Geometric Algebra Computing, 2010 in Engineering and Computer Science

This book presents new results on applications of geometric algebra. The time when researchers and engineers were starting to realize the potential of quaternions for - plications in electrical, mechanic, and control engineering passed a long time ago. Since the publication of Space-Time Algebra by David Hestenes (1966) and Clifford Algebra to Geometric Calculus: A Uni?ed Language for Mathematics and Physics by David Hestenes and Garret Sobczyk (1984), consistent progress in the app- cations of geometric algebra has taken place. Particularly due to the great dev- opments in computer technology and the Internet, researchers have proposed new ideas and algorithms to tackle a variety of problems in the areas of computer science and engineering using the powerful language of geometric algebra. In this process, pioneer groups started the conference series entitled “Applications of Geometric Algebra in Computer Science and Engineering” (AGACSE) in order to promote the research activity in the domain of the application of geometric algebra. The ?rst conference, AGACSE’1999, organized by Eduardo Bayro-Corrochano and Garret Sobczyk, took place in Ixtapa-Zihuatanejo, Mexico, in July 1999. The contri- tions were published in Geometric Algebra with Applications in Science and En- neering, Birkhäuser, 2001. The second conference, ACACSE’2001, was held in the Engineering Department of the Cambridge University on 9–13 July 2001 and was organizedbyLeoDorst,ChrisDoran,andJoanLasenby. Thebestconferencecont- butions appeared as a book entitled Applications of Geometric Algebra in Computer Science and Engineering, Birkhäuser, 2002. The third conference, AGACSE’2008, took place in August 2008 in Grimma, Leipzig, Germany.

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.

Presents novel, pioneering research on the study and applications of Clifford (geometric) algebra Diverse areas of application are discussed, including neural computing and learning, robotics and computer vision, image processing, colour and scene analysis Includes supplementary material: sn.pub/extras