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What is space? Is there space when there are objects to occupy it or is there space only when there are no objects to occupy it? Can there be space without objects? These are old philosophical questions that concern the ontology of space in the philosophical sense of ‘ontology’ – what is the nature of space? Cognitive science in general and arti?cial intelligence in particular are less c- cerned with the nature of things than with their mental conceptualizations. In spatial cognition research we address questions like What do we know about space? How is space represented? What are the representational entities? What are the rep- sentational structures? Answers to these questions are described in what is called ontologies in arti?cial intelligence. Different tasks require different knowledge, and different representations of knowledge facilitate different ways of solving problems. In this book, Jan Oliver Wallgrün develops and investigates representational structures to support tasks of autonomous mobile robots, from the acquisition of knowledge to the use of this knowledge for navigation. The research presented is concerned with the robot mapping problem, the pr- lem of building a spatial representation of an environment that is perceived by s- sors that only provide incomplete and uncertain information; this information usually needs to be related to other imprecise or uncertain information. The routes a robot can take can be abstractly described in terms of graphs where alternative routes are represented by alternative branches in these route graphs.

Engineering. --- Mobile robots -- Programming. --- Spatial data infrastructures. --- Voronoi polygons. --- Robots --- Mobile robots --- Voronoi polygons --- Spatial data infrastructures --- Mechanical Engineering --- Mechanical Engineering - General --- Engineering & Applied Sciences --- Dynamics --- Programming --- Programming. --- Diagrams, Voronoi --- Thiessen polygon method --- Thiessen polygons --- Voronoi diagrams --- SDIs (Geographic information systems) --- Artificial intelligence. --- Robotics. --- Automation. --- Robotics and Automation. --- Artificial Intelligence (incl. Robotics). --- Geographic information systems --- Polygons

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This book, a translation of the German volume n-Ecke, presents an elegant geometric theory which, starting from quite elementary geometrical observations, exhibits an interesting connection between geometry and fundamental ideas of modern algebra in a form that is easily accessible to the student who lacks a sophisticated background in mathematics. It stimulates geometrical thought by applying the tools of linear algebra and the algebra of polynomials to a concrete geometrical situation to reveal some rather surprising insights into the geometry of n-gons. The twelve chapters treat n-gons, classes of n-gons, and mapping of the set of n-gons into itself. Exercises are included throughout, and two appendixes, by Henner Kinder and Eckart Schmidt, provide background material on lattices and cyclotomic polynomials.(Mathematical Expositions No. 18).

Polygons. --- Set theory. --- Aggregates --- Classes (Mathematics) --- Ensembles (Mathematics) --- Mathematical sets --- Sets (Mathematics) --- Theory of sets --- Logic, Symbolic and mathematical --- Mathematics --- Polygonal figures --- Geometry, Plane --- Shapes

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This, the 20th issue of the Transactions on Computational Science journal, edited by Bahman Kalantari, is devoted to the topic of Voronoi Diagrams and their applications. The 10 full papers included in the volume are revised and extended versions of a selection of papers presented at the International Symposium on Voronoi Diagrams 2012, held in Rutgers, NJ, USA, in June 2012. They provide an in-depth overview of current research on topological data structures and a comprehensive evaluation of their applications in the fields of cartography, physics, material modeling, chemistry, GIS, motion planning and computer graphics.

Engineering & Applied Sciences --- Technology - General --- Computer science. --- Artificial intelligence. --- Computer graphics. --- Image processing. --- Computer Science. --- Computer Graphics. --- Image Processing and Computer Vision. --- Artificial Intelligence (incl. Robotics). --- Pictorial data processing --- Picture processing --- Processing, Image --- Imaging systems --- Optical data processing --- Automatic drafting --- Graphic data processing --- Graphics, Computer --- Computer art --- Graphic arts --- Electronic data processing --- Engineering graphics --- Image processing --- AI (Artificial intelligence) --- Artificial thinking --- Electronic brains --- Intellectronics --- Intelligence, Artificial --- Intelligent machines --- Machine intelligence --- Thinking, Artificial --- Bionics --- Cognitive science --- Digital computer simulation --- Logic machines --- Machine theory --- Self-organizing systems --- Simulation methods --- Fifth generation computers --- Neural computers --- Informatics --- Science --- Digital techniques --- Voronoi polygons. --- Computer science --- Mathematics. --- Computer mathematics --- Discrete mathematics --- Diagrams, Voronoi --- Thiessen polygon method --- Thiessen polygons --- Voronoi diagrams --- Polygons --- Mathematics --- Computer vision. --- Artificial Intelligence. --- Machine vision --- Vision, Computer --- Artificial intelligence --- Pattern recognition systems --- Optical data processing. --- Optical computing --- Visual data processing --- Integrated optics --- Photonics --- Computers --- Optical equipment

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This unique book gives a comprehensive account of new mathematical tools used to solve polygon problems. In the 20th and 21st centuries, many problems in mathematics, theoretical physics and theoretical chemistry – and more recently in molecular biology and bio-informatics – can be expressed as counting problems, in which specified graphs, or shapes, are counted. One very special class of shapes is that of polygons. These are closed, connected paths in space. We usually sketch them in two-dimensions, but they can exist in any dimension. The typical questions asked include "how many are there of a given perimeter?", "how big is the average polygon of given perimeter?", and corresponding questions about the area or volume enclosed. That is to say "how many enclosing a given area?" and "how large is an average polygon of given area?" Simple though these questions are to pose, they are extraordinarily difficult to answer. They are important questions because of the application of polygon, and the related problems of polyomino and polycube counting, to phenomena occurring in the natural world, and also because the study of these problems has been responsible for the development of powerful new techniques in mathematics and mathematical physics, as well as in computer science. These new techniques then find application more broadly. The book brings together chapters from many of the major contributors in the field. An introductory chapter giving the history of the problem is followed by fourteen further chapters describing particular aspects of the problem, and applications to biology, to surface phenomena and to computer enumeration methods.

Polygons --- Polyominoes --- Physics - General --- Geometry --- Physics --- Mathematics --- Physical Sciences & Mathematics --- Polygons. --- Polyominoes. --- Polygonal figures --- Physics. --- Chemometrics. --- Numerical analysis. --- Algorithms. --- Combinatorics. --- Statistical physics. --- Dynamical systems. --- Mathematical Methods in Physics. --- Numeric Computing. --- Statistical Physics, Dynamical Systems and Complexity. --- Math. Applications in Chemistry. --- Combinatorial designs and configurations --- Geometry, Plane --- Shapes --- Mathematical physics. --- Electronic data processing. --- Chemistry --- Complex Systems. --- Mathematics. --- Combinatorics --- Algebra --- Mathematical analysis --- Algorism --- Arithmetic --- Physical mathematics --- ADP (Data processing) --- Automatic data processing --- Data processing --- EDP (Data processing) --- IDP (Data processing) --- Integrated data processing --- Computers --- Office practice --- Foundations --- Automation --- Chemistry, Analytic --- Analytical chemistry --- Dynamical systems --- Kinetics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Statics --- Mathematical statistics --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Measurement --- Statistical methods

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Hexagonal Image Processing provides an introduction to the processing of hexagonally sampled images, includes a survey of the work done in the field, and presents a novel framework for hexagonal image processing (HIP) based on hierarchical aggregates. Digital image processing is currently dominated by the use of square sampling lattices, however, hexagonal sampling lattices can also be used to define digital images. The strengths offered by hexagonal lattices over square lattices are considerable: • higher packing density, • uniform connectivity of points (pixels) in the lattice, • better angular resolution by virtue of having more nearest neighbours, and • superlative representation of curves. The utility of the HIP framework is demonstrated by implementing several basic image processing techniques (for the spatial and frequency domain) and some applications. The HIP framework serves as a tool for comparing processing of images defined on a square vs hexagonal grid, to determine their relative merits and demerits. The theory and algorithms covered are supplemented by attention to practical details such as accommodating hardware that support only images sampled on a square lattice. Including a Foreword written by Professor Narendra Ahuja, an eminent researcher in the field of Image Processing and Computer Vision, the book’s fresh approach to the subject offers insight and workable know-how to both researchers and postgraduates.

Image processing --- Hexagons. --- Digital techniques. --- Six-sided polygon --- Polygons --- Digital image processing --- Digital electronics --- Computer vision. --- Computer science. --- Optics, Lasers, Photonics, Optical Devices. --- Image Processing and Computer Vision. --- Computer Imaging, Vision, Pattern Recognition and Graphics. --- Media Design. --- Informatics --- Science --- Machine vision --- Vision, Computer --- Artificial intelligence --- Pattern recognition systems --- Lasers. --- Photonics. --- Optical data processing. --- Multimedia systems . --- Computer-based multimedia information systems --- Multimedia computing --- Multimedia information systems --- Multimedia knowledge systems --- Information storage and retrieval systems --- Optical computing --- Visual data processing --- Bionics --- Electronic data processing --- Integrated optics --- Photonics --- Computers --- New optics --- Optics --- Light amplification by stimulated emission of radiation --- Masers, Optical --- Optical masers --- Light amplifiers --- Light sources --- Optoelectronic devices --- Nonlinear optics --- Optical parametric oscillators --- Optical equipment