Omnidirectional Robot Vision Using Conformal Geometric Computing

In this paper, we show how to use the conformal geometric algebra (CGA) as a framework to model the different catadioptric systems using the unified model (UM). This framework is well suited since it can not only represent points, lines and planes, but also point pairs, circles and spheres (geometric objects needed in the UM). We define our model using the great expressive capabilities of the CGA in a more general and simpler way, which allows an easier implementation in more complex applications. On the other hand, we also show how to recover the projective invariants from a catadioptric image using the inverse projection of the UM. Finally, we present applications in navigation and object recognition. Carlos Alberto López-Franco is a doctoral student at CINVESTAV, GEOVIS Laboratory, Unidad Guadalajara, México. He received in 2003 the M.S. degree in Computer Science from CINVESTAV, Unidad Guadalajara. His scientific interests are in the fields of computer vision, robotics and the applications of geometric algebra for mobile robots. 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. At present is a full professor at CINVESTAV Unidad Guadalajara, México, Department of Electrical Engineering and Computer Science. His current research interest focuses on geometric methods for artificial perception and action systems. It includes geometric neural networks, visually guided robotics, color image processing, Lie bivector algebras for early vision and robot maneuvering. He developed the quaternion wavelet transform for quaternion multi-resolution analysis using the phase concept. He is associate editor of Robotics and Journal of Advanced Robotic Systems and member of the editorial board of Journal of Pattern Recognition, Journal of Mathematical Imaging and Vision, Iberoamerican Journal of Computer and Systems and Journal Of Theoretical And Numerical Approximation. 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 Geometric Computing for Pattern Recognition, Computer Vision, Neurocomputing and Robotics, E. Bayro-Corrochano, Springer Verlag, 2005. He has published over 120 refereed journal, book chapters and conference papers.