Geometric Algebra Computing (eBook, PDF)

in Engineering and Computer Science
Redaktion: Bayro-Corrochano, Eduardo; Scheuermann, Gerik

• Format: PDF

Produktbeschreibung

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 neuralcomputing 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 FullProfessor at the University of Leipzig, Germany. He is the author of the Springer title Topology-Based Methods in Visualization II.

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Produktdetails

• Verlag: Springer London
• Seitenzahl: 526
• Erscheinungstermin: 19. Mai 2010
• Englisch
• ISBN-13: 9781849961080
• Artikelnr.: 37343534

Inhaltsangabe

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.- Parameterization of 3D Conformal Transformations in Conformal Geometric Algebra.- 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.- 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.- Computer Vision.- Image Sensor Model Using Geometric Algebra: From Calibration to Motion Estimation.- Model-Based Visual Self-localization Using Gaussian Spheres.- Conformal mapping and Fluid Analysis.- Geometric Characterization of Geometric Algebra.- Some Applications of Gröbner Bases in Robotics and Engineering.

Rezensionen

From the reviews:

"This book is a result of the edited proceedings of the 2008 conference. It contains many advanced ideas from mathematics, physics, and computer science, and ... serve as a reference book on geometric algebra and its applications. ... includes numerous color illustrations, and the chapters end with references to the literature. ... This book should be treasured for presenting various geometric algebra applications in several areas ... . It will be useful to physicists, computer scientists, and engineers. ... this is a very useful book." (S. V. Nagaraj, ACM Computing Reviews, February, 2012)