Plenary Talk


Modern applications of Clifford geometric algebra


Eckhard Hitzer
International Christian University, Japan

Abstract

In this presentation we give an overview of the 21st century applications of the 19th century geometric algebras introduced by William Kingdon Clifford in the 1870ies, based on the work of Hamilton and Grassmann. These applications include in the field of robotics: real and virtual robot arms, humanoid robots, robot platforms, collision avoidance, pose estimation, robot kinematics and dynamics. In the domain of (color) image processing we review applications to shadowing, ray traycing, visibility computations, image structure, edge detectors, filtering, color reconstruction, texture mapping, image segmentation and video image processing. In the field of computer vision we show applications in: orientation and tracking, motion capture, image object recognition, automatic navigation. In geometry geometric algebra is successfully applied to: uncertain geometries, geometric constraint solving and automatic geometric theorem proving. In material science we give an overview of applications to: optical tomography, space group symmetry visualization, coincidence site lattices, crystal texture (crystal grain orientation analysis), molecular dynamics (computation and feature extraction). In applied physics we explain about: vector field processing, scattering and diffraction of electromagnetic waves, quantum computing, entanglement and light. Finally there are rich applications in: fast computing, telecommunications, graph computations, geographic information systems (data structures and processing).



ISSN 1611 - 4086 | © IKM 2015