Computational Proximity
Excursions in the Topology of Digital Images
Authors: Peters, James F.
Free Preview- 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
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- About this book
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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.
- Table of contents (14 chapters)
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Computational Proximity
Pages 1-62
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Proximities Revisited
Pages 63-96
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Distance and Proximally Continuous
Pages 97-118
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Image Geometry and Nearness Expressions for Image and Scene Analysis
Pages 119-139
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Homotopic Maps, Shapes and Borsuk–Ulam Theorem
Pages 141-173
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Table of contents (14 chapters)
- Download Preface 1 PDF (234.9 KB)
- Download Sample pages 2 PDF (1.9 MB)
- Download Table of contents PDF (188 KB)
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Bibliographic Information
- Bibliographic Information
-
- Book Title
- Computational Proximity
- Book Subtitle
- Excursions in the Topology of Digital Images
- Authors
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- James F. Peters
- Series Title
- Intelligent Systems Reference Library
- Series Volume
- 102
- Copyright
- 2016
- Publisher
- Springer International Publishing
- Copyright Holder
- Springer International Publishing Switzerland
- eBook ISBN
- 978-3-319-30262-1
- DOI
- 10.1007/978-3-319-30262-1
- Hardcover ISBN
- 978-3-319-30260-7
- Softcover ISBN
- 978-3-319-80764-5
- Series ISSN
- 1868-4394
- Edition Number
- 1
- Number of Pages
- XXVIII, 433
- Number of Illustrations
- 215 b/w illustrations, 39 illustrations in colour
- Topics
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