Computational Proximity Excursions in the Topology of Digital Images

Computational Proximity Excursions in the Topology of Digital Images / by James F. Peters.

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 relat...

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Bibliographic Details
Main Author: Peters, James F. (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Cham : Springer International Publishing : Imprint: Springer, 2016.
Edition:1st ed. 2016.
Series:Intelligent Systems Reference Library, 102
Springer eBook Collection.
Subjects:
Computational intelligence.
Artificial intelligence.
Electronic resources (E-books)
Online Access:Click to view e-book
Holy Cross Note:Loaded electronically.
Electronic access restricted to members of the Holy Cross Community.
Table of Contents:
  • 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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