Buch, Englisch, 551 Seiten, Previously published in hardcover, Format (B × H): 155 mm x 235 mm, Gewicht: 855 g
Theoretical Foundations and Applications in Computer Vision and Robotics
Buch, Englisch, 551 Seiten, Previously published in hardcover, Format (B × H): 155 mm x 235 mm, Gewicht: 855 g
ISBN: 978-3-642-07442-4
Verlag: Springer
Clifford algebra, then called geometric algebra, was introduced more than a cenetury 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 representation 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.
Zielgruppe
Research
Autoren/Hrsg.
Fachgebiete
- Technische Wissenschaften Technik Allgemein Mathematik für Ingenieure
- Mathematik | Informatik Mathematik Geometrie Algebraische Geometrie
- Mathematik | Informatik EDV | Informatik Informatik Künstliche Intelligenz
- Technische Wissenschaften Elektronik | Nachrichtentechnik Elektronik Robotik
- Mathematik | Informatik EDV | Informatik Informatik Mathematik für Informatiker
- Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
- Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
Weitere Infos & Material
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.
