Computational Proximity

Excursions in the Topology of Digital Images

  • James F. Peters

Part of the Intelligent Systems Reference Library book series (ISRL, volume 102)

Table of contents

  1. Front Matter
    Pages i-xxviii
  2. James F. Peters
    Pages 1-62
  3. James F. Peters
    Pages 63-96
  4. James F. Peters
    Pages 97-118
  5. James F. Peters
    Pages 141-173
  6. James F. Peters
    Pages 237-258
  7. James F. Peters
    Pages 291-303
  8. James F. Peters
    Pages 317-323
  9. James F. Peters
    Pages 325-342
  10. James F. Peters
    Pages 343-353
  11. Back Matter
    Pages 355-433

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.


Description Descriptive Proximity Spaces Dense Finite Framework Infinite Intelligent Systems Near Sets Nearness Proximity Sets Subsets

Authors and affiliations

  • James F. Peters
    • 1
  1. 1.Engg & Tech Complex, Rm E2-390Univ of Manitoba, Electrical & Comp EnggWinnipegCanada

Bibliographic information

  • DOI
  • Copyright Information Springer International Publishing Switzerland 2016
  • Publisher Name Springer, Cham
  • eBook Packages Engineering Engineering (R0)
  • Print ISBN 978-3-319-30260-7
  • Online ISBN 978-3-319-30262-1
  • Series Print ISSN 1868-4394
  • Series Online ISSN 1868-4408
  • Buy this book on publisher's site
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