of the book series: SpringerBriefs in Mathematics (BRIEFSMATH)
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Table of contents (5 chapters)
Keywords
- theory of currents
- Geometric Measure Theory
- linear functionals
- statistical shape analysis
- Crystal dislocations
- Tumor-driven angiogenesis
- Stochastic Geometry
- Push-forward of a current
- Operations on currents
- Boundary, and Lie derivative of a current
- Gaussian currents in statistical shape analysis
- Random currents on Hilbert spaces
- Gaussian currents
- Elements of measure theory
- Fundamentals of Stochastic Processes
About this book
This book introduces random currents by presenting underlying mathematical methods necessary for applications. The theory of currents is an advanced topic in geometric measure theory that extends distribution to linear functionals within the space of differential forms of any order. Methods to extend random distributions to random currents are introduced and analyzed in this book. Beginning with an overview of mathematical aspects of the theory of currents, this book moves on to examine applications in medicine, material science, and image analysis. Applied researchers will find the practical modern mathematical methods along with the detailed appendix useful to stimulate new applications and research.
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Authors and Affiliations
Bibliographic Information
Book Title: An Introduction to Random Currents and Their Applications
Authors: Vincenzo Capasso
Series Title: SpringerBriefs in Mathematics
DOI: https://doi.org/10.1007/978-3-319-94577-4
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Author(s), under exclusive licence to Springer International Publishing AG, part of Springer Nature 2018
Softcover ISBN: 978-3-319-94576-7Published: 14 August 2018
eBook ISBN: 978-3-319-94577-4Published: 02 August 2018
Series ISSN: 2191-8198
Series E-ISSN: 2191-8201
Edition Number: 1
Number of Pages: XIII, 143
Topics: Measure and Integration, Image Processing and Computer Vision, Probability Theory and Stochastic Processes