Digital and Discrete Geometry

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.

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.