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Proximity spaces. --- Set theory.

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Topology --- Proximity spaces. --- Uniform spaces. --- Espaces de proximité.

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The principal aim of this book is to introduce topology and its many applications viewed within a framework that includes a consideration of compactness, completeness, continuity, filters, function spaces, grills, clusters and bunches, hyperspace topologies, initial and final structures, metric spaces, metrization, nets, proximal continuity, proximity spaces, separation axioms, and uniform spaces.This book provides a complete framework for the study of topology with a variety of applications in science and engineering that include camouflage filters, classification, digital image processing, f

Topological spaces. --- Topology. --- Analysis situs --- Position analysis --- Rubber-sheet geometry --- Geometry --- Polyhedra --- Set theory --- Algebras, Linear --- Spaces, Topological --- Proximity spaces.

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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.

Computer vision -- Mathematics. --- Pattern recognition systems. --- Proximity spaces. --- Computer vision --- Digital images --- Pattern recognition systems --- Proximity spaces --- Topology --- Engineering & Applied Sciences --- Computer Science --- Applied Physics --- Mathematics. --- Mathematical models. --- Spaces, Proximity --- Pattern classification systems --- Pattern recognition computers --- Machine vision --- Vision, Computer --- Engineering. --- Artificial intelligence. --- Image processing. --- Computational intelligence. --- Computational Intelligence. --- Image Processing and Computer Vision. --- Artificial Intelligence (incl. Robotics). --- Intelligence, Computational --- Artificial intelligence --- Soft computing --- Pictorial data processing --- Picture processing --- Processing, Image --- Imaging systems --- Optical data processing --- AI (Artificial intelligence) --- Artificial thinking --- Electronic brains --- Intellectronics --- Intelligence, Artificial --- Intelligent machines --- Machine intelligence --- Thinking, Artificial --- Bionics --- Cognitive science --- Digital computer simulation --- Electronic data processing --- Logic machines --- Machine theory --- Self-organizing systems --- Simulation methods --- Fifth generation computers --- Neural computers --- Construction --- Industrial arts --- Technology --- Nearness spaces --- Pattern perception --- Image processing --- Computer vision. --- Artificial Intelligence. --- Optical data processing. --- Optical computing --- Visual data processing --- Integrated optics --- Photonics --- Computers --- Optical equipment