Intelligent Systems Reference Library

Topology of Digital Images

Visual Pattern Discovery in Proximity Spaces

Authors: Peters, James F.

Free Preview
  • Introduction to the basics of digital images that are viewed as topological spaces
  • Offers a complete entry-level study of digital image processing and the analysis of digital images that are structured sets
  • Includes various Matlab examples
see more benefits

Buy this book

eBook 106,99 €
price for Spain (gross)
  • ISBN 978-3-642-53845-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • Immediate eBook download after purchase and usable on all devices
  • Bulk discounts available
Hardcover 155,99 €
price for Spain (gross)
Softcover 136,06 €
price for Spain (gross)
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 topologies 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 proximity 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 images 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.

Reviews

From the reviews:

“This book presents the recent research results of visual patterns in proximity spaces in a very easy to follow way. … a research exposition for mathematicians, computer scientists, engineers and for all who want to familiarize with the recent research in this field. It can be also treated as the textbook for students and for all who want to deeply understand images through their topology. It can be used for a self studying and as a course book as well.” (Agnieszka Lisowska, zbMATH, Vol. 1295, 2014)

Table of contents (12 chapters)

Table of contents (12 chapters)
  • Topology of Digital Images: Basic Ingredients

    Pages 1-75

    Peters, James F.

  • Structures Arising from Sets of Pixels

    Pages 77-101

    Peters, James F.

  • Visualisations and Covers

    Pages 103-119

    Peters, James F.

  • Linear Filtering and Visual Patterns in Images

    Pages 121-171

    Peters, James F.

  • Edges, Lines, Ridges, and Nearness Structures

    Pages 173-197

    Peters, James F.

Buy this book

eBook 106,99 €
price for Spain (gross)
  • ISBN 978-3-642-53845-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • Immediate eBook download after purchase and usable on all devices
  • Bulk discounts available
Hardcover 155,99 €
price for Spain (gross)
Softcover 136,06 €
price for Spain (gross)
Loading...

Recommended for you

Loading...

Bibliographic Information

Bibliographic Information
Book Title
Topology of Digital Images
Book Subtitle
Visual Pattern Discovery in Proximity Spaces
Authors
Series Title
Intelligent Systems Reference Library
Series Volume
63
Copyright
2014
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-53845-2
DOI
10.1007/978-3-642-53845-2
Hardcover ISBN
978-3-642-53844-5
Softcover ISBN
978-3-662-52250-9
Series ISSN
1868-4394
Edition Number
1
Number of Pages
XVI, 411
Number of Illustrations
92 b/w illustrations, 158 illustrations in colour
Topics