Digital and Discrete Geometry [electronic resource] : Theory and Algorithms / by Li M. Chen.

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.

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.