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ISBN: 354078859X 3540788581 3642097669 Year: 2008 Publisher: Berlin : Springer,
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Stochastic geometry has in recent years experienced considerable progress, both in its applications to other sciences and engineering, and in its theoretical foundations and mathematical expansion. This book, by two eminent specialists of the subject, provides a solid mathematical treatment of the basic models of stochastic geometry -- random sets, point processes of geometric objects (particles, flats), and random mosaics. It develops, in a measure-theoretic setting, the integral geometry for the motion and the translation group, as needed for the investigation of these models under the usual invariance assumptions. A characteristic of the book is the interplay between stochastic and geometric arguments, leading to various major results. Its main theme, once the foundations have been laid, is the quantitative investigation of the basic models. This comprises the introduction of suitable parameters, in the form of functional densities, relations between them, and approaches to their estimation. Much additional information on stochastic geometry is collected in the section notes. As a combination of probability theory and geometry, the volume is intended for readers from either field. Probabilists with interest in random spatial structures, or motivated by the prospect of applications, will find an in-depth presentation of the geometric background. Geometers can see integral geometry "at work" and may be surprised to learn how classical results from convex geometry have elegant applications in a stochastic setting.
Geometric probabilities. --- Integral geometry. --- Stochastic geometry. --- Geometry --- Geometry, Integral --- Geometry, Differential --- Probabilities --- Distribution (Probability theory. --- Discrete groups. --- Probability Theory and Stochastic Processes. --- Convex and Discrete Geometry. --- Groups, Discrete --- Infinite groups --- Distribution functions --- Frequency distribution --- Characteristic functions --- Discrete mathematics --- Probabilities. --- Convex geometry . --- Discrete geometry. --- Combinatorial geometry --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk
ISBN: 0387743782 0387726357 1441924817 Year: 2008 Publisher: New York, NY : Springer New York : Imprint: Springer,
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This book introduces the reader to a recent theory in Computer Vision yielding elementary techniques to analyse digital images. These techniques are inspired from and are a mathematical formalization of the Gestalt theory. Gestalt theory, which had never been formalized is a rigorous realm of vision psychology developped between 1923 and 1975. From the mathematical viewpoint the closest field to it is stochastic geometry, involving basic probability and statistics, in the context of image analysis. The book is intended for a multidisciplinary audience of researchers and engineers. It is self contained in three aspects: mathematics, vision and algorithms, and requires only a background of elementary calculus and probability. A large number of illustrations, exercises and examples are included. The authors maintain a public software, MegaWave, containing implementations of most of the image analysis techniques developed in the book.
Computer vision --- Gestalt psychology. --- Image analysis. --- Stochastic geometry. --- Mathematics. --- Geometry --- Analysis of images --- Image interpretation --- Imaging systems --- Configuration (Psychology) --- Form psychology --- Psychology, Structural --- Structural psychology --- Consciousness --- Ejection (Psychology) --- Knowledge, Theory of --- Perception --- Psychology --- Senses and sensation --- Machine vision --- Vision, Computer --- Artificial intelligence --- Image processing --- Pattern recognition systems --- Computer vision. --- Differential equations, partial. --- Visualization. --- Algorithms. --- Image Processing and Computer Vision. --- Partial Differential Equations. --- Signal, Image and Speech Processing. --- Applications of Mathematics. --- Math --- Science --- Visualisation --- Imagination --- Visual perception --- Imagery (Psychology) --- Partial differential equations --- Algorism --- Algebra --- Arithmetic --- Foundations --- Optical data processing. --- Partial differential equations. --- Signal processing. --- Image processing. --- Speech processing systems. --- Applied mathematics. --- Engineering mathematics. --- Computational linguistics --- Electronic systems --- Information theory --- Modulation theory --- Oral communication --- Speech --- Telecommunication --- Singing voice synthesizers --- Pictorial data processing --- Picture processing --- Processing, Image --- Optical data processing --- Processing, Signal --- Information measurement --- Signal theory (Telecommunication) --- Optical computing --- Visual data processing --- Bionics --- Electronic data processing --- Integrated optics --- Photonics --- Computers --- Engineering --- Engineering analysis --- Mathematical analysis --- Optical equipment --- Mathematics
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