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Engineering - Computational Intelligence and Complexity | Topology of Digital Images - Visual Pattern Discovery in Proximity Spaces

Topology of Digital Images

Visual Pattern Discovery in Proximity Spaces

Peters, James F.

2014, XVI, 411 p. 250 illus., 158 illus. in color.

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  • 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

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.

Content Level » Research

Keywords » Digital Image Analysis - Digital Image Processing - Image Structures - Neighbourhood - Set - Symmetric Proximity - Topology

Related subjects » Artificial Intelligence - Computational Intelligence and Complexity - Image Processing

Table of contents 

1 Topology of Digital Images: Basic Ingredients.-
2 Structures Arising from Sets of Pixels.-
3 Visualisations and Covers.-
4 Linear Filtering and Visual Patterns in Images.-
5 Edges, Lines, Ridges, and Nearness Structures.-
6 Corners and Symmetric Proximity.-
7 Separation of Image Regions and Set Patterns.-
8 Descriptive Raster Spaces.-
9 Component Analysis and Uniform Spaces.-
10 Shapes and Shape Set Patterns.-
11 Texture and Texture Set Patterns.-
12 Pattern-Based Picture Classification.-
13 Appendix: Matlab and Mathematica Scripts.-
14 Notes and Further Readings.

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