Conformal Geometric Algebra for Robotic Vision

In this paper the authors introduce the conformal geometric algebra in the field of visually guided robotics. This mathematical system keeps our intuitions and insight of the geometry of the problem at hand and it helps us to reduce considerably the computational burden of the problems. As opposite to the standard projective geometry, in conformal geometric algebra we can deal simultaneously with incidence algebra operations (meet and join) and conformal transformations represented effectively using spinors. In this regard, this framework appears promising for dealing with kinematics, dynamics and projective geometry problems without the need to resort to different mathematical systems (as most current approaches do). This paper presents real tasks of perception and action, treated in a very elegant and efficient way: body–eye calibration, 3D reconstruction and robot navigation, the computation of 3D kinematics of a robot arm in terms of spheres, visually guided 3D object grasping making use of the directed distance and intersections of lines, planes and spheres both involving conformal transformations. We strongly believe that the framework of conformal geometric algebra can be, in general, of great advantage for applications using stereo vision, range data, laser, omnidirectional and odometry based systems. Eduardo Jose Bayro-Corrochano gained his Ph.D. in Cognitive Computer Science in 1993 from the University of Wales at Cardiff. From 1995 to 1999 he has been Researcher and Lecturer at the Institute for Computer Science, Christian Albrechts University, Kiel, Germany, working on applications of geometric Clifford algebra to cognitive systems.  His current research interest focuses on geometric methods for artificial perception and action systems. It includes geometric neural networks, visually guidevsd robotics, color image processing, Lie bivector algebras for early vision and robot maneuvering. He is editor and author of the following books: Geometric Computing for Perception Action Systems, E. Bayro-Corrochano, Springer Verlag, 2001; Geometric Algebra with Applications in Science and Engineering, E. Bayro-Corrochano and G. Sobczyk (Eds.), Birkahauser 2001; Handbook of Computational Geometry for Pattern Recognition, Computer Vision, Neurocomputing and Robotics, E. Bayro-Corrochano, Springer Verlag, 2005. He authored more than 90 strictly reviewed papers. Leo Hendrick Reyes-Lozano received his degree in Computer Engineering from the University of Guadalajara in 1999. He earned his MSc. and Ph.D. from the Center of Research and Advanced Studies (CINVESTAV) Guadalajara in 2001 and 2004, respectively. His research interests include Computer Vision, Geometric Algebra and Computer Graphics. Julio Zamora-Esquivel received his degree in Electronic Engineering at the Guzman City Institute of Tecnology in 2000. He earned his MSc. at the Center of Research and Advanced Studies (CINVESTAV) in Guadalajara in 2003. He is currently a Ph.D Candidate at CINVESTAV. His research interests include Computer Vision, Geometric Algebra and Robotics.