Geometric computing with Clifford algebras : theoretical foundations and applications in computer vision and robotics
著者
書誌事項
Geometric computing with Clifford algebras : theoretical foundations and applications in computer vision and robotics
Springer, c2001
大学図書館所蔵 全15件
注記
Includes bibliographical references (p. [531]-542) and index
内容説明・目次
内容説明
This monograph-like anthology introduces the concepts and framework of Clifford algebra. It provides a rich source of examples of how to work with this formalism. 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 shows that Clifford algebra provides a universal and powerful algebraic framework for an elegant and coherent representation of various problems occurring in computer science, signal processing, neural computing, image processing, pattern recognition, computer vision, and robotics.
目次
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.
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