Eduardo Bayro Corrochano – författare
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This book presents a unified mathematical treatment of diverse problems in the
general domain of robotics and associated fields using Clifford or geometric alge-
bra. By addressing a wide spectrum of problems in a common language, it offers
both fresh insights and new solutions that are useful to scientists and engineers
working in areas related with robotics.
It introduces non-specialists to Clifford and geometric algebra, and provides ex-
amples to help readers learn how to compute using geometric entities and geomet-
ric formulations. It also includes an in-depth study of applications of Lie group
theory, Lie algebra, spinors and versors and the algebra of incidence using theuniversal geometric algebra generated by reciprocal null cones.
Featuring a detailed study of kinematics, differential kinematics and dynamics
using geometric algebra, the book also develops Euler Lagrangeand Hamiltoni-
ans equations for dynamics using conformal geometric algebra, and the recursive
Newton-Euler using screw theory in the motor algebra framework. Further, it
comprehensively explores robot modeling and nonlinear controllers, and discusses
several applications in computer vision, graphics, neurocomputing, quantum com-
puting, robotics and control engineering using the geometric algebra framework.
The book also includes over 200 exercises and tips for the development of future
computer software packages for extensive calculations in geometric algebra, and a
entire section focusing on how to write the subroutines in C++, Matlab and Maple
to carry out efficient geometric computations in the geometric algebra framework.
Lastly, it shows how program code can be optimized for real-time computations.
An essential resource for applied physicists, computer scientists, AI researchers,
roboticists and mechanical and electrical engineers, the book clarifies and demon-
strates the importance of geometric computing for building autonomous systems
to advance cognitive systems research.2 498 kr
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The goal of Geometric Algebra Applications Vol. III: Integral Transforms, Machine Learning, and Quantum Computing is to present a unified mathematical treatment of diverse problems in the general domain like Clifford Fourier Transforms, Deep Learning and Geometric Algebra Convolutional Neural Networks, Quaternion Quantum Fourier Transform and Geometric Quantum Computing. Topics and features · Introduces nonspecialists to Clifford, or geometric algebra and by example encourages the reader to learn to compute using geometric entities and geometric formulations.· A study in depth for applications of Lie group theory, Lie algebra, projective geometry, and the algebra of incidence using the conformal geometric algebra. · Features the computing frameworks of the linear model n-dimensional affine plane and the nonlinear model of Euclidean space known as the horosphere, and addresses the relationships of these models to conformal, affine, and projective geometries.· Includes a thorough study of Integral transforms: Quaternion and Clifford Transforms, quaternion analytic signal, monogenic signals, Hilbert transform, Riesz transform, Clifford Fourier Transform, Quaternion Wavelet transforms, Quaternion Quantum Fourier Transform, 3D Radon Transform and Hough-Transform in geometric algebra. · Color image processing using the color model HSV, Quaternion Split rotors and motors, and the space-time Lorentz transform.· Geometric neural computing using Split Quaternions, Geometric Algebra neural networks, Clifford Support Vector Machine and Neuro Control.· Thorough discussion of several tasks of computer vision, graphics, neurocomputing, and robotics. machine learning, Deep Learning and CNNs, and Geometric Quantum Computing using the geometric algebra framework.· 130 exercises and hints for the development of future computer software packages for extensive calculations in geometric algebra. An entire section is dedicated to explaining how one should write the subroutines in C++, Phyton, Matlab, and Maple to carry out efficient geometric computations in the geometric algebra framework. Furthermore, it is shown how program code can be optimized for real-time computations.The book is an essential resource for applied mathematicians, physicists, computer scientists, graphics engineering, AI and Machine Learning researchers, roboticists and mechanical and electrical engineers, neurocomputing researchers, neuroscientists, and quantum computing specialists. It clarifies and demonstrates the importance of geometric computing for building autonomous systems and pushes forward advances in geometric cybernetics research.
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Progress in Pattern Recognition, Image Analysis, Computer Vision, and Applications
19th Iberoamerican Congress, CIARP 2014, Puerto Vallarta, Mexico, November 2-5, 2014, Proceedings
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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.
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Many computer scientists, engineers, applied mathematicians, and physicists use geometry theory and geometric computing methods in the design of perception-action systems, intelligent autonomous systems, and man-machine interfaces. This handbook brings together the most recent advances in the application of geometric computing for building such systems, with contributions from leading experts in the important fields of neuroscience, neural networks, image processing, pattern recognition, computer vision, uncertainty in geometric computations, conformal computational geometry, computer graphics and visualization, medical imagery, geometry and robotics, and reaching and motion planning. For the first time, the various methods are presented in a comprehensive, unified manner.
This handbook is highly recommended for postgraduate students and researchers working on applications such as automated learning; geometric and fuzzy reasoning; human-like artificial vision; tele-operation; space maneuvering; haptics; rescue robots; man-machine interfaces; tele-immersion; computer- and robotics-aided neurosurgery or orthopedics; the assembly and design of humanoids; and systems for metalevel reasoning.
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