AGACSE 2008 Proceedings: Geometric Algebra Computing, Springer 2010


Geometric Algebra Computing – in Engineering and Computer Science

Bayro-Corrochano, Eduardo; Scheuermann, Gerik (Eds.)
1st Edition., 2010, XVI, 524 p. 180 illus., Hardcover
ISBN: 978-1-84996-107-3
Price: 119,95 Euro

Contents
Part I Geometric Algebra

New Tools for Computational Geometry and Rejuvenation of Screw Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
David Hestenes

Tutorial: Structure-Preserving Representation of Euclidean Motions Through Conformal Geometric Algebra . . . . . . . . . . . . . . . . 35
Leo Dorst

Engineering Graphics in Geometric Algebra . . . . . . . . . . . . . . . . 53
Alyn Rockwood and Dietmar Hildenbrand

Parameterization of 3D Conformal Transformations in Conformal Geometric Algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
Hongbo Li

Part II Clifford Fourier Transform
Two-Dimensional Clifford Windowed Fourier Transform . . . . . . . . . 93
Mawardi Bahri, Eckhard M.S. Hitzer, and Sriwulan Adji

The Cylindrical Fourier Transform . . . . . . . . . . . . . . . . . . . . . 107
Fred Brackx, Nele De Schepper, and Frank Sommen

Analyzing Real Vector Fields with Clifford Convolution and Clifford–Fourier Transform . . . . . . . . . . . . . . . . . . . . . . . 121
Wieland Reich and Gerik Scheuermann

Clifford–Fourier Transform for Color Image Processing . . . . . . . . . . 135
Thomas Batard, Michel Berthier, and Christophe Saint-Jean
Hilbert Transforms in Clifford Analysis . . . . . . . . . . . . . . . . . . . 163
Fred Brackx, Bram De Knock, and Hennie De Schepper

Part III Image Processing,Wavelets and Neurocomputing

Geometric Neural Computing for 2D Contour and 3D Surface Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191
Jorge Rivera-Rovelo, Eduardo Bayro-Corrochano, and Ruediger Dillmann

Geometric Associative Memories and Their Applications to Pattern Classification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211
Benjamin Cruz, Ricardo Barron, and Humberto Sossa

Classification and Clustering of Spatial Patterns with Geometric Algebra 231
Minh Tuan Pham, Kanta Tachibana, Eckhard M.S. Hitzer, Tomohiro Yoshikawa, and Takeshi Furuhashi

QWT: Retrospective and New Applications . . . . . . . . . . . . . . . . . 249
Yi Xu, Xiaokang Yang, Li Song, Leonardo Traversoni, and Wei Lu

Part IV Computer Vision
Image Sensor Model Using Geometric Algebra: From Calibration to Motion Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . 277
Thibaud Debaecker, Ryad Benosman, and Sio H. Ieng

Model-Based Visual Self-localization Using Gaussian Spheres . . . . . . . 299
David Gonzalez-Aguirre, Tamim Asfour, Eduardo Bayro-Corrochano, and Ruediger Dillmann

Part V Conformal Mapping and Fluid Analysis

Geometric Characterization ofM-Conformal Mappings . . . . . . . . . 327
K. Gürlebeck and J. Morais

Fluid Flow Problems with Quaternionic Analysis—An Alternative Conception . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 345
K. Gürlebeck and W. Sprößig

Part VI Crystallography, Holography and Complexity

Interactive 3D Space Group Visualization with CLUCalc and Crystallographic Subperiodic Groups in Geometric Algebra . . . . . 385
Eckhard M.S. Hitzer, Christian Perwass, and Daisuke Ichikawa

Geometric Algebra Model of Distributed Representations . . . . . . . . . 401
Agnieszka Patyk

Computational Complexity Reductions Using Clifford Algebras . . . . . 431
René Schott and G. Stacey Staples

Part VII Efficient Computing with Clifford (Geometric) Algebra

Efficient Algorithms for Factorization and Join of Blades . . . . . . . . . 457
Daniel Fontijne and Leo Dorst

Gaalop—High Performance Parallel Computing Based on Conformal Geometric Algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . 477
Dietmar Hildenbrand, Joachim Pitt, and Andreas Koch

Some Applications of Gröbner Bases in Robotics and Engineering . . . . 495
Rafał Abłamowicz

Further information (http://www.springer.com/)

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.

Content Level » Research

Keywords » Clifford Algebra – Clifford Fourier Transform – Conformal Geometric Algebra – Geometric Algebra – Geometric Computing – Quaternions

Related subjects » Artificial IntelligenceImage Processing Information Systems and Applications Theoretical Computer Science

Source: 2010-10-05,  http://www.springer.com/computer/information+systems+and+applications/book/978-1-84996-107-3

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