Geometry of Digital Spaces (1998)

There are many areas of science and engineering where multi-dimensional discrete data are collected and analyzed, e.g., neuroscience, medical imaging, industrial inspection, geoscience, and fluid dynamics to name a few. In attempting to design and to prove the validity of computational procedures for visualization and analysis of the information in such data, the need for a mathematical theory of surfaces, objects, and their boundaries in discrete spaces is essential. Such a theory - the geometry of digital spaces - is the subject matter of this new book. Self-contained, accessible, and mathematically precise, this book serves as an introduction to this field, providing information that can be used immediately in the discussion of properties of practical algorithms in spaces. The approach used in "Geometry of Digital Spaces" is strongly application oriented. It presents problems of visualization and analysis of multi-dimensional data sets. The primary areas of mathematics used are graph theory and topology. Scientists and professionals from diverse backgrounds will find the discussions clear and accessible because all concepts and methods are carefully introduced, defined, and illustrated with examples.