Discrete Surfaces and Manifolds: A Theory of Digital-Discrete Geometry and Topology

Along with the development of computer science and information technology, almost everything has its computerized or digitized view. Geometrical objects: curves, surfaces, and manifolds are no exception. This self-contained monograph focuses on the constructive method for digital and discrete objects especially for surfaces and manifolds. This book primarily consists of research done by the author and his collaborators with relation to other researchers' work. It could be a valuable reference for researchers in Image Processing and Computer Vision, Pattern Recognition, Computer Graphics, and Computational and Discrete Geometry. It may be used as a textbook for special topics in discrete mathematics, image processing, and computer vision for undergraduate and graduate students. In this book, the author treads the mathematical objects from a computer scientist's prospective, i.e. each concept and procedure shall be programmable. Within a nearly unified framework, the book includes: Digital spaces and discrete spaces, curves in digital planes, definitions and advanced topics of digital surfaces, digital manifolds, discrete manifolds, gradually varied surfaces, and lambda-connectedness in digital and discrete spaces. ----------------------------- "I looked at chapters 8 and l0 but made no attempt at following your exposition in detail since your theory extends beyond my competence. But what is quite obvious is that your ideas are original and highly interesting. Please accept my congratulations." "P.S. I am taking the liberty of donating your book to our Math Library." Lotfi A. Zadeh Professor in the Graduate School, Computer Science Division Department of Electrical Engineering and Computer Sciences University of California Berkeley, CA 94720 -1776 Director, Berkeley Initiative in Soft Computing (BISC) ---------------------- I think the book is very impressive! Furthermore,I found the last part particularly useful in brain modeling and photonics networking alike! Paul P.Wang Professor Department of Electrical & Computer Engineering Pratt School of Engineering Duke University,Durham ,NC,27708 ,USA ---------------------- Thank you for giving me an opportunity to look into your book. Judging by its table of contents at least, it looks like a very complete and authoritative treatment of digital topology. Jacob E. Goodman Professor of Mathematics, CCNY, The author of the bestselling book: "Handbook of Discrete and Computational Geometry"