Springer, 2018. — 753 p. — ISBN 978-3-319-74828-3The goal of the Volume I Geometric Algebra for Computer Vision, Graphics and Neural Computing is to present a unified mathematical treatment of diverse problems in the general domain of artificial intelligence and associated fields using Clifford, or geometric, algebra. Geometric algebra provides a rich and general mathematical framework for Geometric Cybernetics in order to develop solutions, concepts and computer algorithms without losing geometric insight of the problem in question. Current mathematical subjects can be treated in an unified manner without abandoning the mathematical system of geometric algebra for instance: multilinear algebra, projective and affine geometry, calculus on manifolds, Riemann geometry, the representation of Lie algebras and Lie groups using bivector algebras and conformal geometry. By treating a wide spectrum of problems in a common language, this Volume I offers both new insights and new solutions that should be useful to scientists, and engineers working in different areas related with the development and building of intelligent machines. Each chapter is written in accessible terms accompanied by numerous examples, figures and a complementary appendix on Clifford algebras, all to clarify the theory and the crucial aspects of the application of geometric algebra to problems in graphics engineering, image processing, pattern recognition, computer vision, machine learning, neural computing and cognitive systems. Table of contents Geometric Algebra for the Twenty-First Century Cybernetics Introduction to Geometric Algebra Differentiation, Linear, and Multilinear Functions in Geometric Algebra Geometric Calculus Lie Algebras, Lie Groups, and Algebra of Incidence 2D, 3D, and 4D Geometric Algebras Kinematics of the 2D and 3D Spaces Conformal Geometric Algebra The Geometric Algebras Programming Issues Quaternion–Clifford Fourier and Wavelet Transforms Geometric Algebra of Computer Vision Geometric Neurocomputing Applications of Lie Filters, Quaternion Fourier, and Wavelet Transforms Invariants Theory in Computer Vision and Omnidirectional Vision Geometric Algebra Tensor Voting, Hough Transform, Voting and Perception Using Conformal Geometric Algebra Modeling and Registration of Medical Data Applications in Neurocomputing Neurocomputing for 2D Contour and 3D Surface Reconstruction
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