What can Grassmann, Hamilton and Clifford tell us about Computer Vision and Robotics
نویسندگان
چکیده
Geometric algebra is a universal mathematical language which provides very comprehensive techniques for analyzing the complex geometric situations occurring in robotics and computer vision. The application of the 4D motor algebra for the linearization of the the hand-eye calibration problem is presented. Geometric algebra and its associated linear algebra framework is a very elegant language to express all the ideas of projective geometry. Using purely geometric derivations, the constraints for point and line correspondences in n-views and projective invariants are computed.
منابع مشابه
Mathematical Foundations for Computer Graphics and Computer Vision
• Euclid synthetic geometry 300 BC • Descartes analytic geometry 1637 • Gauss – complex algebra 1798 • Hamilton – quaternions 1843 • Grassmann – Grasmann Algebra 1844 • Cayley – Matrix Algebra 1854 • Clifford – Clifford algebra 1878 • Gibbs – vector calculus 1881 – used today • Sylvester – determinants 1878 • Ricci – tensor calculus 1890 • Cartan – differential forms 1908 • Dirac, Pauli – spin ...
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