Overview
- Introduces descriptive proximity spaces and the generation of set patterns in proximity spaces, leading to new forms of topological spaces and new forms of algebraic structures such as near groups useful in solving pattern generation, pattern recognition, digital image analysis, retrieval and classification problems
- Presents a complete framework for the practical applications in descriptive proximity spaces
- Written by a leading expert in the field
- Includes supplementary material: sn.pub/extras
Part of the book series: Intelligent Systems Reference Library (ISRL, volume 102)
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About this book
This book introduces computational proximity (CP) as an algorithmic approach to finding nonempty sets of points that are either close to each other or far apart. Typically in computational proximity, the book starts with some form of proximity space (topological space equipped with a proximity relation) that has an inherent geometry. In CP, two types of near sets are considered, namely, spatially near sets and descriptivelynear sets. It is shown that connectedness, boundedness, mesh nerves, convexity, shapes and shape theory are principal topics in the study of nearness and separation of physical aswell as abstract sets. CP has a hefty visual content. Applications of CP in computer vision, multimedia, brain activity, biology, social networks, and cosmology are included. The book has been derived from the lectures of the author in a graduate course on the topology of digital images taught over the past several years. Many of the students have provided important insights and valuable suggestions. The topics in this monograph introduce many forms of proximities with a computational flavour (especially, what has become known as the strong contact relation), many nuances of topological spaces, and point-free geometry.
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Table of contents (14 chapters)
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Front Matter
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Back Matter
Authors and Affiliations
Bibliographic Information
Book Title: Computational Proximity
Book Subtitle: Excursions in the Topology of Digital Images
Authors: James F. Peters
Series Title: Intelligent Systems Reference Library
DOI: https://doi.org/10.1007/978-3-319-30262-1
Publisher: Springer Cham
eBook Packages: Engineering, Engineering (R0)
Copyright Information: Springer International Publishing Switzerland 2016
Hardcover ISBN: 978-3-319-30260-7Published: 29 April 2016
Softcover ISBN: 978-3-319-80764-5Published: 22 April 2018
eBook ISBN: 978-3-319-30262-1Published: 20 April 2016
Series ISSN: 1868-4394
Series E-ISSN: 1868-4408
Edition Number: 1
Number of Pages: XXVIII, 433
Number of Illustrations: 215 b/w illustrations, 39 illustrations in colour