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Geometric algebra of points, lines, planes and spheres for computer vision and robotics

Published online by Cambridge University Press:  10 November 2005

Eduardo Bayro-Corrochano
Affiliation:
Centro de Investigación y de Estudios Avanzados Computer Science Department, GEOVIS Lab Guadalajara, Jalisco 45090 (Mexico). E-mail: edb@gdl.cinvestav.mx
Luis Eduardo Falcón
Affiliation:
Tecnológico de Monterrey Mathematics Department Guadalajara, Jalisco 45201 (Mexico). E-mail: luis.eduardo.falcon@itesm.mx

Abstract

This paper introduces conformal geometric algebra (CGA) for applications in computer vision and robotics. The authors show that CGA deals with our intuition and insight of the geometry and it helps us to reduce considerably the computational burden of the problems. The CGA can be applied not only to describe the geometry of the space, but to handle the algebra of incidence, as well as conformal transformations, to deal with kinematics or projective geometry problems. The authors show with real and simulated applications that this system can be of great advantage in robotics and computer vision.

Type
Research Article
Copyright
© 2005 Cambridge University Press

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