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. 


Table of contents:


1. Introduction 


2. Digital spaces, discrete spaces, and finite topologies 


3. Curves in digital planes 


4. Digital surfaces: definitions 


5. Digital surfaces: advanced topics in 3D 


6. Digital manifolds 


7. Generalized discrete manifolds 


8. Gradually varied functions on digital and discrete manifolds 


9. Point digital spaces vs. raster digital spaces 


10. [Lambda]-connectedness in digital and discrete spaces