This book offers a gentle introduction to Clifford geometric algebra, an advanced mathematical framework, for applications in perception action systems. Part I, is written in an accessible way allowing readers to easily grasp the mathematical system of Clifford algebra. Part II presents related topics. While Part 3 features practical applications for Computer Vision, Robotics, Image Processing and Neural Computing.
Topics and Features include: theory and application of the quaternion Fourier and wavelet transforms, thorough discussion on geometric computing under uncertainty, an entire chapter devoted to the useful conformal geometric algebra, presents examples and hints for the use of public domain computer programs for geometric algebra.
The modern framework for geometric computing highlighted will be of great use for communities working on image processing, computer vision, artificial intelligence, neural networks, neuroscience, robotics, control engineering, human and robot interfaces, haptics and humanoids.
Rezensionen / Stimmen
From the reviews: "This book presents the theory and engineering applications of geometric algebra, a very powerful mathematical system. ... The results highlight that geometric algebra is a mathematical tool that can be used very advantageously in many engineering scenarios. ... has a real potential to convince a big audience of the benefits of using geometric algebra in engineering applications, and I hope that it will be successful." (Dietmar Hildenbrand, IAPR Newsletter, Vol. 33 (3), July, 2011) "The theory and applications of geometric algebra (Clifford algebra), an advanced mathematical language, are addressed in this book. ... The book is aimed at a graduate-level audience ... . it can also be well suited for teaching a course or for self-study at the postgraduate level. Each chapter is accompanied by numerous examples and figures ... . also be useful to scientists and engineers who are working in various areas related to the development and building of intelligent machines. I really enjoyed reading it." (George K. Adam, ACM Computing Reviews, October, 2010) "The subject of this interesting book is the application of geometric algebra to image processing, computer vision, neurocomputing and robotics. ... A notation table, a list of useful formulas, a bibliography and an index conclude the book. The book is well structured, rich in data, and it contains many exercises; it is aimed at graduate students." (Patrizio Frosini, Zentralblatt MATH, Vol. 1211, 2011)
Auflage
Sprache
Verlagsort
Zielgruppe
Für Beruf und Forschung
Research
Illustrationen
32
133 farbige Abbildungen, 119 s/w Abbildungen, 32 s/w Tabellen
119 black & white illustrations, 133 colour illustrations, 32 black & white tables, biography
Maße
Gewicht
ISBN-13
978-1-84882-928-2 (9781848829282)
DOI
10.1007/978-1-84882-929-9
Schweitzer Klassifikation
Part I: Fundamentals of Geometric Algebra
Introduction to Geometric Algebra
Geometric Algebra for Modeling in Robot Physics
Part II: Euclidean, Pseudo-Euclidean, Lie and Incidence Algebras and Conformal Geometries
2D, 3D and 4D Geometric Algebras
Kinematics of the 2D and 3D Spaces
Lie Algebras and Algebra of Incidence Using The Null Cone and Affine Plane
Conformal Geometric Algebra
Programming Issues
Part III: Geometric Computing for Image Processing, Computer Vision and Neurocomputing
Clifford Fourier and Wavelet Transforms
Geometric Algebra of Computer Vision
Geometric Neuralcomputing
Part IV: Geometric Computing of Robot Kinematics and Dynamics
Kinematics
Dynamics
Part V: Applications I: Image Processing, Computer Vision, Neurocomputing
Applications of Lie Filters, Quaternion Fourier and Wavelet Transforms
Invariants Theory in Computer Vision and Omnidirectional Vision
Registration of 3D Points Using GA and Tensor Voting
Applications in Neuralcomputing
Neural Computing for 2D Contour and 3D Surface Reconstruction
Part VI: Applications II: Robotics and Medical Robotics
Rigid Motion Estimation Using Line Observations
Tracker Endoscope Calibration and Body-Sensors Calibration
Tracking, Grasping and Object Manipulation
3D Maps, Navigation and Relocalization
Modeling and Registration of Medical Data
Part VII: Appendix
