Computational Proximity: Excursions in the Topology of Digital Images

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.