Autor: G. Sommer
ISBN-13: 9783540411987
Veröffentl: 22.05.2001
Einband: Book
Seiten: 551
Gewicht: 931 g
Format: 242x165x27 mm
Sprache: Deutsch

Geometric Computing with Clifford Algebras

Theoretical Foundations and Applications in Computer Vision and Robotics
 Book
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1. New Algebraic Tools for Classical Geometry.- 2. Generalized Homogeneous Coordinates for Computational Geometry.- 3. Spherical Conformai Geometry with Geometric Algebra.- 4. A Universal Model for Conformai Geometries of Euclidean, Spherical and Double-Hyperbolic Spaces.- 5. Geo-MAP Unification.- 6. Honing Geometric Algebra for Its Use in the Computer Sciences.- 7. Spatial-Color Clifford Algebras for Invariant Image Recognition.- 8. Non-commutative Hypercomplex Fourier Transforms of Multidimensional Signals.- 9. Commutative Hypercomplex Fourier Transforms of Multidimensional Signals.- 10. Fast Algorithms of Hypercomplex Fourier Transforms.- 11. Local Hypercomplex Signal Representations and Applications.- 12. Introduction to Neural Computation in Clifford Algebra.- 13. Clifford Algebra Multilayer Perceptrons.- 14. A Unified Description of Multiple View Geometry.- 15. 3D-Reconstruction from Vanishing Points.- 16. Analysis and Computation of the Intrinsic Camera Parameters.- 17. Coordinate-Free Projective Geometry for Computer Vision.- 18. The Geometry and Algebra of Kinematics.- 19. Kinematics of Robot Manipulators in the Motor Algebra.- 20. Using the Algebra of Dual Quaternions for Motion Alignment.- 21. The Motor Extended Kalman Filter for Dynamic Rigid Motion Estimation from Line Observations.- References.- Author Index.
Clifford algebra, later called geometric algebra, was introduced more than a century ago by William K. Clifford, building on work by Grassmann and Hamilton. Clifford or geometric algebra shows strong unifying aspects and turned out in the 1960s to be a most adequate formalism for describing different geometry-related algebraic systems as specializations of one "mother algebra" in various subfields of physics and engineering. Recent work outlines that Clifford algebra provides a universal and powerfull algebraic framework for an elegant and coherent repre- sentation of various problems occuring in computer science, signal processing, neural computing, image processing, pattern recognition, computer vision, and robotics. This monograph-like anthology introduces the concepts and framework of Clifford algebra and provides computer scientists, engineers, physicists, and mathematicians with a rich source of examples of how to work with this formalism.
Editiert von: G. Sommer
Inhaltsangabe1. New Algebraic Tools for Classical Geometry.- 2. Generalized Homogeneous Coordinates for Computational Geometry.- 3. Spherical Conformai Geometry with Geometric Algebra.- 4. A Universal Model for Conformai Geometries of Euclidean, Spherical and Double-Hyperbolic Spaces.- 5. Geo-MAP Unification.- 6. Honing Geometric Algebra for Its Use in the Computer Sciences.- 7. Spatial-Color Clifford Algebras for Invariant Image Recognition.- 8. Non-commutative Hypercomplex Fourier Transforms of Multidimensional Signals.- 9. Commutative Hypercomplex Fourier Transforms of Multidimensional Signals.- 10. Fast Algorithms of Hypercomplex Fourier Transforms.- 11. Local Hypercomplex Signal Representations and Applications.- 12. Introduction to Neural Computation in Clifford Algebra.- 13. Clifford Algebra Multilayer Perceptrons.- 14. A Unified Description of Multiple View Geometry.- 15. 3D-Reconstruction from Vanishing Points.- 16. Analysis and Computation of the Intrinsic Camera Parameters.- 17. Coordinate-Free Projective Geometry for Computer Vision.- 18. The Geometry and Algebra of Kinematics.- 19. Kinematics of Robot Manipulators in the Motor Algebra.- 20. Using the Algebra of Dual Quaternions for Motion Alignment.- 21. The Motor Extended Kalman Filter for Dynamic Rigid Motion Estimation from Line Observations.- References.- Author Index.

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Autor: G. Sommer
ISBN-13:: 9783540411987
ISBN: 3540411984
Erscheinungsjahr: 22.05.2001
Verlag: Springer-Verlag GmbH
Gewicht: 931g
Seiten: 551
Sprache: Deutsch
Auflage 2001
Sonstiges: Buch, 242x165x27 mm, 89 Abbildungen, 16 Tabellen