Digital and Discrete Geometry

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 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)