Bayesian Inference and Geometric Algebra: An Application to Camera Localization
Chris Doran · Birkhäuser Boston eBooks · 2001
Geometric algebra is an extremely powerful language for solving complex geometric problems in engineering [ 4 , 8 ]. Its advantages are particularly clear in the treatment of rotations. Rotations of a vector are performed by the double-sided application of a rotor , which is formed from the geometric product of an even number of unit vectors. In three dimensions a rotor is simply a normalised element of the even subalgebra of G 3 , the geometric algebra of three dimensional space. In this paper we are solely interested in rotations in space, and henceforth all reference to rotors can be assumed to refer to the 3-d case. Rotors have a number of useful features. They can be easily parameterised in terms of the bivector representing the plane of rotation. Their product is a very efficient way of computing the effect of compound rotations, and is numerically very stable. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.