Topology of Digital Images

Visual Pattern Discovery in Proximity Spaces

  • James F.┬áPeters

Part of the Intelligent Systems Reference Library book series (ISRL, volume 63)

Table of contents

  1. Front Matter
    Pages 1-13
  2. James F. Peters
    Pages 77-101
  3. James F. Peters
    Pages 103-119
  4. James F. Peters
    Pages 121-171
  5. James F. Peters
    Pages 173-197
  6. James F. Peters
    Pages 199-210
  7. James F. Peters
    Pages 211-245
  8. James F. Peters
    Pages 247-263
  9. James F. Peters
    Pages 265-278
  10. James F. Peters
    Pages 279-299
  11. James F. Peters
    Pages 301-315
  12. James F. Peters
    Pages 317-342
  13. Back Matter
    Pages 343-409

About this book


This book carries forward recent work on visual patterns and structures

in digital images and introduces a near set-based a topology of digital

images. Visual patterns arise naturally in digital images viewed as sets

of non-abstract points endowed with some form of proximity (nearness)

relation. Proximity relations make it possible to construct uniform topolo-

gies on the sets of points that constitute a digital image. In keeping with

an interest in gaining an understanding of digital images themselves as a

rich source of patterns, this book introduces the basics of digital images

from a computer vision perspective. In parallel with a computer vision

perspective on digital images, this book also introduces the basics of prox-

imity spaces. Not only the traditional view of spatial proximity relations

but also the more recent descriptive proximity relations are considered.

The beauty of the descriptive proximity approach is that it is possible to

discover visual set patterns among sets that are non-overlapping and non-

adjacent spatially. By combining the spatial proximity and descriptive<

proximity approaches, the search for salient visual patterns in digital im-

ages is enriched, deepened and broadened. A generous provision of Matlab

and Mathematica scripts are used in this book to lay bare the fabric and

essential features of digital images for those who are interested in finding

visual patterns in images. The combination of computer vision techniques

and topological methods lead to a deep understanding of images.


Digital Image Analysis Digital Image Processing Image Structures Neighbourhood Set Symmetric Proximity Topology

Authors and affiliations

  • James F.┬áPeters
    • 1
  1. 1.Department of Electrical and Computer EngineeringUniversity of ManitobaWinnipegCanada

Bibliographic information

  • DOI
  • Copyright Information Springer-Verlag Berlin Heidelberg 2014
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Engineering Engineering (R0)
  • Print ISBN 978-3-642-53844-5
  • Online ISBN 978-3-642-53845-2
  • Series Print ISSN 1868-4394
  • Series Online ISSN 1868-4408
  • Buy this book on publisher's site
Industry Sectors
Materials & Steel
Chemical Manufacturing
Finance, Business & Banking
IT & Software
Consumer Packaged Goods
Energy, Utilities & Environment
Oil, Gas & Geosciences