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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  and
Luis Eduardo Falcón
Eduardo Bayro-Corrochano
Affiliation:
Centro de Investigación y de Estudios Avanzados Computer Science Department, GEOVIS Lab Guadalajara, Jalisco 45090 (Mexico). E-mail: [email protected]
Luis Eduardo Falcón
Affiliation:
Tecnológico de Monterrey Mathematics Department Guadalajara, Jalisco 45201 (Mexico). E-mail: [email protected]
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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.

Keywords

Computer visionClifford (geometric) algebraProjective and affine geometryIncidence algebra3D rigid motionVisually guided robotics
Type
Research Article
Information
Robotica , Volume 23 , Issue 6 , November 2005 , pp. 755 - 770
Copyright
© 2005 Cambridge University Press

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