Book Details :
Title : Geometric Computing: for Wavelet Transforms, Robot Vision, Learning, Control and Action
Author : Eduardo Bayro Corrochano
Hardcover : 643 pages
Publisher : Springer; 1st Edition. edition (March 31, 2010)
Language : English
ISBN-10 : 1848829280
ISBN-13 : 978-1848829282
Size : 18.42 MB.
Type : Pdf.
Upload by : www.boxmaths.com
Book Description :

This book offers a gentle introduction to Clifford geometric algebra, an advanced mathematical framework, for applications in perception action systems. Part I, is written in an accessible way allowing readers to easily grasp the mathematical system of Clifford algebra. Part II presents related topics. While Part 3 features practical applications for Computer Vision, Robotics, Image Processing and Neural Computing. Topics and Features include: theory and application of the quaternion Fourier and wavelet transforms, thorough discussion on geometric computing under uncertainty, an entire chapter devoted to the useful conformal geometric algebra, presents examples and hints for the use of public domain computer programs for geometric algebra. The modern framework for geometric computing highlighted will be of great use for communities working on image processing, computer vision, artificial intelligence, neural networks, neuroscience, robotics, control engineering, human and robot interfaces, haptics and humanoids.

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 Computing for Wavelet Transforms, Robot Vision, Learning, Control and Action presents a unified mathematical treatment of diverse problems in artificial intelligence and associated fields using Clifford, or geometric, algebra. By treating a wide spectrum of problems in a common language, this book offers both new insights and new solutions that should be useful to scientists, and engineers working in different areas related with the development and building of intelligent machines. Each chapter is written in accessible terms and is accompanied by numerous examples and figures. These features, together with a complementary appendix on Clifford algebras, serve to clarify the theory and fundamental aspects of the application of geometric algebra to problems in image processing and related fields. Topics and features: Introduces nonspecialists to geometric algebra and, by examples, encourages readers to learn to compute using geometric entities and geometric formulations Presents a thorough discussion of several tasks for image processing, pattern recognition, computer vision, robotics, neurocomputing, cognitive systems and engineering using the geometric algebra framework Provides exercises and hints for the development of future computer software packages for extensive calculations in geometric algebra Describes applications of geometric algebra to other related areas, such as graphics engineering, aeronautics, mechatronics, biomechanics and quantum computing Features the computing frameworks of the linear model n-dimensional affine plane and the nonlinear model of Euclidean space known as the horosphere, and addresses the relationships of these models to conformal, affine, and projective geometries Includes a thorough study of all existing Clifford Fourier transforms and Clifford wavelet transforms, using the phase concept to show how to disentangle symmetries useful for scene analysis and medical image processing The book is an essential resource for computer scientists, applied physicists, AI researchers and mechanical and electrical engineers. It clarifies and demonstrates the importance of geometric computing for building autonomous systems and pushing forward advances in cognitive systems research. Prof. Dr. Eng. Eduardo Bayro-Corrochano is a Full Professor of Geometric Computing at Cinvestav, Mexico. His published books include Handbook of Geometric Computing.