Digital and Discrete Geometry - Theory and Algorithms

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 (suchas 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.

Inhaltsverzeichnis

Introduction.- Discrete Spaces: Graphs, Lattices, and Digital Spaces.- Euclidean Space and Continuous Space.- Digital Planar Geometry: Curves and Connected Regions.- Surfaces and Manifolds in Digital Space.- Algorithms for Digital Surfaces and Manifolds.- Discrete Manifolds: the Graph-Based Theory.- Discretization, Digitization, and Embedding.- Combinatorial Topology and Digital Topology.- Geometric Measurements and Geometric Computing.- Digital Functions, Data Reconstruction, and Numerical Geometry.- Geometric Search and Geometric Processing.- Discrete Methods in Differential Geometry.- Advanced Digital Topology and Applications.- Select Topics and Future Challenges in Discrete Geometry.

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Zusammenfassung

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 (suchas 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.

Zusatztext

“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)

Bericht

"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)

Produktdetails

• Autoren: Li Chen, Li M Chen, Li M. Chen
• Verlag: Springer, Berlin
• Sprache: Englisch
• Produktform: Taschenbuch
• Erschienen: 01.01.2016
• EAN: 9783319348629
• ISBN: 978-3-31-934862-9
• Seiten: 322
• Abmessung: 155 mm x 18 mm x 235 mm
• Gewicht: 521 g
• Illustration: XVII, 322 p. 130 illus. in color.
• Themen: Naturwissenschaften, Medizin, Informatik, Technik > Informatik, EDV > Anwendungs-Software; B, Datenbanken, Mustererkennung, Mathematik für Informatiker, computer science, Database Management, Computer Vision, Image Processing and Computer Vision, Computer Graphics, pattern recognition, database programming, Algebraic Geometry, Discrete Mathematics in Computer Science, Discrete Mathematics, Discrete geometry, Convex and Discrete Geometry, Convex geometry, Computer science—Mathematics, Maths for computer scientists, Optical data processing, Biometrics, Biometrics (Biology), Graphics programming, Databases