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  TwoDimensional 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  ModelBased Visual SelfLocalization Using Gaussian Spheres  Part V: Conformal Mapping and Fluid Analysis  Geometric Characterization of Mconformal 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 realtime 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 realtime 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 BayroCorrochano 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 TopologyBased 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.) 
