Camera Motion Correction with PGA

In this paper we study the geometry and kinematics of stabilizing a moving camera in order to track a stationary scene both in the 2D and 3D setting. This is being done initially in a rather straightforward manner, using the tools of analytic and differential geometry, after which we discuss the advantages of the so-called ‘projective geometric algebra’ (PGA) approach in this context. In the planar case one can easily get equivalent results with complex numbers, but in 3D it is a convenient substitute for Plücker line geometry and the theory of screws. While a lot can be done using quaternions and differential geometry, PGA is quite handy when there are different rotation or screw axes involved. Its basic constructions and properties are briefly summarized in the appendix.