Topology of Digital Images von James F. Peters

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.

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