Overview
- Explains profound theorems such as Minkowski’s Theorem and solid applications such as persistent analysis
- Provides natural links to profound topics including differential discrete geometry
- Includes case studies and more
- Includes supplementary material: sn.pub/extras
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Table of contents (15 chapters)
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Front Matter
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Basic Geometry
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Front Matter
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Digital Curves, Surfaces, and Manifolds
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Front Matter
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Discretely Represented Objects: Geometry and Topology
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Front Matter
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Geometric Computation and Processing
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Front Matter
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Advanced Topics
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Front Matter
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Keywords
About this book
The author investigates digital geometry and its related constructive methods in discrete geometry, offering detailed methods and algorithms. The book is divided into five sections: basic geometry; digital curves, surfaces and manifolds; discretely represented objects; geometric computation and processing; and advanced topics. Chapters especially focus on the applications of these methods to other types of geometry, algebraic topology, image processing, computer vision and computer graphics.
Digital and Discrete Geometry: Theory and Algorithms targets researchers and professionals working in digital image processing analysis, medical imaging (suchas CT and MRI) and informatics, computer graphics, computer vision, biometrics, and informati
on theory. Advanced-level students in electrical engineering, mathematics, and computer science will also find this book useful as a secondary text book or reference.
Praise for this book:
This book does present a large collection of important concepts, of mathematical, geometrical, or algorithmical nature, that are frequently used in computer graphics and image processing. These concepts range from graphs through manifolds to homology. Of particular value are the sections dealing with discrete versions of classic continuous notions. The reader finds compact definitions and concise explanations that often appeal to intuition, avoiding finer, but then necessarily more complicated, arguments… As a first introduction, or as a reference for professionals working in computer graphics or image processing, this book should be of considerable value." -Prof. Dr. Rolf Klein, University of Bonn.
Reviews
“This book does present a large collection of important concepts, of mathematical, geometrical, or algorithmical nature, that are frequently used in computer graphics and image processing. … As a first introduction, or as a reference for professionals working in computer graphics or image processing, this book should be of considerable value.” (Rolf Klein, zbMATH 1319.68002, 2015)
"This is an informative text covering a surprisingly wide range of topics. The author has succeeded in finding the appropriate (though highly variable) mix of mathematical theory, practical problems, computational approaches, and algorithms. The writing and production quality are generally good …... The book is suitable for an upper-level undergraduate course and a follow-on graduate course. Researchers and practitioners will find it a reasonably adequate introduction (more details would have been useful in several places, especially for readers not enrolledin a college course). Given the considerable mathematical content in this book, it is more readable than might be expected, especially for readers familiar with principles and problems from related domains, especially computer graphics, image processing, and the theory of algorithms. Since the author explains basic concepts (though often rather briefly) before moving on to more advanced ideas, even readers new to much of the background material should be able to make fair headway.” (R. M. Malyankar, ACM Computing Reviews #CR143755)
Authors and Affiliations
About the author
Bibliographic Information
Book Title: Digital and Discrete Geometry
Book Subtitle: Theory and Algorithms
Authors: Li M. Chen
DOI: https://doi.org/10.1007/978-3-319-12099-7
Publisher: Springer Cham
eBook Packages: Computer Science, Computer Science (R0)
Copyright Information: Springer International Publishing Switzerland 2014
Hardcover ISBN: 978-3-319-12098-0Published: 05 January 2015
Softcover ISBN: 978-3-319-34862-9Published: 24 September 2016
eBook ISBN: 978-3-319-12099-7Published: 12 December 2014
Edition Number: 1
Number of Pages: XVII, 322
Number of Illustrations: 130 illustrations in colour
Topics: Image Processing and Computer Vision, Computer Graphics, Convex and Discrete Geometry, Biometrics, Discrete Mathematics in Computer Science, Database Management