Geometric Algebra Applications Vol. I

Geometric Algebra Applications Vol. I: Computer Vision, Graphics and Neurocomputing By 作者: Eduardo Bayro-Corrochano ISBN-10 书号: 3319748289 ISBN-13 书号: 9783319748283 Edition 版本: 1st ed. 2019 出版日期: 2018-08-13 pages 页数: 753 $219.99 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. 1 Geometric Algebra for the Twenty-First Century Cybernetics Part I Fundamentals of Geometric Algebra 2Introduction to Geometric Algebra 3 Differentiation,Linear,and Multilinear Functions in Geometric Algebra 4 Geometric Calculus 5 Lie Algebras,Lie Groups,and Algebra of Incidence Part ll Euclidean,Pseudo-Euclidean Geometric Algebras, Incidence Algebra,Conformal and Projective Geometric Algebras 62D,3D,and 4D Geometric Algebras 7 Kinematics of the 2D and 3D Spaces 8 Conformal Geometric Algebra 9 The Geometric Algebras G6,0,2+,G6,3,G9,3+,G6,0,6+ 10 Programming Issues Part ll Image Processing and Computer Vision 11 Quaternion-Clifford Fourier and Wavelet Transforms 12 Geometric Algebra of Computer Vision Part IV Machine Learning 13 Geometric Neurocomputing Part V Applications of GA in lmage Processing,Graphics and Computer Vision 14 Applications of Lie Filters,Quaternion Fourier,and Wavelet Transforms 15 Invariants Theory in Computer Vision and Omnidirectional Vision 16 Geometric Algebra Tensor Voting,Hough Transform,Voting and Perception Using Conformal Geometric Algebra 17 Modeling and Registration of Medical Data Part VI Applications of GA in Machine Learning 18 Applications in Neurocomputing 19 Neurocomputing for 2D Contour and 3D Surface Reconstruction 20 Clifford Algebras and Related Algebras