Digital Topology

Digital topology deals with properties of digital images that correspond to topological properties of the objects represented in those images. This book is an introduction to and a reference on digital topology. It includes a concise but self-contained introduction that covers the parts of graph theory and topology that are needed in the sequel.

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Digital topology deals with properties of digital images that correspond to topological properties of the objects represented in those images. Concepts and results of digital topology are used to specify and justify important image-processing operations, such as thinning and boundary surface extraction. This book is a coherent introduction to and a reference on digital topology. The book includes a concise but self-contained introduction that covers the parts of graph theory and topology that are needed in the sequel. There is substantial coverage of finite and locally finite topological spaces, which are discussed in very few other texts. Among topics covered are: the boundary tracking problem with applications and methodology; reductive and reductive-augmentative shrinking algorithms; topology-preserving deletion of 1's in 2-4 dimensional digital pictures; topological soundness verification of parallel thinning algorithms; continuous and metric analogs; and the approximation of compact Hausdorff spaces by finite spaces.
Its readership includes both computer scientists concerned with applications of the subject and mathematicians interested in the numerous theoretical questions that arise in connection with those applications.