Computational proximity [electronic resource] : excursions in the topology of digital images / James F. Peters.
Peters, James F., author.
2016
TA1637.5
Available Online

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Title Computational proximity [electronic resource] : excursions in the topology of digital images / James F. Peters.
Author Peters, James F., author.
ISBN 9783319302621 (electronic book)
3319302620 (electronic book)
9783319302607
DOI https://doi.org/10.1007/978-3-319-30262-1
Published Switzerland : Springer, 2016.
Language English
Description 1 online resource (xxviii, 433 pages) : illustrations.
Other Standard Identifiers 10.1007/978-3-319-30262-1 doi
Call Number TA1637.5
Dewey Decimal Classification 621.36/7
Summary 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.
Bibliography, etc. Note Includes bibliographical references and indexes.
Access Note Access limited to authorized users.
Source of Description Online resource; title from PDF title page (SpringerLink, viewed April 26, 2016).
Series Intelligent systems reference library ; v. 102.
Available in Other Form Print version: 9783319302607
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Computational Proximity
Proximities Revisited
Distance and Proximally Continuous.-Image Geometry and Nearness Expressions for Image and Scene Analysis
Homotopic Maps, Shapes and Borsuk-Ulam Theorem
Visibility, Hausdorffness, Algebra and Separation Spaces
Strongly Near Sets and Overlapping Dirichlet Tessellation Regions
Proximal Manifolds.-Watershed, Smirnov Measure, Fuzzy Proximity and Sorted Near Sets
Strong Connectedness Revisited
Helly?s Theorem and Strongly Proximal Helly Theorem
Nerves and Strongly Near Nerves
Connnectedness Patterns
Nerve Patterns- Appendix A: Mathematica and Matlab Scripts
Appendix B: Kuratowski Closure Axioms
Appendix C: Sets. A Topological Perspective
Appendix D: Basics of Proximities
Appendix E: Set Theory Axioms, Operations and Symbols
Appendix F: Topology of Digital Images.

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