Topology of Digital Images

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This book carries forward recent work on visual patterns and structuresin digital images and introduces a near set-based a topology of digitalimages. Visual patterns arise naturally in digital images viewed as setsof 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 withan interest in gaining an understanding of digital images themselves as arich source of patterns, this book introduces the basics of digital imagesfrom a computer vision perspective. In parallel with a computer visionperspective on digital images, this book also introduces the basics of prox-imity spaces. Not only the traditional view of spatial proximity relationsbut also the more recent descriptive proximity relations are considered.The beauty of the descriptive proximity approach is that it is possible todiscover visual set patterns among sets that are non-overlapping and non-adjacent spatially. By combining the spatial proximity and descriptive

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