Design of algorithms of robot vision using conformal geometric algebra

Abstract

In this paper the authors will apply a mathematical system, the Conformal Geometric Algebra (CGA), to propose applications in computer vision and robotics. The CGA keeps our intuition and insight of the problem’s geometry at hand, besides helping us to reduce the computational problems’ burden. Matrix and vector algebras, complex numbers, rigid and conformal transformations, Euclidean and projective spaces, to name some, are different mathematical tools to model and solve almost any problem in robotic vision. Now, CGA is a mathematical system where all those systems are embedded. We use this compact system following the Occam’s razor philosophy that mathematical ‘entities should not be multiplied unnecessarily’. In this work we handle simulated and real tasks for perception-action systems, treated in a single and efficient way. The authors show that this framework can be of great advantage for applications using stereo vision, range data, laser, omnidirectional and odometry based systems.