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Bayro-Corrochano E. Geometric Algebra Applications Vol. I: Computer Vision, Graphics and Neurocomputing

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Bayro-Corrochano E. Geometric Algebra Applications Vol. I: Computer Vision, Graphics and Neurocomputing
Springer, 2018. — 753 p. — ISBN 978-3-319-74828-3
The 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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