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Title Geometric algebra computing : in engineering and computer science / Eduardo Bayro-Corrochano, Gerik Scheuermann, editors
Published London ; New York : Springer, [2010]
©2010
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Description 1 online resource (xxii, 526 pages) : illustrations (some color)
Contents Part I: Geometric Algebra -- New Tools for Computational Geometry and Rejuvenation of Screw Theory -- Tutorial: Structure Preserving Representation of Euclidean Motions through Conformal Geometric Algebra -- Engineering Graphics in Geometric Algebra -- Parametrization of 3D Conformal Transformations in Conformal Geometric Algebra -- Part II: Clifford Fourier Transform -- Two-Dimensional Clifford Windowed Fourier Transform -- The Cylindrical Fourier Transform -- Analyzing Real Vector Fields with Clifford Convolution and Clifford Fourier Transform -- Clifford Fourier Transform for Color Image Processing -- Hilbert Transforms in Clifford Analysis -- Part III: Image Processing, Wavelets and Neurocomputing -- Geometric Neural Computing for 2D Contour and 3D Surface Reconstruction -- Geometric Associative Memories and their Applications to Pattern Classification -- Classification and Clustering of Spatial Patterns with Geometric Algebra -- QWT: Retrospective and New Applications -- Part IV: Computer Vision -- Image Sensor Model using Geometric Algebra: from Calibration to Motion Estimation -- Model-Based Visual Self-Localization Using Gaussian Spheres -- Part V: Conformal Mapping and Fluid Analysis -- Geometric Characterization of M-conformal Mappings -- Fluid Flow Problems with Quaternionic Analysis: An Alternative Conception -- Part VI: Cristalography, Holography and Complexity -- Interactive 3D Space Group Visualization with CLUCalc and Crystallographic Subperiodic Groups in Geometric Algebra -- Geometric Algebra Model of Distributed Representations -- Computational Complexity Reductions using Clifford Algebras -- Part VII: Efficient Computing with Clifford (Geometric) Algebra -- Efficient Algorithms for Factorization and Join of Blades -- Gaalop -- High Performance Parallel Computing based on Conformal Geometric Algebra -- Some Applications of Gröbner Bases in Robotics and Engineering
Summary Geometric algebra provides a rich and general mathematical framework for the development of solutions, concepts and computer algorithms without losing geometric insight into the problem in question. Many current mathematical subjects can be treated in an unified manner without abandoning the mathematical system of geometric algebra, such as multilinear algebra, projective and affine geometry, calculus on manifolds, Riemann geometry, the representation of Lie algebras and Lie groups using bivector algebras, and conformal geometry. Geometric Algebra Computing in Engineering and Computer Science presents contributions from an international selection of experts in the field. This useful text/reference offers new insights and solutions for the development of theorems, algorithms and advanced methods for real-time applications across a range of disciplines. The book also provides an introduction to advanced screw theory and conformal geometry. Written in an accessible style, the discussion of all applications is enhanced by the inclusion of numerous examples, figures and experimental analysis. Topics and features: Provides a thorough discussion of several tasks for image processing, pattern recognition, computer vision, robotics and computer graphics using the geometric algebra framework Introduces nonspecialists to screw theory in the geometric algebra framework, offering a tutorial on conformal geometric algebra and an overview of recent applications of geometric algebra Explores new developments in the domain of Clifford Fourier Transforms and Clifford Wavelet Transform, including novel applications of Clifford Fourier transforms for 3D visualization and colour image spectral analysis Presents a detailed study of fluid flow problems with quaternionic analysis Examines new algorithms for geometric neural computing and cognitive systems Analyzes computer software packages for extensive calculations in geometric algebra, investigating the algorithmic complexity of key geometric operations and how the program code can be optimized for real-time computations The book is an essential resource for computer scientists, applied physicists, AI researchers and mechanical and electrical engineers. It will also be of value to graduate students and researchers interested in a modern language for geometric computing. Prof. Dr. Eng. Eduardo Bayro-Corrochano is a Full Professor of Geometric Computing at Cinvestav, Mexico. He is the author of the Springer titles Geometric Computing for Perception Action Systems, Handbook of Geometric Computing, and Geometric Computing for Wavelet Transforms, Robot Vision, Learning, Control and Action. Prof. Dr. Gerik Scheuermann is a Full Professor at the University of Leipzig, Germany. He is the author of the Springer title Topology-Based Methods in Visualization II
Bibliography Includes bibliographical references and index
Notes Print version record
Subject Clifford algebras -- Data processing.
Form Electronic book
Author Bayro Corrochano, Eduardo.
Scheuermann, Gerik.
LC no. 2010926690
ISBN 9781849961080
1849961085
(hbk.)
(hbk.)