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Topology of Digital Images: Visual Pattern Discovery in Proximity Spaces
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From the Back Cover
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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