Geometric Computing with Clifford Algebras: Theoretical Foundations and Applications in Computer Vision and Robotics. - gebunden oder broschiert

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. TOC:Part I. A Unified Algebraic Approach for Classical Geometries: New Algebraic Tools for Classical Geometry, Generalized Homogeneous Coordinates for Computational Geometry, Spherical Conformal Geometry with Geometric Algebra, A Universal Model for Conformal Geometries of Euclidean, Spherical and Double-Hyperbolic Spaces, Geo-MAP Unification, Honing Geometric Algebra for Its Use in the Computer Sciences, Part II. Algebraic Embedding for Signal Theory and Neural Computation: Spatial-Color Clifford Algebras for Invariant Image Recognition, Non-commutative Hypbercomplex Fourier Transforms of Multidimensional Signals, Commutative Hypercomplex Fourier Transforms of Mulitdimensional Signals, Fast Algorithms fo Hypercomplex Fourier Transforms, Local Hypercomplex Signal Representations and Applications, Introduction to Neural Computation in Clifford Algebra, Clifford Algebra Mulitlayer Perceptrons, etc.