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Digital and Discrete Geometry

Theory and Algorithms

Authors: Chen, Li

  • 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
  •    
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Buy this book

eBook $99.00
price for USA in USD (gross)
  • ISBN 978-3-319-12099-7
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $119.99
price for USA in USD
  • ISBN 978-3-319-12098-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $129.00
price for USA in USD
  • Customers within the U.S. and Canada please contact Customer Service at 1-800-777-4643, Latin America please contact us at +1-212-460-1500 (Weekdays 8:30am – 5:30pm ET) to place your order.
  • Due: November 11, 2016
  • ISBN 978-3-319-34862-9
  • Free shipping for individuals worldwide
About this book

This book provides comprehensive coverage of the modern methods for geometric problems in the computing sciences. It also covers concurrent topics in data sciences including geometric processing, manifold learning, Google search, cloud data, and R-tree for wireless networks and BigData.
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 (such as CT and MRI) and informatics, computer graphics, computer vision, biometrics, and information 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.

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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 enrolled in 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)


Table of contents (15 chapters)

  • Introduction

    Chen, Li M.

    Pages 3-15

  • Discrete Spaces: Graphs, Lattices, and Digital Spaces

    Chen, Li M.

    Pages 17-34

  • Euclidean Space and Continuous Space

    Chen, Li M.

    Pages 35-46

  • Digital Planar Geometry: Curves and Connected Regions

    Chen, Li M.

    Pages 49-66

  • Surfaces and Manifolds in Digital Space

    Chen, Li M.

    Pages 67-88

Buy this book

eBook $99.00
price for USA in USD (gross)
  • ISBN 978-3-319-12099-7
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $119.99
price for USA in USD
  • ISBN 978-3-319-12098-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $129.00
price for USA in USD
  • Customers within the U.S. and Canada please contact Customer Service at 1-800-777-4643, Latin America please contact us at +1-212-460-1500 (Weekdays 8:30am – 5:30pm ET) to place your order.
  • Due: November 11, 2016
  • ISBN 978-3-319-34862-9
  • Free shipping for individuals worldwide
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Bibliographic Information

Bibliographic Information
Book Title
Digital and Discrete Geometry
Book Subtitle
Theory and Algorithms
Authors
Copyright
2014
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing Switzerland
Distribution Rights
Distribution rights for India: Researchco Book Centre, New Delhi, India
eBook ISBN
978-3-319-12099-7
DOI
10.1007/978-3-319-12099-7
Hardcover ISBN
978-3-319-12098-0
Softcover ISBN
978-3-319-34862-9
Edition Number
1
Number of Pages
XVII, 322
Number of Illustrations
130 illustrations in colour
Topics